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2 years ago

Find the circumference of the circle. area = 121pi ft2

Mathematics

1 answer:

Free_Kalibri [48]2 years ago

7 0

Answer: 11,499.0145103 ft ( $60.5^{2}\pi$ )

Step-by-step explanation:

$a = \pi r^{2}$
121 = d, d = rx2
121/2 = 60.5
$60.5^{2}$ = 3660.25
3660.25 x $\pi$ = 11,499.0145103

Answer: 11,499.0145103 ft

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3. Why does it tako 3 copies of; to show the same amount as 1 copy of ?? Explain your answer in words

Amanda [17]

Because 3/6 is equal to 1/2.
You multiply the 1 (in 1/2) by 3, and the 2 (in 1/2) by 3 to get 3/6. You need to have a common denominator, and 6 was the common denominator.

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2 years ago

4. a) A ping pong ball has a 75% rebound ratio. When you drop it from a height of k feet, it bounces and bounces endlessly. If t

Klio2033 [76]

First part of question:

Find the general term that represents the situation in terms of k.

The general term for geometric series is:

$a_{n}=a_{1}r^{n-1}$

$a_{1}$ = the first term of the series

$r$ = the geometric ratio

$a_{1}$ would represent the height at which the ball is first dropped. Therefore:

$a_{1} = k$

We also know that the ball has a rebound ratio of 75%, meaning that the ball only bounces 75% of its original height every time it bounces. This appears to be our geometric ratio. Therefore:

$r=\frac{3}{4}$

Our general term would be:

$a_{n}=a_{1}r^{n-1}$

$a_{n}=k(\frac{3}{4}) ^{n-1}$

Second part of question:

If the ball dropped from a height of 235ft, determine the highest height achieved by the ball after six bounces.

$k$ represents the initial height:

$k = 235\ ft$

$n$ represents the number of times the ball bounces:

$n = 6$

Plugging this back into our general term of the geometric series:

$a_{n}=k(\frac{3}{4}) ^{n-1}$

$a_{n}=235(\frac{3}{4}) ^{6-1}$

$a_{n}=235(\frac{3}{4}) ^{5}$

$a_{n}=55.8\ ft$

$a_{n}$ represents the highest height of the ball after 6 bounces.

Third part of question:

If the ball dropped from a height of 235ft, find the total distance traveled by the ball when it strikes the ground for the 12th time. 

This would be easier to solve if we have a general term for the <em>sum </em>of a geometric series, which is:

$S_{n}=\frac{a_{1}(1-r^{n})}{1-r}$

We already know these variables:

$a_{1}= k = 235\ ft$

$r=\frac{3}{4}$

$n = 12$

Therefore:

$S_{n}=\frac{(235)(1-\frac{3}{4} ^{12})}{1-\frac{3}{4} }$

$S_{n}=\frac{(235)(1-\frac{3}{4} ^{12})}{\frac{1}{4} }$

$S_{n}=(4)(235)(1-\frac{3}{4} ^{12})$

$S_{n}=910.22\ ft$

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3 years ago

The people on this app are mean for not answering

Nataly [62]

aggreed very mean.....

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2 years ago

Read 2 more answers

If UV=x+13 and RT=x-37, What is the value of x?

liberstina [14]

Answer:

x = 87

Step-by-step explanation:

the ratio SR / RV is equal the ratio ST / TU (both ratios are equal to 1), and the angle in the vertex S is the same for both triangles SUV and STR, so we can affirm that these triangles are similar (case S-A-S).

Then, we have that the ratio SR / SV is the same as RT / UV:

SR / SV = RT / UV = 1 / 2

RT * 2 = UV

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2x - 74 = x + 13

x = 87

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I need below help!!!

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