Answer:
10x-20
Step-by-step explanation:
(5×2x)-(5×4)
10x-20
Answer:
4/14
Step-by-step explanation:
2+1+7+4=14
red marbles are 4/14
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![V=x^2z](https://tex.z-dn.net/?f=V%3Dx%5E2z)
Volume of the box![=12 ft^3\\](https://tex.z-dn.net/?f=%3D12%20ft%5E3%5C%5C)
![Therefore, x^2z=12\\z=\frac{12}{x^2}](https://tex.z-dn.net/?f=Therefore%2C%20x%5E2z%3D12%5C%5Cz%3D%5Cfrac%7B12%7D%7Bx%5E2%7D)
The material for the base costs
, the material for the sides costs
, and the material for the top costs
.
Area of the base ![=x^2](https://tex.z-dn.net/?f=%3Dx%5E2)
Cost of the Base ![=\$0.17x^2](https://tex.z-dn.net/?f=%3D%5C%240.17x%5E2)
Area of the sides ![=4xz](https://tex.z-dn.net/?f=%3D4xz)
Cost of the sides=![=\$0.10(4xz)](https://tex.z-dn.net/?f=%3D%5C%240.10%284xz%29)
Area of the Top ![=x^2](https://tex.z-dn.net/?f=%3Dx%5E2)
Cost of the Base ![=\$0.13x^2](https://tex.z-dn.net/?f=%3D%5C%240.13x%5E2)
Total Cost, ![C(x,z) =0.17x^2+0.13x^2+0.10(4xz)](https://tex.z-dn.net/?f=C%28x%2Cz%29%20%3D0.17x%5E2%2B0.13x%5E2%2B0.10%284xz%29)
Substituting ![z=\frac{12}{x^2}](https://tex.z-dn.net/?f=z%3D%5Cfrac%7B12%7D%7Bx%5E2%7D)
![C(x) =0.17x^2+0.13x^2+0.10(4x)(\frac{12}{x^2})\\C(x)=0.3x^2+\frac{4.8}{x} \\C(x)=\dfrac{0.3x^3+4.8}{x}](https://tex.z-dn.net/?f=C%28x%29%20%3D0.17x%5E2%2B0.13x%5E2%2B0.10%284x%29%28%5Cfrac%7B12%7D%7Bx%5E2%7D%29%5C%5CC%28x%29%3D0.3x%5E2%2B%5Cfrac%7B4.8%7D%7Bx%7D%20%5C%5CC%28x%29%3D%5Cdfrac%7B0.3x%5E3%2B4.8%7D%7Bx%7D)
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: ![z=\frac{12}{x^2}=\frac{12}{2^2}=3\\](https://tex.z-dn.net/?f=z%3D%5Cfrac%7B12%7D%7Bx%5E2%7D%3D%5Cfrac%7B12%7D%7B2%5E2%7D%3D3%5C%5C)
Therefore, the dimensions that minimizes the cost of the box are:
(a)Length =2 feet
(b)Width =2 feet
(c)Height=3 feet
Answer:
153 miles
Step-by-step explanation:
36 * 4.25 = 153