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2 years ago

PLS HELP DUE ASAP! WILL MARK BRAINLIEST

Mathematics

1 answer:

snow_tiger [21]2 years ago

3 0

Answer:

24º

Step-by-step explanation:

C = (1/2)(56 + 116)

C = 86

4x - 10 = 86

4x = 96

x = 24

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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

3 years ago

The population of Farmersville can be modeled by the inequality y > 2,000x + 2,100, where x is the number of years since 2010

Kaylis [27]

Answer:

The population can be greater than 6,100 but less than 6,300, and thus, we cannot determine if the population of Farmersville will be greater than 6,300 in 2012.

Step-by-step explanation:

Inequality for the population of Farmsville:

The inequality for the population of Farmsville in x years after 2010 is given by:

$y(x) > 2000x + 2100$

Will the population of Farmersville be greater than 6,300 in 2012?

2012 is 2012-2010 = 2 years after 2010, so we have to find y(2).

$y(2) > 2000(2) + 2100$

$y(2) > 6100$

The population can be greater than 6,100 but less than 6,300, and thus, we cannot determine if the population of Farmersville will be greater than 6,300 in 2012.

3 0

3 years ago

HELP FAST. ILL GIVE BRAINLIST. 100 pts for each answer.

Aleonysh [2.5K]

Ok so
The first division problem’s answer is 12.
The second division problems answer is 9.
The third division problem’s answer is 8.
Now put those as the denominators of the fractions.
If that isn’t what they’re asking for then I don’t know but I hope this helps!

5 0

2 years ago

Read 2 more answers

The expression 3(x-9) is equivalent to

11111nata11111 [884]

Answer:

3(x)-3(9)

Step-by-step explanation:

The brackets means you times everything within the brackets with everything outside it. So it would be 3 times x take away 3 times 9

8 0

3 years ago

If the slope of a proportional relationship is 3, what is the equation that represents that line?

adelina 88 [10]

Answer:

y = 3x

Step-by-step explanation:

A proportional function has the equation

y = kx, where k is the constant of proportionality and also the slope of the line.

Answer: y = 3x

5 0

3 years ago