Math 11
Chapter 3
Study Guide answers
1.
V = lwh
25000 = (92 – 2x)(72 – 2x)x
Use window settings with mins at zero
x max is 37 (after that y values are neg)
∴ y1 = (92 – 2x)(72 – 2x)x
Y2 = 25000
y max is 40 000
Intersection points are : 4.89 and 24.16
Correct answers are: 82.22 cm x 62.22cm x 4.89cm
or 43.68 cm x 23.68 cm x 24.16cm
2.
V = (88-2x)(72 – 2x)x
Enter this in your calculator and find the max (13.13, 37078.96). Use the x value from the max
to find the length and width. (88 – 2x13.13) and (72 – 2x 13.13)
61.74cm x 45.74cm x 13.13cm
3.
If 1000ml = 9cm x 6cm x 20cm
Then 2000 = (9 +x)(6 + x)(20 + x)
∴ y1 = (9 +x)(6 + x)(20 + x)
y2 = 2000
find the intersection point of the 2 graphs (x = 2.13) and use that value of x to find the new
dimensions. The closest answer is 11.2cm x 8.2cm x 22.2cm
4.
The reciprocal would be
5. The domain is all real numbers, the range is -3 ≤ y ≤3
6. The graph as drawn has a slope of -1 and a y intercept of zero.
Therefore the equation of the graph is y = -x.
The inverse would be y =
7.
8.
9.
10.
. This matches graph a.
C
y = 0 only a horizontal asymptote can be crossed by the graph
x = -3
7.5n = 2000 +5.5n
2n = 2000
n = 1000
11. If V = 1200, then h =
h = 3.7
so the equation is 1200 = (18 – x)2(3.7 + h) where h is the change in height
Solving the equation for h results in the equation:
h=
- 3.7
12. You need a function similar to the one in question #11
If v = 1600, then h =
h=4
so the equation is 1600 = (20-x) 2 (4 + h)
solving for h we get:
h=
–4
Substitute 1.3 for x and solve for h
h = 0.58
13. If
4
= x2 + 3x – 2 then
= 4(x2 + 3x – 2)
4x2 + 12x – 8
14.
= x2 – x + 2 and
= 3x – 5
Then the sum of the 2 functions is x2 – x + 2 + 3x – 5
x2 + 2x -3
15.
–
x – 5x – 3 – (6 – 3x)
x 2 – 5x – 3 – 6 +3x
x2 – 2x – 9
2
16.
x
(x – 4)(2x2 + 5)
2x4 - 3x2 – 20
2
17.
= 2(x2 + 2x – 3) - 5
= 2x2 + 4x – 11