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Liono4ka [1.6K]
3 years ago
10

What is the answer for #7?

Mathematics
1 answer:
Karo-lina-s [1.5K]3 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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Ede4ka [16]

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Hope this helped!

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3 years ago
Find the area of the shaded regions below. Give your answer as a completely simplified exact value in terms of π (no approximati
Svetach [21]

Answer:

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Step-by-step explanation:

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and this triangle is a right triangle so side A=B

that means the other leg is 6.Knowing that we can solve

The formula for the area of a triangle is (base×height)÷2

so that means 6×6 equals 36 and if you divide that by 2 you get the 18.

Now we will deal with the semicircle. We know that both of the legs are 6 so that means the diameter is 6 and now we solve 6 divided by 2 equals 3 and we will have to square that and we will 9 and since it is a semicircle we have to divide it by 2  and that will give us 4.5 and since we have to express it in terms of pi it will be 4.5(pi) and then we add both of the areas

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8 0
3 years ago
On a 16 scale drawing of a bike, one part is 3 inches long. How long will the actual bike part be?
Oksanka [162]
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4 0
3 years ago
Read 2 more answers
14, 8, 17, 21, x, 11,<br> 3, 13; range: 20​
MakcuM [25]

Answer:

x = 1

Step-by-step explanation:

When you subtract the smallest number from the biggest number, the answer is called the range. Here the largest number is 21. The smallest is 3. Then the range should be 18. But since it's 20. This mean that x is 1. Because 21 - 1 will equal 20, making 20 the range. So the correct answer is 1.

6 0
3 years ago
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Kobotan [32]

Answer:

You should put "no solution" into the parallel lines box,

you should put "infinite solutions" into the coinciding lines box,

you should put the "(0,0)" and the "(3,-2)" into the intersecting lines box.

Step-by-step explanation:

5 0
3 years ago
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