Arthur drops a ball from a height of 81 feet above the ground. it’s height, , is given by the equation h=16ft^2+81, where t is the time in seconds. for which interval of the time is the height of the ball less than 17 feet

The height of the ball is less than 17 feet for t > 2 seconds.

Step-by-step explanation:

The height of the ball after t seconds is given by the following equation:

For which interval of the time is the height of the ball less than 17 feet

This is t for which:

So

Multiplying by -1

The height of the ball is less than 17 feet for t > 2 seconds.

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4