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Furkat [3]
3 years ago
9

The radius of a sphere is increasing at a rate of 5 mm/s. How fast is the volume increasing (in mm3/s) when the diameter is 40 m

m
Mathematics
1 answer:
jeka943 years ago
4 0

9514 1404 393

Answer:

  8000π mm^3/s ≈ 25,133 mm^3/s

Step-by-step explanation:

The rate of change of volume is found by differentiating the volume formula with respect to time.

  V = 4/3πr^3

  V' = 4πr^2·r'

For the given numbers, this is ...

  V' = 4π(20 mm)^2·(5 mm/s) = 8000π mm^3/s ≈ 25,133 mm^3/s

_____

<em>Additional comment</em>

By comparing the derivative to the area formula for a sphere, you see that the rate of change of volume is the product of the area and the rate of change of radius. This sort of relationship will be seen for a number of different shapes.

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Answer:

Number of $5 bills = 32

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Number of $20 bills = 8

Step-by-step explanation:

Let x number of $5, y number of $10 and z number of $20

The number of $5 bills exceeds twice the number of $10 bills by 4.

Therefore, x = 2y + 4

The number of $20 bills is 6 fewer than the number of $10 bills.

Therefore, z = y - 6

A wallet contains $460 in $5, $10, and $20 bills.

Therefore,

5x + 10y + 20z = 460

Substitute x and y into equation

    5(2y+4) + 10y + 20(y-6) = 460

10y + 20 + 10y + 20y - 120 = 460

                           40y - 100 = 460

                                    40y = 460 + 100

                                    40y = 560

                                      y = 14

  • Put the value of y into x = 2y + 4 and solve for x

                                      x = 2(14) + 4

                                      x = 32

  • Put the value of y into z = y - 6 and solve for z

                                      z = 14 - 6

                                      z = 8

Hence, the each type of bills,

Number of $5 bills = 32

Number of $10 bills = 14

Number of $20 bills = 8

3 0
3 years ago
Read 2 more answers
Please help me solve for x
ohaa [14]

Answer:

You would do this problem like a normal varible problem. x=10

Step-by-step explanation:

Since 9x is a right angle the inside would also be 9x

9x+4x+10+40=180

180 because that is how much a triangle equals

combine like terms

13x+50=180

subtract 50 from both sides

13x=130

divide by 13

x=10

<u>Hope this helps!</u>

7 0
3 years ago
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Cloud [144]

Answer:

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Step-by-step explanation:

The perimeter of the square base of a pyramid = 7.3 ft

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The perimeter of a square is given by :

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Here, l = b = 1.825 ft

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V=\dfrac{1.825\times 1.825\times 6}{3}\\\\V=6.66\ ft^3

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Answer:

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3 0
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!!!*BRAINLIEST*!!!
sweet-ann [11.9K]

Answer:

I'm pretty sure the answer is [B] 10,368.

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