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
enyata [817]
3 years ago
12

Find the average rate of change of the area of a circle with respect to its radius r as r changes from 3 to each

Mathematics
1 answer:
GarryVolchara [31]3 years ago
5 0

Answer:

Step-by-step explanation:

The question is incomplete. Here is the complete question.

Find the average rate of change of the area of a circle with respect to its radius r as r changes from 3 to each of the following.

(i)    3 to 4

(ii)    3 to 3.5

(iii)    3 to 3.1

(b) Find the instantaneous rate of change when r = 3.  A'(3)

Area of a circle A(r)= πr²

The average rate of change of the area of a circle with respect to its radius

ΔA(r)/Δr = πr₂²-πr₁²/r₂-r₁

ΔA(r)/Δr = π(r₂²-r₁²)/r₂-r₁

i) If the radius changes from 3 to 4

ΔA(r)/Δr = π(r₂²-r₁²)/r₂-r₁

ΔA(r)/Δr = π(4²-3²)/4-3

ΔA(r)/Δr = π(16-9)/1

ΔA(r)/Δr = 7π

<em>Hence, average rate of the area of a circle when the radius changes from 3 to 4 is 7π</em>

ii) If the radius changes from 3 to 3.1

ΔA(r)/Δr = π(r₂²-r₁²)/r₂-r₁

ΔA(r)/Δr = π(3.5²-3²)/3.5-3

ΔA(r)/Δr = π(12.25-9)/0.5

ΔA(r)/Δr = 3.25π/0.5

ΔA(r)/Δr = 6.5π

<em>Hence, average rate of the area of a circle when the radius changes from 3 to 3.5 is </em>6.5π

iii) If the radius changes from 3 to 3.1

ΔA(r)/Δr = π(r₂²-r₁²)/r₂-r₁

ΔA(r)/Δr = π(3.1²-3²)/3.1-3

ΔA(r)/Δr = π(9.61-9)/0.1

ΔA(r)/Δr = 0.61π/0.1

ΔA(r)/Δr = 6.1π

<em>Hence, average rate of the area of a circle when the radius changes from 3 to 3.1 is </em> 6.1π

iv) Instantaneous rate of change A'(r) = 2πr

When r = 3;

A'(3) = 2π(3)

A'(3) = 6π

<em>Hence, the instantaneous rate of change when r = 3 is 6π </em>

You might be interested in
The ratio of the same side angles of two parallel lines is 33:3. Find all angles.
alex41 [277]

Answer:

15 degrees, 165 degrees.

Step-by-step explanation:

The same side angles add up to 180.

So one  side = 3/(33+3)

= 3/36

= 1/12

= 15 degrees.

The  other angle = 180 - 15

= 165 degrees.

6 0
3 years ago
If you had $500 to put into a savings account with 8% interest , how would you know which bank to choose, if you plan to withdra
Yuki888 [10]

Answer:

Compound interest because you earn more over time

Step-by-step explanation:

8 0
3 years ago
Which input value produces the same output value for the
USPshnik [31]

Answer:

x = 4

Step-by-step explanation:

The 2 graphs have the same output, y = 3 at the point of intersection

This occurs when the input is x = 4

8 0
3 years ago
Read 2 more answers
A bag contains 1 blue, 2 green, and 3 red marbles, as shown. What is the probability of drawing a green marble out of the bag wi
Doss [256]

ANSWER

P(G)=  \frac{1}{3}

EXPLANATION

The number of green marbles in the bag is

n(G) = 2

The total number of marbles in the bag is

n(S)=1+2+3 = 6

The probability of selecting a green marble from the bag without looking is

P(G)=  \frac{n(G)}{n(S)}

Substitute the values to get,

P(G)=  \frac{2}{6}

P(G)=  \frac{1}{3}

8 0
3 years ago
Read 2 more answers
DECIDE WHETHER THE CONGRUENCE STATEMENT IS TRUE. EXPLAIN YOUR REASONING.​
kaheart [24]
Yes it is because ejehhjekeb
6 0
3 years ago
Other questions:
  • 1 1/4 3 1/2. additon
    13·2 answers
  • When x = 8, y = 18. find y when x = 84?
    15·1 answer
  • which set of rectangular coordinates describes the same location as the polar coordinates 3sqrt2 5pi/4
    15·1 answer
  • ABCD is a rectangle. Find the measure of angle CAD
    8·2 answers
  • What is the solution to the inequality of 2n+5&gt;1 please help
    13·1 answer
  • Which value represents |-100|?
    9·2 answers
  • Solve the equation:<br> -4x - 12 = 8
    10·2 answers
  • 6 is 15% of what number
    6·1 answer
  • Make u the subject of formula in <br>M=m(v-u).u​
    6·1 answer
  • Use triangle XYZ to answer questions 1-3
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!