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3 years ago

ASAP 10 POINTS IF YOU ANSWER

Mathematics

2 answers:

kiruha [24]3 years ago

5 0

Step-by-step explanation:

-18.4,-17.3,-1.4,7.8,15.8,16.2

Nana76 [90]3 years ago

4 0

Answer:

-18.4 < -17.3 < -1.4 < 7.8 < 15.8 < 16.2

Step-by-step explanation:

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Solve 3^2x+3=243 for x. A. x = 10 B. x = 2 C. x = 2/5 D. x = 1

telo118 [61]

I think its B but im not 100% sure

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3 years ago

A hot air balloon descends from an altitude of 2,000 feet at a constant rate of 90 feet per minute. The graph shows the altitude

liberstina [14]

Answer:

y=90x+2,000

Step-by-step explanation:

90 is the rate of change because the hot air balloon descends 90 feet per minute.

And 2,000 is the starting point because the hot air balloon started the descent at 2,000 feet.

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3 years ago

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Could anyone tell me where these numbers would go? domain or range?

Free_Kalibri [48]

Independent, x-coordinate, input, domain.
Dependent, y-coordinate, output, range.

Domain: {0.5, 1, 4, 6, 8}
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3 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 sum 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

What is the equation of a line that passes through (6,3) and has a slope of -2/3

goldenfox [79]

Answer:

y=mx+b = 3y=6x+-2/3

Step-by-step explanation:

hope this is better

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3 years ago