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
we know the triangle is an isosceles, so it has twin sides, and then the hypotenuse, since it's a right-triangle, we can just use the pythagorean theorem for that.
![\bf \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies c=\sqrt{a^2+b^2} \qquad \begin{cases} c=hypotenuse\\ a=\stackrel{adjacent}{3\sqrt{2}}\\ b=\stackrel{opposite}{3\sqrt{2}}\\ \end{cases} \\\\\\ c=\sqrt{(3\sqrt{2})^2+(3\sqrt{2})^2}\implies c=\sqrt{(3^2\cdot 2)+(3^2\cdot 2)}\implies c=\sqrt{18+18} \\\\\\ c=\sqrt{36}\implies c=6](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7Busing%20the%20pythagorean%20theorem%7D%20%5C%5C%5C%5C%20c%5E2%3Da%5E2%2Bb%5E2%5Cimplies%20c%3D%5Csqrt%7Ba%5E2%2Bb%5E2%7D%20%5Cqquad%20%5Cbegin%7Bcases%7D%20c%3Dhypotenuse%5C%5C%20a%3D%5Cstackrel%7Badjacent%7D%7B3%5Csqrt%7B2%7D%7D%5C%5C%20b%3D%5Cstackrel%7Bopposite%7D%7B3%5Csqrt%7B2%7D%7D%5C%5C%20%5Cend%7Bcases%7D%20%5C%5C%5C%5C%5C%5C%20c%3D%5Csqrt%7B%283%5Csqrt%7B2%7D%29%5E2%2B%283%5Csqrt%7B2%7D%29%5E2%7D%5Cimplies%20c%3D%5Csqrt%7B%283%5E2%5Ccdot%202%29%2B%283%5E2%5Ccdot%202%29%7D%5Cimplies%20c%3D%5Csqrt%7B18%2B18%7D%20%5C%5C%5C%5C%5C%5C%20c%3D%5Csqrt%7B36%7D%5Cimplies%20c%3D6)
Answer:
(3)(5) + (1/3)(5) + (3)(1/4) + (1/3)(1/4)
Step-by-step explanation:
I'm pretty sure that's the correct answer..
Answer:
A. The top 8 Olympic shot putters in the preliminary round threw further on average than the top 8 U.S qualifiers
Step-by-step explanation:
Answer:
c
Step-by-step explanation: