PLEASE HELP ME THANK YOU, GUYS!❤️❤️❤️

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:

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

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

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

$S_{n}=910.22\ ft$

8 0

3 years ago

H(x)=x-1 is a factor of f(x)=x^5+1. Please select the best answer from the choices provided.

Zanzabum

Answer:true

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

I need help with this question and no link or I’ll report u

Ugo [173]

It would be 35 because we can assume that both y’s on the left side are parallel to the right side, and so they would have to be a 35 on each side

3 0

3 years ago

Write down a pair of integers whose

liubo4ka [24]

<span>The pair of integers that I chose are:

(a) sum is –3
5 + (-8) = -3

(b) difference is –5
2 - 7 = -5

(c) difference is 2
14 -12 = 2

(d) sum is 0
2 - 2 = 0</span>

3 0

3 years ago

pH measurements of a chemical solutions have mean 6.8 with standard deviation 0.02. Assuming all pH measurements of this solutio

aalyn [17]

Answer: 2.14 %

Step-by-step explanation:

Given : pH measurements of a chemical solutions have

Mean : $\mu=6.8$