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iren [92.7K]
3 years ago
15

6. A super-bouncy-ball is thrown 25m into the air. The ball falls, rebounds to 70% of the height of the previous bounce and fall

s again. If the ball continues to rebound and fall in this manner, find the total distance the ball has travelled after it hits the ground the 5th time. This may be answered in decimal form. Round your answer to 2 decimal places.
Mathematics
1 answer:
inn [45]3 years ago
8 0

Answer:

The total distance the ball has travelled after it hits the ground the 5th time is of 48.53m.

Step-by-step explanation:

Geometric sequence:

In a geometric sequence, the quotient of consecutive terms is the same. The nth term of a geometric sequence is given by:

a_n = a_1q^{n-1}

In which a_1 is the first term and q is the common ratio.

A super-bouncy-ball is thrown 25m into the air. The ball falls, rebounds to 70% of the height of the previous bounce and falls again.

This means that:

q = 0.7, a_1 = 25*0.7 = 17.5

Then

a_n = a_1q^{n-1}

a_n = 17.5(0.7)^{n-1}

First 5 terms:

a_1 = 17.5

a_2 = 17.5(0.7)^{2-1} = 12.25

a_3 = 17.5(0.7)^{3-1} = 8.58

a_4 = 17.5(0.7)^{4-1} = 6

a_5 = 17.5(0.7)^{5-1} = 4.2

Find the total distance the ball has travelled after it hits the ground the 5th time.

T = 17.5 + 12.25 + 8.58 + 6 + 4.2 = 48.53

The total distance the ball has travelled after it hits the ground the 5th time is of 48.53m.

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Henry had 20 convertibles and 5 trucks in his miniature car collection. After Henry's aunt bought him some more miniature trucks
saw5 [17]

Answer:

Her aunt buy <u>75</u> trucks.

Step-by-step explanation:

Given:

Henry had 20 convertibles and 5 trucks in his miniature car collection. After Henry's aunt bought him some more miniature trucks, Henry noticed that a fifth of his collection were convertible.

Now, to find the trucks her aunt buy.

Let the total collection of Henry be x.

<em>Number of trucks Henry had in his collection = 5.</em>

<em>Number of convertibles Henry had in his collection = 20.</em>

As, Henry's \frac{1}{5} collection were convertible.

Now, to get the total number of collection:

\frac{1}{5}\ of\ x=20.

\frac{1}{5} \times x=20

<em>Multiplying both sides by 20 we get:</em>

x=100.

<em>Total collection of Henry = 100.</em>

So, the total number of trucks he had in his collection is:

<u><em>Total collection of Henry - number of convertibles Henry had in his collection.</em></u>

=100-20

=80.

<em>Hence, Henry had total 80 trucks in his collection.</em>

<em>And 5 trucks he had already in his miniature car collection.</em>

Now, to get the number of trucks her aunt buy we subtract trucks he had already in his miniature car collection from the total number of trucks in Henry's collection:

<u><em>Total number of trucks in Henry's collection - Number of trucks already in his miniature car collection.</em></u>

=80-5

=75.

Therefore, her aunt buy 75 trucks.

8 0
3 years ago
A scale factor of less than one means
podryga [215]

Answer:

The sides get smaller

Step-by-step explanation:

Because anything times 1 gets smaller and it's no different for scale factor

8 0
3 years ago
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2. what is the solution to to equation -2(x + 4)= -20?​
aleksley [76]

Answer:

x=6

Step-by-step explanation:

-2(x + 4)= -20

<u>Divide both sides by -2:</u>

<u />x+4=\cfrac{-20}{-2}<u />

<u>Divide -20 by -2 = 10</u>

<u />x+4=10<u />

<u>Subtract 4 from both sides:</u>

<u />x=10-4<u />

<u />x=6<u />

<u>______________________</u>

7 0
3 years ago
Plz help i gotta turn dis in now (no links)
soldier1979 [14.2K]

Answer:

1.368 × 10^4

Step-by-step explanation:

i blink 38 times a muinet so i blink 2280 an hour so i blink 13680 every 16 hours

4 0
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Myles has $40 already. He needs to save a total of $448 to buy the newest baseball bat. The baseball season starts in six months
SIZIF [17.4K]

Answer:

408 dollars

Step-by-step explanation:

448-40 is 408

3 0
3 years ago
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