Given the function f(x) = 5(x+4) − 6, solve for the inverse function when x = 19.
1 answer:
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The formula we need is
, where <em>v</em>₀ is the starting velocity and <em>h</em>₀ is the initial height. Using the velocity and starting height from our problem we have
. The path of this rocket will be a downward facing parabola, so there will be a maximum. This maximum will be at the vertex of the graph. To find the vertex we start out with 
, which in our case is 
. It will take 5 seconds for the rocket to reach its maximum height. Plugging this back into our formula gives us
The rocket's maximum height is 400 feet.
We set our formula equal to zero to find the time it takes to hit the ground, then we factor:
Using the zero product property, we know that either -16t =0 or t-10=0. When -16t=0 is at t=0, when the rocket is launched. t-10=0 gives us an answer of t=10, so the rocket reaches the ground again at 10 seconds.
The rocket's maximum height is 400 feet.
We set our formula equal to zero to find the time it takes to hit the ground, then we factor:
Using the zero product property, we know that either -16t =0 or t-10=0. When -16t=0 is at t=0, when the rocket is launched. t-10=0 gives us an answer of t=10, so the rocket reaches the ground again at 10 seconds.