James Stewart-Calculus_ Early Transcendentals-Cengage Learning (2015)

A122 Appendix I Answers to Odd-Numbered Exercises
3. vstd − k2t, 1 l
astd − k21, 0 l
| vstd | − st 2 1 1
5. vstd − 23 sin t i 1 2 cos t j
astd − 23 cos t i 2 2 sin t j
| vstd | − s5 sin2 t 1 4
y
v(2)
(_2, 2)
a(2)
y
π
3c3 (0, Ans 2) 10.4.3 v” ’
3
9.13.04
0
0
π
a” ’
3
x
3
” , œ„3’
2
(3, 0)
x
37.
4 1 18t 2
s4 1 9t 2 ,
6t
39. 0, 1 41.
s4 1 9t 2
43. 4.5 cmys 2 , 9.0 cmys 2 45. t − 1
Chapter 13 Review • page 881
True-False Quiz
1. True 3. False 5. False 7. False
9. True 11. False 13. True
Exercises
1. (a)
z
Î 7
s30 , 131
30
(0, 1, 0)
7. vstd − i 1 2t j
astd − 2 j
| vstd | − s1 1 4t
2
x
z
3c3 Ans 10.4.5
9.13.04
a(1)
(1, 1, 2)
v(1)
9. k2t 1 1, 2t 2 1, 3t 2 l, k2, 2, 6t l, s9t 4 1 8t 2 1 2
11. s2 i 1 e t j 2 e 2t k, e t j 1 e 2t k, e t 1 e 2t
3c3 Ans 10.4.7
13. e t fscos t 2 sin tdi 1 ssin t 1 cos tdj 1 st 1 1dkg,
9.13.04
e t f22 sin t i 1 2 cos t j 1 st 1 2dkg, e t st 2 1 2t 1 3
15. vstd − s2t 1 3d i 2 j 1 t 2 k,
rstd − st 2 1 3td i 1 s1 2 td j 1 ( 1 3 t 3 1 1) k
17. (a) rstd − ( 1 3 t 3 1 t) i 1 st 2 sin t 1 1d j 1 ( 1 4 2 1 4 cos 2t) k
(b)
z
0.6
0.4
0.2
0
19. t − 4
200
0
x
_200
10
_10
0 y
21. rstd − t i 2 t j 1 5 2 t 2 k, | vstd | − s25t 2 1 2
23. (a) <3535 m 3c3 Ans (b) 10.4.15b <1531 m (c) 200 mys
25. 30 mys
9.13.04
27. < 544 ftys
29. 13.0° , , 36.0°, 55.4° , , 85.5°
31. s250, 250, 0d; 10s93 < 96.4 ftys
33. (a) 16 m (b) <23.6° upstream
20
12
0
40
_4
_12
35. The path is contained in a circle that lies in a plane perpendicular
ca100427a to c with center on a line through ca100427b the origin in the direction
10.13.00
10.13.00
of c.
0
y
40
x
y
(2, 1, 0)
(b) r9std − i 2 sin t j 1 cos t k,
r0std − 2 ca10r01a
2 cos t j 2 2 sin t k
3. rstd − 10.13.00 4 cos t i 1 4 sin t j 1 s5 2 4 cos tdk, 0 < t < 2
5. 1 3 i 2 s2y 2 dj 1 s2ydk 7. 86.631 9. 90°
1
11. (a) k3 sin t, 23 cos t, 2l (b) kcos t, sin t, 0l
s13
1
(c) k22 sin t, 2 cos t, 3l
s13
3
(d)
or 3 sec t csc t
13 sin t cos t 13
13. 12y17 3y2 15. x 2 2y 1 2 − 0
17. vstd − s1 1 ln td i 1 j 2 e 2t k,
| vstd | − s2 1 2 ln t 1 sln td2 1 e 22t , astd − s1ytdi 1 e 2t k
19. rstd − st 3 1 td i 1 st 4 2 td j 1 (3t 2 t 3 ) k
21. 37.3°, 157.4 m
23. (c) 22e 2t v d 1 e 2t R
Problems PLUs • page 884
1. (a) v − Rs2sin t i 1 cos t jd (c) a − 2 2 r
3. (a) 90°, v 2 0 ys2td
5. (a) <0.94 ft to the right of the table’s edge, <15 ftys
(b) <7.6° (c) <2.13 ft to the right of the table’s edge
7. 56°
9. sa 2b 3 2 a 3b 2dsx 2 c 1d 1 sa 3b 1 2 a 1b 3dsy 2 c 2d
1 sa 1b 2 2 a 2b 1dsz 2 c 3d − 0
Chapter 14
Exercises 14.1 • page 899
1. (a) 227; a temperature of 215°C with wind blowing at
40 kmyh feels equivalent to about 227°C without wind.
(b) When the temperature is 220°C, what wind speed gives a
wind chill of 230°C? 20 kmyh
(c) With a wind speed of 20 kmyh, what temperature gives a wind
chill of 249°C? 235°C
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