tag:blogger.com,1999:blog-82232916333811099252018-03-06T05:28:26.645-08:00Emily Pearce emily pearcenoreply@blogger.comBlogger20125tag:blogger.com,1999:blog-8223291633381109925.post-76470938869127831942016-10-25T17:23:00.002-07:002016-10-25T17:23:39.398-07:00what's up docOne night, when I was ten or so, I woke up to the sheep crying outside. We owned several sheep and goats, as well as a few cats and dogs. Our home was a mini farm of sorts. That night was early spring, or as I knew it, lambing season. So at 3 am, hearing the sheep making that much noise, I figured that one of them was giving birth. Needless to say I jumped out of bed and ran to check on them. I rarely ever wore shoes at home and that night was no different. Unfortunately for me, that night one of our cats had decided to gift us with a dead bird. So when I ran outside I stepped on the bird and when I lifted my foot the bird came with. One of the birds bones had stuck into my foot! I broke the bird off, leaving a piece in my foot, and promptly informed my mom of what had happened. That morning she took me to the doctor and we were told the chunk of bone would work its way out. It did not... though it did eventually dissolve.emily pearcehttps://plus.google.com/102901842240418615625noreply@blogger.com0tag:blogger.com,1999:blog-8223291633381109925.post-85006464915328709192016-10-22T19:36:00.002-07:002016-10-22T19:36:20.200-07:00Coursera Creative Writing: Plot assignment one Escalator Jonah had just finished building a castle out of blocks and playdoh when his mother walked in carrying a box that was bigger than he was. Excited, Jonah reached towards the box and made the sign for "please" but she took one look at his <span style="color: blue;">filthy</span> hands and sent him to the bathroom to clean up. Jonah ran to the bathroom and climbed the steps to the sink. He turned on the water but there was no soap so he <span style="color: blue;">pretended</span> there had been and scrubbed anyway. Back in the kitchen Jonah spotted the box on top of the table but his mother was no where to be seen. Jonah was sure his mom wouldn't mind if he took one peek inside so he pushed the dog <span style="color: blue;">cage</span> closer and crawled on top to get a better look. The box was covered in jungle print paper complete with Jonahs favorite animal, a <span style="color: blue;">tiger</span>. Jonah reached for the box just as strong hands with gold <span style="color: blue;">rings</span> picked him up and set him back on the floor. "Wait, it's a surprise" his mother signed. She pulled out a tray of veggies, complete with <span style="color: blue;">carrots</span>, and told him to have a snack while he waited. Jonah wasn't hungry but he ate anyway and wondered what was in the giant box. He imagined he was a pirate and the box was a treasure chest <span style="color: purple;">aboard</span> his ship but he didn't have a ladder to climb the side. He was just about to send his <span style="color: blue;">crow</span>, (parrots talked too much and Jonah being deaf couldn't hear them anyway) to retrieve the box when his grandpa tapped him on the shoulder. His Grandpa smiled and said some things but Jonah wasn't very good at reading lips and just looked at him confused. Grandpa pointed at the box and signed "for you". Jonah jumped up and down as Grandpa opened the box and peered inside. Jonah thought he might explode with excitement. His eyes went wide and his mouth gaped as Grandpa pulled out a giant stuffed tiger and handed it to Jonah. Best birthday ever!emily pearcehttps://plus.google.com/102901842240418615625noreply@blogger.com0tag:blogger.com,1999:blog-8223291633381109925.post-39765941727460683752014-07-25T22:55:00.000-07:002014-07-25T23:09:17.392-07:00Herbalism 07.25.14<div class="separator" style="clear: both; text-align: center;"><a href="http://2.bp.blogspot.com/-13UGp_8RIAk/U9NFbPHo9OI/AAAAAAAAAGQ/ouBHNLYJq2M/s1600/violet+and+Nettle+infusion+07.25.14.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://2.bp.blogspot.com/-13UGp_8RIAk/U9NFbPHo9OI/AAAAAAAAAGQ/ouBHNLYJq2M/s1600/violet+and+Nettle+infusion+07.25.14.jpg" height="180" width="320" /></a></div><br /><br /><br />So about a week ago I ordered some Nettle, Violet, Sage, Rosemary and Astragalus Root from Mountain Rose Herbs in order to try a few infusions and decoctions. So far I have made two different infusions, one from the Nettle and one from the Violet. I like the taste of the nettle a little better but the violet isn't bad.<br /><br />Nourishing Infusions are made by pouring boiling water over one ounce of the plant material and letting it steep for at least 4 hours. <br /><br />I've also learned that Nettle has been used effectively for arthritis, lowering blood pressure, regulating blood sugar, helping with dandruff, and curbing allergies among other things. In addition it's packed with calcium and vitamin C.<br /><br />I've only read a little on violet but from what I've read it seems to be famous for breaking up cysts.<br /><br />In the pictures I took the violet is on the left and the nettle is on the right. The knife in the background was used to help distribute the heat from the boiling water so that the glass wouldn't crack.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/-9XkkoXsxN3U/U9NF2gV8clI/AAAAAAAAAGY/JdttklQfsRE/s1600/violet+and+Nettle+infusion2+07.25.14.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://1.bp.blogspot.com/-9XkkoXsxN3U/U9NF2gV8clI/AAAAAAAAAGY/JdttklQfsRE/s1600/violet+and+Nettle+infusion2+07.25.14.jpg" height="320" width="180" /></a></div><br /><br /><br /><br /><br />emily pearcehttps://plus.google.com/102901842240418615625noreply@blogger.com0tag:blogger.com,1999:blog-8223291633381109925.post-82625183015095139142014-07-20T18:26:00.000-07:002014-07-25T22:30:32.843-07:00Wiccan/Mindfulness Education 07.20.14I wanted to make a comment on how daily meditation is affecting me. I've heard many people say it makes them feel calmer or more at peace but it seems to have a different affect on me. I feel more focused and alert, I get things done faster and recognize problems quicker. I've noticed this at work where my job seems easier and I'm more "in touch" with what's going on, it's like an increase in awareness. I'm getting my work done faster and more efficiently. At home I notice that I want to do more, I have more focus on what is going on and find myself more alert.emily pearcehttps://plus.google.com/102901842240418615625noreply@blogger.com0tag:blogger.com,1999:blog-8223291633381109925.post-74787020005742363552014-07-17T09:40:00.001-07:002014-07-25T22:30:07.392-07:00Wiccan/Herbalism/Mindfulness Education 07.16.14In my quest to learn for the sake of learning and to figure out what I want out of life I came across Wicca. Now I'm not big into the whole "there's a higher being out there watching over us" thing though I do pray for my children on a daily basis. I've always thought that the "higher power" was more of an energy or force like in Star Wars. Not good, not bad, just there. So at any rate I've looked through several different religions and never really found my place though the closest I've come so far was Buddhism. Now I'm giving Wicca a try and I'm going to journal what I've learned so far, what I've done, what I think about it and how I feel about it.<br /><br />Contrary to some claims, Wicca is not an old religion and really started with Gerald Gardner. From there it branched off to many different sects with different rituals and beliefs. At the core of each is the Wiccan Rede, which states "An it harm none, do as you will". This in particular struck a cord with me as I have seen it in many other religions in different forms "do unto others as you would have others do unto you" though this is more freeing as it allows all conduct that does not harm others.<br /><br />Wiccans believe in many gods and goddesses though some choose to follow just one or two. Their belief system is different than Christianity and other "Religions of the book" as they do not require worship. I'm still wrapping my head around that as it runs contrary to how I was brought up.<br /><br />I should make a note that I have so far based my studies primarily off of Witchschool.com and MagickaSchool.com. Witch School was founded on the Correlian Nativist tradition of Wicca and I am taking Correlian Wicca First Degree, Living the Wiccan Life, Basic Meditations and Basic Herbs. I am also doing some study of Herbalism as it fascinates me.