1. The height in feet, of a t-shirt launched from a t-shirt cannon high in the stands at a football stadium is given by h(x)= -16x^2 + 64x + 80, where x is the time in seconds after the t-shirt is launched. How long will it take before the t-shirt reached the ground?

2. A penny is dropped from the top of a ne building. Its height in feet can be modeled by the equation y = 256 - 16x^2, where x is the time in seconds since the penny was dropped. How long does it take for the penny to reach the ground>

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tramserran tramserran · Answer 1 · 2020-09-23T14:51:41+02:00

Answer: 1) 5 seconds 2) 4 seconds

Step-by-step explanation:

When the object hits the ground, the height is zero.

Since the y-value is the height, set the equation equal to zero and solve for x.

A negative x-value can be disregarded since time cannot be negative (unless you have a time machine - LOL).

1) y = -16x² + 64x + 80

0 = -16x² + 64x + 80

0 = -16(x² - 4x - 5)

0 = x² - 4x - 5

0 = (x - 5)(x + 1)

0 = x - 5 0 = x + 1

x = 5 x = -1

↓

Disregard

The t-shirt reaches the ground in 5 seconds.

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2) y = 256 -16x²

0 = 256 -16x²

0 = 16(16 - x²)

0 = 16 - x²

0 = (4 - x)(4 + x)

0 = 4 - x 0 = 4 + x

x = 4 x = -4

↓

Disregard

The penny lands on the ground in 4 seconds.