Nate tosses a ball up a hill for his dog to chase. The path of the
ball is modeled by the function y=-1/4x^2 + 33/5x, where x is
the ball's horizontal distance from Nate in feet and y is the ball's
height in feet. The hill is modeled by the line y
2. How far
does the ball travel horizontally before it hits the ground? (in
feet, round to tenth place if necessary)

Answers

Answer 1

Answer:

26.4 m

Step-by-step explanation:

The path the ball follows is given by the function

[tex]y=-\dfrac{1}{4}x^2+\dfrac{33}{5}x[/tex]

Before it hits the ground means y will be zero.

[tex]0=-\dfrac{1}{4}x^2+\dfrac{33}{5}x\\\Rightarrow x(-\dfrac{1}{4}x+\dfrac{33}{5})=0\\\Rightarrow x=0, -\dfrac{1}{4}x+\dfrac{33}{5}=0\\\Rightarrow x=0, x=\dfrac{33}{5}\times4\\\Rightarrow x=0, 26.4[/tex]

There are two points where the vertical displacement is zero the point at which Nate tosses the ball and the point where it lands.

So, the ball travels 26.4 m horizontally before it hits the ground.

Answer 2

Solving the quadratic equation, it is found that the ball travels 26.4 feet horizontally before it hits the ground.

The height of the ball, after an horizontal distance of x feet, is given by:

[tex]y(x) = -\frac{1}{4}x^2 + \frac{33}{5}x[/tex]

Converting the fractions to decimal:

[tex]y(x) = -0.25x^2 + 6.6x[/tex]

It hits the ground when:

[tex]y(x) = 0[/tex]

Then:

[tex]-0.25x^2 + 6.6x = 0[/tex]

[tex]0.25x^2 - 6.6x = 0[/tex]

[tex]x(0.25x - 6.6) = 0[/tex]

[tex]x = 0[/tex], or:

[tex]0.25x - 6.6 = 0[/tex]

[tex]0.25x = 6.6[/tex]

[tex]x = \frac{6.6}{0.25}[/tex]

[tex]x = 26.4[/tex]

The ball travels 26.4 feet horizontally before it hits the ground.

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Step-by-step explanation:

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Simplify your answer as much as possible

Answers

Answer:

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Step 1: Simplify both sides of the equation.

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Step-by-step explanation:

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Answers

Answer:

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Answers

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Step-by-step explanation:

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Answer:

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Answers

Answer:

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Step-by-step explanation:

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Answer:

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Answers

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Answer:

A number that is less than zero

Step-by-step explanation:

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Answers

Answer:

B

Step-by-step explanation:

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Answers

Answer: kim made $6,900 in commission for selling the house

Step-by-step explanation:i took the test

What is the value of the expression
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Simplify your answer.​

Answers

Answer:

[tex]\frac{4}{25}[/tex]

Step-by-step explanation:

Given expression:

          [tex]-\frac{1s }{20r}[/tex]  

   r  = [tex]-\frac{1}{4}[/tex] , s = [tex]\frac{4}{5}[/tex]

Now;

     [tex]-\frac{1s }{20r}[/tex]    = [tex]-\frac{s}{20r}[/tex]

              Insert the parameters:

                = [tex]-\frac{\frac{4}{5} }{20 x (-\frac{1}{4} )}[/tex]  

               = - [tex]\frac{\frac{4}{5} }{-5}[/tex]  

              -x - = +

                = [tex]\frac{4}{5}[/tex] x [tex]\frac{1}{5}[/tex]

                = [tex]\frac{4}{25}[/tex]

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Answers

Answer:

B. 12.40

Step-by-step explanation:

Add all the hours

Total profit divided by the amount of hours

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Answers

Answer:

y= -5/4x + 6

Step-by-step explanation:

y= mx + b

m= -5/4 (rise over run/slope)

b= 6 (y-intercept)

-I hope this helps have a great day!

Answer:

y = -5/4(x)+6

Step-by-step explanation:

to find the equation of this line, we must first find the slope

We can write the equation of this line y = mx + b where m is the slope and b is the y-intercept

m = (y2-y1)/(x2-x1)

m = (-4-6)/(8-0)

m = -10/8

m = -5/4

b is the y intercept which is at 6

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Answers

Answer:

9%

Step-by-step explanation:

Convert the fraction to a decimal, then multiply by  

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