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Reil [10]
3 years ago
5

Pls answer with explanation!

Mathematics
1 answer:
patriot [66]3 years ago
4 0

Answer:

3,750 cars.

Step-by-step explanation:

We are given that the equation:

y=9000-2.4x

Models the relationsip between <em>y</em>, the number of unfilled seats in the stadium, and <em>x</em>, the number of cars in the parking lot.

We want to determine the number of cars in the parking lot when there are no unfilled seats in the stadium.

When there are no unfilled seats in the stadium, <em>y</em> = 0. Thus:

0=9000-2.4x

Solve for <em>x</em>. Subtract 9000 from both sides:

-2.4x=-9000

Divide both sides by -2.4:

x=3750

So, there will be 3,750 cars in the parking lot when there are no unfilled seats in the stadium.

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9. A home improvement store advertises 60 square
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C. $5.55

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About 2.9362 seconds.

Step-by-step explanation:

The equation  \displaystyle h(t)=-5t^2+14t+2  models the height h in meters of the ball t seconds after its launch.

Part A)

To determine whether or not the ball reaches a height of 14 meters, we can find the vertex of our function.

Remember that the vertex marks the maximum value of the quadratic (since our quadratic curves down).

If our vertex is greater than 14, then, at some time t, the ball will definitely reach a height of 14 meters.

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So, let’s find our vertex. The formula for vertex is given by:

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\displaystyle h(t)=-5t^2+14t+2

Hence: a=-5, b=14, and c=2.

Therefore, the x-coordinate of our vertex is:

\displaystyle x=-\frac{14}{2(-5)}=\frac{14}{10}=\frac{7}{5}

To find the y-coordinate and the maximum height, we will substitute this value back in for x and evaluate. Hence:

\displaystyle h(\frac{7}{5})=-5(\frac{7}{5})^2+14(\frac{7}{5})+2

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\displaystyle \begin{aligned} h(\frac{7}{2})&=-5(\frac{49}{25})+\frac{98}{5}+2 \\ &=\frac{-245}{25}+\frac{98}{5}+2\\ &=\frac{-245}{25}+\frac{490}{25}+\frac{50}{25}\\&=\frac{-245+490+50}{25}\\&=\frac{295}{25}=\frac{59}{5}=11.8\end{aligned}

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Part B)

To find out how long the ball is in the air, we can simply solve for our t when h=0.

When the ball stops being in the air, this will be the point at which it is at the ground. So, h=0. Therefore:

0=-5t^2+14t+2

A quick check of factors will reveal that is it not factorable. Hence, we can use the quadratic formula:

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Hence, our zero is approximately 2.9362.

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