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3 years ago

OMGGG!!! ACTUALLY SOMEONE PLEASE HELP!!! PLEASE!!! THIS IS PAST DUE!!! HELLLLP!! ANSWER ALL!!!!! HELP ME!!!!

Mathematics

1 answer:

8_murik_8 [283]3 years ago

5 0

y-intercept: 8

slope: 1/2

equation: 1/2x + 8

Hope this helps! :)

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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

2 years ago

Square RSTU is translated to form R'S'T'U', which has vertices R'(–8, 1), S'(–4, 1), T'(–4, –3), and U'(–8, –3). If point S has

Zarrin [17]

Answer:

C. (-1, -6)

Step-by-step explanation:

Hope this helps :)

7 0

2 years ago

Simplify 7.021 x 0.15 25pts

Helen [10]

Answer:

1.05315

Step-by-step explanation:

Simply multiply the two numbers to receive your answer

6 0

2 years ago

Read 2 more answers

How do you solve 3 (x - 4) = 12?<br> I'm really stuck on these type of questions

jolli1 [7]

Answer:

Step-by-step explanation:

Here you go mate

Use PEMDAS

Parenthesis,Exponent,Multiplication,Division,Addition,Subtraction

Step 1

3(x-4)=12 Equation/Question

Step 2

3(x-4)=12 Remove parenthesis

3x-12=12

Step 3

3x-12=12 Add 12 to sides

3x=24

Step 4

3x=24 Divide sides by 3

answer

x=8

Hope this helps

5 0

2 years ago

There are 180 calories in 3 scoops of vanilla ice cream. How many calories are in 7 scoops.

harkovskaia [24]

Answer:

420 calories

Step-by-step explanation:

180 / 3 = 60 calories

60 x 7 =420 calories

8 0

3 years ago