1
MATH 209 INDIVIDUAL TEXTBOOK
SOLUTIONS WEEK 4
Chapters 9 & 10 of Dugo 3rd Ed
Section 9.1: Exercises 12, 24, 36, 64, 84, 108, 110, 112, and 114
Section 9.2: Exercises 22, 38, 104, 128, 130, 132, and 134
Section 9.3: Exercises 6, 36, 88, 94, 112, 114, and 116
Section 9.4: Exercises 12, 30, 60, 76 and 110
Section 9.5: Exercises 16, 30, 100, 102, and 104
Section 10.1: Exercises 80, 86, 96, and 102
Section 10.2: Exercises 10, 30, 42, 48, 84, and 88
Section 10.3: Exercises 64 70, 92, and 94
Section 9.1 Page 549-551, #12, 24, 36, 64, 84, 108, 110, 112, and 114
12 -√25 = -5
24
√m6 =m3
36
√16n = 4√n
2
64
√12x8 = 2x4√3
84
=
108 Comparing wind chills
Wind chill formula is
Where does the wind chill make one feel colder?
Minneapolis: t=10F, v = 15mph
Or Chicago: t= 20F, v = 25mph
Calculation for Minneapolis is
W=91.4 – 109.8 = -18.4
The wind chill in Minneapolis is -18F when the actual temperature is 10F and the
wind is 15mph
110 Using the formula, t=√(h/16), determine the time, t, for a skydiver to fall
17,000 ft, h.
t= √(17000/16) = √17000/4 = 130.38/4 = 32.6 seconds
3
112 The dimensions for yachts in the America’s Cup competition are determined
by the formula
Determine if a boat that has a displacement, D = 21.44m3
a sail area , S = 320.13 m2
and a length, L= 21.22m
meet the requirements
21.22 +22.36 – 27.24 < 16.296
16.34 < 16.296 ? NO
Trim sail to meet requirements
S < ((16.296 +27.24 -21.22)/1.25)2
S< (22.3/1.25)2
S< 318.27 m
Sail area must be decreased by 320.13-318.27 = 1.86 m2
114 The formula for small plane landing speed in terms of gross weight is
_____
V= √1.496L
a) For a gross weight of 7000 lbs the landing speed is
___________
V= √1.496*7000
= 102.3 ft/sec.
b) The gross weight for a landing speed of 115 ft/sec. is
L = V2/1.496 = (115)2/1.496 = 13225/1.496 = 8840 lbs
Section 9.2 Page 559-562 # 22, 38, 104, 128, 130, 132, and 134
4
22 (-16)1/4 is not a real number
38 25-3/2 = 1/√253 =1/√15625 = 1/125
104 (-27x9)1/3 = -3x3
128 Find the radius of a spherical tank, using the formula
Where the volume, V= 32π/3 m3
130 The radius of the orbit of a planet around the sun is modeled by the formula
R = T2/3
a) What is the radius of the Mars orbit if it takes 1.881 years to complete its orbit?
________
R =3√ (1.881)2
= 1.52 Astronomical Units
b) From the graph it seems that Saturn takes approximately 27 years to orbit the sun.
132 Determine the average annual return of a $10000(P) investment if it was
worth $24780 (S) after 5 years(n). Use the formula
5
The 5-year average return is 19.9%
134
Use the same formula for population growth
S = 32.5 M
P = 19.9 M
n = 30 years
=
= .0165
Population rate of growth was 1.65%
Section 9.3 Page 567-569, #6, 36, 88, 94, 112, 114, and 116
6
36
88
94
112 V =
114 A =
116 a) and d) are identities. In each case there is a square that can be removed
from under the radical sign.
6
Section 9.4 Page 567-569, #12, 30, 60, 76 and 110
12
30
=
60
76
110
a)
b)
c)
d)
e)
can be written x4/3
can be written x3/4 <<is not equivalent to the others
can be written x4/3
is written
x4/3
can be written x4/3
Section 9.5 Page 576-578, # 16, 30, 100, 102, and 104
16 a2-40 = 0
a2 = 40
a = +2√10
30
a-1 = 36
a = 37
100 The length of the diagonal of a square patio with an area of 40m2
x2 =40
the diagonal = √2x2 = √80 =4√5m2
7
102 The length of the side of a cube whose volume = 80ft3
x3 = 80
The length of one side, x =
104 Length of a diagonal billboard whose sides are 5 m and 12m
52 + 122 = (length of diagonal)2
25 + 144 = 169
The length of the diagonal is 13m
Section 10.1 Page 617-620, #80, 86, 96, and 102
80 w2 = - 225 The square root of a negative number is not a real number. It is
called an imaginary number and we’ll study about such in some future math
class.
86 3v2 +4v -1 =0
_____
v = -4 ±√16+12
6
v = -2 ±√7
3
96
7x + 29 = (x + 3 )2
7x + 29 = x2 +6x + 9
x2 –x – 20 = 0
(x+4)(x-5) = 0
x = 5 ( x = -4 does not check, gives the root of a negative number, and is
therefore extraneous)
102 100x2 -60x + 9 = 0 can be factored
(10x – 3)2 =0
x =0.3
8
Section 10.2 Pages 628-630, #10, 30, 42, 48, 84, and 88
10. The solution for x2 + 4x + 3 = 0 is x =-1, -3
30 The solution for -3x2-2x -5 = 0 isn’t a real number
42 The solution 9m2 -24m + 16 = 0 is m=4/3
48 The solution for -3x2 + 7x = 0 is x = 0, 7/3
84 Find length of the side of the square whose diagonal is 2m longer than the
side.
(x+2)2 = 2x2
2x2 –x2 – 4x – 4 = 0
x2 -4x – 4 = 0
The length of a side of the square is 4.8m.
88 Using the formula S = -16t2 + v0 t +s0 , calculate the time, for a ball to drop for
s0 = 12ft and v0 = 16 ft/sec (S = 0)
0 = -16t2 + 16 t +12
Simplify
0 = 4t2 – 4t - 3
9
The ball is in the air for 1.5 sec.
Section 10.3 Pages 637-639, #64 70, 92, and 94
64 Find the value of x in the expression
Let x2 + x = z2
z2 + z -2 = 0
(z+2)(z-1) = 0
Z= -2,1
x2 +x +4 = 0
not a real number
x2
+ x -1 = 0
70
b is not a real number
92
Rate to
Time Work
do Payroll
Cicely 1/x
8
8/x
Eva
1/(x+3)
6
6/(x+3)
10
hr
Therefore, their combined rate to do the entire job is
1/14.4 + 1/17.4 = 0.1268 payroll per hour
1/0.128 = 7.8 hr per payroll
It will take the two women 0.78 hrs to complete the last 10% of the payroll.
94 Length of rectangular painting is 36 inches. What is width required to make
golden rectangle?