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anonymous

  • 5 years ago

a rocket is fired into the air from the top a building. The equation H= -16t2 + 96t + 120 gives H, the height of the rocket in feet, t seconds after it was fired. a) How tall was the building? b) What was the maximum height of the rocket? c) When did the rocket hit the ground?

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  1. anonymous
    • 5 years ago
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    a) substitue t=0 into the equation. b) dH/dt = 0

  2. anonymous
    • 5 years ago
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    a. well when time = 0 the rocket has not fired yet and it is sitting on top of the building so H = -16(0) + 96(0) + 120

  3. anonymous
    • 5 years ago
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    Are you in Algebra or Calculus?

  4. anonymous
    • 5 years ago
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    im in algebra

  5. anonymous
    • 5 years ago
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    c) let H =0, the solve the quadratic equation

  6. anonymous
    • 5 years ago
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    OK. so we need to find the maximum of the parabola. It is found when x = -b/2a (x in this case is t) so t = -96/-32 which is t = 3 that means when t = 3 or after 3 seconds, it is at its highest point. to find out how high that point is put in 3 for t H = -16(3^2) + 96(3) + 120

  7. anonymous
    • 5 years ago
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    To find out when it hits the ground, we need to find out when H = 0 0 = -16t^2 + 96t + 120 we need to factor this or use the quadratic formula. which do you want to do?

  8. anonymous
    • 5 years ago
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    factor

  9. anonymous
    • 5 years ago
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    OK.. you always want the t^2 to be positive so we are going to take it over to the other side of the equation

  10. anonymous
    • 5 years ago
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    16t^2 - 96t - 120 = 0 OK?

  11. anonymous
    • 5 years ago
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    ok

  12. anonymous
    • 5 years ago
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    8(2t^2 - 12t - 15) factor out the GCF which is 8

  13. anonymous
    • 5 years ago
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    Well... it doesn't factor so we have to use the quadratic formula. I am going back to the original 16t^2 - 96t - 120 = 0

  14. anonymous
    • 5 years ago
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    x = -b +- sqrt(b^2 - 4ac) ------------------ 2a

  15. anonymous
    • 5 years ago
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    x = 96 +- sqrt((-96)^2 - 4(16)(-12)) ----------------------------- 2(16)

  16. anonymous
    • 5 years ago
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    x = 96 +- sqrt(9216 + 768) ---------------------- 32

  17. anonymous
    • 5 years ago
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    x = 96 +- sqrt(9984) --------------- 32

  18. anonymous
    • 5 years ago
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    x = 96 +- 99.92 ------------ 32 x = -.1225 or x = 6.1225 since x represents seconds then it would be on the ground at 6.1 seconds

  19. anonymous
    • 5 years ago
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    thank you very much

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