Mathematics, 31.10.2019 03:31 faithtunison

Arectangular box with a square base and a cover is to be built to contain 640 cubic feet. if the cost per square foot for the bottom is $15 and for the top and the sides is $10, what is the minimum cost of the constructed box?

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Answer from: maguilarz2005

$4800

Step-by-step explanation:

The cost is minimized when any pair of opposite faces of the box costs the same as any other pair. Since the top+bottom total $25 per square foot and the sides (left+right or front+back) total $20 per square foot, the area of a side must be 25/20 = 5/4 times the area of the top or bottom.

If we let x represent the length of one side of the square bottom, then 5/4x will be the height of the box. Its volume will be ...

(5/4x)(x²) = 640 ft³

x³ = (4/5)(640 ft³) = 512 ft³ . . . . . . multiply by 4/5

x = 8 ft . . . . . . . . . . . . . . . . . . . . . . . take the cube root

The base area is then (8 ft)² = 64 ft², and the cost of the top+bottom is ...

64 ft² × $25/ft² = $1600

The three pairs of opposite sides will cost 3×$1600 = $4800.

The minimum cost of the constructed box is $4800.

_____

You can also write an equation for the total cost in terms of x, the side length of the base. That cost function will be ...

c(x) = 15x² + 10x² + 10·4x(640/x²)

This simplifies to ...

c(x) = 25x² +25600/x

A graph shows the minimum is c(8) = 4800 (as above).

Algebraically, you can set the derivative to zero to find the value of x.

dc/dx = 0 = 50x -25600/x²

512 = x³ . . . . multiply by x²/50 and add 512

8 = x . . . . . . . take the square root. Same solution as above. Cost is minimized when the side length of the base is 8 ft.

Arectangular box with a square base and a cover is to be built to contain 640 cubic feet. if the cos

Answer from: Quest

Heidi’s has to come to a party tomorrow night at the navy house i was like going home i have ig

Answer from: Quest

correct choice is b

step-by-step explanation:

when you calculate the average rate of change of a function, you are finding the slope of the secant line between the two points. for the function $y=f(x)$ the average rate of change from point $a(a,f(a))$ to point $b(b,f(b))$ can be calculated as

$\text{average rate of change}=\dfrac{f(b)-f(a)}{b-a}.$

to find the average rate of change from day 2 to day 10, note that at day 2, 8 houses were sold, so a(2,8) and at day 10, 2 houses were sold, so b(10,2). thus,

$\text{average rate of change}=\dfrac{2-8}{10-2}=\dfrac{-6}{8}=-\dfrac{3}{4}.$

The graph below shows the number of houses sold over x days. what is the average rate of change from

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