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Alexxx [7]
3 years ago
14

A ball was dropped from a height of 60m. Each time it hit the ground, it bounced up 1/2 (half) of the height that it dropped. Ho

w far had the ball travelled when it hit the ground for the fifth time?
Mathematics
1 answer:
asambeis [7]3 years ago
4 0

Answer:

The ball traveled 116.25 m when it hit the ground for the fifth term

Step-by-step explanation:

This is a geometric progression exercise and what we are asked to look for is the sum of a GP.

The ball was dropped from a height of 60 m. This means that the initial height of the ball is 60 m.

First value, a = 60

Each time it hit the ground, it bounced up 1/2 (half) of the height that it dropped.

This is the common ratio, r = 1/2 = 0.5

The number of terms it hits the ground is the number of terms in the GP.

number of terms, n = 5

The distance traveled by the ball when it hit the ground for the fifth term will be modeled by the equation:

S_n = \frac{a(1 - r^n) }{1 - r} \\S_5 =  \frac{60(1 - 0.5^5) }{1 - 0.5}\\S_5 =  \frac{58.125}{0.5} \\S_5 = 116.25 m

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An aluminum can has a capacity of 2.37 L. What is the capacity of the can in milliliters?
sasho [114]

Answer:

2,370 mL

Step-by-step explanation:

1000mL = 1 L, so I multiplied 1000 by 2.37

If they ask for it to be set up as a proportion, I would write 1/1000 = 2.37/x and cross multiply. x = 2,370

5 0
2 years ago
8th grade math . Pythagorran practice <br>​
Serhud [2]

The answers according to rows are:

  • ROW 1 : diameter of base = 10,  base area = 25π, volume of cylinder = 175π    volume of cone = \frac{175}{3}π
  • ROW 2 : base radius = 3, base area = 9π, height = 40/3, volume of cylinder = 120π
  • ROW 3 : base radius = 6, base diameter = 12, height = 4, volume of cylinder = 144π

<h3>What is mensuration?</h3>

Mensuration is an aspect of geometry that deals with measurement of volumes and area.

Analysis:

Row 1

Diameter of base = 2 x radius = 2 x 5 = 10

Base area = πr^{2} = π(5)^{2} = 25\pi

Volume of cylinder = base area x height = 25π x 7 = 175π

Volume of cone  = 1/3 x volume of cylinder = 175π/3

Row 2

Base radius = base diameter/2 = 6/2 = 3

Base area = πr^{2} = π(3)^{2} = 9π

Volume of cone = 1/3 x base area x height

base area x height  = 3 x volume of cone

base area x height = 3 x 40π

Height = 120π/9π = 40/3

Cylinder volume = 3 x cone volume = 3 x 40π = 120π

Row 3

Base area = πr^{2}

36π =  πr^{2}

r2 = \sqrt{36}

r = 6

Base diameter = 2 x 6 = 12

Volume of cone  = 1/3 x base area x height

48π = 1/3 x 36π x height

Height = 4

Cylinder volume = 3 x 48 = 144π

In conclusion,

ROW 1 : diameter of base = 10,  base area = 25π, volume of cylinder = 175π

volume of cone = \frac{175}{3}π

ROW 2 : base radius = 3, base area = 9π, height = 40/3, volume of cylinder = 120π

ROW 3 : base radius = 6, base diameter = 12, height = 4, volume of cylinder = 144π

Learn more about mensuration: brainly.com/question/18541562

#SPJ1

4 0
2 years ago
What is 62,810 rounded to the nearest
sweet-ann [11.9K]
62,810 rounded up is 60,00
3 0
3 years ago
Liam babysat for 3 1/2 hours and made $31.50. How much money does he make per hour?
anzhelika [568]

Answer:

$9 per hour

Step-by-step explanation:

31.50/3.5 = 3150/350 = 630/70 = 63/7 = 9

Hope this helps!      :3

plz mark as brainliest!

5 0
3 years ago
Wich is greater 4\10 or 32\10 explain how u know·
Zigmanuir [339]

Answer:

32/10

Step-by-step explanation:

simplify them

4/10= 2/5= 0.4 (as a decimal)

32/10= 3.2 (as a decimal)

3.2>0.4

4 0
2 years ago
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