Which ordered pair is a solution to the system?<br> x – 2y = –2<br> 3x

We assume the height of the volleyball is described by the equation for ballistic motion. We want to find the time it takes for the height to become zero.

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<h3>motion equation</h3>

The general form of the equation of height for ballistic motion is ...

$h(t)=-16t^2+v_0t+h_0\qquad\text{$v_0$ and $h_0$ are the initial velocity and height}$

The coefficient 16 in the equation is an approximation of 1/2g, where g is the acceleration due to gravity in ft/s². This means the units of time and distance are expected to be seconds and feet.

For the problem at hand, the initial velocity and height are 10.5 ft/s and 5 ft. Then the height equation is ...

h(t) = -16t² +10.5t +5

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<h3>reaction time</h3>

Marsha has until the ball hits the ground to react to the serve. To find out how long that is, we need to solve the height equation for t when h=0. This is most easily done using the quadratic formula with ...

a = -16
b = 10.5
c = 5

The solution is ...

$t=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}= \dfrac{-10.5\pm\sqrt{10.5^2-4(-16)(5)}}{2(-16)}\\\\=\dfrac{10.5\pm\sqrt{430.25}}{32}=\dfrac{21\pm\sqrt{1721}}{64}$

The positive solution is ...

t ≈ 0.976327 ≈ 0.98

Marsha has about 0.98 seconds to react before the volleyball hits the ground.

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<em>Additional comment</em>

After about 0.33 seconds, Marsha knows she doesn't need to react at all. The serve will not clear the net. Its maximum height is about 6' 8 5/8". A women's volleyball net is 7' 4 1/8" high. Jennifer's serve velocity must be at least 12.3 ft/s for the ball to go over the net. With that upward velocity, Marsha has about 1.06 seconds to react.

4 0

2 years ago

PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU B

Irina-Kira [14]

First one is graph C second one is graph B third is graph D

3 0

3 years ago

A masonry contractor is preparing an estimate for building a stone wall and gate. He estimates that the job will take a

Kamila [148]

Based on the number of hours in the work week, the cost of the laborers and masons, worth of the materials and the profit, the estimated cost of the job can be written as a mathematical statement of A. 3 x $15 x 40 + 4 x $25 x 40 + $3,268 + $700 = $

The total estimated cost is $9,768

<h3>What is the total estimated cost?</h3>

The total estimated cost of the job can be found by the formula:

= (Number of laborers needed x Cost of laborers x Number of hours in work week) + (Number of masons x cost of masons x number of hours in work week) + materials worth + Required profit

The total estimated cost is therefore:

= (3 x $15 x 40) + (4 x $25 x 40) + $3,268 + $700

= 1,800 + 4,000 + 3,268 + 700

= $9,768

Find out more on total estimated cost at brainly.com/question/20950074.

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3 0

1 year ago

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Which ordered pair is a solution to the system? x – 2y = –2 3x – 2y = 2