SOLUTION: the height h(t), in feet, of an airborne tee-shirt t seconds after being launched can be approximated by h(t)= -15t^2+105t+10,0≤t≤10 find the times when the tee-shirt w

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Question 921914: the height h(t), in feet, of an airborne tee-shirt t seconds after being launched can be approximated by h(t)= -15t^2+105t+10,0≤t≤10 find the times when the tee-shirt will reach a fan 160 feet above ground level.
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
h(t)= -15t^2+105t+10,0≤t≤10 find the times when the tee-shirt will reach a fan 160 feet above ground level.
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h(t)= -15t^2+105t+10 = 160
-3t^2 + 21t + 2 = 32
-3t^2 + 21t - 30 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=81 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 2, 5. Here's your graph:

==================
t = 2 seconds going up
t = 5 second coming down

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