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
Answer:
112.5 deg
Step-by-step explanation:
First we find the area of the entire circle.
A = pi * r^2
A = pi * (4 m)^2
A = 16pi m^2
The entire circle has area = 16pi m^2.
The sector has area 5pi m^2.
Now we find the fraction the area of the sector is of the entire circle.
fraction = (5pi m^2)/(16pi m^2) = 5/16 = 0.3125
The full circle has a central angle of 360 deg, the entire circle.
The measure of the central angle of the arc of the sector is the same fraction of the entire circle.
measure of sector angle = 0.3125 * 360 deg = 112.5 deg
Answer:
The table on the right, the green table, is the one that shows a proportional relationship
Step-by-step explanation:
Step-by-step explanation:
We will use pythagoras' Theorem for this question
where c is the longest side (in this case, the diagonal)
a and b are the 2nd and 3rd longest side (interchangeable)
given a = 10.6, b = 16.8,
