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guajiro [1.7K]
3 years ago
12

Find a equation for the line below

Mathematics
1 answer:
LenaWriter [7]3 years ago
3 0

Answer:

y = - \frac{1}{2} x - \frac{13}{2}

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 5, - 4) and (x₂, y₂ ) = (- 1, - 6)

m = \frac{-6+4}{-1+5} = \frac{-2}{4} = - \frac{1}{2}, thus

y = - \frac{1}{2} x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (- 1, - 6), then

- 6 = \frac{1}{2} + c ⇒ c = - 6 - \frac{1}{2} = - \frac{13}{2}

y = - \frac{1}{2} x - \frac{13}{2} ← equation of line

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Answer:

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Step-by-step explanation:

37999

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Jennifer serves the volleyball to Marsha with an upward velocity of 10.5 ft/s. The ball is 5 feet above the ground when she stri
Katarina [22]

Answer:

  0.98 seconds

Step-by-step explanation:

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 ...

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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.

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1 year ago
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Answer:

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Step-by-step explanation:

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ikadub [295]

Use Ga_thMath(u) (brainly doesn't allow me to type it) To use the app u need to take a pic of the problem and then it will process it and you'll get ur answer ASAP(most of the time).

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