Select the best interpretation of the following equation.<br> 11

The ratio of the circumference of two circles is 3:2.What is the ratio of their area

Nezavi [6.7K]

The ratio of their area is 9/4

<h2>Explanation:</h2>

We use ratios to compares values. In this exercise, we are comparing the circumference of two circles, which is:

$3:2$

and we want to know what is the ratio of their area. Recall that the circumference of a circle is given by:

$C=2\pi r \\ \\ \\ Where: \\ \\ C:Circumference \\ \\ r:Radius \ of \ the \ circle$

If we define:

$C_{1}: \ Circumference \ of \ circle \ 1 \\ \\ C_{2}: \ Circumference \ of \ circle \ 2 \\ \\ r_{1}: \ Radius \ of \ circle \ 1 \\ \\ r_{2}: \ Radius \ of \ circle \ 2$

Then, the ratio of the circumference of two circles is 3:2 is:

$\frac{C_{1}}{C_{2}}=\frac{2\pi r_{1}}{2\pi r_{2}}=\frac{3}{2} \\ \\ \therefore \frac{r_{1}}{r_{2}}=\frac{3}{2}$

The area of a circle is given by:

$A=\pi r^2 \\ \\ A:Area \\ \\ r:Radius$

So the ratio of their area can be found as:

$\frac{A_{1}}{A_{2}}=\frac{\pi r_{1}^2}{\pi r_{2}^2} \\ \\ \\ A_{1}:Area \ of \ circle \ 1 \\ \\ A_{2}:Area \ of \ circle \ 2$

So:

$\frac{A_{1}}{A_{2}}=\frac{r_{1}^2}{r_{2}^2}=\left( \frac{r_{1}}{r_{2}} \right)^2 \\ \\ \frac{A_{1}}{A_{2}}=\left(\frac{3}{2}\right)^2 \\ \\ \boxed{\frac{A_{1}}{A_{2}}=\frac{9}{4}}$

<h2>Learn more:</h2>

Unit rate: brainly.com/question/13771948#

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5 0

4 years ago

I need help asap please!

Sunny_sXe [5.5K]

Answer:

Check the attachment as solved.

brainliest please ;)

5 0

3 years ago

Twenty-six students apply to serve as an usher at a school function. Eight of the those applying are freshmen, 7 are sophomores,

Gelneren [198K]

Answer:

d

Step-by-step explanation:

from usatestprep:

The situation is not an example of uniform probability because freshmen, sophomores, juniors, and seniors do not have equal probabilities of being selected.; Uniform probability → equal probability of being selected

P(freshman) =

8/

26

; P(sophomore) =

7 /

26

; P(junior) =

6 /

26

; P(senior) =

5 /

26

; unequal probabilities → not uniform

6 0

3 years ago

Read 2 more answers

Sue walked from her home to her school at a constant rate of 2 miles per hour, picked up her bicycle and rode back at a constant

Nady [450]

Answer:

15 miles

Step-by-step explanation:

the 2 mph is a red herring. If there is a rate of 10 mph, and the trip took 1.5 hours, the 1 hour=10 miles, and the .5=5 miles, add em up and its 15 miles

8 0

3 years ago

Read 2 more answers

Solve the equation below for the variable "x". *<br> - 2x + 10 = 8

Brums [2.3K]

Answer:

x = 1

Step-by-step explanation:

Subtract 10 from 8 to get -2. Then divide -2x by itself so it will cancel out. Whatever you do to one side of the equation, do to the other so divide -2 by -2 to get your answer of 1

3 0

3 years ago

Read 2 more answers

Select the best interpretation of the following equation. 11 - y = 3