<br /><br />So far I have learned some history of Wicca as well as a few spells (which I liken more to concentrated meditation). I took a Tai-Chi class with my dad and learned a meditation to cleanse the body and store Chi that involves visualizing my body filled with water and draining out through my palms and feet. There's more to it than that but that's the basic idea. I found the same concept in the Wicca referred to as grounding. It appears that Gerald Gardner spent some time in Asia learning about eastern thought and religion and integrated that into Wicca. So magic, in Wiccan thought, is similar to chi or energy in eastern thought, also Wiccans subscribe to the concept of Karma though they call it the law of three. That which you do will come back to you three fold, most don't take this as a literal equation but rather as the classical version of Karma but in this lifetime rather than the next.<br /><br />I also learned a shielding spell which is a meditation concerned with strengthening ones aura. The other one I learned but have not tried is the cleansing spell involving Rosemary, Sage, Salt, Oil and a warm bath. Prior to attempting this I looked up the medical uses of Rosemary and Sage. I found that Rosemary has been used effectively to treat baldness, and some skin conditions while Sage has been used for cold sores as well as a treatment for Alzheimer's. I believe that the medical properties of the plants themselves along with the words/ritual/meditation (creating somewhat of a Placebo effect) is what causes the persons "spell" to work. I'm personally fascinated by the mix of herbalism and meditation for healing purposes and this seems to be a lot of what Wicca is about. <br /><br />So far I've spent the last three days doing the aura strengthening exercise and the grounding exercise. I can say that immediately after I feel a sense of calm that I usually experience after meditation. For the time being that's the only benefit I've experienced. I've also made a conscious effort to try and view everything as being aware though that has been a little bit more difficult for me. I have sat in my kitchen, bathroom, and computer room and asked the room what it wanted and needed from me. That was a strange experience though I believe what I got out of it was more what I envisioned the room to be rather than the room actually responding to me. I have also contemplated the eternal cycle of water in that the same water (in a sense) was around in ancient times just the way it is today.<br /><br />One other thought I had was that in a way, we are depriving ourselves of healing opportunities by stepping away from belief when it comes to medicine. When we perform prayers, rituals and other such actions in tandem with whatever medicine we are taking I believe it increases the effect. Simply by believing it will work people have seen results from placebos, be it sugar pills or prayer, and combining that with medicine or herbs I believe would have an added effect. While I consider my self fairly grounded in science and reality I can see from that standpoint why religions and rituals come about.emily pearcehttps://plus.google.com/102901842240418615625noreply@blogger.com0tag:blogger.com,1999:blog-8223291633381109925.post-8632464400234966622013-12-25T23:20:00.003-08:002013-12-25T23:20:36.740-08:00Book ReviewsJust wanted to leave a quick note to let you all know that the book reviews have moved to my new blog <a href="http://little-book-worms.blogspot.com/">http://little-book-worms.blogspot.com/</a>emily pearcehttps://plus.google.com/102901842240418615625noreply@blogger.com0tag:blogger.com,1999:blog-8223291633381109925.post-5339126315773600842013-11-30T01:09:00.003-08:002013-11-30T01:09:32.484-08:00Introduction to Computer Science 11.29.13 23:26I restarted the class on computer science from Udacity this past week. So far this course discussed the difference between a toaster and a computer in that a toaster is designed to do one thing while a computer can do anything we program it to do. A program is a code that tells the computer what to do in a given situation. I also got to do a little bit of programming in Python which is the language they use for the course. We started out with arithmetic, typing in <span style="color: orange;">print 1 + 1</span> and running it in the interpreter produces the result <span style="color: orange;">2</span> . The<span style="color: orange;"> print</span> function is a way to see what the code we built is doing. Then it moved on to assignment statements. Typing in any word (name for example) an equals symbol and an expression assigns that expression to that word so if we write<span style="color: orange;"> name = 5 * 3</span><span style="color: blue;"> </span>and then <span style="color: orange;">print name</span> it will evaluate to <span style="color: orange;">15</span>.<br /><br />So lets say we wanted to print out more than just numbers, this is where we need to use strings. To create a string we could just use <span style="color: orange;">print 'This is a test'</span> and the output would be <span style="color: orange;">This is a test</span>. To create a string it needs to have quotes or double quotes on each side so<span style="color: orange;"> 'the'</span>, <span style="color: orange;">"isn't"</span> and <span style="color: orange;">'"simple" she said.'</span> would all be valid strings. As long as the string starts and ends with the same type of quote it will work. Simple enough, but what if we have a really long string and we don't want to type it out each time? Then we could assign the string to a name and just print the name. For example: <span style="color: orange;">einstein_quote = '"</span><span style="font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 14px; line-height: 20px;"><span style="color: orange;">Education is what remains after one has forgotten what one has learned in school." Albert Einstein'</span> we can then run <span style="color: orange;">print einstein_quote </span>and the string<span style="color: orange;"> </span></span><span style="color: orange;">"<span style="font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 14px; line-height: 20px;">Education is what remains after one has forgotten what one has learned in school." Albert Einstein</span></span><span style="font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 14px; line-height: 20px;"> </span><span style="font-size: 14px; line-height: 20px;"><span style="font-family: inherit;">will be the result. </span></span><br /><span style="background-color: white; font-size: 14px; line-height: 20px;"><span style="font-family: inherit;"><br /></span></span>This brings us to another question, what if we have an entire page as a string and we want to find where a specific word or link first appears? We can use the find function, so starting with the string we just used we could then write <span style="color: orange;">einstein_quote.find('one')</span> and the output would be the location of the first instance of the word <span style="color: orange;">one</span> in our string. Of course we would have to print that piece of code to actually see the location as a number. I'm going to explain this using a shorter string, <span style="color: blue;"> </span><span style="color: orange;">'one'</span> for example, if I typed in<span style="color: orange;"> print 'one'.find(n)</span> I would get <span style="color: orange;">1</span> as the result because the location is initialized by numbers starting at zero and <span style="color: orange;">n</span> is the second letter in the word one. We could type <span style="color: orange;">print 'one'[1:]</span> and this would result in <span style="color: orange;">ne</span>, because it would print starting from position one through the rest of the string. If we typed <span style="color: orange;">print 'one'[1:2]</span> we would get <span style="color: orange;">n</span> because the end point (2 in this case) prints up to but not including that position. We could also write <span style="color: orange;">print 'one'[:2]</span> and get <span style="color: orange;">on</span>, because it would display from the start of the string up to position 2.