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3 years ago

Help please :) about to post more too

Mathematics

1 answer:

yKpoI14uk [10]3 years ago

5 0

Answer:

Lets say test tubes = t, and beakers = b

1 pack of (t) is $4 less than 1 pack of (b)

Since i have no prior information we are going to use variables for this equation:

1t (1 pack of test tubes) is $4 less than 1b (1 set of beakers)

so to quantify the equation, we have 8t and 12b.

if b is a number that IS quantifiable such as $5 we can easily figure out this answer.

Lets use and example that 1 set of beakers is $8, if we multiply $8 by 12 (the number of sets of beakers), we get: 96

Using the same example, if 1t is $4 less than 1b than 1t = $4. So, if we multiply $4 by 8 (the amount of packs of test tubes), we get: 32

If you take both of those numbers: 96, and 32 and you divide them you get 3. so that means that 1t = 3b

Answer = 1t = 3b

This may not be correct due to the little information that i got however i hope that, that works out for you :)

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First part of question:

Find the general term that represents the situation in terms of k.

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$a_{1}$ = the first term of the series

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$a_{1}$ would represent the height at which the ball is first dropped. Therefore:

$a_{1} = k$

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$r=\frac{3}{4}$

Our general term would be:

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Second part of question:

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$n$ represents the number of times the ball bounces:

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Plugging this back into our general term of the geometric series:

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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:

$S_{n}=\frac{(235)(1-\frac{3}{4} ^{12})}{1-\frac{3}{4} }$

$S_{n}=\frac{(235)(1-\frac{3}{4} ^{12})}{\frac{1}{4} }$

$S_{n}=(4)(235)(1-\frac{3}{4} ^{12})$

$S_{n}=910.22\ ft$

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