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
KonstantinChe [14]
2 years ago
12

The radius of a circle is changing at the rate of 1/π inches per second. At what rate, in square inches per second, is the circl

e’s area changing when the radius is 5 inches?
Mathematics
1 answer:
MAXImum [283]2 years ago
4 0

Answer:

10 square inches per second.

Step-by-step explanation:

The radius of the circle is given by the equation:

r(t) = (1/π  in/s)*t

Where time in seconds.

Remember that the area of a circle of radius R is written as:

A = π*R^2

Then the area of our circle will be:

A(t) = π*( (1/π  in/s)*t)^2 = π*(1/π  in/s)^2*(t)^2

Now we want to find the rate of change (the first derivation of the area) when the radius is equal to 5 inches.

Then the first thing we need to do is find the value of t such that the radius is equal to 5 inches.

r(t) = 5 in =  (1/  in/s)*t

       5in*(π s/in) = t

        5*π s = t

So the radius will be equal to 5 inches after 5*π seconds, let's remember that.

Now let's find the first derivate of A(t)

dA(t)/dt = A'(t) = 2*(π*(1/π  in/s)^2*t = (2*π*t)*(1/π  in/s)^2

Now we need to evaluate this in the time such that the radius is equal to 5 inches, we will get:

A'(5*π s) = (2*π*5*π s)*((1/π  in/s)^2

              = (10*π^2  s)*(1/π^2  in^2/s^2) = 10 in^2/s

The rate of change is 10 square inches per second.

You might be interested in
If a=8 and b=4, evaluate the following expression:2a−3b​
Nata [24]

Answer:

4

Step-by-step explanation:

2(8)-3(4)

16-12

4

7 0
3 years ago
Read 2 more answers
The volume for the above figure is?
lara [203]
The area of the circle is πr², ie. 144π.
The volume of the cilinder is 12×144π = 1728π cm³.

I vote for answer A.
7 0
3 years ago
Factor the GCF:<br> 24x3 + 8x
disa [49]

Answer:

8x(3x^2 +1)

Step-by-step explanation:

24x^3 + 8x

We can factor out 8x

8x(3x^2 +1)

4 0
3 years ago
Compare: (4x10 to the 3rd power) + (2x100) + (3x1/10) ____ (4x1000) + (2x10 to the 2nd power) + (3x1/10)
postnew [5]

Answer:

Take your time to complete the equation. Don't rush. This is very easy you just need to be patient..

Step-by-step explanation:

5 0
3 years ago
4(х +Зу) = 2(3х-y)<br> Solve for x
Fittoniya [83]

Answer:

7y

Step-by-step explanation:

use distributive property:

4x+12y=6x-2y

2x=14y

x=7y

6 0
3 years ago
Other questions:
  • Please help. ASAP.<br> PLEASE HELP <br> Question :<br> Write function for this.<br><br> Thanks.
    6·1 answer
  • To shift the graph of an equation a certain number of units _____, you need to subtract that number from the functions equation
    6·2 answers
  • UV and RV are secant segments that intersect at point V.
    5·2 answers
  • A flower bed is in the shape of a triangle with one side twice the length of the shortest​ side, and the third side is 18 feet m
    11·1 answer
  • What is the volition of -3 (2x + 5)=-3?<br><br> 5
    9·2 answers
  • What is 224% in its simplest form?
    13·1 answer
  • The average distance of the Moon from Earth is 386,242,560 m. Represent 386,242,560 in scientific notation.
    8·1 answer
  • Which expressions are equivalent to -6n+(-12)+4n
    7·1 answer
  • 9 + 7 × ( 15 + 3 )÷3 2= Giving brainliest
    7·1 answer
  • I tried to do it and I don’t understand??
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!