Please help!! will mark branliest 6.7 problem 13
A rubber ball is dropped onto a hard surface from a height of 8 feet, and it bounces up and down. At each bounce it rises to 85% of the height from which it fell. (Hint: Read all units carefully!)

(a) Find a formula for h(n), the height in inches reached by the ball on bounce n.
h(n)=

(b) How high will the ball bounce on the 8th bounce?
h=

(c) How many bounces before the ball rises no higher than an inch?

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

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

c. The solution to this point requires using exponential and logarithm equations; a more basic way would be trial and error using the previous 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:

Let's first isolate the fraction by dividing by 72.

 Now, to get numbers we can plug in a calculator, let's take the natural logarithm of both sides:

. Now the two quantities are known - or easy to get with any calculator, replacing them and solving for n we get:

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.

reduce the friction between its moving parts

step-by-step explanation:

in fact, by reducing the friction between the moving parts of the machine, it is possible to reduce the energy wasted due to this friction; therefore, more input energy is converted into useful work, and this will improve the efficiency of the machine.

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step-by-step explanation:

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