Problem Statement:
A rectangle has one corner on the graph of y=16-x2 , another at the origin, a third on the positive y-axis, and the fourth on the positive x-axis. If the area of the rectangle is a function of x, what value of x yields the largest area for the rectangle.
This was the question that was given to us and basically what we had to do was to find the maximum area of the rectange and the maximum perimeter.
This was the question that was given to us and basically what we had to do was to find the maximum area of the rectange and the maximum perimeter.
Initial Attempts:
Next what we did from the first graph we multiplied the positive numbers, 1 x 15= 15,
2 x 12= 24, 3 x 7=21 and 4 x 0=0 and we got this new x,y graph which helped us find the maximum area. From that table we did another one to find the actual number using number bigger than 2 so we started with 1.1 and plugged this into the equation which is (16(x)squared) times X. We went on until we found that 2.3 was the biggest it could get so the maximum area is 24.63. This part of the problem of finding the decimal number was challenging because at first I didnt get why we had to modiify the equation a little but then Azzael explained it to me and I got it. |
To find the perimeter we came up with a new equation, we made a graph table to find the maximum perimeter and we got 28.
This part of the problem was the most challenging because I didn't understand how we came up with the equation but with the practice and the explanations that I got from my group everything cleared up, and it tuned out to be very easy I just needed a push. |
Final Solution:
Individual Test/Group Test:
For the Group test it was very good because our group work was excellent we were all helping each other to find the answers it was challenging but having all of us complementing really helped the process of finding the equations and answers.
|
For the Individual test I didn't do very well because I forgot how to create an equation for the perimeter part the test; I felt like if I had more practice I could of done it better but I didn't practice a lot so I forgot, also not having the support from the group made me feet like I was doing everything wrong.
|
Reflection:
If I were to get a grade myself in a scale from 1-10, I would give myself an 8.5 because I know I could of done a lot better on this problem.