Mathematics, 20.09.2020 14:01 ruslffdr

A rectangular box with a depth of 10 inches and a square base is to be manufactured by the Bold Box Company. The top of the box costs $1.20 per square inch, the bottom costs $.95 per square inch and the sides cost $.75 per square inch. Express the cost of manufacturing this box as a function of length.

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Answer from: Tsumiki

The cost function of manufacturing this box is:

$C_{T} = 2.15\cdot x^{2}+30\cdot x$ , where is the length of the box, measured in US dollars.

Step-by-step explanation:

From the statement we know that:

1) The box has a square base ( w = l = x ).

2) The box has a depth of 10 inches ( $h = 10\,in$ ).

3) The cost of manufacturing the top of the box is $ 1.20 per square inch.

4) The cost of manufacturing the bottom of the box is $ 0.95 per square inch.

5) The cost of manufacturing each side of the box is $ 0.75 per square inch.

The total cost of manufacturing the box is:

$C_{T} =C_{bottom} + C_{top} + 4\cdot C_{side}$

Where:

$C_{bottom}$ - Cost of the bottom of the box, measured in US dollars.

$C_{top}$ - Cost of the top of the box, measured in US dollars.

$C_{side}$ - Cost of the side of the box, measured in US dollars.

Dimensionally, cost equals unit cost, measured in US dollars by square inch, multiplied by surface area, measured in square inches. Now, the expression is expanded:

$C_{T} = c_{bottom}\cdot x^{2}+c_{top}\cdot x^{2}+4\cdot c_{side}\cdot h\cdot x$

$C_{T} =(c_{bottom}+c_{top})\cdot x^{2}+4\cdot c_{side}\cdot h \cdot x$

If we know that $c_{bottom} = \$\,0.95\,in^{-2}$ , $c_{top} = \$\,1.20\,in^{-2}$ , $c_{side} = \$\,0.75\,in^{-2}$ and $h = 10\,in$ , the cost function of manufacturing this box is:

$C_{T} = 2.15\cdot x^{2}+30\cdot x$ , where is the length of the box, measured in US dollars.

Answer from: Quest

pentagon

step-by-step explanation:

the coordinates a(5, -2), b(3,-1),c(-4,-4) d(-3,8) and e(-1,4) forms the vertices of the polygon when they are connected in order.

in order to classify that which polygon is it with the given coordinates, first count the number of vertices and then count the number of sides it can make with these vertices.

since, the given coordinates have five vertices, therefore, it will make five sides. moreover, pentagon is regular in nature therefore it will be convex.

now, a polygon with five sides is known as pentagon, therefore, the given polygon is the pentagon.

Answer from: Quest

the terms of a geometric sequence can be found by beginning with the first term and multiplying by the common ratio repeatedly. a recursive formula for a geometric sequence with common ratio r is given by an=ran−1 a n = r a n − 1 for n≥2 n ≥ 2 .

step-by-step explanation:

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A rectangular box with a depth of 10 inches and a square base is to be manufactured by the Bold Box...

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