In each of these graphs their is a use of different mathematics equations that create interesting pictures that some could define as art and others define as boring. For the top left graph it starts of as R=theta which gives it the swirls, next their is r=a+1costheta which gives the graphs the the small circles at the center of the graph, and last for the this graph their is the equation r=11sin14theta which gives the graph the flower circling around it. For the top right graph the equation used is r=asinbtheta, with the b=1.7 and the a=-8 it gives the graph the spiraling circles that overlap each other to make a big flower. For the final graph at the bottom it uses the equation r is <= sin(a/btheta) with a=5 and b=6 being multiplied by sin creates a group of circles around the center axis that when come together and shaded form a flower within the circles from the equation. At the beginning of the trimester the art that we were making on desmos was simple lines like cos and sin that would make waves. As the trimester progressed we learned how to create waves that could go in certain direction and had the ability to go on different angles. We were taught various equations and formulas that would expand our knowledge and give us the ability to to create more creative art graphs on desmos which led us to being able to create the beautiful graphs you see on this assignment.
Desmos Art Portfolio
In each of these graphs their is a use of different mathematics equations that create interesting pictures that some could define as art and others define as boring. For the top left graph it starts of as R=theta which gives it the swirls, next their is r=a+1costheta which gives the graphs the the small circles at the center of the graph, and last for the this graph their is the equation r=11sin14theta which gives the graph the flower circling around it. For the top right graph the equation used is r=asinbtheta, with the b=1.7 and the a=-8 it gives the graph the spiraling circles that overlap each other to make a big flower. For the final graph at the bottom it uses the equation r is <= sin(a/btheta) with a=5 and b=6 being multiplied by sin creates a group of circles around the center axis that when come together and shaded form a flower within the circles from the equation. At the beginning of the trimester the art that we were making on desmos was simple lines like cos and sin that would make waves. As the trimester progressed we learned how to create waves that could go in certain direction and had the ability to go on different angles. We were taught various equations and formulas that would expand our knowledge and give us the ability to to create more creative art graphs on desmos which led us to being able to create the beautiful graphs you see on this assignment.
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For the first picture I used 3 different equations
Using these three equations I was able to make the swirling effect go out of the center along with the two circles in the middle that have circles within their circles. Finally I used a variation of the equation asinbtheta to make the rose in the middle. For the second image I used only the equation asinbtheta and then changed what a and b was in the equation.
h=2.415sin(pi/6(t-2.5670))+12.25
Jan- 2.415sin(pi/6(1-2.5670))+12.25 10 hours Feb-2.415sin(pi/6(2-2.5670))+12.25 11 hours Mar- 2.415sin(pi/6(3-2.5670))+12.25 12 hours Apr-2.415sin(pi/6(4-2.5670))+12.25 13 hours May-2.415sin(pi/6(5-2.5670))+12.25 14 hours Jun-2.415sin(pi/6(6-2.5670))+12.25 14 hours Jul-2.415sin(pi/6(7-2.5670))+12.25 13 hours Aug-2.415sin(pi/6(8-2.5670))+12.25 12 hours Sep-2.415sin(pi/6(9-2.5670))+12.25 11 hours Oct-2.415sin(pi/6(10-2.5670))+12.25 10 hours Nov-2.415sin(pi/6(11-2.5670))+12.25 10 hours Dec-2.415sin(pi/6(12-2.5670))+12.25 10 hours You can move to Yuma because 6 months out of the year half the day or more will be sunny for more than half the day. Summary and Reflection are at the end of the presentation, google would not let me embed the presentation so here is the link to it. The circle graphs can be used with the 30,60,90 triangle and the 45,45,90 triangle to find the point of the problem on the Cartesian plane. The Cartesian plane can be used to find points on the circle graph. That sin can be used as 1 when the finding what the point is on the y-axis of the Cartesian point. This gave me a different view, a more visual one that I could not get from the book on this subject. Using my partner we were able to talk our way through all the problems to find an answer we were confident in.
