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For the simple harmonic motion described by the trigonometric function,find the maximum displacement.? d=8cos6π5td = 8 \cos \frac { 6 \pi } { 5 } t ?


A) 55 ?
B) 65\frac { 6 } { 5 }
C) 8
D) 18\frac { 1 } { 8 }
E) 56\frac { 5 } { 6 }

F) A) and B)
G) A) and D)

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For the simple harmonic motion described by the trigonometric function,find the frequency per second.? d=14sin6πtd = \frac { 1 } { 4 } \sin 6 \pi t ?


A) 33
B) 66
C) 3π3 \pi
D) 6π6 \pi
E) 2π2 \pi

F) A) and D)
G) B) and C)

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Find the angle α\alpha between two nonvertical lines L1L _ { 1 } and L2L _ { 2 } .The angle α\alpha satisfies the equation? tanα=m2m11+m2m1\tan \alpha = \left| \frac { m _ { 2 } - m _ { 1 } } { 1 + m _ { 2 } m _ { 1 } } \right| ? where m1m _ { 1 } and m2m _ { 2 } are slopes of L1L _ { 1 } and L2L _ { 2 } ,respectively. (Assume that m1m21m _ { 1 } m _ { 2 } \neq 1 . ) ?? L1:2xy=8L _ { 1 } : 2 x - y = 8 L2:x5y=4L _ { 2 } : x - 5 y = - 4 ? Round your answer to one decimal place. ?


A) 54.1o
B) ?53.1o
C) 55.1o
D) 52.1o
E) 56.1o

F) A) and B)
G) B) and C)

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You are holding one of the tethers attached to the top of a giant character balloon in a parade.Before the start of the parade the balloon is upright and the bottom is floating approximately 20 feet above ground level.You are standing approximately a = 130 feet ahead of the balloon (see figure) .?  You are holding one of the tethers attached to the top of a giant character balloon in a parade.Before the start of the parade the balloon is upright and the bottom is floating approximately 20 feet above ground level.You are standing approximately a = 130 feet ahead of the balloon (see figure) .?   ? Find an expression for the angle of elevation from you to the top of the balloon. ? A)   \theta = \arccos \left( \frac { 130 } { l } \right)   B)   \theta = \arccos \left( \frac { l } { 130 } \right)   C)   \theta = \arcsin \left( \frac { l } { h + 17 } \right)   D)   \theta = \arcsin \left( \frac { h + 20 } { l } \right)   E)   \theta = \arctan \left( \frac { 130 } { h + 20 } \right) ? Find an expression for the angle of elevation from you to the top of the balloon. ?


A) θ=arccos(130l) \theta = \arccos \left( \frac { 130 } { l } \right)
B) θ=arccos(l130) \theta = \arccos \left( \frac { l } { 130 } \right)
C) θ=arcsin(lh+17) \theta = \arcsin \left( \frac { l } { h + 17 } \right)
D) θ=arcsin(h+20l) \theta = \arcsin \left( \frac { h + 20 } { l } \right)
E) θ=arctan(130h+20) \theta = \arctan \left( \frac { 130 } { h + 20 } \right)

F) A) and E)
G) A) and D)

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A granular substance such as sand naturally settles into a cone-shaped pile when poured from a small aperture.Its height depends on the humidity and adhesion between granules.The angle of elevation of a pile,θ,is called the angle of repose.If the height of a pile of sand is 11 feet and its diameter is approximately 34 feet,determine the angle of repose.Round answer to nearest degree. A granular substance such as sand naturally settles into a cone-shaped pile when poured from a small aperture.Its height depends on the humidity and adhesion between granules.The angle of elevation of a pile,θ,is called the angle of repose.If the height of a pile of sand is 11 feet and its diameter is approximately 34 feet,determine the angle of repose.Round answer to nearest degree.   A) 29<sup>o</sup> B) 30<sup>o</sup> C) 31<sup>o</sup> D) 32<sup>o</sup> E) 33<sup>o</sup>


