Question

1. a penny is dropped from the top of a new building. its height in feet can be modeled by the equation y = 256 - 16x², where x is the time in seconds since the penny was dropped. how long does it take for the penny to reach the ground? see example 4

Explanation:

Step1: Set height y to 0

When the penny reaches the ground, its height $y = 0$. So we set up the equation $0=256 - 16x^{2}$.

Step2: Rearrange the equation

Add $16x^{2}$ to both sides of the equation: $16x^{2}=256$.

Step3: Solve for $x^{2}$

Divide both sides by 16: $x^{2}=\frac{256}{16}=16$.

Step4: Solve for x

Take the square - root of both sides. Since $x$ represents time, we consider the positive value only. $x=\sqrt{16}=4$.

Answer:

4 seconds