Solutions Manual Problem Set 34 (a) y + Z = 65 2 y + z = 130 y = 130 - z 2. RET = concoctions (25) concoctions R = ET 20 (3)(5) 4 concoctions 3 eater-hr R = = Use substitution to solve. RET = concoctions (b) z-Y=24 2 z- y = 48 z - (130 - z) = 48 2z = 178 z = 89 T= concoctions RE T=~=21hr (~}5) 10 y = 130 - z y = 130 - (89) y = 41 3. RsT + RBT = jobs (25) (~)T + (~)T = 10 29. ~ = 4 (1) b a = 4b !2T= 10 30 300 hr T = 17 A and B are equal. Therefore the answer is C. $120 4. B = -- = $7.50 per call (18) 16 Ix! ~c A 30. (1J 3 3 A =- B = - ($7.50) = $11.25 per call 2 2 12A = 12($11.25) = $135 Since AB = BC, mLBAC = mLBCA = yO. X O = mLBAC - mLDAC = yO _ mLDAC 7 5. L 3 = 3 + 3 + 3 + 3 + 3 + 3 + 3 = 21 (34) i=l XO < yO Therefore the answer is B. 2 3j 3(0) 3(1) 3(2) 6. L 1- 2j = 1 - 2(0) + 1 - 2(1) + 1 - 2(2) (34) }=o 1 3 9 = -+-+- 1 -1 -3 =1-3-3= -5 Problem Set 34 1. Distance = m (28) Rate = z 7. (34) From the graph of the line we pick two ordered pairs: (70, 850) and (90, 700). m = 850 - 700 = -7.5 70 - 90 Mo = -7.5Zr + b 700 = -7.5(90) + b b = 1375 Mo = -7.5Zr + 1375 Time = m Z New distance = m New time = m_ 3 = m- 3z z z m _ New rate = m- 3z - z mz mi --- m - 3z hr Advanced Mathematics, Second Edition 113
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Solutions Manual Problem Set 34Solutions Manual Problem Set 34 (a) y + Z = 65 2 y + z = 130 y = 130 - z 2. RET = concoctions (25) concoctions R = ET 20 (3)(5) 4 concoctions 3 eater-hr
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From the graph of the line we pick two orderedpairs: (70, 850) and (90, 700).
m = 850 - 700 = -7.570 - 90
Mo = -7.5Zr + b700 = -7.5(90) + b
b = 1375
Mo = -7.5Zr + 1375
Time = mZ
New distance = m
New time = m _ 3 = m - 3zz z
m _New rate = m - 3z -
z
mz mi---
m - 3z hr
Advanced Mathematics, Second Edition 113
Problem Set 34Solutions Manual
8. From the graph of the line we pick two ordered(34) pairs: (102, 100) and (105, 120).
m = 120 - 100 = 6.67105 - 102
H = 6.67C + b100 = 6.67(102) + b
b = -580
H = 6.67C - 580
(b) y
a
(3~j I(x) = -fX tan ( Arcsin ~) = tan () = !g(x) = x + 1
(c) y
10.(33)
A property of a rectangle is that it has 4 right angles.The square also has 4 right angles. However, we arenot told anything about the sides or diagonals.Therefore the answer is A.
-+-r"T"T--- x
-3
111. Median = -(Bl + B2)(33) 2
3x + 5 = .!.[(2x - 1) + (6x - 9)]2
13x + 5 = -(8x - 10)
23x + 5 = 4x - 5
x = 10
-90° < () < 90°
1cos [Arctan (-3)] = cos () = .JlO = M10
12. 1 5 14. (a) x axis, yes.y = -x - -(31)
9x2 + (_y)2 = 9 is equivalent to 9x2 + y2 = 9.(32) 3 61 5 y axis, yes.--x = -y - -3 6
9(-x)2 + y2 = 9 is equivalent to 9x2 + y2 = 9.x = 3y +
5Origin, yes.-
29(-x)2 + (_y)2 = 9 is equivalent to
Interchange x and y.9x2 + y2 = 9.
y = 3x + 5 (b) x axis, no.-2
-y = x3 is not equivalent to y = x3.
y axis, no.13. (a) y y = (_x)3 is not equivalent to y = x3.(32)
Origin, yes.-y = (_x)3 is equivalent to y = x3.
x
15. Replace y with y + 3.(31)
-90° < () < 90° y + 3 = IxlArctan 1 = 45° y = Ixl - 3
114Advanced Mathematics, Second Edition
Solutions Manual Problem Set 34
16. g(x) = x2 - 2(31)
119. log2 - = a(26) 32
2a = J.32
2a = _125
a = -5
y
I \ I I I! I • x
20. log , P = -2(26) "5
17. -3/-135° - 2/-140°(30)
= -3/-135° + (-2/-140°)
y
P = (~r2=15-2 = 25
y
,I,I
/
21. (a) Not a function(21)
(b) Not a function
(c) Function, 1 to 1(d) Function, not 1 to 1/
/
/
DB
>tV'. I I ••• X .,v ". - I I •• X
A = 3 cas 45° = 2.1213
B = 3 sin 45° = 2.1213C = 2 cas 40° = 1.5321
D = 2 sin 40° = 1.2856
22. x + 11 ~ 0(21)
x ~ -11
x2 - x - 12 i' 0
(x - 4 )(x + 3) i' 0x i' 4,-3
{x E IR I x ~ -11, x i' 4, -3 }Resultant = (2.1213 + 1.5321) i