Chapter 5.1, Problem 84E

In Exercises 71-90, use the following notations: $\theta$ = central angle of circle, r = radius of circle, s = length of the intercepted arc, v = linear velocity, $\omega$ = angular velocity, A = area of the sector of a circle, and t = time.

In each case, find the missing quantity. Find the exact answer.

71. $r=25\text{in},s=7\text{in},\theta =?$

72. $r=5\text{ft},s=6\text{ft},\theta =?$

73. $r=10.5\text{cm},s=22\text{cm},\theta =?$

74. $r=60\text{m},s=120\text{m},\theta =?$

75. $r=3\text{m},\theta =25°,s=?$

76. $r=0.7\text{m},\theta =357°,s=?$

77. $r=6.5\text{m},\theta =12\text{radians},s=?$

78. $r=6\text{m},\theta =\frac{\pi }{6}\text{radians},s=?$

79. $\theta =\frac{1}{2}\text{radians},s=3\text{centimeters},r=?$ 5.

80. $\theta =\frac{1}{5}\text{radians},s=2\text{feet},r=?$

81. $\theta =30°,s=\frac{3\pi }{2}\text{meters},r=?$

82. $\theta =120°,s=20\text{inches},r=?$

83. $r=10in,\theta =4rad,A=?$

84. $r=1.5\text{ft},\theta =60°,A=?$

85. $A=20{\text{ft}}^{\text{2}},\theta =60°,r=?$

86. $A=60m^2,\theta =2\text{rad},r=?$

87. $r=6m,\omega =10rad/\min ,v=?$

88. $r=3.2\text{ft},\omega =5rad/\sec ,v=?$

89. $v=20\text{ft}/\sec ,r=10\text{f}t,\omega =?$

90. $v=10m/\min ,r=6m,\omega =?$