Answer:
(a)Length =2 feet
(b)Width =2 feet
(c)Height=3 feet
Step-by-step explanation:
Let the dimensions of the box be x, y and z
The rectangular box has a square base.
Therefore, Volume of the box
Volume of the box

The material for the base costs
, the material for the sides costs
, and the material for the top costs
.
Area of the base 
Cost of the Base 
Area of the sides 
Cost of the sides=
Area of the Top 
Cost of the Base 
Total Cost, 
Substituting 

To minimize C(x), we solve for the derivative and obtain its critical point
![C'(x)=\dfrac{0.6x^3-4.8}{x^2}\\Setting \:C'(x)=0\\0.6x^3-4.8=0\\0.6x^3=4.8\\x^3=4.8\div 0.6\\x^3=8\\x=\sqrt[3]{8}=2](https://tex.z-dn.net/?f=C%27%28x%29%3D%5Cdfrac%7B0.6x%5E3-4.8%7D%7Bx%5E2%7D%5C%5CSetting%20%5C%3AC%27%28x%29%3D0%5C%5C0.6x%5E3-4.8%3D0%5C%5C0.6x%5E3%3D4.8%5C%5Cx%5E3%3D4.8%5Cdiv%200.6%5C%5Cx%5E3%3D8%5C%5Cx%3D%5Csqrt%5B3%5D%7B8%7D%3D2)
Recall: 
Therefore, the dimensions that minimizes the cost of the box are:
(a)Length =2 feet
(b)Width =2 feet
(c)Height=3 feet
we have
<u>The system of equations</u>
-------> equation 
-------> equation 
Substitute equation
in equation 

subtract
both sides


Divide by
both sides

the solution is the point 
therefore
the answer is
the solution to the system of equations is the point 
Answer:
D) L+S=9 ; 6L+3S=9
Step-by-step explanation:
Given this information, we know that the total number of large and small Ubers must be 9, so we can eliminate choices A and C as the first part of the system of equations is L+S=9
Also, since the large Ubers can fit only 6 people per vehicle and the small Ubers can only fit 3 people per vehicle, then we can eliminate choice B as the second part of the system of equations is 6L+3S=39
Therefore, the only correct choice is D
treat the tree trunk as a cylinder
v= pi x r^2 x h
using 3.14 for pi
3.14 x 3^2 x 10 = 282.6 cubic feet
282.6 * 45 = 12, 717 pounds
f' = -4x+8=0 => x=2
=> f(2) is the maximum = 11