Chapter 5.5, Problem 6E

Reminder Round all the answers to two decimal places unless otherwise indicated.

A Leaking Can The side of a cylindrical can full of water springs a leak, and the water begins to stream out. (See Figure $5.73$.) The depth $H$, in inches, of water remaining in the can is a function of the distance $D$ in inches (measured from the base of the can) at which the stream of water strikes the ground. Here is a table of values of $D$ and $H$:

Distance D, in inches	Depth H, in inches
$0$	$1.00$
$1$	$1.25$
$2$	$2.00$
$3$	$3.25$
$4$	$5.00$

a. Use regression to find a formula for $H$ as a quadratic function of $D$.

b. When the depth is $4$ inches, how far from the base of the can will the water stream strike the ground?

c. When the water stream strikes the ground $5$ inches from the base of the can, what is the depth of water in the can?