Problem Statement
A rectangle has one corner on the graph of Y=16-X squared, another at the origin, a third on the positive Y-axis, and the fourth on the X-axis. If the area of the rectangle is a function of X, what value of X yields the largest area.
Process
Initial Attempt/s:
When I first got this problem I had no idea what to do or where to start, I looked at the equation again and noticed that you can almost plug anything in for X in the function so I made a t-table with the numbers 0-5 as X and used the formula in the problem above to find the Y-intercepts. Doing this we soon got point's to be able to put onto a graph, creating an upside-down parabola, soon after plotting the points we were able to find the area of each rectangle in the parabola using the formula of A=Y*X. With all of this information we were able to create a second table with just the X intercepts and the area's we found and tried to see which one had the largest area and it was 2, we then tried to calculate an in between number somewhere between 1 and 2 or 2 and 3 and we found that 2.31 was the biggest number we could get. To find this out we used the original function of Y=16-X^2. |
Solution
Maximum Area:With all of this information we were able to create a second table with just the X intercepts and the area's we found and tried to see which one had the largest area and it was 2, we then tried to calculate an in between number somewhere between 1 and 2 or 2 and 3 and we found that 2.31 was the biggest number we could get. To find this out we used the original function of Y=16-X^2.
Maximum Perimeter:
To find the maximum perimeter we had to use p=2(X(16-x^2)), we used this equation because to solve the perimeter you use P=2(length x Width) aka P=2(XxY), you end up plugging in the original function for Y. We ended up doing the same thing we had done for maximum area, trying to find the biggest outcome which was 5.
Maximum Perimeter:
To find the maximum perimeter we had to use p=2(X(16-x^2)), we used this equation because to solve the perimeter you use P=2(length x Width) aka P=2(XxY), you end up plugging in the original function for Y. We ended up doing the same thing we had done for maximum area, trying to find the biggest outcome which was 5.
Group Test/ Individual Test
In preparation for the quiz we went over the original problem as much as we could to make sure we all knew what we had to do the next day for the group quiz. We discussed things that we were all confused about and we tried to clarify any questions anyone had as much as we could. During the group test we all collaborated really well and tried to all stay at the same pace and same question's, I think the group test overall helped everyone "digest" what we had to do and how to do it before the individual test.
The individual test was quite easy for me especially since we had done the group quiz before hand, it was a really good refresher for me and helped me not blank during the test which I happen to do a lot. Doing a group test before an individual test is very helpful because it gives me a little more time to "study" and go over things before hand.
The individual test was quite easy for me especially since we had done the group quiz before hand, it was a really good refresher for me and helped me not blank during the test which I happen to do a lot. Doing a group test before an individual test is very helpful because it gives me a little more time to "study" and go over things before hand.
Evaluation/Reflection
I feel like this really pushed me to use a lot some things that I learned in sophomore year, and this problem really challenged my thinking by having to use something I learned almost about a year ago. If I was to grade myself on this unit I think i'd give myself an A because I worked really hard to understand the concept and how to do it, I contributed a lot to the group work and helped others in group understand how to solve it which I think really shows how well I understood the concept.