Download = · = = / / 5x + 1 = 4 -→ 5x + 1 = 16 -→ x = 3 / / 3x + 1 = 4

Math 152A Ch. 10 Test Part 2
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1. Find all the complex square roots of −49.
Solution:
7i or − 7i
2. Perform the division of complex numbers
Solution:
3 − 2i
.
4 + 3i
3 − 2i
3 − 2i 4 − 3i
12 − 8i − 9i + 6i2
6 − 17i
=
·
=
=
4 + 3i
4 + 3i 4 − 3i
16 + 9
25
3. Solve the following. The answers should be real numbers, not complex numbers.
√
(a) 5x + 1 = 4
Solution:
(b)
√
√
3x + 1 = 4
Solution:
(c)
5x + 1 = 4 −→ 5x + 1 = 16 −→ x = 3
p
3
√
3x + 1 = 4 −→
√
3x = 3 −→ 3x = 9 −→ x = 3
y+3 = 2
Solution:
p
3
(d) 7 +
√
y + 3 = 2 −→ y + 3 = 8 −→ y = 5
x−5 = x
Solution:
7+
√
√
x−5 = x
x−5 = x−7
x − 5 = x2 − 14x + 49
x2 − 15x + 54 = 0
( x − 6)( x − 9) = 0 −→ The only solution is x = 9.
(e)
√
2x + 1 =
Solution:
√
x+4−1
√
√
x+4−1
√
2x + 1 = x + 4 − 2 x + 4 + 1
√
x − 4 = −2 x + 4
2x + 1 =
x2 − 8x + 16 = 4( x + 4)
x2 − 12x = 0
x ( x − 12) = 0 −→ x = 0 or x = 12
Checking shows the only solution is x = 0.
4. (pg. 471.32) In recent years, Las Vegas has become a popular location for conventions. The number of
convention attendees in Las Vegas rose from 4.6 million in 2002 to 6.1 million in 2006. Let v(t) represent
the number of convention attendees in Las Vegas t years after 2000.
Math 152A
Ch. 10 Test Part 2
Page 2 of 2
(a) Find a linear function v(t) that fits the data. Be sure to write your answer in terms of t and v.
Solution: Using the points (2, 4.6) and (4, 6.1), the slope is
m=
6.1 − 4.6
= 0.75
4−2
Using the point-slope formula for line
v − 4.6 = 0.75(t − 2) −→ v(t) = 0.75t + 3.1
(b) In what year will there be 18.1 million convention attendees in Las Vegas?
Solution: Solving the equation 18.1 = 0.75t + 3.1 gives t = 20 so the year will be 2022.
5. Set up the equation for the following word problems. DO NOT SOLVE!
(a) Etch Clean Graphics uses one cleanser that is 25% acid and a second that is 50% acid. How many
liters of each should be mixed to get 30 liters of a solution that is 40% acid?
(
x + y = 30
Solution: pg. 533 #26 Answer =
0.25x + 0.50y = 0.40(30)
(b) A self-employed contractor nearing retirement made two investments totaling $15,000. In one year,
those investments yielded $1023 in simple interest. Part of the money was invested at 6% and part
at 7.5%. How much was invested at each rate?
(
x + y = 15, 000
Solution: pg. 533 #30 Answer =
0.06x + 0.075y = 1023
6. (pg. 493.77) The stopping distance d of a car after the brakes have been applied varies directly as the
square of the speed r. Once the brakes are applied, a car traveling 50 mph can stop in 128 feet. Write
the equation for that models the stopping distance. Be sure to find the value of k.
Solution:
d = kr2 −→ 128 = k(50)2 −→ k = 0.0512 −→ d = 0.0512r2
7. Set up the algebra equations AND SOLVE the following.
A train leaves Danville at noon and travels north at a speed of 75 km/hr. Another train leaves Danville
at noon, heading west at 100 km/hr. How far will the northbound train have traveled when the two
trains are 1000 km apart?
Solution:
(75t) + (100t)2 = 10002
5625t2 + 10, 000t2 = 1, 000, 000
15, 625t2 = 1, 000, 000
t2 = 64
t = 8 hours
Therefore the northbound train will have traveled 75(8) = 600 miles.