• Jul 7th 2008, 03:47 PM
bliks
Was wondering if someone could please walk me through how you would do this question:

A ball is thrown into the air. A sensor measures the height of the ball above the ground. The height of the ball is described by the equation y = -5x(x-4), where x represents the time in seconds. Determine the intervals of time when the ball is above a height of 15m.

• Jul 7th 2008, 03:50 PM
Jhevon
Quote:

Originally Posted by bliks
Was wondering if someone could please walk me through how you would do this question:

A ball is thrown into the air. A sensor measures the height of the ball above the ground. The height of the ball is described by the equation y = -5x(x-4), where x represents the time in seconds. Determine the intervals of time when the ball is above a height of 15m.

you need to solve \$\displaystyle -5x(x - 4) > 15\$ ...........this is where the height is greater than 15

\$\displaystyle \Rightarrow -5x^2 + 20x - 15 > 0\$ or \$\displaystyle x^2 - 4x + 3 < 0\$

can you continue?
• Jul 7th 2008, 03:52 PM
bliks
I can thank you for your time.
• Jul 7th 2008, 05:15 PM
OnMyWayToBeAMathProffesor
I think there might be a mistake some where. either with Jhevon or bliks. when you graph \$\displaystyle \Rightarrow -5x^2 + 20x - 15 > 0\$ the highest point is 5 when x is 1.999999. Maybe I did it wrong but that is what i got.
• Jul 7th 2008, 06:31 PM
Reckoner
Quote:

Originally Posted by OnMyWayToBeAMathProffesor
I think there might be a mistake some where. either with Jhevon or bliks. when you graph \$\displaystyle \Rightarrow -5x^2 + 20x - 15 > 0\$ the highest point is 5 when x is 1.999999. Maybe I did it wrong but that is what i got.

You are correct that 5 is the maximum of that parabola (but it occurs at \$\displaystyle x = 2\$, not 1.999999, as simple differentiation will show), but I fail to see how this affects the problem.
• Jul 8th 2008, 06:04 AM
OnMyWayToBeAMathProffesor
so wouldn't that mean that the ball never passes over the 15m mark?
• Jul 8th 2008, 01:23 PM
Reckoner
Quote:

Originally Posted by OnMyWayToBeAMathProffesor
so wouldn't that mean that the ball never passes over the 15m mark?

The ball's height will be greater than 15 m at those values \$\displaystyle x\$ which satisfy

\$\displaystyle -5x(x - 4) > 15\$.

So we solve the inequality:

\$\displaystyle -5x(x - 4) > 15\$

\$\displaystyle \Rightarrow -5x^2 + 20x - 15 > 0\$ (As you can see, we need this parabola to give values greater than 0, not 15)

\$\displaystyle \Rightarrow x^2 - 4x + 3 < 0\$

\$\displaystyle \Rightarrow(x - 3)(x - 1) < 0\$

\$\displaystyle \Rightarrow1 < x < 3\$

and we have our solution.