We are currently working with Polar Graphs. We did a project where we made roses on Desmos by using the equation r=a *cos(n*theta). After playing around with this we used different equations to get different shapes. For example we used the equation r= a+bcos theta to produce a circle inside a circle. We even made the "Spiral of Archimedes" by using the equation r=theta. Now onto the image below. I used the equation r= 2+tan3theta to start out. Then I used the same equation four more times while increasing the numbers. So my next one was r=3+tan2theta.
If you want to find the cos you look at the x values on the circle. So for example if you wanted to know cos 30 the x value would be (square root of 3)/2. So cos 30=(square root of 3)/2. Then if you wanted to find the sin of something you look at the y values on the circle. For example if you wanted to find the sin 30 the y value would be 1/2. So then sin 30=1/2. To find tan of something life gets a bit more difficult. This is because tan theta= sin theta/cos theta. I'd give an example but I'm not to skilled in this field. :P
Subsidized vs Unsubsidized Subsidized loans government pays the interest. When the person is in school or the economic hardship deferments. Unsubsidized is the responsibility of the borrower. Subsidized is the least expensive option. During subsidized responsibility to repay back the government is suspended as long as you're in school half time. Payments are delayed until the end of grace period after graduation. Subsidized loans the government pays the interest as it accrues. And Unsubsidized loans increase if the interest is not paid. Gov vs Bank Federal loans funded by government, private loans are from the bank. Federal loans include many benefits such as fixed interest rates and income based repayment plans. Bank loans are usually more expensive. Federal loans pay when graduate and/or change your enrollment status to less than half time. Bank loans you pay while still in college. Dont need a credit check for most federal loans. Interest rate is fixed and lower than private loans. You might need a cosigner for bank loans. Bank loans are not subsidized. Federal loans you maybe able to postpone or lower your payments. There is no prepayment penalty fee for federal loans Interest Rates Subsidized- 4.66% Unsubsidized- 4.66% Bank loans- 5.99%-11.24% In the picture above it shows how much I would have to pay back in students for 4 years and 10 years. It is kind of hard to see but for 4 years I would have to pay back $500 a month. Then for 10 years I would have to pay back $262 a month. So clearly paying back more money is cheaper in a sense.
What are Limits? Limits are numbers that get closer and closer to another number but never actually get to it. You can tell if a limit exists by seeing if a number gets really really close to another number but does not reach it. Limits help describe the behavior of points of discontinuity by showing on the graph when it cannot reach a number. When it cannot reach the number that is the limit.
I.) Factors lead the way to finding the zeros. By setting the factor to equal zero then you are able to find the zero. So let us take x+5=0 for example. So the zero of that factor would be -5.
II.) Division helps us to factor polynomials by bringing them down to their simplest forms, which in turn helps us find the zeros. III.) The degree of the polynomial tells us how many zeros we need to look for. IV.) The degree does not show the number factors, because there are repeating factors. To look at this graph you must be thinking someone was crazy. In a sense they were, you have to use three equations to make a graph like this. You have to us neagtive x squared plus 2. Then you have to use the square root of -x squared plus 2 squared. Then finally you have to use (x squared minus 2) squared.
The object of this activity was to see if the basketball would make it in or not. I made this diagram by using GeoGebra. It took a minute to figure out even after watching the video, haha. Anywho we had to see if the ball would make it into the hoop or not. By the diagram the ball appears to miss the hoop, but not by much. Maybe if we're lucky the ball will bounce off the back board.
In this activity I had to find the inverse function of y equals x squared. To find the inverse I had to switch the y and the x. My observations concluded that the graph flipped on its side. In the bottom picture I folded the graph along the dotted line to see if the graphs lined up. As you can see they are slightly off, this is because my dotted line was off centered. |
Amber CI am in Pre Calculus and this is my blog. Archives
April 2015
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