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
yawa3891 [41]
3 years ago
11

Related rates(calculus)

Mathematics
1 answer:
telo118 [61]3 years ago
7 0

Answer:

The volume increases at a rate of 125663.71 mm^ 3 / s

Step-by-step explanation:

The rate of change of the radius with respect to time is 4 mm / s.


So:


\frac{dr}{dt} = 4mm / s

Now we must find a relationship between the volume of a sphere and its radius.


The equation of the volume of a sphere is:


V = \frac{4}{3}\pi r^ 3

So:


\frac{dV}{dt} = \frac{4}{3}\pi * 3r ^ 2 * \frac{dr}{dt}\\\frac{dV}{dt} = 4\pi r ^ 2 * 4\\\frac{dV}{dt} = 16\pi r ^ 2

The diameter of the sphere is 100 mm. Therefore its radius is 100/2 = 50 mm.


So:


\frac{dV}{dt} = 16\pi (50) ^ 2\\\frac{dV}{dt} = 40000\pi mm^3 / s


The volume increases at a rate of :

40000 π mm ^ 3 / s = 125663.71 mm^3/s

You might be interested in
Please help me with these questions I am begging anyone please help
Y_Kistochka [10]

Answer:

1)rs.6000

Step-by-step explanation:

1)30 000*20/100=rs.6000

Sorry I don't know the answers for other questions cause I don't know outright price

5 0
3 years ago
Find the area of each polygon​
sweet [91]

Answer:

5 in^2

Step-by-step explanation:

Area of square: 2*2=4

Area of triangle: 2*1/2=1

4+1=5

4 0
3 years ago
Find the measure of angle of GDE
nikdorinn [45]
I would think it is a 90 degree angle, sorry if I’m wrong.
3 0
3 years ago
Does the table represent a linear relationship (3,15) (9,45) (21,105) why or why not?
Tasya [4]
Sysydystistisitw58w58w693636e59e5969e69
7 0
3 years ago
How to solve this problem
Alex777 [14]

Answer:

Step-by-step explanation:

Use the laws of exponents and simplify \frac{a^8}{a^6} to a^(8-6) to a^2

3 0
2 years ago
Other questions:
  • What do you need to find out before you can solve the problem? Show a way to find this. You can use a tool to help.
    5·1 answer
  • Suppose that G(x) = F(x + 4) + 2. Which statement best compares the graph of G(x) with the graph of F(x)?A. The graph of G(x) is
    5·2 answers
  • What is the value of the expression below when simplified?<br><br> 4[5(3 − 1)]2 − 23
    13·2 answers
  • How do I solve 3x2+4x=1
    9·2 answers
  • What is the y-intercept of the graph of the function f(x) = x2 + 3x + 5?
    7·2 answers
  • The perimeter of this figure is 42.5 cm. Find the area of this figure.
    7·1 answer
  • Rectangle A has length 12 and width 8. Rectangle c has lenth 30 and width 15.
    13·2 answers
  • Question: A book contains 10 photograph , some in color and some in black-and-white. Each
    5·1 answer
  • What is the value of x in the equation shown below<br> 0.75x + 3 = 6(x - 3)
    8·1 answer
  • 44% of the 25 buildings in the Forum are preserved. How many buildings are preserved?
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!