Question 819280: A ball is thrown from an initial height of 4 feet with an initial upward velocity of 37ft/s . The ball's height H (in feet) after T seconds is given by the following. H=4+37t-16t^2. Find all values of for which the ball's height is 24feet?
Answer by TimothyLamb(4379)   (Show Source):
You can put this solution on YOUR website! ---
H(t) = -16t^2 + 37t + 4
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H(t) = 24 feet:
24 = -16t^2 + 37t + 4
-16t^2 + 37t - 20 = 0
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the above quadratic equation is in standard form, with a=-16, b=37, and c=-20
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to solve the quadratic equation, by using the quadratic formula, plug this:
-16 37 -20
into this: https://sooeet.com/math/quadratic-equation-solver.php
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the two real roots (i.e. the two x-intercepts), of the quadratic are:
t = 0.86143809
t = 1.45106191
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the ball is at 24 feet of height 0.861 seconds after being thrown (on it's way up),
and is at 24 feet of height again 1.451 seconds after being thrown (on it's way down.)
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Solve quadratic equations, quadratic formula:
https://sooeet.com/math/quadratic-formula-solver.php
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Calculate and graph the linear regression of any data set:
https://sooeet.com/math/linear-regression.php
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