Question

At the start of the basketball game, the referee tosses a ball for a jump ball. The equation that models the height of the ball is
h(t) = -16t2 + 24t + 5
During what time interval is the height of the ball above 9 feet? (Round your answer to the nearest tenth of a second.)
a) .4 seconds to 1.9 seconds
b) .5 seconds to 2.1 seconds
c) .6 seconds to 1.8 seconds
d) .2 seconds to 1.3 seconds

Answer 1

ok, here we have quadratic inequalities (jeez.... lol, just kidding)
Basically, the question asks for the value of t for which
h(t) > 9
so...
-16t^2 + 24t + 5 > 9
-16t^2 + 25t - 4 > 0
Now we want to get what we call critical numbers (not sure what you call them)
Critical numbers are numbers for which h(t) is 0 or undefined.
By our quadratic formula, h(t) would be 0 at...
-25+sqrt(625 - 256)/-32 and -25-sqrt(625-256)/-32
= 0.18095 and 1.38154...
You'll see that if you pick t less than 0.18095, or t greater than 1.38154 that
h(t) would be less than 9, and if you pick t in between 0.18095 and 1.38154 that h(t) is indeed above 9, so pick that interval
And then round them off to then nearest tenth: (0.2, 1.4) to which (d) is closest, so I think I'll go with (d)

If I made an error, please notify me :)

Answer 2

yha u right thanks a lot :)

Answer 3

No problem :)