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jok3333 [9.3K]
3 years ago
8

A soccer ball is kicked off from the ground in an arc defined by the function, h(x)=-8x^2+64x. At what point does the ball hit t

he ground?
(0,4) , (0,8) , (4,0) , (8,0)
Mathematics
1 answer:
tangare [24]3 years ago
6 0

Answer:

(8,0)

Step-by-step explanation:

The equation that models the path traced by the ball is

h(x)=-8x^2+64x

To find the point at which the ball hit the ground, we must equate the function to zero.

-8x^2+64x=0

Factor;

-8x(x-8)=0

-8x=0,(x-8)=0

This implies that;

x=0,x=8,

At x=0, the ball was not yet kicked.

So we take x=8, to be the time the ball hit the ground.

We substitute x=8 into the function to get;

h(8)=-8(8)^2+64(8)=0

Hence the point at which the ball hit the ground is (8,0)

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<em><u>Solution:</u></em>

Given that,

You are choosing between two mugs

<em><u>The volume of cylinder is given as:</u></em>

V = \pi r^2h

Where,

r is the radius and h is the height

<em><u>One has a base that is 5.5 inches in diameter and a height of 3 inches</u></em>

radius = \frac{diameter}{2}

Therefore,

r = \frac{5.5}{2}\\\\r = 2.75

Also, h = 3 inches

<em><u>Thus volume of cylinder is given as:</u></em>

V = \pi \times 2.75^2 \times 3\\\\V = 3.14 \times 22.6875\\\\V = 71.23875 \approx 71.24

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<em><u>The other has a base of 4.5 inches in diameter and a height of 4 inches</u></em>

Radius = \frac{4.5}{2}\\\\r = 2.25

h = 4 inches

Therefore,

V = 3.14 \times 2.25^2 \times 4\\\\V = 3.14 \times 20.25\\\\V = 63.585

Thus the second mug holds 63.585 cubic inches

On comparing, volume of both mugs,

Volume of first mug > volume of second mug

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