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:

To find the time \( t \) when the rock is 89 feet above the water, set \( h(t) = 89 \): \[ -16t^2 + 30t + 225 = 89 \] Rearranging gives: \[ -16t^2 + 30t + 136 = 0 \] Next, we can use the quadratic formula \( t = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \), where \( a = -16 \), \( b = 30 \), and \( c = 136 \). Calculating the discriminant: \[ b^2 - 4ac = 30^2 - 4(-16)(136) = 900 + 8704 = 9604 \] Now, take the square root: \[ \sqrt{9604} = 98 \] Plugging into the quadratic formula: \[ t = \frac{-30 \pm 98}{2(-16)} \] Calculating the two possible values for \( t \): 1. \( t = \frac{-30 + 98}{-32} = \frac{68}{-32} = -2.125 \) (not valid) 2. \( t = \frac{-30 - 98}{-32} = \frac{-128}{-32} = 4 \) The valid solution is \( t = 4 \) seconds. So, the final answer is: Answer: 4 Units: seconds