The amplitude and periods of the graphs
sin- the amplitude consistently goes up to 1 and down to negative 1, the period is every 4 blocks on the x-axis the lines meets up with it cos- the amplitude repeatedly goes up to 1 and down to negative 1, the period is every 4 blocks it crosses the x-axis tan-the amplitude goes off the graph at an asymptote repeatedly, the period is every 5 blocks where it crosses the x-axis csc-the amplitude seems to go off the graph at 2 separate points and is then followed by small humps, the period seems to cross the x-axis twice at an area of two blocks then skips 8 blocks and repeats the process sec-the amplitude is 2 and negative 2 then after leaves the graph at an asymptote, the period seems to be every 8 blocks then flips to the opposite side of the x-axis cot-the amplitude seems to leave the graphs then go to the point of 1.5 then negative 1.5, the period is that it continues to cross the x-axis every six blocks sine and cosine- it seems that these are basically the same graph with the exception that cosine meets up with the y-axis half way through ones of its positive intervals the vertical asymptotes are located where they are due to the type of graphthey are they often have errors that cause the graphs to have blank spaces where the errors occur
For my final project I chose the activity of skateboarding and what it has to do with math. Skateboarding has a lot to do with the pushes and pulls of gravity and the wooden board on wheels travels at the various paces and the various ways it does. This diagram helps explain how math can be used to calculate various things you can do in skate by using the key components Speed, Distance, and Time. Using these components one can determine how long it will take to skate up a hill, how far you can go with the speed going down a hill, or how much speed it is going to take to skate from point to point.
For skating up a hill the equation that will be used is Distance/Speed For speed you can get going down a hill equation is Distance/Time For flat land covered on a skateboard it is Speed x Time These equation will help determine various things skateboards can be and are used for along with how they can be used in the pre-calc domain which connects to many characteristics of physics. PART 1
1. Direct subsidized loan-loans available to undergraduates Terms to pay it back can be chosen during the time loan is taken or after, Interest rate: After 7/1/13 and before 7/1/14-3.86% after 7/1/14 and before 7/1/15-4.66% Parents along with student can take out loans Direct Un subsidized loans- loans available to undergraduates, graduates, or professionals Terms are first six months out of school (grace period), After 7/1/13 and before 7/1/14-3.86% After 7/1/13 and before 7/1/15-4.66% Parents can Take out These loans Direct plus loan- loans available to Parents and Graduate or Professional Students Terms are up to 10 years to pay back Interest Rate: After 7/1/13 and before 7/1/14-6.41% After 7/1/13 and before 7/1/15-7.21% Undergraduates along with professional students can take out these loans 2. interest is calculated by x number of days since last payment times x interest rate factor= interest amount Payment is calculated by the principle amount times monthly interest over 1-(1+Monthly payment) to the power of amount of months Interest can work like a graph where the longer it is put off being payed the more it will increase like a linear graph of a linear equation, quarterly interests will normally be lower than that of an annual interest based upon the type and variation of loan Direct subsidized loan-Loan is subsidized while in college Direct Un subsidized loans-Loan is unsubsidized so it can be payed in college or after Direct plus loan- Loan is lenient and allows payment during college or after Interest Rates Direct subsidized loan-After 7/1/13 and before 7/1/14-3.86%, 7/1/14 and before 7/1/15-4.66% Direct Un subsidized loans- After 7/1/13 and before 7/1/14-3.86% ,7/1/14 and before 7/1/15-4.66% Direct plus loan-After 7/1/13 and before 7/1/14-6.41%, After 7/1/13 and before 7/1/15-7.21% PART 2 P(1+r/n)^t*n-(monthly Payment)nt Loan Balance:$2,333.37 Adjusted Loan Balance:$2,333.37 Loan Interest Rate:3.86%Loan Fees:0.00%Loan Term:4.3 years Minimum Payment:$50.00 Enrollment Status:In Repayment Degree Program:Bachelor's Degree Total Years in College:4 years Average Debt per Year:$583.34 Monthly Loan Payment:$50.00Number of Payments:51 Cumulative Payments:$2,532.36 Total Interest Paid:$198.99 |
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March 2015
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