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2 years ago

Ryan is going to invest in an account paying an interest rate of 1.5%

Mathematics

1 answer:

lana [24]2 years ago

6 0

Step-by-step explanation:

2,360×8=2,360 two thundered three hundred and sixty

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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

What is the domain of y = -x – 4+9

cupoosta [38]

Answer:

Step-by-step explanation:

5 0

2 years ago

295 X 3 =<br> What is the distributive property of multiplication

frosja888 [35]

Answer:

295 x 3 = 885

The distributive property is when you distriute numbers if they are getting multiplied by the same number.

Example:

Original Equation: A(B+C)

Distribute the equation so that B and C are by itself.

New Equation: AxB + AxC

This is distributive property.

7 0

2 years ago

Peter lives in San Mateo. He bought an item for $528.9 and when the clerk calculated the sales tax it came out to exactly $55.67

velikii [3]

560.00

It will be 560.00 because when you round up the 6 it it will be 560.00

8 0

2 years ago

Read 2 more answers

Choose the definition for the function.

Yuki888 [10]

Answer:

The definition for the all functions is 86

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2 years ago