If a fire hose is held horizontally, then the distance the stream will travel depends on the water pressure and on thehorizontal factorfor the nozzle. The horizontal factorHdepends on the diameter of the nozzle. For a 0.5-inch nozzle, the horizontal factor is 56. For each 1/8-inch increase in nozzle diameter, the horizontal factor increases by 6.

(a) Explain why the function giving the horizontal factorHin terms of the nozzle diameterd(measured in inches) is linear.

(Because the horizontal factorHalways increases by 6, whendincreases by 1/8, the horizontal factor has a constant rate of change.)

(b) Use a formula to expressHas a linear function ofd.

$\displaystyle H= \frac{1}{8}d+6 $

(c) Once the horizontal factorHis known, we can calculate the distanceSin feet that a horizontal stream of water can travel by using the following formula wherepis pressure in pounds per square inch.

$\displaystyle S=\sqrt{Hp}$

How far will a horizontal stream travel if pressure is 45 pounds per square inch and the nozzle diameter is 1.75 inches? (Round your answer to one decimal place.)

8.9

(Of course... all of these answers are wrong... what am I doing?)