Question

Abigail tosses a coin off a bridge into the stream below. The distance, in feet, the coin is above the water is modeled by the equation y = -16x^2 + 96x + 112. Where x represents time in seconds. What is the greatest height of the coin? Your answer

Answer 1

Answer:

The greatest height is 256 Feets

Explanations:

The distance of the coin above the water is modeled by the equation:

`\begin{gathered} y=-16x^2+96x\text{ + 112} \\ \text{Where x = the time} \end{gathered}`

The distance (y) is maximum when dy/dx = 0

`\begin{gathered} (dy)/(dx)=-32x\text{ + 96} \\ \text{Let }(dy)/(dx)=0 \\ -32x\text{ + 96 = 0} \\ 32x\text{ = 96} \\ x\text{ = }(96)/(32) \\ x\text{ = 3} \end{gathered}`

x = 3 seconds

To calculate the maximul height, substitute x = 3 into the given height equation

`\begin{gathered} y=-16(3)^2+96(3)+112 \\ y\text{ = -16(9) }+\text{ 96(3) + 112} \\ y\text{ = }-144+288+112 \\ y\text{ = 256} \end{gathered}`

The greatest height is 256 Feet