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Studentka2010 [4]

3 years ago

15

Sally pays $38 per hour for dance class after paying the enrollment fee of $100. Identify the constant of proportionality that r

elates her dance class charges (y) to the number of hours (x) she goes to class.
A) x
B) y
C) $38
D) $138

1 answer:

lakkis [162]3 years ago

8 0

C because y=mx+b and the constant is the slope which is m. The equation is y =38x+100

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Volume of the Square-Based box=171,500 cubic cm

Let the length of a side of the base=x cm

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Surface Area of the Sides=4xh

Cost of the sides=$2.50 X 4xh =10xh

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Therefore, total Cost of the box

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To find the minimum total cost, we solve for the critical points of C(x). This is obtained by equating its derivative to zero and solving for x.

$C'(x)=\dfrac{40x^3-1715000}{x^2}\\\dfrac{40x^3-1715000}{x^2}=0\\40x^3-1715000=0\\40x^3=1715000\\x^3=1715000\div 40\\x^3=42875\\x=\sqrt[3]{42875}=35$

Recall that:

$h=\dfrac{171500}{x^2}\\Therefore:\\h=\dfrac{171500}{35^2}=140cm$

The dimensions that will lead to minimum costs are base length of 35cm and height of 140cm.

Therefore, the minimum total cost, at x=35cm

$C(35)=\dfrac{20(35)^3+1715000}{35}=\$29,400$

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