<br /><br />So why and how would we use this? Well, for lesson one the goal is to be able to extract a link from a webpage. Let's go back to our <span style="color: orange;">einstein_quote</span> string and say we wanted to print just the part <span style="color: orange;">one has forgotten what one has learned in school.</span> we could write some code to do this as follows.<br /><br /><span style="color: orange;">first_one = einstein_quote.find('one')</span><br /><span style="color: orange;">end_point = einstein_quote.find('.') + 1</span><br /><span style="color: orange;">print einstein_quote[first_one:end_point]</span><br /><br />This should produce the result we are looking for. The reason the second step includes a <span style="color: orange;">+ 1</span> is because the end point of an index (the <span style="color: orange;">[:]</span> used to show parts of a string ) prints up to that position and we want to include that position.<br /><br />emily pearcehttps://plus.google.com/102901842240418615625noreply@blogger.com0tag:blogger.com,1999:blog-8223291633381109925.post-20485120812514695432013-11-21T06:24:00.001-08:002013-11-21T08:22:35.446-08:00Algebra 11.21.13This past week I reviewed graphing basics and how to find the distance between two points. Let's start with some graphing basics. Points on a graph are denoted (x,y) where x is the distance a point is from the origin (0,0) on the x or horizontal axis and y is the distance from the origin on the y or vertical axis. A graph has 4 quadrants. Points in quadrant 1 will have both a positive x and y value so (x,y). Points in quadrant 2 will have a negative x and positive y (-x,y). In quadrant 3 both the x and y values are negative (-x,-y) and in quadrant 4 the y value is negative while the x value is positive (x,-y). It is important to note that while a graph will not show all the numbers the x and y axis extend indefinitely in both the negative and positive directions.<br /><div class="separator" style="clear: both; text-align: center;"><a href="http://2.bp.blogspot.com/-Gjut0qa8px0/Uo4R91sBZlI/AAAAAAAAADY/X8D20LOdLcI/s1600/graph.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="225" src="http://2.bp.blogspot.com/-Gjut0qa8px0/Uo4R91sBZlI/AAAAAAAAADY/X8D20LOdLcI/s400/graph.jpg" width="400" /></a></div><br />We can find the distance between two points using the Pythagorean Theorem a squared plus b squared = c squared where c is the hypotenuse of a right triangle. No matter which two points we look at they all can be looked at as being a part of a right triangle. So if we were going to find the distance between the point (1,2) and (2,4) we need to look at the big picture. The distance between the two x coordinates 1 and 2 is one and the distance between the two y coordinates 2 and 4 is 2. 1 squared is 1 and 2 squared is 4, one plus 4 is 5. Then we take the square root of 5 to get the distance between those two points. 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height: 1px; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: 0px; width: 0.2px;"></span></span><span style="border: 0px; display: inline-block; height: 62px; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; left: 14.8px; margin: 0px; padding: 0px; position: absolute; top: -55.4px; vertical-align: 0px;"><span class="mn" id="MathJax-Span-31" style="border: 0px; display: inline; font-family: MathJax_Main; font-size: 20px; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">1</span><span style="border: 0px; display: inline-block; height: 62px; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span></span></span><span class="msubsup" id="MathJax-Span-32" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span style="border: 0px; display: inline-block; height: 0px; margin: 0px; padding: 0px; position: relative; vertical-align: 0px; width: 23.1px;"><span style="border: 0px; clip: rect(40.3px 27664px 73.9px -7.5px); left: 0px; margin: 0px; padding: 0px; position: absolute; top: -64px; vertical-align: 0px;"><span class="mo" id="MathJax-Span-33" style="border: 0px; display: inline; font-family: MathJax_Main; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">)</span><span style="border: 0px; display: inline-block; height: 64px; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; left: 11px; margin: 0px; padding: 0px; position: absolute; top: -75.2px; vertical-align: 0px;"><span class="mn" id="MathJax-Span-34" style="border: 0px; display: inline; font-family: MathJax_Main; font-size: 20px; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">2</span><span style="border: 0px; display: inline-block; height: 62px; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span></span></span></span><span style="border: 0px; display: inline-block; height: 64px; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; clip: rect(100.5px 27664px 110.4px -9px); left: 28px; margin: 0px; padding: 0px; position: absolute; top: -137.8px; vertical-align: 0px;"><span style="border: 0px; display: inline-block; height: 0px; margin: 0px; padding: 0px; position: relative; vertical-align: 0px; width: 281.7px;"><span style="border: 0px; font-family: MathJax_Main; left: -2.3px; margin: 0px; padding: 0px; position: absolute; top: -111px; vertical-align: 0px;">−<span style="border: 0px; display: inline-block; height: 111px; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; font-family: MathJax_Main; left: 262.5px; margin: 0px; padding: 0px; position: absolute; top: -111px; vertical-align: 0px;">−<span style="border: 0px; display: inline-block; height: 111px; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; font-family: MathJax_Main; left: 11.7px; margin: 0px; padding: 0px; position: absolute; top: -111px; vertical-align: 0px;">−<span style="border: 0px; display: inline-block; height: 111px; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; font-family: MathJax_Main; left: 26.5px; margin: 0px; padding: 0px; position: absolute; top: -111px; vertical-align: 0px;">−<span style="border: 0px; display: inline-block; height: 111px; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; font-family: MathJax_Main; left: 41.2px; margin: 0px; padding: 0px; position: absolute; top: -111px; vertical-align: 0px;">−<span style="border: 0px; display: inline-block; height: 111px; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; font-family: MathJax_Main; left: 56px; margin: 0px; padding: 0px; position: absolute; top: -111px; vertical-align: 0px;">−<span style="border: 0px; display: inline-block; height: 111px; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; font-family: MathJax_Main; left: 70.7px; margin: 0px; padding: 0px; position: absolute; top: -111px; vertical-align: 0px;">−<span style="border: 0px; display: inline-block; height: 111px; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; font-family: MathJax_Main; left: 85.5px; margin: 0px; padding: 0px; position: absolute; top: -111px; vertical-align: 0px;">−<span style="border: 0px; display: inline-block; height: 111px; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; font-family: MathJax_Main; left: 100.2px; margin: 0px; padding: 0px; position: absolute; top: -111px; vertical-align: 0px;">−<span style="border: 0px; display: inline-block; height: 111px; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; font-family: MathJax_Main; left: 115px; margin: 0px; padding: 0px; position: absolute; top: -111px; vertical-align: 0px;">−<span style="border: 0px; display: inline-block; height: 111px; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; font-family: MathJax_Main; left: 129.7px; margin: 0px; padding: 0px; position: absolute; top: -111px; vertical-align: 0px;">−<span style="border: 0px; display: inline-block; height: 111px; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; font-family: MathJax_Main; left: 144.5px; margin: 0px; padding: 0px; position: absolute; top: -111px; vertical-align: 0px;">−<span style="border: 0px; display: inline-block; height: 111px; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; font-family: MathJax_Main; left: 159.2px; margin: 0px; padding: 0px; position: absolute; top: -111px; vertical-align: 0px;">−<span style="border: 0px; display: inline-block; height: 111px; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; font-family: MathJax_Main; left: 174px; margin: 0px; padding: 0px; position: