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3 years ago

Joseph says that in the number 9,999,999,all the digits have the same value?Is Joseph correct? explain

1 answer:

galina1969 [7]3 years ago

5 0

No because the first nine means 9,000,000 (nine million)and the last nine means just 9 meaning the first"nine's" value is a lot greater

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Punnett Square

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2 years ago

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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 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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2 years ago

PLEASE HELP!!!! 100 ÷ 25 • 20 + 4 ÷ 2 – 14

Zolol [24]

The answer is 38

Hope this helps : )

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3 years ago

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Are rectangle or garden has a length of 10.25 feet and a width of 6.2 feet. Another rectangle or garden has a length of 20.5 fee

Alinara [238K]

Hello!

The formula for finding area of a rectangle is length × width

1st garden
l = 10.25
w = 6.2

6.2 × 10.25 = 63.55

Area = 63.55 ft²

2nd garden

l = 20.5
w = 12.4

20.5 × 12.4 = 254.2

Area = 254.2 ft²

Divide the bigger area by the smaller area

254.2 ÷ 63.55 = 4

$\framebox {4 times greater}$

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3 years ago

1/8th of Rs.1,64,350

aleksklad [387]

Answer:

₹20543.75

Hope you got your answer.

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