A) 29o
B) 30o
C) 31o
D) 32o
E) 33o

F) C) and D)
G) A) and C)

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Find the altitude of the isosceles triangle shown below if θ=38\theta = 38 ^ { \circ } and b=8 centimeters b = 8 \text { centimeters } .Round your answer to two decimal places.  Find the altitude of the isosceles triangle shown below if  \theta = 38 ^ { \circ }  and  b = 8 \text { centimeters }  .Round your answer to two decimal places.   A) 5.12 centimeters B) 6.25 centimeters C) 3.13 centimeters D) 2.46 centimeters E) 1.38 centimeters


A) 5.12 centimeters
B) 6.25 centimeters
C) 3.13 centimeters
D) 2.46 centimeters
E) 1.38 centimeters

F) None of the above
G) B) and E)

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Find the length of the sides of a regular hexagon inscribed in a circle of radius 29 inches. ​


A) 30 in.
B) 31 in.
C) 32 in.
D) 33 in.
E) 29 in.

F) None of the above
G) A) and E)

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Find a model for simple harmonic motion satisfying the specified conditions. ? Displacement (t = 0) : 0 Amplitude: 5 meters Period: 10 seconds ?


A) d=5sin(πt5) d = 5 \sin \left( \frac { \pi t } { 5 } \right) ?
B) d=5sin(2πt) d = 5 \sin ( 2 \pi t ) ?
C) ? d=5sin(πt12) d = 5 \sin \left( \frac { \pi t } { 12 } \right) ?
D) d=10sin(πt) d = 10 \sin ( \pi t ) ?
E) d=5cos(2πt) d = 5 \cos ( 2 \pi t ) ?

F) A) and C)
G) D) and E)

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Find the lengths of all the unknown members of the truss. Round your answer to one decimal place.?  Find the lengths of all the unknown members of the truss. Round your answer to one decimal place.?   ?  A = 30  ? A)   b \approx 22.0 , a \approx 37.6  B)   b \approx 21.0 , a \approx 36.6  C)   b \approx 24.0 , a \approx 39.6  D)   b \approx 36.6 , a \approx 21.0  E)   b \approx 23.0 , a \approx 38.6 ? A=30A = 30 ?


A) b22.0,a37.6b \approx 22.0 , a \approx 37.6
B) b21.0,a36.6b \approx 21.0 , a \approx 36.6
C) b24.0,a39.6b \approx 24.0 , a \approx 39.6
D) b36.6,a21.0b \approx 36.6 , a \approx 21.0
E) b23.0,a38.6b \approx 23.0 , a \approx 38.6

F) B) and D)
G) A) and E)

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Determine the angle between the diagonal of a cube and its edge,as shown in the figure,where a=12a = 12 .Round your answer to one decimal place.?  Determine the angle between the diagonal of a cube and its edge,as shown in the figure,where  a = 12  .Round your answer to one decimal place.?   ? A) 56.7<sup>o</sup> B) 57.7<sup>o</sup> C) 55.7<sup>o</sup> D) 54.7<sup>o</sup> E) 58.7<sup>o</sup> ? ?


A) 56.7o
B) 57.7o
C) 55.7o
D) 54.7o
E) 58.7o ?

F) B) and C)
G) A) and E)

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Find the angle ? between two nonvertical lines L1L _ { 1 } and L2L _ { 2 } .The angle ? satisfies the equation? tanα=m2m11+m2m1\tan \alpha = \left| \frac { m _ { 2 } - m _ { 1 } } { 1 + m _ { 2 } m _ { 1 } } \right| ? where m1m _ { 1 } and m2m _ { 2 } are slopes of L1L _ { 1 } and L2L _ { 2 } ,respectively. (Assume that m1m21m _ { 1 } m _ { 2 } \neq 1 . ) ? L1L _ { 1 } : 5x - 4y = 5 L2L _ { 2 } : x + y = 1 ? Round your answer to one decimal place. ?


