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3 years ago

You have traveled 150 miles per gallon. how far did you travel per gallon?

Mathematics

1 answer:

anyanavicka [17]3 years ago

8 0

Answer:

If you are looking for an equation, 150g=m

Step-by-step explanation:

g=gallons

m=gallons

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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

shirin bought a fruit smoothie. she paid $5.40 plus sales tax. the sales tax was %5. how much does she pay in sales tax?

Kitty [74]

Answer:

0.27

Step-by-step explanation:

5%of 5.40

=(5/100) *5.40

=$0.27

5 0

3 years ago

Read 2 more answers

The product of two numbers is 891 . if one one of them is 9,find the others

yaroslaw [1]

Answer:

Step-by-step explanation:

99 x 9= 891

Just divide 891 by 9 to give you your answer;)

3 0

3 years ago

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What is six less than three raised to the third power?

Nataliya [291]

Answer:

Step-by-step explanation:

Three raise to third power can be written as $3^3$ . In this three is the base which is raised to third power.

$3^3 = 3*3*3 = 27$

Next we need to subtract 6 from Three raise to third power(i.e from 27)

which can be written mathematically as

$3^3 - 6 = 3*3*3 - 6 \\=> 27 - 6 = 21$

Hence 6 less than three raised to the third power is 21 as explained above.

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3 years ago

Determine the quadrants in which each angle lies

Vinvika [58]

0 to 90 degrees is located in quadrant one. 90 to 180 degrees is located in quadrant two. 180 to 270 degrees is located in quadrant three. 270 to 360 degrees is located in quadrant four. Is this what you were after?

8 0

3 years ago

You have traveled 150 miles per gallon. how far did you travel per gallon? ​

You have traveled 150 miles per gallon. how far did you travel per gallon?