mao (tm23477) – HW01 – gualdani – (57180)
1
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Welcome to Quest
001
10.0 points
±ind the solution set oF the inequality
x
2
<
−
3
x
+ 10
,
expressing your answer in interval notation.
1.
(
−∞
,
−
5]
2.
(
−∞
,
−
5)
∪
(2
,
∞
)
3.
(
−
5
,
2)
correct
4.
(2
,
∞
)
5.
[
−
5
,
2]
Explanation:
AFter Factoring we can rewrite the inequal
ity in the Form
(
x
+ 5)(
x
−
2)
<
0
.
Now the leFt hand side changes sign at its
zeros,
i.e.
, at
x
=
−
5
,
2, and the sign chart
−∞
∞
−
5
2
+
−
+
determines which sign it takes on a given
interval. Consequently, the given inequality
has
solution set = (
−
5
,
2)
.
002
10.0 points
A company manuFacturing computers has
fxed costs $21000 per month and variable
costs oF $800 per computer.
How many computers must be manuFac
tured and sold each month For the company
to break even iF the selling price oF a computer
is $1500?
1.
breakeven point = 40
2.
breakeven point = 50
3.
breakeven point = 60
4.
breakeven point = 20
5.
breakeven point = 30
correct
Explanation:
Let
x
be the number oF computers produced
each month. Then the production costs are
given by
C
(
x
) = 21000 + 800
x,
while the revenue From selling these comput
ers is given by
R
(
x
) = 1500
x.
±or the company to break even the cost oF
production should be equal to the revenue;
i.e.
,
C
(
x
) =
R
(
x
), in other words when
21000 + 800
x
= 1500
x.
Solving For
x
we see that the
breakeven point = 30.
003
10.0 points
A car purchased For $17000 has a resale value
oF $3000 aFter 10 years.
Assuming its resale value decreased linearly
over these years, what was the resale value oF
the car aFter 7 years?
1.
$7400
2.
$7000
3.
$7100
4.
$7300
5.
$7200
correct
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2
Explanation:
If the resale value
y
decreases linearly over
time, its value
x
years after purchase is given
by
y
=
mx
+
b
.
Initially,
i.e.
, at
x
= 0,
the value of the car is $17000, so
b
= 17000.
On the other hand, over 10 years the value
decreases to $3000, so
m
=
3000
−
17000
10
=
−
1400
.
Thus the resale value is given by
y
=
−
1400
x
+ 17000
.
After 7 years, therefore, the resale value is
−
1400
·
7 + 17000 = $7200.
004
10.0 points
Find the function
g
that is ±nally graphed
after the following transformations are ap
plied in the order given to the graph of a
function
f
:
(1) re²ect about the
x
axis;
(2) shift down 3 units;
(3) stretch vertically by a factor 8;
(4) re²ect about the
y
axis.
1.
g
(
x
) = 8
f
(
x
)
−
24
2.
g
(
x
) = 24
−
8
f
(
x
)
3.
g
(
x
) = 24
−
3
f
(
−
x
)
4.
g
(
x
) =
−
24
−
8
f
(
−
x
)
correct
5.
g
(
x
) = 24 + 8
f
(
−
x
)
Explanation:
Beginning with a function
y
=
f
(
x
), the
four transformations change
f
(
x
) as follows:
f
(
x
)
(1)
−→ −
f
(
x
)
(2)
−→ −
3
−
f
(
x
)
(3)
−→
8(
−
3
−
f
(
x
))
(4)
−→ −
24
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 Fall '08
 schultz
 Trigonometry, 3 2

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