SOLUTION: The height of an object thrown in the air is given by h = t2 – 7t + 3, where h is in feet and t is the time in seconds the object has been in motion. At what time (to the nearest

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: The height of an object thrown in the air is given by h = t2 – 7t + 3, where h is in feet and t is the time in seconds the object has been in motion. At what time (to the nearest       Log On


   

Question 224467: The height of an object thrown in the air is given by h = t2 – 7t + 3, 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?
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
The height of an object thrown in the air is given by h=t%5E2-7t%2B3, 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 h=10 into h=t%5E2-7t%2B3.

Step 2. Then, 10=t%5E2-7t%2B3 which is quadratic equation with two solutions.

The final quadratic equation is t%5E2-7t-7=0 after subtracting 10 from both sides of the equation.

Step 3. To solve, use the quadratic formula given as

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

where a=1, b=-7, and c=-7

Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-7x%2B-7+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-7%29%5E2-4%2A1%2A-7=77.

Discriminant d=77 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--7%2B-sqrt%28+77+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-7%29%2Bsqrt%28+77+%29%29%2F2%5C1+=+7.88748219369606
x%5B2%5D+=+%28-%28-7%29-sqrt%28+77+%29%29%2F2%5C1+=+-0.887482193696061

Quadratic expression 1x%5E2%2B-7x%2B-7 can be factored:
1x%5E2%2B-7x%2B-7+=+1%28x-7.88748219369606%29%2A%28x--0.887482193696061%29
Again, the answer is: 7.88748219369606, -0.887482193696061. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-7%2Ax%2B-7+%29



Selecting the positive time is 7.9 seconds

Step 4. ANSWER: The time is 7.9 seconds.

I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Good luck in your studies!

Respectfully,
Dr J