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The height of an object thrown in the air is given by
, where h is in feet and t is the time in seconds the object has been in motion. At what time (to the nearest tenth) is the object 10 feet in the air?
Step 1. Substitute
Step 2. Then,
which is quadratic equation with two solutions.
The final quadratic equation is
after subtracting 10 from both sides of the equation.
Step 3. To solve, use the quadratic formula given as
where a=1, b=-7, and c=-7
|Solved by pluggable solver: SOLVE quadratic equation with variable|
|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=77 is greater than zero. That means that there are two solutions: .
Quadratic expression can be factored:
Again, the answer is: 7.88748219369606, -0.887482193696061.
Here's your graph:
Selecting the positive time is 7.9 seconds
Step 4. ANSWER: The time is 7.9 seconds.
I hope the above steps were helpful.
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