Answer:
48∛9 ft²
Step-by-step explanation:
The length (L) and width (W) are given by:
![L = 4\sqrt[3]{24}\\ W= 6\sqrt[3]{3}](https://tex.z-dn.net/?f=L%20%3D%204%5Csqrt%5B3%5D%7B24%7D%5C%5C%20W%3D%206%5Csqrt%5B3%5D%7B3%7D)
Since this is a rectangular region, the area is given by:
![A=L*W=L \\A=4\sqrt[3]{24}* 6\sqrt[3]{3}\\A=24\sqrt[3]{72}\ ft^2](https://tex.z-dn.net/?f=A%3DL%2AW%3DL%20%5C%5CA%3D4%5Csqrt%5B3%5D%7B24%7D%2A%206%5Csqrt%5B3%5D%7B3%7D%5C%5CA%3D24%5Csqrt%5B3%5D%7B72%7D%5C%20ft%5E2)
The answer can be further simplified by factoring as follows:
![A=24\sqrt[3]{72} = \\A=24\sqrt[3]{2*2*2*3*3}= 24\sqrt[3]{2^3*9}\\A=48\sqrt[3]{9}\ ft^2](https://tex.z-dn.net/?f=A%3D24%5Csqrt%5B3%5D%7B72%7D%20%3D%20%5C%5CA%3D24%5Csqrt%5B3%5D%7B2%2A2%2A2%2A3%2A3%7D%3D%2024%5Csqrt%5B3%5D%7B2%5E3%2A9%7D%5C%5CA%3D48%5Csqrt%5B3%5D%7B9%7D%5C%20ft%5E2)
The exact area is its simplest form is 48∛9 ft²
One function you would be trying to minimize is
<span>f(x, y, z) = d² = (x - 4)² + y² + (z + 5)² </span>
<span>Your values for x, y, z, and λ would be correct, but </span>
<span>d² = (20/3 - 4)² + (8/3)² + (-7/3 + 5)² </span>
<span>d² = (8/3)² + (8/3)² + (8/3)² </span>
<span>d² = 64/3 </span>
<span>d = 8/sqrt(3) = 8sqrt(3)/3</span>
Area= i^2 + 4i
Area= length x width
Length (y)= i + 4
Width (i)=i
