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koban [17]
3 years ago
11

A bouncing ball reaches a height of 27 feet at its first peak, 18 feet at its second peak, and 12 feet at its third peak. Descri

be how a sequence can be used to determine the height of the ball when it reaches its fourth peak
Mathematics
2 answers:
Mrrafil [7]3 years ago
7 0

Answer:

There is a common ratio of 2/3 between the height of the ball at each bounce. So, the bounce heights form a geometric sequence: 27, 18, 12. Two-thirds of 12 is 8, so on the fourth bounce, the ball will reach a height of 8 feet.

Step-by-step explanation:

astraxan [27]3 years ago
5 0

Sample Response: There is a common ratio of 2/3 between the height of the ball at each bounce. So, the bounce heights form a geometric sequence: 27, 18, 12. Two-thirds of 12 is 8, so on the fourth bounce, the ball will reach a height of 8 feet.

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Niki makes the same payment every two months to pay off his $61,600 loan. The loan has an interest rate of 9. 84%, compounded ev
elena-14-01-66 [18.8K]

Niki pays $39,467 interest will he have paid in total.

Given that,

Niki makes the same payment every two months to pay off his $61,600 loan.

The loan has an interest rate of 9.84%, compounded every two months.

If Niki pays off his loan after exactly eleven years.

We have to determine,

How much interest will he have paid in total?

According to the question,

The total interest will be paid is determined by,

\rm PV = \dfrac{P\left(1 - (1 + \dfrac{r}{t})^{-nt}\right) }{ \dfrac{r}{t}}

Where, PV = $61,600,  r = interest rate = 9.84% = 0.0984;

t = number of payments in a year = 6; n = number of years = 11 years and P is the periodic payment.

Substitute all the values in the formula;

\rm PV = \dfrac{P\left(1 - (1 + \dfrac{r}{t})^{-nt}\right) }{ \dfrac{r}{t}}\\\\\rm 61600 = \dfrac{P\left(1 - (1 + \dfrac{0.0984}{6})^{-11 \times 6}\right) }{ \dfrac{0.0986}{6}}\\\\61600 = \dfrac{P\left(1 - (1 + {0.0164})\right^{-66} }{0.0164}\\\\61600 = \dfrac{P\left(1 - (1.01640))^{-66}}{0.0164}\\\\ 61600 \times 0.0164 = P (1-0.341769)\\\\1010.24 = 0.658231P\\\\P = \dfrac{1010.24}{0.6582}\\\\P = 1534.78

Therefore,

Niki pays $1,534.78 every two months for eleven years,

The total payment made by Niki = 11 x 6 x 1,534.78 = $101,295.48

Therefore, interest paid by Niki = $101,295.48 - $61,600 = $39,695.48.

Hence, Niki pays $39,467 interest will he have paid in total.

For more details about Interest rates refer to the link given below.

brainly.com/question/10302432

6 0
2 years ago
Find the volume (show work)
Karo-lina-s [1.5K]

V = 1/3 × base × height

V = 1/3 × ( 8 × 8 ) × 7

V = 1/3 × 64 × 7

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3 years ago
Please help!!
vesna_86 [32]
1. have you ever borrowed money from a friend?
6 0
3 years ago
Which system of equations is represented by the graph?
melomori [17]
B) y=x-4 not sure how to explain it, but because the y intercept is -4, it is almost certain that the last number will ne -4 and since x is equal to 4 y must equal x-4. Might be wrong though ('o')
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3 years ago
Ronaldo has 50/250 BI liability insurance. He loses control of his car and injures 18 children
Alex73 [517]

Answer:

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<u><em></em></u>

  • <u><em>Ronaldo will be personally responsible for $110,000.</em></u>

Explanation:

<em>BI</em> stands for bodily injury.

Bodily Injury <em>liability</em> <em> insurance</em> covers the damages caused to third parties (other drivers or persons not including you).

In the format <em>50/250</em>, the first number is the amount covered for one person in the accident, and the second number is the limit that the insurance company covers in the same accident.

Since <em>each child is awarded $20,000 as a result of a lawsuit</em>, the total legal responsability is 18 × $20,000 = $360,000.

Hence, the limit of $ 250,000 covered by the insurance company is exceeded meaning that <em>the insurance company will pay</em> the limit of $250,000.

Therefore, <em>Ronaldo will be personally responsible for</em> the difference: $360,000 - $250,000 = $110,000.

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3 years ago
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