Question

Please help ASAP

A toy cannon ball is launched from a cannon on top of a platform.
The function h(t) =-5+ 2 + 20+ + 4 gives the height, in meters, of the ball t seconds after it is launched.
Write and solve an inequality to find the times where the ball is more than 12 meters above the ground.
Round to the nearest hundredth.

Answer 1

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Explanation:

Answer 2

An inequality to find the times when the ball is more than 12 meters above the ground is
`h(t) < -5t^2+20t-8`.

The times when the ball is more than 12 meters above the ground is 0.45 seconds < t < 3.55 seconds.

In order to find the times when the ball would attain a height that is more than 12 meters above the ground, we would have to set up an inequality as follows;

h(t) > 12 meters.

By applying the substitution method, we have the following:

`-5t^2+20t+4 > 12\\\\-5t^2+20t+4-12 > 0\\\\-5t^2+20t-8 > 0`

where:

a = -5, b = 20, and c = -8

By solving the quadratic function using the quadratic formula, we have:

`t = (-b\; \pm \;√(b^2 - 4ac))/(2a)\\\\t = (-20\; \pm \;√(20^2 - 4(-5)(-8)))/(2(-5))\\\\t = (-20\; \pm \;√(400 - 160))/(-10)\\\\t = (-20\; \pm \;√(240))/(-10)\\\\t=2\pm ((4√(15) )/(-10) )`

t = 2 - 1.55

t = 0.45 seconds.

t = 2 + 1.55

t = 3.55 seconds.

Therefore, the times when the ball is more than 12 meters above the ground can be written as follows;

0.45 seconds < t < 3.55 seconds.