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Nutka1998 [239]
2 years ago
6

Please help!! will mark branliest

Mathematics
1 answer:
Mashcka [7]2 years ago
7 0

Answer:

a. After the first bounce, the ball will be at 85% of 8 ft. After 2 bounces, it'll be at 85% of 85% of 8 feet. After 3 bounces, it'll be at (85% of) (85% of) (85% of 8 feet).  You can see where this is going. After n bounces the ball will be at

h(n) = (85\%)^n 6ft = (\frac{17}{20})^n(6ft\times 12\frac{in}{ft}) = (\frac{17}{20})^n\times72'

b. After 8 bounces we can apply the previous formula with n = 8 to get

h(8)=(\frac{17}{20})^8\times 72' = 19.62'

c. The solution to this point requires using exponential and logarithm equations; a more basic way would be trial and error using the previous h(n)increasing the value of n until we find a good value. I recommend using a spreadsheet for that; the condition will lead to the following inequality:

1>(\frac{17}{20})^n\times 72 Let's first isolate the fraction by dividing by 72.

(\frac{17}{20})^n  Now, to get numbers we can plug in a calculator, let's take the natural logarithm of both sides:

ln ((\frac{17}{20})^n) < ln \frac 1{72} \rightarrow n\times ln (\frac{17}{20}) < -ln72. Now the two quantities are known - or easy to get with any calculator, replacing them and solving for n we get:

-(0.16)n < - 4.27 \rightarrow n>26.31 Now, since n is an integer - you can't have a fraction of a bounce after all, you pick the integer right after that, or n>27.

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