Part A
The four plastic sides comprises of two equal squares of area
![x^{2}](https://tex.z-dn.net/?f=%20x%5E%7B2%7D%20)
each and two equal rectangles of area
![xy](https://tex.z-dn.net/?f=xy)
each.
Given that t<span>he total area of the four plastic sides is to be
![1200in^2](https://tex.z-dn.net/?f=1200in%5E2)
, thus:
![2x^2+2xy=1200 \\ \\ \Rightarrow x^2+xy=600 \\ \\ \Rightarrow xy=600-x^2](https://tex.z-dn.net/?f=2x%5E2%2B2xy%3D1200%20%5C%5C%20%20%5C%5C%20%5CRightarrow%20x%5E2%2Bxy%3D600%20%5C%5C%20%20%5C%5C%20%5CRightarrow%20xy%3D600-x%5E2)
The volume of the figure is given by: Volume = Area of base x depth
![V=(xy)x=x(600-x^2)=600x-x^3](https://tex.z-dn.net/?f=V%3D%28xy%29x%3Dx%28600-x%5E2%29%3D600x-x%5E3)
Part B:
For maximum volume, the derivative of V with respect to x will equal 0.
![\frac{dV}{dx} =0 \\ \\ \Rightarrow600-3x^2=0 \\ \\ \Rightarrow3x^2=600 \\ \\ \Rightarrow x^2=200 \\ \\ \Rightarrow x=\pm \sqrt{200} =\pm14.14](https://tex.z-dn.net/?f=%20%5Cfrac%7BdV%7D%7Bdx%7D%20%3D0%20%5C%5C%20%20%5C%5C%20%5CRightarrow600-3x%5E2%3D0%20%5C%5C%20%20%5C%5C%20%5CRightarrow3x%5E2%3D600%20%5C%5C%20%20%5C%5C%20%5CRightarrow%20x%5E2%3D200%20%5C%5C%20%20%5C%5C%20%5CRightarrow%20x%3D%5Cpm%20%5Csqrt%7B200%7D%20%3D%5Cpm14.14)
But dimensions has to be positive, thus the value of x which produces maximum volume is x = 14.14
Recall that
![xy=600-x \\ \\ \Rightarrow y= \frac{600}{x} -x \\ \\ = \frac{600}{14.14} -14.14 \\ \\ =42.43-14.14 \\ \\ =28.29](https://tex.z-dn.net/?f=xy%3D600-x%20%5C%5C%20%20%5C%5C%20%5CRightarrow%20y%3D%20%5Cfrac%7B600%7D%7Bx%7D%20-x%20%5C%5C%20%20%5C%5C%20%3D%20%5Cfrac%7B600%7D%7B14.14%7D%20-14.14%20%5C%5C%20%20%5C%5C%20%3D42.43-14.14%20%5C%5C%20%20%5C%5C%20%3D28.29)
Therefore, the </span><span>dimensions that will maximize the volume of the shelter is x = 14.14 and y = 28.29</span>
The answer is 125 because u divide 625 by 5
Answer:
D
Step-by-step explanation:
just do it. (Nike supports you)
Answer:
100y - 16
Step-by-step explanation:
Answer: 93.6
Step-by-step explanation:
26% = 26/100 = 0.26
0.26 * 360 = 93.6