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
Which pair of the following tests is used to test for normality?
marissa [1.9K]

Answer: the answer is b( a quantile - quantile plot and a p- value test

Step-by-step explanation:

8 0
2 years ago
11 minus what number is 7
MA_775_DIABLO [31]
Eleven minus four equal seven
11-4=7
4 0
3 years ago
What is 34 divided by 45
Mrrafil [7]
34 ÷ 45 \frac{34}{45}= 0.7555555555556 ≈ 0.76
7 0
3 years ago
144 flowers in a vase the ratio of yellow to pink flowers is 5 to 6 how many yellow flowers are in the vase
azamat

\frac{5}{11}  \times 144 \: is \: the \: amount \: of \: yellow \: flowers \\  \\  \frac{5}{11}  \times 144 = 65.45 = 65
therfore there is 65 yellow flowers
4 0
3 years ago
Explain how to find which value is greater (5/6)*81 or (9/10)*81 without multiplying?
8_murik_8 [283]

The value (9/10)*81 is greater than (5/6)*81

<h3>How to determine the greater value?</h3>

The values are given as:

(5/6)*81 and (9/10)*81

Remove the common factor in both values

So, we have:

5/6 and 9/10

Convert to decimals

0.83 and 0.9

0.9 is greater than 0.83

Hence, (9/10)*81 is greater than (5/6)*81

Read more about expressions at:

brainly.com/question/723406

#SPJ1

8 0
2 years ago
Other questions:
  • F(x) = <br> sin 4x/2x<br> x-intercepts?
    15·1 answer
  • Amanda leaned a 15-foot ladder against the top of her house so she could get on the roof, which is 12 feet from the ground.
    5·1 answer
  • 72000 divided by what = 200
    13·1 answer
  • 2a+3b=10<br> 2a+3b=23<br> How to isolate them and substitute it
    6·1 answer
  • Give triangle abc is congruent to triangle def find x
    10·1 answer
  • Use the volume formula to find the volume of the prism
    12·2 answers
  • Shannon is asked to draw a quadrilateral with the following specifications.
    8·2 answers
  • What could be the dimensions of a triangle with an area of 12in square?
    8·1 answer
  • 42 of the 50 coffee mugs at Nicole's Pancake House are dirty. What percentage of the
    12·2 answers
  • This is a substitution problem
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!