absolute; top: -111px; vertical-align: 0px;">−<span style="border: 0px; display: inline-block; height: 111px; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; font-family: MathJax_Main; left: 188.7px; margin: 0px; padding: 0px; position: absolute; top: -111px; vertical-align: 0px;">−<span style="border: 0px; display: inline-block; height: 111px; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; font-family: MathJax_Main; left: 203.5px; margin: 0px; padding: 0px; position: absolute; top: -111px; vertical-align: 0px;">−<span style="border: 0px; display: inline-block; height: 111px; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; font-family: MathJax_Main; left: 218.2px; margin: 0px; padding: 0px; position: absolute; top: -111px; vertical-align: 0px;">−<span style="border: 0px; display: inline-block; height: 111px; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; font-family: MathJax_Main; left: 233px; margin: 0px; padding: 0px; position: absolute; top: -111px; vertical-align: 0px;">−<span style="border: 0px; display: inline-block; height: 111px; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; font-family: MathJax_Main; left: 247.7px; margin: 0px; padding: 0px; position: absolute; top: -111px; vertical-align: 0px;">−<span style="border: 0px; display: inline-block; height: 111px; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span></span><span style="border: 0px; display: inline-block; height: 111px; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; clip: rect(76.2px 27664px 132px -5.9px); left: 0px; margin: 0px; padding: 0px; position: absolute; top: -113.1px; vertical-align: 0px;"><span style="border: 0px; font-family: MathJax_Size2; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"> Distance = √</span><span style="border: 0px; color: #330099; display: inline-block; height: 111px; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span></span></span></span><span style="border: 0px; color: #330099; display: inline-block; height: 64px; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span></span><span style="background-color: #ccccff; border-left-style: solid; border-width: 0px; color: #330099; display: inline-block; font-family: Verdana, Arial, Helvetica, sans-serif; font-size: 21px; height: 52.2px; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: -16.9px; white-space: nowrap; width: 0px;"></span><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/-0SLCDJFVVgg/Uo4UkkVlQSI/AAAAAAAAADk/eAUBn4AwIH0/s1600/Graph+2x=y.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="180" src="http://1.bp.blogspot.com/-0SLCDJFVVgg/Uo4UkkVlQSI/AAAAAAAAADk/eAUBn4AwIH0/s320/Graph+2x=y.jpg" width="320" /></a></div>emily pearcehttps://plus.google.com/102901842240418615625noreply@blogger.com0tag:blogger.com,1999:blog-8223291633381109925.post-13483418224145530592013-11-21T05:36:00.002-08:002013-11-21T05:36:49.082-08:00Mandarin Chinese 11.21.13I started the Rosetta Stone Mandarin Chinese course today. So far I'm having trouble pronouncing some of the sounds but I'm starting to grasp word meaning. So here are the words I remember as close as I can get to what they sound like to me.<br /><br />nu ren - woman<br />nan ren - man<br />nu hi zi - girl<br />nan hi zi - boy<br />you yong - swim<br />pao bu - run<br />hu - drink<br />ni hao - hello<br />si chen - goodbye<br />kan - read<br />shu - book<br />shuay - water<br />che - tea<br /><br />As I learn more I will try to put in a few complete sentences.emily pearcehttps://plus.google.com/102901842240418615625noreply@blogger.com0tag:blogger.com,1999:blog-8223291633381109925.post-88765388265122541302013-11-15T04:55:00.000-08:002013-11-15T04:55:38.304-08:00Algebra 08.04.13An equation is two expressions that are set equal to each other. Conditional equations, identities, and not equations. A Conditional equation is such that its truth is dependent on which number x stands for. For example 2x+1=5 is only true when x = 2. An Identity is when both sides are exactly the same so 3n+1=3n+1 because when we simplify we get 0=0. x-3 and 2/x +1= 2/x +2 are not equations simply because they do not equal anything or are false.emily pearcehttps://plus.google.com/102901842240418615625noreply@blogger.com0tag:blogger.com,1999:blog-8223291633381109925.post-60504959109615183332013-08-02T09:02:00.001-07:002013-08-02T14:49:22.284-07:00Twins 08.02.13My girls are 7 months old today and very different. Rain is intense in her attention to things and small details, she is quiet and is always off exploring (even though she only scoots and rolls). Sometimes she squeaks when she is excited, she doesn't like sweet food as much as veggies. Her favorites are peas and plain cereal. Rain was the first to escape from the car seat when she's not strapped in and the first to figure out how to hold her own bottle. She's always examining objects and even her own hands just to see how they work. Today I watched her examine a Lego block for a good twenty minutes, just rolling it around putting her hand and fingers in all the holes.<br /><br />River is more vocal and always wants to be the center of attention, where Rain examines new things River shakes them and tries to get them to make noise. She was the first to vocalize and giggle, her belly is ticklish too. River also growls at people and things, not an angry growl but just a very guttural sound, it's very comical, like a tiny dinosaur trying to be heard. She loves juice and the sweet fruity foods, when she doesn't want to eat something she blows raspberries to get it out of her mouth. Today while I was feeding her and Rain mixed veggies she blew most of it out and I got more on me then she ate. River is goofy, personable and loves to cuddle.<br /><br />It's crazy to see how different they are. Rain is the little scientist trying to figure out how the world works and River is the social butterfly trying to mimic the big people.emily pearcehttps://plus.google.com/102901842240418615625noreply@blogger.com0tag:blogger.com,1999:blog-8223291633381109925.post-81974133892152464332013-08-02T06:05:00.000-07:002013-08-02T06:05:14.874-07:00Algebra 08.02.13The last part of lesson two focuses on exponents. When a dealing with several variables multiplied together that have exponents the exponents can be added together to simplify the expression. For example if I have x^2*y^4*x^9*3 (where ^ is used to show there is an exponent) I can simplify to x^11*y^4*3.<br /><br />Lesson three is about polynomials. The distributive property allows us to take the expression a(b+c) and simplify it to ab+ac. For example say we have the expression 5-(6-x) we can think of the negative sign as a -1 and distribute it to get 5-6+x or -1+x. When multiplying polynomials together make sure to multiply every term in the first polynomial by every term in the second polynomial. For example (x+2)(x+5)= x^2+5x+2x+10 which simplified is x^2+7x+10.Emily Pearcehttp://www.blogger.com/profile/09765482929763666188noreply@blogger.com0tag:blogger.com,1999:blog-8223291633381109925.post-701422981719807082013-08-01T08:00:00.001-07:002013-08-02T05:22:12.935-07:00Algebra 08.01.13Lesson 2 in Udacity's College Algebra course is about expressions. It starts by going back over the commutative property of both addition and multiplication. As a reminder the commutative property just means that the order of terms or factors doesn't matter. So a+b+c is the same thing as b+a+c and a*b*c is the same as c*a*b and so on. When combining like terms it is important to remember that they need to have the same variable and power (x cannot be added to x squared). So 2x+3x+4-2y can be simplified to 5x-2y+4 but no further.