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Mrs.Peterson dropped a ball from the top of a tower. At the same time, her son, Drake, launches a rocket from a different level of the tower.
The height of the tennis ball in feet after t seconds can be represented by the quadratic function: b(t)=-t^2-2t+26.
The height of Drakes rocket after t seconds can be represented by the linear function: p(t)=-2t+10.
What are the two solutions to this system? Show your work.
Explain which solution is not reasonable in this situation.
After how many seconds do the rocket and the ball reach the same height.

Respuesta :

sqdancefan

9514 1404 393

Answer:

  • two solutions: t = -4, t = 4
  • t = -4 is not reasonable
  • 4 seconds

Step-by-step explanation:

A graphing calculator shows the two solutions to be ...

  (t, h) = (-4, 18) and (4, 2)

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The two heights will be equal when ...

  p(t) = b(t)

  -2t +10 = -t^2 -2t +26

  t^2 -16 = 0 . . . . subtract the right side expression

  (t -4)(t +4) = 0 . . . factor the difference of squares

  t = 4 or -4 . . . . values of t that make the factors zero

At these times, the heights will be ...

  p(t) = -2{4, -4} +10 = {-8, 8} +10 = {2, 18}

The solutions are ...

  (t, height) = (-4, 18) and (4, 2).

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We generally discount solutions for negative time, because we start counting time when the objects are launched. t = -4 is an extraneous solution.

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The rocket and ball reach the same height after 4 seconds.

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