Applying Radical Functions to Real-World Situations

Kriz watched a series about fire fighting and became super interested in the high pressure water systems used to fight fires. The maximum flow

Q

of such systems is

200

liters per minute. The following formula presents the relationship between

Q

and the diameter

d

of the fire hose.

Q = \frac{π d ^{2} v}{4}

In this formula,

v

is the speed of the water. What is the diameter of the hose that allows a maximum flow of water at a speed of

\frac{6 4 0}{3 π}

decimeters per second? Write the exact answer in decimeters as a decimal.

Option	Statement
A	The average increase in profit of the first company will be greater over the next $10$ years.
B	The average increase in profit of the second company will be greater over the next $10$ years.
C	On average, the profit of the companies increases at the same rate.
D	On average, the annual profit of the second company is about $0.175$ millions of dollars.

How to Calculate the Speed of a Car?

	8 Theory slides
	8 Exercises - Grade E - A
	Each lesson is meant to take 1-2 classroom sessions

Interval $[t_{1}, t_{2}]$	$\frac{P _{1} ( t _{2} ) - P _{1} ( t _{1} )}{t _{2} - t _{1}}$	Substitute and Evaluate
$[2, 10]$	$\frac{P _{1} ( 1 0 ) - P _{1} ( 2 )}{1 0 - 2}$	$\frac{3 - 2}{1 0 - 2} = 0.125$
$[10, 18]$	$\frac{P _{1} ( 1 8 ) - P _{1} ( 1 0 )}{1 8 - 1 0}$	$\frac{3 . 2 6 - 3}{1 8 - 1 0} \approx 0.033$

$t$	$\frac{1}{2} 3 t - 2 + 2$	$P_{1} (t)$
$0$	$\frac{1}{2} 3 0 - 2 + 2$	$\approx 1.37$
$10$	$\frac{1}{2} 3 10 - 2 + 2$	$3$

Profit Function	$\frac{f ( x _{2} ) - f ( x _{1} )}{x _{2} - x _{1}}$	Substitute and Evaluate
$P_{1}$	$\frac{P _{1} ( 1 0 ) - P _{1} ( 0 )}{1 0 - 0}$	$\frac{3 - 1 . 3 7}{1 0 - 0} = 0.163$
$P_{2}$	$\frac{P _{2} ( 1 0 ) - P _{2} ( 0 )}{1 0 - 0}$	$\frac{3 - 1 . 2 5}{1 0 - 0} = 0.175$

Input	$18 d$	$v_{1} (d)$	$16 3 p$	$v_{2} (p)$
$0$	$18 (0)$	$0$	$1630$	$0$
$216$	$18 (216)$	$\approx 62.35$	$163216$	$96$

Function	$\frac{f ( x _{2} ) - f ( x _{1} )}{x _{2} - x _{1}}$	Substitute and Evaluate
$v_{1}$	$\frac{v _{1} ( 2 1 6 ) - v _{1} ( 0 )}{2 1 6 - 0}$	$\frac{6 2 . 3 5 - 0}{2 1 6 - 0} \approx 0.29$
$v_{2}$	$\frac{v _{2} ( 2 1 6 ) - v _{2} ( 0 )}{2 1 6 - 0}$	$\frac{9 6 - 0}{2 1 6 - 0} \approx 0.44$

Metabolic Rate
The rate at which a person or an animal burns calories to maintain its body weight.