<br /><br />A polynomial is an expression with constants and/or variables that are combined using addition, subtraction and multiplication, where all exponents are non-negative integers. The degree of a term is the sum of exponents on the variables in that term. So x squared times y cubed would have a degree of 5 because the exponents 2 and 3 add up to 5. The degree of a polynomial is equal to the highest degree of any of its terms. the standard form of a polynomial is to put the terms in order from highest degree to lowest degree.emily pearcehttps://plus.google.com/102901842240418615625noreply@blogger.com0tag:blogger.com,1999:blog-8223291633381109925.post-63612696109016694162013-08-01T04:38:00.000-07:002013-08-01T17:37:49.242-07:00Psychology 08.01.13So over the last few days I have been working on Lesson 3 "The Biology of Behavior". Last post I talked about colorblindness which is a trait controlled by one gene. There are, however, many traits that are controlled by multiple genes such as eye color or height, these are called polygenic traits. Traits are not just affected by genes but also by the environment. Identical twins can posses very different traits because of their life choices, if one overeats and smokes while the other doesn't they are going to look very different. Epigenetics is the study of how our environment can turn different traits on and off. There is a study about two genetically identical mice whose mothers were fed different diets while pregnant, one high in methyl groups and one without. The end result was that one mouse came out obese and yellow while the other was normal and brown. These mice have the same genotype but different phenotypes. The same principals hold true for personality traits, there is a gene that is referred to as the warrior gene, this gene was thought to cause aggressive behavior but as it turns out many people have the gene without displaying aggressive behavior. In fact it takes an abusive childhood coupled with the Monoamine Oxidase A (warrior gene) to cause the more aggressive personality, making this an excellent example of how the environment can affect the gene expression.<br /><br />The next part of Lesson 3 had to do with the nervous system. The nervous system can be broken down as into the Central and Peripheral nervous systems. The central nervous system consists of the brain and spinal cord while the peripheral accounts for all the other nerves. The peripheral system can be broken into the somatic and autonomic systems, the autonomic system controls functions like heart beat, breathing, digestion etc... the somatic is responsible for voluntary functions. Both of these systems have motor and sensory nerves. The autonomic nervous system has both a sympathetic and parasympathetic nervous system. The sympathetic nervous system is responsible for the fight or flight response, when activated it does things like dilate the pupils, increase heart rate, inhibit digestion and relax the bronchi to make taking in more oxygen possible. When the parasympathetic nervous system is activated it has the opposite effect, the pupils and bronchi are restricted, heart rate is slowed and digestion is stimulated.<br /><br />There are two types of cells that make up the nervous system, Glial cells and Neurons. Glial cells provide structural support and remove debris while Neurons process and transmit information. There are three different types of neurons; sensory, motor and interneurons, the interneurons connect neurons to one another. Below is a very rough drawing of a neuron. The Soma is the center of the cell and contains the nucleus. Branching off of the soma are the Dendrites, dendrites connect to other neurons and are the receivers for the cell. The axon transmits the electrical charge (when a neuron fires) to the terminal buttons, the mylin sheath (not present on all neurons) helps to speed up this process. The terminal buttons release neurotransmitters to neighboring neurons and the process repeats. Neurotransmitters can be either inhibitory or excitatory, excitatory neurotransmitters increase the chance that a neuron will fire while inhibitory ones decrease that chance. So to put it all together lets say an excitatory neurotransmitter is received by the dendrites of a neuron, if enough are received the neuron will fire off an electrical signal that runs down the axon and tells the terminal buttons to release more neurotransmitters once they do the cycle repeats with the next neuron. <br /><br /><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="http://2.bp.blogspot.com/-_gmPD9fK4XM/UfpEzTaDtpI/AAAAAAAAADI/IvxZbxgUrbk/s1600/Neuron.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="225" src="http://2.bp.blogspot.com/-_gmPD9fK4XM/UfpEzTaDtpI/AAAAAAAAADI/IvxZbxgUrbk/s400/Neuron.jpg" width="400" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Neuron</td></tr></tbody></table><br /><br />emily pearcehttps://plus.google.com/102901842240418615625noreply@blogger.com0tag:blogger.com,1999:blog-8223291633381109925.post-52467859559108039582013-07-28T06:52:00.000-07:002013-08-01T17:38:16.840-07:00Algebra 07.28.13Yesterday I finished up the Introductory Algebra Review on Udacity ( I know the certificate says 07.25.13 but that was for getting 80% of the questions right, I finished out the last unit and test on the 27th), I'm starting the College Algebra course today. Lesson one is about numbers, numbers are a construct in that they do not exist in the real world, we use the concept of numbers to do everything from balancing our checkbooks to launching satellites into orbit. Natural numbers are the numbers 1 to infinity, increasing by 1 at each step so 1, 34 and 375 are natural numbers but -3, 3.6, and 0 are not. Whole numbers are all natural numbers and the number 0. Integers are all whole numbers and negative numbers that are not fractions or decimals so they range from -infinity to +infinity. These are all sets of numbers, of course a set can be made up of any combination of numbers. Another way to express the relationship of of one set of numbers to another is to say x is a sub-set of y, for example whole numbers are a subset of integers because all whole numbers are integers. Rational numbers are any number that can be written as a/b where a and b are integers and b is not 0. Irrational numbers cannot be written as ratios of integers, so any square root that is not a perfect square is an irrational number, pi is also an irrational number. <br /><br />There is also a review of variables, constants, expressions and equations. I am not going to go back over them because that information is in my previous algebra posts.emily pearcehttps://plus.google.com/102901842240418615625noreply@blogger.com0tag:blogger.com,1999:blog-8223291633381109925.post-57599582226304860982013-07-28T03:29:00.001-07:002013-08-01T17:37:49.240-07:00Psychology 07.28.13Today in the Intro to Psychology class I went over good practices in experiments, specifically in reference to psychological experiments. Randomly assigning participants to either the experimental or control group can help insure that both groups are similar. Not telling participants which group they are in eliminates bias on their part, having both the participants and the experimenter in the dark is called a double blind study and this eliminates bias on both parts. An important thing to note about psychology is that a review board has to okay any experiments, the benefits must outweigh the risks and participants must sign informed consent. Participants must also be able to leave the study at anytime without negative consequences.<br /><br />Lesson 3 starts out with an introduction into how long modern humans have been around as compared to other humans. Modern humans have existed for the last 200,000 years, before that were Neanderthals, homo-erectus and homo-habilus. Homo habilus, the first humans, lived from about 2.4 to 1.4 million years ago. Our closest relative would be the Neanderthals and we actually interbred with them before they died off around 28,000 years ago so many of us have Neanderthal DNA. Our closest living relative is the chimp, with whom we share about 98% of our DNA, the other 2% is what makes us uniquely human. These changes happened over a long period of time due to mutations and natural selection, in other words, we evolved.<br /><br />The changes to our brains is probably what makes us most human. Our brains are bigger than our ancestors and the most differences between our brains and theirs is in the frontal lobe. Having a bigger brain did not come without consequences, childbirth is more painful because of larger skulls and we need more food to fuel our brains.