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3 years ago

5

An electronics store offers students a discount

1 answer:

salantis [7]3 years ago

5 0

Answer:

83.9357% increase for the buyer

Step-by-step explanation:

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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

Each chicken eats about 6 pounds of chicken feed in a month.how many pounds of chicken feed will be left after 3 months? Write a

NARA [144]

Dear Vegafred77, use 3x6=18 since a chicken eats 6 lbs of chicken.

6 0

3 years ago

X^lg(x)=100^x find x

Wittaler [7]

$x^lg(x)=100^x$ <span>
</span>

$X^lg(x)=100^x:x$ $|Solve \ for \ x|$

<span> $|Use \ logarithms \ of \ both \ sides \ of \ the \ base \ 10|

$ </span>

<span>
</span>

<span> $lg (x ^ lg (x)) = lg (100x)

$ </span>

<span>
</span>

<span> $lg ^ 2 (x) = 2 + lgx$ </span>

<span>
</span>

$lg 2 ^ x-lg x -2 = 0$

$lg x = 2 x = 100$

$lg x = -1 x = \dfrac{1}{10} = 0.1$

3 0

3 years ago

Find the probability of throwing a sum of 4 at least 6 times in 9 throws of a pair of fair dice.

lora16 [44]

4/6 with 2 throws left i think.

4 0

3 years ago

Rewrite the following using the GCF and distributive properly : <br><br> 63+ 27

Yuki888 [10]

The answer is 90 i think
explain: none

3 0

3 years ago