Aball is launched at 20 m/sec from a 50 m tall platform. the function of the ball’s height (h) at time (t) seconds after launch is h(t) = -5t2 + 20t + 50. what is the domain of this situation?

The domain, since t<0 has no real context, is from zero to the time, t, when the height is equal to zero.  Height equals zero when:

-5t^2+20t+50=0  using the quadratic equation for simplicity:

t=(-20±√1400)/-10, since t>0 when h=0

t=(-20-10√14)/-10

t=2+√14 seconds

t≈5.74 seconds

So the domain is:

t=[0, 2+√14]

t≈[0, 5.74]  (to the nearest hundredth of a second)

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