<br /><br />There is a section on DNA structure, from the nucleotides Thymine, Adenine, Guanine, Cytosine to the 23 chromosomes that make up our DNA. Also it is not the amount of DNA but the sequence that makes us more complex, in fact some amoeba's have more DNA than than anything else on earth. Only about 2% of our genome actually codes for proteins (these portions are called genes), most of the rest regulates which genes are activated, but some of this remaining 98% we're not really sure as to what its purpose is. Alleles are versions of genes, for example my dad has the allele for colorblindness where as my mom does not, so being that this allele only exists on the x chromosome (of which I have 2) I have one allele for colorblindness and one for normal vision. Luckily for me the colorblindness allele is recessive which means that I would need two in order to be colorblind. However this also means that there is a 50/50 chance my daughters will also carry the colorblindness allele and 50/50 chance that any sons I would have would be colorblind. Why? Because males have an x and a y chromosome so they only get one chance at a good allele, where as the x chromosome from my mom allows me to recognize all the colors males don't have a second x chromosome to cancel out or hide the colorblindness allele. This is why more men than women are colorblind, for a woman to be color blind her father would have to be colorblind and her mother would have to carry the colorblind allele. emily pearcehttps://plus.google.com/102901842240418615625noreply@blogger.com0tag:blogger.com,1999:blog-8223291633381109925.post-29911570073222700942013-07-27T01:27:00.000-07:002013-08-01T17:38:16.838-07:00Algebra 07.27.13<span style="font-family: Times, Times New Roman, serif;">Yesterday we learned a bit about slope and how horizontal lines will always have a slope of zero because if you divide zero by any number it is still zero. This brings us to vertical lines, these lines have a change in x of zero, because we can't divide by zero the slope of any vertical line is undefined. Given two points <span style="line-height: 115%;">(x</span><sub style="line-height: 115%;">1</sub><span style="line-height: 115%;">, y</span><sub style="line-height: 115%;">1</sub><span style="line-height: 115%;">) (x</span><sub style="line-height: 115%;">2</sub><span style="line-height: 115%;">,y</span><sub style="line-height: 115%;">2</sub><span style="line-height: 115%;">) we can then find the slope using this equation where "m" stands for slope, m=(y</span><sub style="line-height: 115%;">1</sub><span style="line-height: 115%;">-y</span><sub style="line-height: 115%;">2</sub><span style="line-height: 115%;">)/(x</span><sub style="line-height: 115%;">1</sub><span style="line-height: 115%;">-x</span><sub style="line-height: 115%;">2</sub><span style="line-height: 115%;">). So how do we find the graph or visual representation of a line from this information? We use the slope of a line and a point on the line, we can also represent a line using slope-intercept form. This uses the slope and the y intercept to represent a line or y=mx+b where again m is slope and b is the value of y at the y intercept. We can also use point-slope form y-</span></span><span style="font-family: Times, 'Times New Roman', serif; line-height: 18px;">y</span><sub style="font-family: Times, 'Times New Roman', serif; line-height: 14px;">1</sub><span style="font-family: Times, 'Times New Roman', serif; line-height: 18px;">=m(x-</span><span style="font-family: Times, 'Times New Roman', serif; line-height: 18px;">x</span><sub style="font-family: Times, 'Times New Roman', serif; line-height: 14px;">1</sub><span style="font-family: Times, 'Times New Roman', serif; line-height: 18px;">) where </span><span style="font-family: Times, 'Times New Roman', serif; line-height: 18px;">(x</span><sub style="font-family: Times, 'Times New Roman', serif; line-height: 14px;">1</sub><span style="font-family: Times, 'Times New Roman', serif; line-height: 18px;">, y</span><sub style="font-family: Times, 'Times New Roman', serif; line-height: 14px;">1</sub><span style="font-family: Times, 'Times New Roman', serif; line-height: 18px;">) is any point on the line. If we solve for y we can convert point-slope form to slope-intercept form. </span>emily pearcehttps://plus.google.com/102901842240418615625noreply@blogger.com0tag:blogger.com,1999:blog-8223291633381109925.post-818108992320019102013-07-26T06:22:00.003-07:002013-08-01T17:37:49.244-07:00Psychology 07.26.13I'm going through Udacity's Introduction to Psychology so here are my notes. Psychology is a field of science that explores the questions of why we do what we do. Psychology covers a wide area, from developmental psychologists who study why children acquire different skills at different times to industrial psychologists who review workplace dynamics to create a more productive environment, the classic image of a Freudian character asking a patient how that made them feel is only a small part of what psychologists do. <br /><br />Lesson 2 is about research methods. The first part of the lesson is about correlations. Let's say that the price of pickles went up 2 dollars and the price of milk went up 1 dollar, so looking back we can see that as the price of pickles goes up so does the price of milk. So if we were to plot the data points on the price of pickles to milk we would likely see a correlation. However, that does not mean that one caused the other, the price of milk could be going up because of the economy or higher fuel prices, pickles could be in higher demand recently or a million other things could have affected the price. Correlation does not imply causation.<br /><br />To determine whether one thing causes another is often more difficult than plotting points on a graph. One way is through an experiment. A good experiment starts with a testable hypothesis. I want to know what the best time to feed my girls vegetables is, I've noticed that they tend to eat more vegetables if they have them before meals or as snacks. So my hypothesis is, My girls will eat more of their vegetables if they are fed to them before their meals. Now I set up my experiment, I will feed my children vegetables before meals one week, during meals another week and after meals another week.. The independent variable (the one I will manipulate) in this experiment is the time they are fed vegetables. I will measure how much they eat by how much is left afterwards making quantity remaining my dependent variable. To ensure that my data actually measures what I want it to measure I will control the time of day they eat, what vegetables are served, and what the environment is while they are eating (tv on or off, living room or kitchen), these are my control variables. If in fact they do eat more when they are fed veggies before meals I will have proved my hypothesis. The difference between a hypothesis and a theory is that a theory encompasses many proven hypothesis to come up with an idea that ties them all together. Saying for example that evolution is a theory is really saying that it is the best explanation we have for all the data and proven hypothesis currently available to us. As an aside, during my hypothetical experiment I recorded measurable data (how much of the veggies were left), if I wanted to know how much my kids like veggies I would have to find a way to measure "liking a food" liking something is a construct in that we know what someone means when they say they like something but it isn't a quality that we can measure. So we use operational definitions, in this case we could say kids will eat more of the foods they like so we will measure how much they eat.emily pearcehttps://plus.google.com/102901842240418615625noreply@blogger.com0tag:blogger.com,1999:blog-8223291633381109925.post-77103793112336327532013-07-26T02:46:00.000-07:002013-08-01T17:38:16.844-07:00Algebra 07.26.13Unit 5 Section 1 starts out by introducing t-charts and ordered pairs for displaying data points. A t-chart looks like a t with the two variables (x and y) on the top and numbers on the bottom. This t-chart shows some data points for the equation 2x = y.<br /><a href="http://3.bp.blogspot.com/-C5cWW3fFHbA/UfIybsacaiI/AAAAAAAAAC4/_JPAlNgMj14/s1600/Graph+2x=y.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="112" src="http://3.bp.blogspot.com/-C5cWW3fFHbA/UfIybsacaiI/AAAAAAAAAC4/_JPAlNgMj14/s200/Graph+2x=y.jpg" width="200" /></a><a href="http://4.bp.blogspot.com/-6zIuH15sDtU/UfIvoazoDsI/AAAAAAAAACo/TTbTAKrZ6PM/s1600/T-chart.