1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
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.

You might be interested in
When an article is sold for $132.00, a profit of 10% is made. The cost of the<br> article is?
Orlov [11]

Answer:

118.8

Step-by-step explanation:

Profit=10%

=10/100 × $132

=$13.2

Cost price=Selling price- Cost price

=$132-$13.2

=$118.8

3 0
2 years ago
Help please will mark brainliest.
swat32

Answer: the ANSWER IS 11 sqt

Step-by-step explanation:

Factor 1331 into its prime factors

          1331 = 113

To simplify a square root, we extract factors which are squares, i.e., factors that are raised to an even exponent.

Factors which will be extracted are :

          121 = 112

Factors which will remain inside the root are :

          11 = 11

To complete the simplification we take the squre root of the factors which are to be extracted. We do this by dividing their exponents by 2 :

          11 = 11

The simplified SQRT looks like this:

        11 • sqrt (11)  

Simplified Root :

11 • sqrt(11)

7 0
3 years ago
Read 2 more answers
4) Solve radical equations
blondinia [14]
R - 10 = 18 - r
2r = 28
r = 14
7 0
3 years ago
Here’s a graph of a linear function. Write the equation that describes that function
inessss [21]

Answer:

The equation of the line is y = 1/4x - 4

Step-by-step explanation:

In order to find this, start with two points that are on the line. We'll use (0, -4) and (4, -3). Now we can use the slope formula to find the slope.

m(slope) = (y2 - y1)/(x2 - x1)

m = (-4 - -3)/(0 - 4)

m = -1/-4

m = 1/4

Now that we have this, we can use that slope and a point in point-slope form. Then we solve for y to get the equation.

y - y1 = m(x - x1)

y - -4 = 1/4(x - 0)

y + 4 = 1/4x

y = 1/4x - 4

8 0
3 years ago
Given the perimeter of a rectangle and either the length or​ width, find the unknown measurement using the appropriate formula.
Ad libitum [116K]
The width is 18.

step by step:
1. 2 lengths are 20 which is 20+20 that's 40.
2. 76-40= 36
3. Two widths are 36 cm.
4. so do 36÷2 and that equals 18
8 0
3 years ago
Read 2 more answers
Other questions:
  • Consider the following data: 14 21 23 19 16 15 20 20 21 25 24 18 17 23 26 18 16 15 24 21 16 19 21 23 20 23 14 13 14 14 12 26 19
    10·1 answer
  • What is the area of a trapezoid ABCD with bases AB and CD , if: m∠C=m∠D=60°, AB = BC = 8 cm
    5·2 answers
  • How do you solve X-2&gt;5
    9·1 answer
  • Please help im confused\
    13·1 answer
  • jordan is mailing a package at the post office .The box measures 8 3/4 inches long ,2 6/7 inches wide and 5 inches high.What is
    11·2 answers
  • involving flipping a fair coin. Assume that the coin is flipped 9 times. What is the probability that both heads and tails occur
    11·1 answer
  • 8n- (4n+7)=17 how do I solve
    9·2 answers
  • <img src="https://tex.z-dn.net/?f=%20%5Cfrac%7B42%7D%7B%20%5Csqrt%7B28%7D%20%7D%20%2B%20%5Cfrac%7B60%7D%7B45%7D%20-%202%20%5Csqr
    5·1 answer
  • Help me please <br> PLEASEEE
    13·2 answers
  • Given the function f(x) = 5^x, write the equation of the new function after you shift f(x) to the left six units and down thirte
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!