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h(t)=-4.9t^(2)+9.8 t+39.2
Kaia throws a stone vertically upward from a bridge. The height, in meters, of the stone above the water
t seconds after the throw can be modeled by the quadratic function given. How many seconds after the throw does the stone hit the water?
Choose 1 answer:
(A) 1
(B) 2
(C) 4
(D) 8

$h(t)=-4.9 t^{2}+9.8 t+39.2$ $\newline$ Kaia throws a stone vertically upward from a bridge. The height, in meters, of the stone above the water $t$ seconds after the throw can be modeled by the quadratic function given. How many seconds after the throw does the stone hit the water? $\newline$ Choose $1$ answer: $\newline$ (A) $1$ $\newline$ (B) $2$ $\newline$ (C) $4$ $\newline$ (D) $8$

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Properties of matrices

Full solution

Q.

h(t)=-4.9 t^{2}+9.8 t+39.2

\newline

Kaia throws a stone vertically upward from a bridge. The height, in meters, of the stone above the water

t

seconds after the throw can be modeled by the quadratic function given. How many seconds after the throw does the stone hit the water?

\newline

Choose

1

answer:

\newline

(A)

1

\newline

(B)

2

\newline

(C)

4

\newline

(D)

8

Find when stone hits water: To find when the stone hits the water, we need to find when $h(t) = 0$ .
Set equation to $0$ : Set the equation to $0$ and solve for $t$ : $-4.9t^2 + 9.8t + 39.2 = 0$ .
Divide and simplify: Divide the entire equation by $-4.9$ to simplify: $t^2 - 2t - 8 = 0$ .
Factor quadratic equation: Factor the quadratic equation: $(t - 4)(t + 2) = 0$ .
Solve for $t$ : Set each factor equal to $0$ and solve for $t$ : $t - 4 = 0$ or $t + 2 = 0$ .
Ignore negative solution: Solving $t - 4 = 0$ gives $t = 4$ seconds.
Final result: Solving $t + 2 = 0$ gives $t = -2$ seconds, but time can't be negative, so we ignore this solution.
Final result: Solving $t + 2 = 0$ gives $t = -2$ seconds, but time can't be negative, so we ignore this solution.The stone hits the water after $4$ seconds.

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