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="112" src="http://4.bp.blogspot.com/-6zIuH15sDtU/UfIvoazoDsI/AAAAAAAAACo/TTbTAKrZ6PM/s200/T-chart.jpg" width="200" /></a><br /><br /><br /><br /><br /><br /><br />This can also be shown with ordered pairs, for example (0,0) (1,2) (2,4). Both represent the same data and this data can then be plotted on a graph as shown above. An intercept is where the line crosses the x and y axis, in this case both the x and y intercepts are at (0,0). In any linear equation the x and y intercepts can be found by setting x or y to zero. If you set x to 0 and solve the result will be the y intercept, and if you set y to 0 and solve the result will be the x intercept of the line. Not all lines will have an x and y intercept, vertical lines will only cross the x axis and horizontal lines will only cross the y axis. Vertical lines will have equations that look like x=2 while horizontal lines will have equations that look like y=5.<br /><br />Unit 5 Section 2 is about slope. Slope is how steep a line is and is calculated by rise/run, or the change in y divided by the change in x. Horizontal lines will always have a slope of 0 because the y value does not change and 0 divided by any number is still 0.emily pearcehttps://plus.google.com/102901842240418615625noreply@blogger.com0tag:blogger.com,1999:blog-8223291633381109925.post-8389719243139990122013-07-25T22:15:00.001-07:002013-08-01T17:38:16.845-07:00Algebra learning journal to date. <div lang="en-US" style="line-height: 115%; margin-bottom: 0.14in;"><span style="font-family: Times, Times New Roman, serif; font-size: 11pt;">07.12.13 6:58 </span></div><div lang="en-US" style="line-height: 115%; margin-bottom: 0.14in;"><span style="font-family: Times, Times New Roman, serif;"><span style="font-size: 11pt;"> I am reviewing some basic algebra through the Udacity site. Some notes: the commutative property means that order of any two variables will not change the outcome. Addition and Multiplication both have and commutative property. Associative property means that the order of any three or more variables will not change the outcome, and again both addition and multiplication but not subtraction or division share this property. For example </span></span></div><div lang="en-US" style="line-height: 115%; margin-bottom: 0.14in;"><span style="font-family: Times, Times New Roman, serif;"><span style="font-size: 11pt;">5+2 = 7 and 2+5 = 7, also 2*5 = 10 and 5*2 = 10, this is an example of the commutative property. 5-2= 3 and 2-5 = -3, 3 is not = to -3 to subtraction does not have the commutative property. Just like 10/2 = 5 and 2/10 = 0.2 so division also does not share this property.</span></span></div><div lang="en-US" style="line-height: 115%; margin-bottom: 0.14in;"><span style="font-family: Times, Times New Roman, serif;"><br /></span></div><div lang="en-US" style="line-height: 115%; margin-bottom: 0.14in;"><span style="font-family: Times, Times New Roman, serif;"><span style="font-size: 11pt;"> The next section is about powers, any thing to the first power is itself and anything to the zero power is one. So 3</span><sup><span style="font-size: 11pt;">1 </span></sup><span style="font-size: 11pt;">is 3 and 3</span><sup><span style="font-size: 11pt;">0</span></sup><span style="font-size: 11pt;">is 1. </span></span></div><div lang="en-US" style="line-height: 115%; margin-bottom: 0.14in;"><span style="font-family: Times, Times New Roman, serif;"><span style="font-size: 11pt;"> Order of operations: ( ) and [ ] first, simplify exponents, multiply and divide from left to right, add and subtract from left to right. </span></span></div><div lang="en-US" style="line-height: 115%; margin-bottom: 0.14in;"><span style="font-family: Times, Times New Roman, serif;"><span style="font-size: 11pt;"> Area of a square is l</span><sup><span style="font-size: 11pt;">2 </span></sup><span style="font-size: 11pt;">or l*l (length</span><sup><span style="font-size: 11pt;">2</span></sup><span style="font-size: 11pt;">).</span></span></div><div lang="en-US" style="line-height: 115%; margin-bottom: 0.14in;"><span style="font-family: Times, Times New Roman, serif; font-size: 11pt;"> Area of a rectangle is l*w or Length times Width</span></div><div lang="en-US" style="line-height: 115%; margin-bottom: 0.14in;"><span style="font-family: Times, Times New Roman, serif;"><span style="font-size: 11pt;"> Area of a triangle is 1/2 base times height. </span></span></div><div lang="en-US" style="line-height: 115%; margin-bottom: 0.14in;"><span style="font-family: Times, Times New Roman, serif; font-size: 11pt;">07.14.13 3:08</span></div><div lang="en-US" style="line-height: 115%; margin-bottom: 0.14in;"><span style="font-family: Times, Times New Roman, serif;"><span style="font-size: 11pt;"> This section is about fractions. An improper fraction is one in which the numerator is larger than the denominator. For example 4/3, this can be simplified to 1 1/3. 1 and 1/3 is a mixed number, which is a whole number and a fraction. </span></span></div><div lang="en-US" style="line-height: 115%; margin-bottom: 0.14in;"><span style="font-family: Times, Times New Roman, serif; font-size: 11pt;"> The denominator must be the same to add or subtract fractions, this is done by finding the lowest common denominator (the smallest number that both denominators go into). For example if I'm going to add 1/3 and 1/2 I have to find a number that both 3 and 2 go into. 12 is one but it's high and that would make the fraction more difficult so the lowest common denominator is 6. So to change both fractions I look first at what I have to multiply 3 by to get 6, that’s 2 so I multiply both the numerator and denominator by 2 to get 2/6. Going through the same process for 1/2 give me 3/6 then I just add the numerators, leaving me with 5/6.</span></div><div lang="en-US" style="line-height: 115%; margin-bottom: 0.14in;"><span style="font-family: Times, Times New Roman, serif;"><span style="font-size: 11pt;"> Multiplying fractions is pretty straight forward just multiply the numerators together and the denominators together. Dividing fractions is the same as multiplying by the reciprocal. so if I want multiply 1/3 by 1/2 I get 1/6 (1*1 is 1 and 3*2 is 6) but if I divide 1/3 by 1/2 I get 2/3. This is because the reciprocal or 1/2 is 2/1 and then I multiply, so 2*1 is 2 and 1*3 is 3 so the answer is 2/3. </span></span></div><div lang="en-US" style="line-height: 115%; margin-bottom: 0.14in;"><span style="font-family: Times, Times New Roman, serif; font-size: 11pt;">07.15.13 09:36</span></div><div lang="en-US" style="line-height: 115%; margin-bottom: 0.14in;"><span style="font-family: Times, Times New Roman, serif;"><span style="font-size: 11pt;"> This section is on decimals and rounding. Starting with a decimal such as 3.462 and rounding up to the nearest whole number gives us 3, rounding to the first place gives us 3.5, this is because if a number to the right of the decimal is less than 5 it is rounded down and if it is greater than five it is rounded up. </span></span></div><div lang="en-US" style="line-height: 115%; margin-bottom: 0.14in;"><span style="font-family: Times, Times New Roman, serif;"><span style="font-size: 11pt;"> The second part is about circles, Circumference is the distance around a circle or the perimeter of a circle. Diameter is the length of a line that passes through the center and whose end points lie on the circle. Radius is the distance of a line with one end point on the center of the circle or origin and the other on the circle. </span></span></div><div lang="en-US" style="line-height: 115%; margin-bottom: 0.14in;"><span style="font-family: Times, Times New Roman, serif;"><span style="font-size: 11pt;"> Pi equals circumference/diameter. Circumference = 2*pi*r . Area equals pi*r</span><sup><span style="font-size: 11pt;">2</span></sup><span style="font-size: 11pt;">. </span></span></div><div lang="en-US" style="line-height: 115%; margin-bottom: 0.14in;"><span style="font-family: Times, Times New Roman, serif; font-size: 11pt;">07.19.13 07:52</span></div><div lang="en-US" style="line-height: 115%; margin-bottom: 0.14in;"><span style="font-family: Times, Times New Roman, serif;"><span style="font-size: 11pt;"> This part of section 2 is about scientific notation. Scientific notation takes a number and simplifies is down to a decimal times 10</span><sup><span style="font-size: 11pt;">x</span></sup><span