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2 years ago

For the given equation, find the values of a, b, and c, determine the direction in which

Mathematics

1 answer:

Shkiper50 [21]2 years ago

7 0

Answer: Table D

Step-by-step explanation:

The coefficient of x^2 is -9, the coefficient of x is 7, and the constant is 0, so we know a = -9, b = 7, c = 0.

This eliminates tables A, B, and C.

Thus, table D is the answer.

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katen-ka-za [31]

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(a)Length =2 feet

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Step-by-step explanation:

Let the dimensions of the box be x, y and z

The rectangular box has a square base.

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Volume of the box $=12 ft^3\\$

$Therefore, x^2z=12\\z=\frac{12}{x^2}$

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Area of the sides $=4xz$

Cost of the sides= $=\$0.10(4xz)$

Area of the Top $=x^2$

Cost of the Base $=\$0.13x^2$

Total Cost, $C(x,z) =0.17x^2+0.13x^2+0.10(4xz)$

Substituting $z=\frac{12}{x^2}$

$C(x) =0.17x^2+0.13x^2+0.10(4x)(\frac{12}{x^2})\\C(x)=0.3x^2+\frac{4.8}{x} \\C(x)=\dfrac{0.3x^3+4.8}{x}$

To minimize C(x), we solve for the derivative and obtain its critical point

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Recall: $z=\frac{12}{x^2}=\frac{12}{2^2}=3\\$

Therefore, the dimensions that minimizes the cost of the box are:

(a)Length =2 feet

(b)Width =2 feet

(c)Height=3 feet

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