A ball is dropped form a height of 100 inches. The ball bounces, each time reaching a lower and lower height. The height of each bounce is 75% of the previous bounce. What height will the ball reach after bouncing four times? How many bounces does it take for the ball to reach a height of less than one inch?

Answers

Answer 1

Answer: After the 'n'th bounce, the ball returns to a maximum height of

   (100) times (0.75)^n .

-- After 4 bounces, the maximum height is (100) (0.75)^4 = 31.64 inches.

-- To look for the maximum height of 1 inch,    (100) (0.75)^x = 1

Let's take the log of each side: log(100) + x log(0.75) = 0

Subtract log(100) from each side: x log(0.75) = -log(100)

Divide each side by log(0.75) :     x = -log(100) / log(0.75).

log(100) = 2 . So ... x = -2 / log(0.75) = -2 / -0.124939 = 16.00785

So the ball returns to a slim hair more than 1 inch high on the 16th bounce,
and returns to definitely less than 1 inch high on the 17th bounce.

Answer 2

Answer: 75% of a number is as much as 3/4 of the same number, so:

1st bounce: 3/4 * 100 = 75
2nd bounce: 3/4 * 75 = 56,25
3rd bounce: 3/4 * 56,25 = 42,1875
4th bounce: 3/4 * 42,1875 = 31,640625
5th bounce: 3/4 * 31,640625 = 23,73046875
6th bounce: 3/4 * 23,73046875 = 17,7978515625
7th bounce: 3/4 * 17,7978515625 = 13,348388671875
8th bounce: 3/4 * 13,348388671875 = 10,01129150390625
9th bounce: 3/4 * 10,01129150390625 = 7,508468627929688
10th bounce: 3/4 * 7,508468627929688 = 5,631351470947266
11th bounce: 3/4 * 5,631351470947266 = 4,223513603210449
12th bounce: 3/4 * 4,223513603210449 = 3,167635202407837
13th bounce: 3/4 * 3,167635202407837 = 2,375726401805878
14th bounce: 3/4 * 2,375726401805878 = 1,781794801354408
15th bounce: 3/4 * 1,781794801354408 = 1,336346101015806
16th bounce: 3/4 * 1,336346101015806 = 1,002259575761855
17th bounce: 3/4 * 1,002259575761855 = 0,7516946818213909

Answers:

After bouncing four times, the ball will reach a height of 31,640625 inches.
The ball will reach a height of less than one inch after 17 bounces.

PS: I know it's kind of a walk-around, by it still gives us the answer :)

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Answers

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Happy learning

A fruit company delivers its fruit in two types of boxes : large and small. A delivery of 6 large boxes and 5 small boxes has a total weight of 190 kilograms. A delivery of 2 large boxes and 3 small boxes has a total of 84 kilograms. How much does each type of boxes weigh ?

Answers

4 large and 8 small weigh 113kg
so
2 large and 4 small weigh 56.5 kg
but
2 large and 3 small weigh 50 kg
so taking the difference
1 small weighs 56.5 - 50 = 6.5 kg.

Substitute :
2 large and 3 small weight 50 kg
2 large weigh 50 - 3*6.5 = 50 - 19.5 = 30.5 kg
1 large weighs 15.25 kg

We have this system

6L + 5S = 190 (1)

2L + 3S = 84 multiply through by -3 ⇒ -6L - 9S = -252 (2)

Add (1) and (2) and we get that

-4S = -62

S = -62 / -4 = 15.5 kilos for a small box

And

2L + 3S = 84

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2L = 84 - 46.5

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Which is bigger 31/100 or 5/10

Answers

♥ Solve:
31/100
50/100
50 is larger than 31
Therefore 5/10 is larger than 31/100

31/100
5/10=50/100

Is 50 bigger than 31? Yes.

5/10>31/100

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Answers

Answer:

(x,y) = (-2,4)

Step-by-step explanation:

We have two equations:

$(1).\:2x+5y=16\n(2).-5x-2y=2$

Now let us us multiply equation (1) by 5, and equation (2) by 2:

$(1).\:5(2x+5y=16)\rightarrow\:10x+25y=80\n\n(2).2(-5x-2y=2)\rightarrow\:-10x-4y=4$

and add the two equations to get:

$21y=84$

$\boxed{y=4}$

Now we put this value of $y$ into equation(1) and solve for $x$ :

$2x+5(4)=16$

$2x=-4$

$\boxed{x=-2}$

Thus the solution to our system of equations is

$\boxed{(x,y)=(-2,4)}$

Answer:

Make sure that you enter just (-2,4)

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Answers

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Cammile wants to make fruit drinks.The direction to make one drink include mixing 4 cup of yogurt and 1 cup of ice with the amount of each fruit shown8
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Answers

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