style="font-size: 11pt;">. For example 535,000,000 can be written as 5.35 * 10</span><sup><span style="font-size: 11pt;">8</span></sup><span style="font-size: 11pt;">. The key to remember is that only one number should come before the decimal in scientific notation. Small numbers can also be written in scientific notation. For example .000632 can be written as 6.32 * 10</span><sup><span style="font-size: 11pt;">-4</span></sup><span style="font-size: 11pt;">, and again remember only one number comes before the decimal. </span></span></div><div lang="en-US" style="line-height: 115%; margin-bottom: 0.14in;"><span style="font-family: Times, Times New Roman, serif;"><span style="font-size: 11pt;"> Section 3 starts out with rates. Rates are things like miles per hour or diapers per package, they are used to compare two quantities with different units. So I can go 67 mph which would be the same as saying I went 67 miles in one hour. 16 diapers per 4 packages is the same as saying there are 4 diapers in each package or 4 diapers per package. Both of these are examples of a rate because miles, hours, diapers and packages are all different units. </span></span></div><div lang="en-US" style="line-height: 115%; margin-bottom: 0.14in;"><span style="font-family: Times, Times New Roman, serif;"><span style="font-size: 11pt;"> A "Unit Rate" is any rate where the value of the denominator is equal to one. </span></span></div><div lang="en-US" style="line-height: 115%; margin-bottom: 0.14in;"><span style="font-family: Times, Times New Roman, serif; font-size: 11pt;"> A ratio is used when comparing two quantities with the the same units. For example 2 out 3 of my girls wear diapers, this is a ratio because there is only one unit, in this case it is "my girls". Ratios can also be written with colons so 2/3 of my girls can be written as 2:3.</span></div><div lang="en-US" style="line-height: 115%; margin-bottom: 0.14in;"><span style="font-family: Times, Times New Roman, serif; font-size: 11pt;">07.19.13 04:56</span></div><div lang="en-US" style="line-height: 115%; margin-bottom: 0.14in;"><span style="font-family: Times, Times New Roman, serif; font-size: 11pt;"> This part of section 3 is about Conversion Factors, a conversion factor is a number that relates the quantity of one thing to the quantity of another thing and it always equals one. For example 12 eggs /1 carton is a conversion factor because 12 eggs is equal to 1 carton.</span></div><div lang="en-US" style="line-height: 115%; margin-bottom: 0.14in;"><span style="font-family: Times, Times New Roman, serif;"><span style="font-size: 11pt;"> The last part of section three is about converting decimals and percents. To change a decimal to a percent move the decimal 2 places to the right, and to change a percent to a decimal move the decimal to places to the left. So if I want to say that 2 of my 3 children wear diapers that equals .667 of my children which is 66.7%. If my oldest daughter finishes 75% of her homework she has finished .75 of it and so on. </span></span></div><div lang="en-US" style="line-height: 115%; margin-bottom: 0.14in;"><span style="font-family: Times, Times New Roman, serif;"><span style="font-size: 11pt;"> Unit 4 starts out with variables. A variable is a symbol or letter that can be used to represent an unknown value. </span></span></div><div lang="en-US" style="line-height: 115%; margin-bottom: 0.14in;"><span style="font-family: Times, Times New Roman, serif; font-size: 11pt;">07.23.13</span></div><div lang="en-US" style="line-height: 115%; margin-bottom: 0.14in;"><span style="font-family: Times, Times New Roman, serif; font-size: 11pt;"> Unit 4 section one is about algebraic expressions, an algebraic expression has terms that include numbers and variables that are connected by addition, subtraction, multiplication and division. 3x-4 is an algebraic expression. To evaluate an expression the value of the variable is plugged in. For example if x=3 evaluate 3x-4 it would be 3(3)-4 or 9-4 which is 5. 4x+3(x-2) to simplify this I need to combine like terms, like terms are variables that are raised to the same power so x and 2x are like terms but not x^2 or 2y. So to simplify combine the coefficients of like terms (coefficients are numbers that variables are multiplied by) but leave the variable alone. Constants are numbers with out variables so in our example 4x+3(x-2), 4 is a coefficient and 2 is a constant. To simplify we follow the order of operations. So 4x+3x-6 turns into 7x-6, and our original expression is simplified.</span></div><div lang="en-US" style="line-height: 115%; margin-bottom: 0.14in;"><span style="font-family: Times, Times New Roman, serif; font-size: 11pt;"> Unit 4 Section two is about linear equations, linear equations have an equals sign, an expression on both sides of the equals sign and no variable has an exponent higher than one. So 5x+3=40 is a linear equation. These can be solved for the variable. There are some that don't have a real answer and others where x (the variable) can be all real numbers and still make the equation true. For example 2x-3=-3+2x, simplified down this is all real numbers because no matter what number is x is substituted for the equation remains true. Now 2x=2x +2 doesn't have a solution because if we simplify it we get 0=2 which is not true.</span></div><div lang="en-US" style="line-height: 115%; margin-bottom: 0.14in;"><span style="font-family: Times, Times New Roman, serif;"><span style="font-size: 11pt;"> The same principles that apply to linear equations also apply to inequalities. Such as, if you do something to one side then you have to do the same thing to the other side. The only difference is that if you divide or multiply by a negative in an inequality the sign flips. So -3x<9 simplifies/ solves to x>-3. </span></span></div><div lang="en-US" style="line-height: 115%; margin-bottom: 0.14in;"><span style="font-family: Times, Times New Roman, serif;"><span style="font-size: 11pt;"> Unit 4 Section three is about proportions and similar triangles. Proportions start with a rate and then can be used to find other data by cross multiplying and dividing. For example if I work out and lose 3 pounds a week how many days will it take me to lose 23 pounds. So 3 pounds/7 days = 23 pounds/x days. This problem can be made into a proportion. So now I multiply 23 pounds by 7 days to get 161 and then divide by 3 pounds, so because I have the variable pounds on the top and bottom of the equation I can cancel it out and I get 53 2/3 days. </span></span></div><div lang="en-US" style="line-height: 115%; margin-bottom: 0.14in;"><span style="font-family: Times, Times New Roman, serif; font-size: 11pt;">07.25.13</span></div><div lang="en-US" style="line-height: 115%; margin-bottom: 0.14in;"><span style="font-family: Times, Times New Roman, serif;"><span style="font-size: 11pt;"> Continuing with Unit 4 section three, Similar triangles are triangles that have the same angles but different sides. The angles will all have the same measure and the sides will be in proportion to each other. This is important because similar triangles can be used to find heights in the real world among other things. Lets say that we hold up a yard stick and it casts a 10 foot long shadow, we can then find the height of anything else by measuring its shadow because the sun is at the same angle to the yardstick as it is to every other vertical object. So lets say that we want to know how tall the tree outside is. We measure the shadow and it is 60 feet long, so now we can set up a proportion, 3/10 = x/60. Now we cross multiply and divide, 60 * 3 is 180, divided by 10 is 18. So the tree is 18 feet tall. </span></span></div><div lang="en-US" style="line-height: 115%; margin-bottom: 0.14in;"><span style="font-family: Times, Times New Roman, serif; font-size: 11pt;"> Unit 4 Section 4 is about the Pythagorean Theorem which states that in a right triangle a² + b² = c², where c is the length of the hypotenuse. The Hypotenuse is the longest side of a triangle and in a right triangle it is opposite the 90 degree angle.</span></div><br /><div lang="en-US" style="line-height: 115%; margin-bottom: 0.14in;"><span style="font-family: Times, Times New Roman, serif;"><br /></span></div>emily pearcehttps://plus.google.com/102901842240418615625noreply@blogger.com0