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2 years ago

What is the answer for #7?

Mathematics

1 answer:

Karo-lina-s [1.5K]2 years ago

3 0

Answer:

radius: 1.84 in
height: 3.68 in

Step-by-step explanation:

After you've worked a couple of "optimum cylinder" problems, you find that the cylinder with the least surface area for a given volume has a height that is equal to its diameter. So, the volume equation becomes ...

V = πr²·h = 2πr³ = 39 in³

Then the radius is ...

r = ∛(39/(2π)) in ≈ 1.83779 in ≈ 1.84 in

h = 2r = 3.67557 in ≈ 3.68 in

_____

The total surface area of a cylinder is ...

S = 2πr² + 2πrh

For a given volume, V, this becomes ...

S = 2π(r² +r·(V/(πr²))) = 2πr² +2V/r

The derivative of this with respect to r is ...

S' = 4πr -2V/r²

Setting this to zero and multiplying by r²/2 gives ...

0 = 2πr³ -V

r = ∛(V/(2π)) . . . . . . . . looks a lot like the expression above for r

If we substitute the equation for V into the equation just above this last one, we have ...

0 = 2πr³ - πr²·h

Dividing by πr² gives ...

0 = 2r - h

h = 2r . . . . . generic solution for cylinder optimization problems

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Based on the fact that the radius of the snowball increases by 0.36 inches every second, the linear function can be found to be y = 0.36x + 1.66

<h3>How to find the linear function?</h3>

The linear function is the function that shows how to change in the rate of the independent variable would affect the rate of change in the dependent variable.

The linear function takes the form:

y = mx + b

y = dependent variable

m = slope or change in radius of snowball

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Solving for the y-intercept gives:

3.1 = 0.36(4) + b

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1 year ago

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Answer:

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Step-by-step explanation:

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