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Jlvesh is analyzing the flight of a few of his model rockets with various equations. In each equation, h is

the height of the rocket in centimeters, and the rocket was fired from the ground at timet = 0, where t is

measured in seconds.

Jivesh also has a more powerful Model B rocket. For this rocket, he uses the equation h=-90t4 + 300t.

When is the height of the Model B rocket 250 centimeters? Round your answers to the nearest

hundredth.

After t =

seconds, the rocket will have reached a height of 250 centimeters.

Respuesta :

MrRoyal

Answer:

After t =  1.67 seconds, the rocket will have reached a height of 250 centimeters.

Step-by-step explanation:

Given

[tex]h = -90t^2 + 300t[/tex] --- correct expression

Required: When does height = 250 cm

To do this, we have:

[tex]h = 250[/tex]

This gives:

[tex]250 = -90t^2 + 300t[/tex]

Rewrite as:

[tex]90t^2 - 300t + 250 = 0[/tex]

Divide through by 10

[tex]9t^2 - 30t + 25 = 0[/tex]

Expand

[tex]9t^2 - 15t - 15t + 25 = 0[/tex]

Factorize:

[tex]3t(3t - 5) -5(3t - 5) = 0[/tex]

[tex](3t - 5)(3t - 5) = 0[/tex]

This gives:

[tex]3t - 5 = 0[/tex]

Solve for 3t

[tex]3t = 5[/tex]

Solve for t

[tex]t = \frac{5}{3}[/tex]

[tex]t = 1.67s[/tex]

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