Name_______________________________period___
Algebra II UNIT 3-2 Solving Radicals
PAP ASSIGNMENT #3
Word Problems: Define x & y, Table, Graph, Domain/Range, Answer the question
1. The speed in miles per hour of a tsunami wave can be modeled by the function below.
d = the average depth in feet of water over which the tsunami travels. s = speed in miles per hour. Graph
values for d = 0, 1000, 2000, 3000 to create a table & graph. Predict the speed of the tsunami over water with a
depth of 1200ft.
s (d )  3.46 d
d
s
0
1000
2000
3000
2. The equation below is used to approximate the velocity needed to escape a planet. The gravity of Saturn is 11.08. Mars has a gravity of - 3.77. Remember the gravity changes the further away you are from the planet.
v  4909 gR . Use gravity to create the equations for Saturn & Mars. Graph both equations on the same
graph. Use values of R = 0, 5K, 10K, 15K on the table & graph.
Saturn
Mars
R
v
R
v
0
0
5K
5K
10K
10K
15K
15K
3. A company manufactures cans for pet food. The function
R
3
v 
5
40
models the radius in centimeters of a
can holding a volume of dog food. The graph of the corresponding function for cans of cat food is compressed
by a factor of about 3 . Write the corresponding function g(x) for cans of cat food, and use v = 0, 100, 200,
5
300, 400 to create the table & graph. Use the equation to estimate the radius of a can holding 216 cm3 of cat
food.
v
0
100
200
300
400
R
4. Pilots use the function D ( A)  3.56 A to approximate the distance D in kilometers to the horizon from an
altitude A in meters. Use A = 0, 1500, 3000, 7000, 10000 to create a table & a graph.
A
0
1500
3000
7000
D
10000
Define x & y, &Answer the question
5. For a spinning amusement park ride, the velocity v in meters per second of a car moving around a curve with
a radius r meters is given by v  ar , where a is the car’s acceleration in m/s2.
a) For safety reasons, a ride has a maximum acceleration of 39.2 m/s2. If the cars on the ride have a
velocity of 14 m/s, what is the smallest radius that any curve on the ride may have?
b) What is the acceleration of a car moving at 8 m/s around a curve with a radius of 2.5 m?
6. For 12  4 p  y , what is the value of y when p = -16? For what value of p does y = 8?
*7. New stars can form inside an interstellar cloud of gas when a cloud fragment, called a clump, has a mass
(T  273)3
,
1000
where T is the temperature of the gas in degrees Celsius and n is the density of the gas in molecules per cubic
centimeter. n=1000, Use T = -263, -262, -261, -260 to create the table & graph. An astronomer discovers a gas
clump with M=137 at what temperature will a star form.
greater than what is known as the Jean’s mass. The Jean’s mass, Mj is given by (137) j  100
T
-263
-262
-261
-260
j
*8. The sum of a number, m, and its square root can be represented by the equation y  m  m . Find the value
of m if y = 14.
*9. The surface area, S, of a cone is given by π times the square root of the sum of the radius squared and the
height squared. What is the height of the cone with a surface area of 40 square inches and a base radius of 8
inches?