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Kira is a lovable dog who is full of energy. Her owner thought it would be fun to train her by throwing a frisbee for her to catch. When the frisbee is thrown, it follows a parabolic path that is modeled by the function h(t) = – 0.145t2 + 0.019t + 5.5. How many seconds will it take for the frisbee to hit the ground?

–6.2 seconds
–6.1 seconds
5.5 seconds
6.2 seconds

Respuesta :

fieryanswererft

Answer:

6.2 seconds

Explanation:

             Given function: h(t) = – 0.145t² + 0.019t + 5.5

  • Here h(t) which determines the height, when Frisbee touches the ground, the height shall be 0.

solve the quadratic equation:  

using the formula:  [tex]\left[\begin{array}{ccc} t = \frac{ -b \pm \sqrt{b^2 - 4ac}}{2a}\end{array}\right][/tex]

Solving steps:

→  –0.145t² + 0.019t + 5.5 = 0

→  [–0.145t² + 0.019t + 5.5 = 0 ]* 100

→  -145t² + 19t + 5500 = 0

→  [tex]t = \frac{ -19 \pm \sqrt{19^2 - 4 ( -145)(5500)}}{2(-145)}[/tex]

→  [tex]t_1=\frac{-19+\sqrt{3190361}}{2\left(-145\right)},\:t_2=\frac{-19-\sqrt{3190361}}{2\left(-145\right)}[/tex]

→  [tex]t = -6.09[/tex] , [tex]t = 6.2[/tex]

→  [tex]t = 6.2[/tex]

Time cannot be negative here.

  • So time taken: 6.2 seconds.
mhanifa

Answer:

  • D. 6.2 seconds

Step-by-step explanation:

When the frisbee hits the ground, the value of h is zero.

Find the time required:

  • – 0.145t² + 0.019t + 5.5 = 0
  • 145t² - 19t - 5500 = 0
  • t = (19 + √(19² + 4*145*5500))/290 = (19 + 1786,1)/290 = 6.2 seconds (rounded)
  • Note, taking positive root only as time is never negative

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