The function $$ h(t) $$ gives the height of a rock thrown off the Golden Gate Bridge in feet above the water at $$ t $$ seconds after it is thrown. $$ h(t)=-16 t^{2}+30 t+225 $$ Question: How long until the rock is 89 feet above the water? Enter your final answer rounded to the nearest tenth (one decimal place.) Enter the correct units for your answer in the second box. IF there is no valid answer enter N/A in all blanks. *Remember: When calculating, do not do any rounding until the end of your calculations. Answer:

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Given the function $$ h(t) = -16t^2 + 30t + 225 $$ that represents the height of a rock thrown off the Golden Gate Bridge in feet above the water at $$ t $$ seconds after it is thrown, we need to find how long it takes for the rock to be 89 feet above the water.

To find the time when the rock is 89 feet above the water, we set the function $$ h(t) $$ equal to 89 and solve for $$ t $$:

$$ -16t^2 + 30t + 225 = 89 $$

Now, we can solve this quadratic equation to find the value of $$ t $$ when the rock is 89 feet above the water.
Solve the quadratic equation by following steps:
- step0: Solve by factoring:
  $$-16t^{2}+30t+225=89$$
- step1: Move the expression to the left side:
  $$-16t^{2}+30t+136=0$$
- step2: Factor the expression:
  $$-2\left(t-4\right)\left(8t+17\right)=0$$
- step3: Divide the terms:
  $$\left(t-4\right)\left(8t+17\right)=0$$
- step4: Separate into possible cases:
  $$\begin{align}&t-4=0\&8t+17=0\end{align}$$
- step5: Solve the equation:
  $$\begin{align}&t=4\&t=-\frac{17}{8}\end{align}$$
- step6: Rewrite:
  $$t_{1}=-\frac{17}{8},t_{2}=4$$
The solutions to the equation are $$ t_1 = -\frac{17}{8} $$ and $$ t_2 = 4 $$.

Since time cannot be negative, the valid solution is $$ t = 4 $$ seconds.

Therefore, it takes 4 seconds for the rock to be 89 feet above the water.

The answer is: 4 seconds.
It takes 4.0 seconds for the rock to be 89 feet above the water.

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