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# algebra

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A rock is thrown from a roof and follows a parabolic through the air. The path of the rock is modeled by h(t)=-t^2 +9t+2, where h gives the height of the rock after t seconds since its release. when does the rock first reach a hight higher than 22 meters? for how long does it stay above 22 meters?.

Apr 25, 2022

#1
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$$22=-t^2+9t+2$$

$$t^2 - 9t + 20 = 0$$

$$-4 \cdot -5 = 20, -4-5=-9$$

$$(t-4)(t-5) = 0$$

$$t - 4 = 0$$

$$t = 4$$

$$t - 5 = 0$$

$$t = 5$$

The rock will reach a height higher than 22 meters $$\boxed{4}$$ seconds after it's released. It will stay above 22 meters for $$5 - 4 = \boxed{1}$$ seconds.

Apr 25, 2022

#1
+1

$$22=-t^2+9t+2$$

$$t^2 - 9t + 20 = 0$$

$$-4 \cdot -5 = 20, -4-5=-9$$

$$(t-4)(t-5) = 0$$

$$t - 4 = 0$$

$$t = 4$$

$$t - 5 = 0$$

$$t = 5$$

The rock will reach a height higher than 22 meters $$\boxed{4}$$ seconds after it's released. It will stay above 22 meters for $$5 - 4 = \boxed{1}$$ seconds.

Guest Apr 25, 2022