9.1-­‐9.3 Review Answers Name: ________________________________ Algebra 2 CP 1. The number of calories, C, a person burns and the time, T (in minutes), the person spends performing an activity vary directly. A 150-­‐pound person can burn off 75 calories by sitting in class for 30 minutes. How long must a 150-­‐pound person sit in class to burn off 545 calories? 5
C = kt
C= t
2
5
75 = k(30)
545 = t
2
5
=k
t = 218 min.
2
2. A bicycle uses two gears so that a shaft can turn at a different speed than the pedals. The speed of the gears varies inversely as the number of teeth in the gear. If one gear has 35 teeth and is moving at 50 revolutions per minutes, how fast is the second gear going if it has 25 teeth? €
1750
t
k
1750
50 =
S=
35
25
1750 = k
t = 70 rev / min.
3. The amount of heat necessary to change the temperature of an aluminum can is jointly proportional to the product of the mass of the can and the temperature change desired. It takes 1.54 kilocalories of heat € to change the temperature of a 0.028 kilogram aluminum can 250 degrees Celsius. Find the heat necessary to change the temperature of a 0.054 kilogram can 300 degrees Celsius. S=
k
t
S=
H = kMT
H = .22 MT
1.54 = k(.028)(250)
H = .22(.054)(300)
.22 = k
H = 3.564 kilocalories
4. When air is pumped into a tire, the pressure required varies inversely as the volume of the air. If the pressure is 30 lb per square inch when the volume is 140 cubic inches, find the pressure when the volume is 100 cubic inches. €
k
4200
P=
P=
V
V
k
4200
30 =
P=
140
100
4200 = k
P = 42 lbs / in 2
5. The power of an electrical circuit varies jointly as the resistance and the square of the current. For a 600-­‐watt microwave oven that draws a current of 5.0 amperes, the resistance is 24 ohms. What is the resistance of a 200-­‐watt refrigerator that draws a current of 1.7 amperes? €
P = krc2
P = rc2
600 = k(24)(5)2
1= k
€
200 = (r )(1.7)2 r = 69.204 ohms
6. Intensity varies inversely with the square of its distance. At a distance of 1 meter, the intensity of jet engine noise is 10 watts per square meter. An airport cargo worker is 15 meters from the jet engine. What is the sound intensity at 15 meters? k
10
I= 2
I= 2
d
d
k
10
10 = 2
I= 2
1
15
10 = k
I = .04 watts / m2
2
Write an equation for a translation of y = that has the given asymptotes. x
€
7. x = -­‐3; y = -­‐4 8. x = 0; y = 4 y=
€
2
−4
x +3
y=
2
+4
x
Sketch the asymptotes and the graph of each equation. 9. €
y=−
1
+ 2 x
€
10. y=
1
− 5 2x + 2
€ €
11. y=
4
+ 4 x −5
12. € € y=−
2
− 3 x +4
Find the vertical asymptotes, horizontal asymptote, or holes for the graph of each rational function. If there are none, write “none”. 13. x −5
( x −1)( x +1)
=
14. =
( x − 3)( x +1)
( x − 2)
Vertical: x = -­‐1 & x = 1 Vertical: x = 2 €
Horizontal: y = 0 €
Horizontal: NONE Holes: NONE Holes: NONE 15. =
x +3
1
=
( x − 3)( x + 3) x − 3
16. =
( x − 2)( x + 2)
x2 + 4
€
Vertical: x = 3 €
Vertical: NONE Horizontal: y = 0 Horizontal: y = 1 Holes: x = -­‐3 Holes: NONE 2x 2 + 3
=
( x − 4)( x + 4)
18. 17. €
Vertical: x = 4 & x = -­‐4 Vertical: x = -­‐6 Horizontal: y = 2 Horizontal: y = 0 Holes: NONE Holes: NONE 19. =
( x + 3)( x − 2) x + 3
=
( x − 2)( x +1) x +1
20. € x = -­‐1 Vertical: Vertical: x = 5/2 Horizontal: y = 1 Horizontal: NONE Holes: x = 2 Holes: NONE