Answer:
c
d
e
Step-by-step explanation:
Answer:
Area = 2500 square feet is the largest area enclosed
Step-by-step explanation:
A rectangular piece of land borders a wall. The land is to be enclosed and to be into divided 3 equal plots with 200 feet of fencing
Let x be the length of each box and y be the width of the box
Perimeter of the box= 3(length ) + 4(width)
![200=3x+4y](https://tex.z-dn.net/?f=200%3D3x%2B4y)
solve for y
![200=3x+4y](https://tex.z-dn.net/?f=200%3D3x%2B4y)
![200-3x=4y](https://tex.z-dn.net/?f=200-3x%3D4y)
divide both sides by 4
![y=50-\frac{3x}{4}](https://tex.z-dn.net/?f=y%3D50-%5Cfrac%7B3x%7D%7B4%7D)
Area of the rectangle = length times width
![Area = 3x \cdot y](https://tex.z-dn.net/?f=Area%20%3D%203x%20%5Ccdot%20y)
![Area = 3x \cdot (50-\frac{3x}{4})](https://tex.z-dn.net/?f=Area%20%3D%203x%20%5Ccdot%20%2850-%5Cfrac%7B3x%7D%7B4%7D%29)
![A=150x-\frac{9x^2}{4}](https://tex.z-dn.net/?f=A%3D150x-%5Cfrac%7B9x%5E2%7D%7B4%7D)
Now take derivative
![A'=150-\frac{9x}{2}](https://tex.z-dn.net/?f=A%27%3D150-%5Cfrac%7B9x%7D%7B2%7D)
Set it =0 and solve for x
![0=150-\frac{9x}{2}](https://tex.z-dn.net/?f=0%3D150-%5Cfrac%7B9x%7D%7B2%7D)
![150=\frac{9x}{2}](https://tex.z-dn.net/?f=150%3D%5Cfrac%7B9x%7D%7B2%7D)
multiply both sides by 2/9
![x=\frac{100}{3}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B100%7D%7B3%7D)
![A''=-\frac{9}{2}](https://tex.z-dn.net/?f=A%27%27%3D-%5Cfrac%7B9%7D%7B2%7D)
For any value of x, second derivative is negative
So maximum at x= 100/3
, replace the value of x
![A=150(\frac{100}{3})-\frac{9(\frac{100}{3})^2}{4})](https://tex.z-dn.net/?f=A%3D150%28%5Cfrac%7B100%7D%7B3%7D%29-%5Cfrac%7B9%28%5Cfrac%7B100%7D%7B3%7D%29%5E2%7D%7B4%7D%29)
Area = 2500 square feet is the largest area enclosed
Equation B could be used to solve the equation
No cos and ran are different values
Cos is 0.9and sin is 0.017 they aren’t exact figures but a rough estimate