This was by far my favorite math project this year. I thought it was really interesting that the different coefficients moved the graph around. My favorite was the butt graph we did but I didn't manage to get a picture, but it was a lot of fun to create. Pictured above from left to right, is the original "Spiral of Archimedes" which is r=theta. The middle picture is an adapted "Spiral of Archimedes", the equation is r=0.5theta. The last picture is a rose that I graphed, the equation is r=asinbtheta. Thank you Mr. Kelly! :)
These past couple weeks in out Pre Calculus class, we have been learning about periods, amplitudes, and frequencies of the sin wave. In this Arduino project, we were give code that repeats the sound of the sin wave over and over, and out project was to make the Arduino sound like a siren, for example, going really fast for a few seconds, then slowing down for a few more, etc. However, our project did not go quite as planned and our wonderful teacher, Mr. Kelly, had to write our code for us, which is shown below. The amplitude is changed by changing the number that is in front of the sin, where the code says sinVal. The period of changed by changing the number in front of x in the same spot. Don't try this at home. float sinVal; int toneVal; int k=0; void setup () { pinMode(8,OUTPUT); } void loop () { while (k< 2000){ for (int x=0;x<180;x++) { // convert degrees to radians then obtain sin value sinVal = (sin(x*(3.1412/180))); // generate a frequency from the sin value toneVal = 2000+(int(sinVal*1000)); tone(8, toneVal); k++; delay(2); }} for (int x=0;x<180;x++) { // convert degrees to radians then obtain sin value sinVal = (sin(x*(3.1412/180))); // generate a frequency from the sin value toneVal = 2000+(int(sinVal*1000)); tone(8, toneVal); delay(5);} }
Using a unit circle is a very easy skill to master. As long as you know sine, cosine, and tangent it will be as simple as pie. For example, if you are looking for the sine, cosine, and tangent of 30, first, to find the sine of 30, look at the y coordinate above the sine of 30. Next, for the cosine of 30, look at the x coordinate of the numbers above 30. The trickiest part, by far, is tangent. So, to find the tangent of 30, take the sine and divide it by the cosine, and that will get you the tangent.
Government subsidised and unsubsidised are loans are different because subsidised loan's amounts are decided by the school the individual is attending and the U.S. Department of Education pays the interest until the individual graduates from the college they were attending. Unsubsidised loans have no requirements to demonstrate financial need and they are offered to graduate and undergraduate students. Interest rates are the same for both loans, undergrad students are 4.66% and grad students are 6.21%, while private bank loans are 5% interest. If I were to take out 5,000 dollars in subsidised loans for all four years of college, and paid it back every month, I would pay $262 per month paying a total of $31,538.
If you folded a paper 42 times, it would reach the moon, which is physically impossible because the most folds of paper anyone got in our class was 7 and there is a big difference between 42 and 7, it's just not physically possible to fold a piece of printing paper that much because the paper is just too small. The paper would be super MEGA wide, 2 to the 42nd power, is 4.39804651x10 to the 12th power. THAT IS SO BIG. It doesn't exactly matter because it's not physically possible, however it is still huge. Thanks a million to our lovely math teacher, Mr. Kelly. :)
#SelfieGameTooStrong #LandyAndEve #AllThoseZeros
A limit is a point on a graph that we look at from the left and the right and we see the numbers approaching the point on the graph we looked at. We can tell if a limit exists by looking at the point and seeing if the left hand numbers and the right hand numbers approach the same number. Limits help us explain function behavior at points of discontinuity by showing what happens at the right side and the left side at the point of discontinuity. Thanks for everything Mr. Kelly. What did zero say to eight? Hey, nice belt. Haha.
So.. zeros. The factors show where the zeros are, that's the connection between the two, for example, (x+1), means that at -1, there is a zero. Division helps us factor polynomials because we need to use the quadratic formula to completely factor it and to use sed formula, we need three variables, and long division or synthetic division helps us find those three variables. The degree of the polynomial shows us how many zeros we need to find, for example, if the formula was f(x)=x^4-3x^3-x^2-2x-4 we could tell by looking at the first variable that we need to find four zeros because the first x is raised to the fourth power. That always tells us how many factors there are, even though multiplicity counts and some zeros may be repeated. Thanks Mr. Kelly, have a great day! :) Today, Cress and Little (Mr. Kelly and his BFF) entertained us with a video of extreme sports, which was really them just shooting a basketball and trying to get it in the hoop and wearing crazy clothes. Our job was to find out if the ball was going to go into the hoop so we took the picture they provided for us of the ball at different heights on it's travel to the hoop, and inserted it into GeoGebra. I used the base of the ball to make the points, and then proceeded to put those points in a chart, made a list of the points, and then let GeoGebra do the math for me and come up with a function for me, it's depicted above but the function is f(x)=0.08x^2+1.29x+3.86. So, judging from the picture, and the line running into the backboard, I'm going to make an educated guess that the ball did not go into the hoop. Thanks to Cress and Little for coming up with these interesting activities for us and applying them to math! We really appreciate it! :)
The equation for this graph is y= -2x+2 is x< or equal to 0, square root of 4-x squared if 0 < or equal to 0 < or equal to 2, (x-2) squared is x > or equal to 2. This is called a piece wise function, hence the title piece wise functions.
This week's activity consisted of us learning about inverse's and their functions; how better to learn about that than actually physically doing it? Our math teacher, Mr. Kelly, had us graph the function x^2, and then find the inverse. The inverse is found by switching out the xs for the ys, for example, the function is y=x^2 therefore the formula becomes x=y^2. Now, to get y by itself, square rooting the x and y to get rid of the squared is necessary. When a variable is square rooted, it has to be + or - so the formula is now, + or - square root of x = y, then we graphed both of those functions, the + or -. It looked like the same function sideways, then we had to draw the y=x which is a diagonal line with a slope of 1 that passes through the origin. Folding our graph along that line, our two graphs should have lined up, however my dotted line sucked and it didn't line up remotely, but if I had drew it right, it would have. This is how to graph the inverse of a function. The function that we drew, x^2 passes the vertical line test, making it a function, but since the inverse does not pass the vertical line test, it is not a function. However there are functions that pass both, for example, y=x or practically any straight line, they pass the vertical and horizontal line test. Big thanks to our teacher for being creative and for being great at what he does!
|
AuthorMy name is Evelyn Bradley and I'm in pre calculus! Archives
April 2015
Categories |