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Mathematics

1 answer:

Over [174]2 years ago

3 0

Answer:

Step-by-step explanation:

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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

asambeis [7]

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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2 years ago

Find the volume of the given solid: Bounded by the cylinder y^2+z^2=4 and the planes x = 2y, x = 0, z = 0 in the first octant.

rodikova [14]

The solution would be like this for this specific problem:

V = ∫ dV 
= ∫0→2 ∫ 0→π/2 ∫ 0→ 2·r·sin(φ) [ r ] dzdφdr 
= ∫0→2 ∫ 0→π/2 [ r·2·r·sin(φ) - r·0 ] dφdr 
= ∫0→2 ∫ 0→π/2 [ 2·r²·sin(φ) ] dφdr 
= ∫0→2 [ -2·r²·cos(π/2) + 2·r²·cos(0) ] dr 
= ∫0→2 [ 2·r² ] dr 
= (2/3)·2³ - (2/3)·0³ 
= 16/3

So the volume of the given solid is 16/3. I am hoping that these answers have satisfied your query and it will be able to help you in your endeavors, and if you would like, feel free to ask another question.

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3 years ago

The seventh grade boys at colonial Christian school removed 1/3 of the 558 chairs in the auditorium how many chairs did they rem

vekshin1