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zaharov [31]
3 years ago
6

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

Mathematics
1 answer:
Nezavi [6.7K]3 years ago
5 0

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#

#LearnWithBrainly

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Answer:

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Step-by-step explanation:

From the given information:

Number of term N = 3 (0.5)^{5} + 3 (0.5)^{6} + 3 (0.5)^{7} + \cdots + 3 (0.5)^{13}

Number of term N = 3 (0.5)^{5} + 3 (0.5)^{6} + 3 (0.5)^{7} +3 (0.5)^{8}+3 (0.5)^{9} +3 (0.5)^{10} +3 (0.5)^{11}+3 (0.5)^{12}+ 3 (0.5)^{13}

Number of term N = 9

The Value of the sum can be determined by using the expression for geometric series:

\sum \limits ^n_{k=m}ar^k =\dfrac{a(r^m-r^{n+1})}{1-r}

here;

m = 5

n = 9

r = 0.5

Then:

\sum \limits ^n_{k=m}ar^k =\dfrac{3(0.5^5-0.5^{9+1})}{1-0.5}

\sum \limits ^n_{k=m}ar^k =\dfrac{3(0.03125-0.5^{10})}{0.5}

\sum \limits ^n_{k=m}ar^k =\dfrac{(0.09375-9.765625*10^{-4})}{0.5}

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Hello from MrBillDoesMath!

Answer:

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Discussion:

Given

64v^3 + 192v^2 - 56 v - 168      

Factor 64v^2 from the first two terms. Factor 56 from the last two terms:

64v^2(v+3) - 56(v  + 3)     => factor (v+3) from both terms

(v+3) (64v^2 - 56)             => factor 8 from both terms in the right ()

8(v+3)(8v^2-7)                   => factor 8y^2-7

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Answer:

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Step-by-step explanation:

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Meaning a group = 4 persons

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