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abruzzese [7]
3 years ago
6

A circle has a circumference of 11{,}30411,30411, comma, 304 units. What is the diameter of the circle?

Mathematics
1 answer:
tigry1 [53]3 years ago
8 0

Answer:

The diameter of the circle is 3,600\ units

Step-by-step explanation:

we know that

The circumference of a circle is equal to

C=\pi D

where

D is the diameter

In this problem we have

C=11,304\ units

assume \pi=3.14

substitute the values and solve for D

11,304=(3.14)D

D=11,304/(3.14)=3,600\ units

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Step-by-step explanation:

The following laws of exponent are useful to this problem:

\displaystyle \large{ {(mn)}^{b} =  {m}^{b} {n}^{b}   } \\  \displaystyle \large{ {n}^{ - b} =   \frac{1}{ {n}^{b} }    }

We are given the expression:

\displaystyle \large{( {m}^{8}  {n}^{ - 4} )^{ \frac{1}{4} } }

Use the first law of exponent above.

\displaystyle \large{( {m}^{8}  {n}^{ - 4} )^{ \frac{1}{4} } =  {m}^{(8)( \frac{1}{4}) } {n}^{ ( - 4)( \frac{1}{4}) }   } \\  \displaystyle \large{( {m}^{8}  {n}^{ - 4} )^{ \frac{1}{4} } =  {m}^{2 } {n}^{  - 1}   }

Make sure to recall the important necesscary fundamental math such as operation with negative numbers/integers, basic division, fraction, etc.

From the expression, apply the second law of exponent to n^-1.

\displaystyle \large{( {m}^{8}  {n}^{ - 4} )^{ \frac{1}{4} } =  {m}^{2 } ( \frac{1}{ {n}^{1} } )} \\   \displaystyle \large{( {m}^{8}  {n}^{ - 4} )^{ \frac{1}{4} } =  {m}^{2 } ( \frac{1}{ {n} } )} \\

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