Review for exam # 4
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Solve.
1) For a resistor in a direct current circuit that does not vary its resistance, the power that a
resistor must dissipate is directly proportional to the square of the voltage across the
1
resistor. The resistor must dissipate
watt of power when the voltage across the resistor
16
1)
is 8 volts. Find the power that the resistor must dissipate when the voltage across it is 16
volts.
2) While traveling at a constant speed in a car, the centrifugal acceleration passengers feel
while the car is turning is inversely proportional to the radius of the turn. If the passengers
feel an acceleration of 12 feet per second per second when the radius of the turn is 100 feet,
find the acceleration the passengers feel when the radius of the turn is 300 feet.
2)
3) The amount of simple interest earned on an investment over a fixed amount of time is
jointly proportional to the principle invested and the interest rate. A principle investment
of $3700.00 with an interest rate of 6% earned $666.00 in simple interest. Find the amount
of simple interest earned if the principle is $2000.00 and the interest rate is 3%.
3)
1
Solve the compound inequality. Graph the solution set.
4) x + 8 < 6 and -8x < -40
5) -
1
3
4)
5x - 1 1
<
12
3
6) -5x + 1
11 or 6x + 3
5)
6)
-21
Solve the absolute value equation.
3x + 1
= |-3|
7)
9
7)
8) |-3x + 9| = |8 - 4x|
8)
2
9) |7x + 5| + 3 = 11
9)
10) |8x + 6| + 18 = 9
10)
Solve the inequality. Graph the solution set.
11) |4k - 8| + 8 < 11
12) |x - 3|
11)
12)
0
3
13) |3k - 2| + 8 > 17
13)
9y + 36
>9
4
14)
15) |3x - 5| > 0
15)
14)
4
Graph the solution of the system of linear inequalities.
16) y < 2x + 7
y x-8
17)
x
3x + 2y
16)
3
-4
17)
Find the cube root.
3 x12
18)
125y6
18)
Find the root. Assume that all variables represent nonnegative real numbers.
4
19) - 16x12y8
19)
Rewrite the expression with a positive rational exponent. Simplify, if possible.
20)
16a 2 b-4 1/2
a -2 b4
20)
5
Identify the domain and then graph the function.
3
21) f(x) = x - 5; use the following table.
x f(x)
4
5
6
13
21)
Rewrite the expression with a positive rational exponent. Simplify, if possible.
2 1/8 -2
y-7/2
r
22)
-7/4
r
y1/7
22)
Use rational exponents to simplify the following.
25
y10z 25
23)
23)
Use the product rule to simplify the expression. Assume that the variables can be any real number.
3
24) -216x4 y5
24)
Use the quotient rule to divide and simplify.
4 625x4
25)
y12
25)
6
Write with positive exponents. Simplify if possible.
26) -32-4/5
26)
Simplify the radical expression. Assume that all variables represent positive real numbers.
56x5 y6
27)
2y4
Find the distance between the pair of points.
28) (-5, -7) and (1, 2)
28)
Find the midpoint of the line segment whose endpoints are given.
9 4
7
29) - 1, , , 5 3
5
Add or subtract. Assume all variables represent positive real numbers.
30) 5x2 - 3 20x2 - 4 20x2
31) 5
3
x3 y7 - 3xy
3
27)
27y4
29)
30)
31)
7
Multiply, and then simplify if possible. Assume all variables represent positive real numbers.
32) 3( 75 + 15)
33) ( 6 -
12)( 2 +
3)
32)
33)
Rationalize the denominator. Assume that all variables represent positive real numbers.
34) 3
5
34)
9x2
Rationalize the denominator and simplify. Assume that all variables represent positive real numbers.
7x
35)
35)
3y
36)
7 7+
3 7-
35
35
36)
Solve the equation.
37) 4x - 11 = 4 - x
37)
Solve.
38)
3
2x + 4 - -2 = 0
38)
8
39)
2x + 3 = 1 +
x+1
39)
40) A balloon is secured to rope that is staked to the ground. A breeze blows the balloon so
that the rope is taut while the balloon is directly above a flag pole that is 50 feet from where
the rope is staked down. Find the altitude of the balloon if the rope is 120 feet long.
9
40)
Answer Key
Testname: REVIEW FOR EXAM # 4 125
1)
1
watt
4
2) 4 feet per second per second
3) $180.00
4)
5) -
3
,1
5
6) (- , )
7)
26
28
,3
3
8) - 1,
9)
10)
11)
17
7
3
13
,7
7
5 11
,
4 4
12) 3
7
3
11
,
3
14) (- , -8)
(0, )
13) - , -
15) - ,
5
3
5
,
3
10
Answer Key
Testname: REVIEW FOR EXAM # 4 125
16)
17)
18)
x4
5y2
19) -2x3 y2
4a 2
20)
b4
21) (- , )
22)
r13/4
y47/7
23) y2/5 z
11
Answer Key
Testname: REVIEW FOR EXAM # 4 125
3
24) -6xy xy2
5x
25)
y3
26) -
1
16
27) 2x2 y 7x
28) 3 13 units
1 1
29) ,
6 5
30) -13x 5
3
31) -4 xy2 y
32) 15 + 3 5
33) 2 3 + 3 2 - 2 6 - 6
3
15x
34)
3x
35)
21xy
3y
36)
13 + 5 5
2
37) {3}
38) - 6
39) -1, 3
40) 10 119 ft
12