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
Letter D
1-sin^2(x) = cos^2(x)
= sin^2(x)/cos^2(x)
= tan^2(x)
Answer:
90
Step-by-step explanation:
Start with changing 35% and 30% to a decimal.
35% = .35%
30% = .30%
Then multiply 105 by .30%. ( but don't put the percent sign in the calculator when multiplying)
105 x .30% = 31.5
Then you want to divide 31.5 by .35%
31.5 / .35% = 90
Answer:
F = 110°
I'm not sure, but since no one answered, here it goes...
Step-by-step explanation:
∵ FD = FE (Given in Diagram)
∴ ΔDFE is isosceles , ∴m∠E = m∠D
1 ) 3x + 14 = 5x
14 = 5x - 3x
14 = 2x
14 / 2 = x
7 = x
m∠E = 3*7 + 14 = 35°
m∠D = 5*7 = 35°
m∠F = 180 - (35+35)
m∠F = 110°
