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leva [86]
3 years ago
7

A ball is thrown into the air. The path of the ball is represented by the equation h(t)= -t^2+8t. How long is the ball in the ai

r?
Mathematics
1 answer:
BARSIC [14]3 years ago
8 0

Answer:

<em>The ball is 8 seconds in the air.</em>

Step-by-step explanation:

<u>Equations</u>

The height of a ball thrown in the air is given by the equation:

h(t)=-t^2+8t

We assume the time is expressed in seconds.

The ball will be in the air while its height is positive. When its height is zero, it means the ball could be at launch time or returning to the ground level.

Setting h(t)=0:

-t^2+8t=0

Factoring:

t(-t+8)=0

There are two possible solutions:

t=0, t=8 sec

The first solution corresponds to the moment the ball is being thrown, the second solution corresponds to the moment the ball is returning to the ground, thus:

The ball is 8 seconds in the air.

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Katie wants to collect over 100 seashells. She already has 34 seashells in her collection. Each day, she finds 12 more seashells on the beach. Katie can use fractions of days to find seashells.

Write an inequality to determine the number of days, d, it will take Katie to collect over 100 seashells

<em><u>Answer:</u></em>

Kathie needs more than 5 days to get over 100 shells

The required inequality is 34 + 12d > 100

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

Given that,

Katie wants to collect over 100 seashells.

She already has 34 seashells in her collection.

Each day, she finds 12 more seashells on the beach

Let "d" be the number of days she takes to cover 100 sea shells

From given statement,

She finds 12 seashells each day

Then for "d" days, the number of sea shells she collected is 12d

She already had = 34

So, the equation can be framed as:

34 + 12d > 100

Here we used "greater than" symbol, since she wants to collect over 100 seashells

Solve the inequality

12d >100-34\\\\12d>66\\\\d>\frac{66}{12}\\\\d>5.5

This means she won't have more than  100 shells until the 6th day

Thus she needs more than 5 days to get over 100 shells

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3 years ago
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The GCF of 8x and 40 is 8
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Solve:
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4x+11 is The answer

-2x-(-6x) two negatives make a positive so -2x-(-6x) is now -2x+6x
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Container A and container B are right circular cylinders. A has a radius of 4 inches and a height of 5 inches while container B
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Answer:

8 in

Step-by-step explanation:

RA = 4 in, RB = 2 in

oil height in A = hA = 2 in

Find oil height in B = hB

volume of oil in A = VA = π*RA² * hA

equal amount means volume of oil in B VB = VA

But VB = π*RB² * hB

so π*RA² * hA = π*RB² * hB

then

hB = hA *(RA/RB)² = 2 * (4/2)² = 8 in

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