1
1
Math 70 : Intermediate Algebra
Test 4: Solution
Part I : Simplify the following expressions.

(1)
x2 5

2
2a 27ab5  3b 3a 3b 3
(2)
x  20  4 5 x
9ab 2 3ab
6
2x
(3)
2 x
2 x
(4)
4 x4 x
4 x
3 2x
x
(5) 5  2i 3  i 

17  i
(8)
3
5i
(6)
 16 a 2 b 4 3

 9a 4 b  2 3





1
(9)
1
2 i
2 1
 i
3
3
3
i
5
2
3a 3
4b
(7)

 
40   98 
90   32

 10  11i 2
Part II :
1. [2 points] Write 2 y x 3 as an exponential expression.
2
5
2. [2 points] Write 3 y as a radical expression.
Answer : 2 yx
Answer:
3
5
3
2
y2
3. Simplify(Use factoring technique.)
[5] (i)
6  x  x2
3x 2  10x  8

1
Fall 2010
x3
3x  4
[5] (ii)
x 2  5x  4 3x 2  2 x  8

4  x  3x 2
x2  4x

x2
x
2
[5] (iii)
[5] (iv)
6
x  32 x  3
4. [5] Solve for x,
5. [5] Solve for x,
6. [5] Solve for x,
1 1 1
 
a b x
3
9
2x  3
5
x  3
2x  3
x3
x4
x4
1
1
 2
2
x  6x  9 x  9
x
ab
ab
3x  2  4  2 .
x=–2
x 2  3x  3  1  2 x . Check your answer. x = 1
7. [5] Find the length of a pendulum that makes one swing in 4s. The equation for the time of one swing of a
L
pendulum is T  2
, where T is the time in seconds and L is the length in feet. Round your answer to
32
the
128
L  2 ft  12.97 ft
nearest hundredth.

8. [5] A new machine can package transistors four times a s fast as an old machine. Working together, the
machine can package the transistors in 8 hours. How long would it take the new machine, working alone, to
package the transistors? (Hint: Faster means less time.)
Let’s assume that the new machine will take x hours, working alone, to finish the job.
How many hours would it take the old machine, working alone, to finish the same job? 4x hours
Old machine
New machine
Rate
1/(4x)
1/x
Time
8
8
Portion of the job completed
8/(4x)
8/x
8 8
 1
It will take the new machine 10 hours, working alone, to package the transistors.
4x x
9. [6] The intensity (I) of a light source is inversely proportional to the square of the distance (d) from the
source. If the intensity is 10 lumens at a distance of 4 m, what is the intensity when the distance is 6 m?
a. Write the equation that describes the relation between I and d. I 
b. Find the constant of variation k.
k
d2
k = 160
c. Rewrite the equation and solve the problem. (Round your answer to the nearest hundredth.)
The intensity of the light source is 4.44 lumens.