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3 years ago

13

A dance school charges a registration fee in addition to a fee per lesson. The equation LaTeX: y=30x+25 y = 30 x + 25 represents

the total cost y of x lessons. What is the cost per lesson?

1 answer:

klasskru [66]3 years ago

7 0

The equation is 30x + 25
since the x is with the 30, that would be the cost per lesson, because you would multiply 30 by the number of lessons(x)

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. A right cylindrical drum is to hold 7.35 cubic feet of liquid. Find the dimensions (radius of the base and height) of the drum

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$V=\pi r^2h\\\Rightarrow h=\dfrac{V}{\pi r^2}\\\Rightarrow h=\dfrac{7.35}{\pi r^2}$

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So, the value of the function is minimum at $r=1.05$

$h=\dfrac{7.35}{\pi r^2}=\dfrac{7.35}{\pi 1.05^2}\\\Rightarrow h=2.12$

So, the radius and height which would minimize the surface area is 1.05 feet and 2.12 feet respectively.

Surface area

$A=2\pi r^2+2\pi rh\\\Rightarrow A=2\pi \times 1.05^2+2\pi 1.05\times 2.12\\\Rightarrow A=20.91\ \text{ft}^3$

The minimum surface area is $20.91\ \text{ft}^3$ .

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