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Svetllana [295]
3 years ago
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 90

% of the height from which it fell.
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 14th bounce? (in inches)
c. How many bounces before the ball rises no higher than an inch? 
Mathematics
1 answer:
Setler [38]3 years ago
7 0
A. 8 feet * 0.9 = distance after first bounce
h(n) = 8 * 0.9^n

b. 8 * 0.9^14 = 1.83 feet to 2 d.p.
1.83 * 12 = 21.96 inches

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Step-by-step explanation:

Given as :

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Let The interest earn at 7% = I_1

And The interest earn at 6% = I_2

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Let The time period = 1 year

Now,<u> From Simple Interest method</u>

Simple Interest = \dfrac{\textrm principal\times \textrm rate\times \textrm time}{100}

Or,  I_1 = \dfrac{\textrm p_1\times \textrm 7\times \textrm 1}{100}

Or,  I_1 = \dfrac{\textrm A\times \textrm 7\times \textrm 1}{100}

And

I_2 = \dfrac{\textrm p_2\times \textrm 6\times \textrm 1}{100}

Or,  I_2 = \dfrac{\textrm (13,957 - A)\times \textrm 6\times \textrm 1}{100}

∵  I_1 -  I_2 = $833.73

So, \dfrac{\textrm A\times \textrm 7\times \textrm 1}{100} -  \dfrac{\textrm (13,957 - A)\times \textrm 6\times \textrm 1}{100} = $833.73

Or, 7 A - 6 (13,957 - A) = $833.73 × 100

Or, 7 A - $83,742 + 6 A = $83373

Or, 13 A = $83373 + $83742

Or, 13 A = $167,115

∴ A = \dfrac{167115}{13}

i.e A = $12,855

So, The Amount invested at 7% interest = A = $12,855

And The Amount invested at 6% interest = ($13,957 - A) = $13,957 - $12,855

I.e The Amount invested at 6% interest = $1,102

Hence,The Amount invested at 7% interest is $12,855

And The Amount invested at 6% interest = $1,102   . Answer

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