A) 83.7º
B) 84.7º
C) 85.7º
D) 86.7º
E) 87.7º

F) A) and B)
G) None of the above

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You are holding one of the tethers attached to the top of a giant character balloon in a parade.Before the start of the parade the balloon is upright and the bottom is floating approximately 20 feet above ground level.You are standing approximately a = 130 feet ahead of the balloon (see figure) .?  You are holding one of the tethers attached to the top of a giant character balloon in a parade.Before the start of the parade the balloon is upright and the bottom is floating approximately 20 feet above ground level.You are standing approximately a = 130 feet ahead of the balloon (see figure) .?   ? Find the length l of the tether you are holding in terms of h,the height h of the balloon from top to bottom. ? A)   \sqrt { h ^ { 2 } + 34 h + 17,189 }  B)   \sqrt { h ^ { 2 } + 17 h + 17,189 }  ? C)   \sqrt { h ^ { 2 } + 20 h + 689 }  D)   \sqrt { h ^ { 2 } + 40 h + 689 }  ? E)   \sqrt { h ^ { 2 } + 34 h + 289 } ? Find the length l of the tether you are holding in terms of h,the height h of the balloon from top to bottom. ?


A) h2+34h+17,189\sqrt { h ^ { 2 } + 34 h + 17,189 }
B) h2+17h+17,189\sqrt { h ^ { 2 } + 17 h + 17,189 } ?
C) h2+20h+689\sqrt { h ^ { 2 } + 20 h + 689 }
D) h2+40h+689\sqrt { h ^ { 2 } + 40 h + 689 } ?
E) h2+34h+289\sqrt { h ^ { 2 } + 34 h + 289 }

F) A) and D)
G) B) and D)

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For the simple harmonic motion described by the trigonometric function,find the least positive value of t for which d = 0.? d=112sin14πtd = \frac { 1 } { 12 } \sin 14 \pi t ?


A) 114\frac { 1 } { 14 }
B) 112\frac { 1 } { 12 }
C) 1212
D) 16\frac { 1 } { 6 }
E) 1414

F) A) and D)
G) A) and E)

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Solve the right triangle shown in the figure for all unknown sides and angles.Round your answers to two decimal places.?  Solve the right triangle shown in the figure for all unknown sides and angles.Round your answers to two decimal places.?   ??  A = 30 ^ { \circ } , b = 12  ? A)   a \approx 13.86 , c \approx 6.93 , B = 60 ^ { \circ }  B)   a \approx 0.59 , c \approx 1.16 , B = 60 ^ { \circ }  ? C)   a \approx 6.93 , c \approx 13.86 , B = 60 ^ { \circ }  D)   a \approx 6.93 , c \approx 13.86 , B = 45 ^ { \circ }  E)   a \approx 6.93 , c \approx 13.86 , B = 30 ^ { \circ } ?? A=30,b=12A = 30 ^ { \circ } , b = 12 ?


A) a13.86,c6.93,B=60a \approx 13.86 , c \approx 6.93 , B = 60 ^ { \circ }
B) a0.59,c1.16,B=60a \approx 0.59 , c \approx 1.16 , B = 60 ^ { \circ } ?
C) a6.93,c13.86,B=60a \approx 6.93 , c \approx 13.86 , B = 60 ^ { \circ }
D) a6.93,c13.86,B=45a \approx 6.93 , c \approx 13.86 , B = 45 ^ { \circ }
E) a6.93,c13.86,B=30a \approx 6.93 , c \approx 13.86 , B = 30 ^ { \circ }

F) B) and C)
G) A) and B)

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For the simple harmonic motion described by the trigonometric function,find the frequency per second.? d=9cos8π5td = 9 \cos \frac { 8 \pi } { 5 } t ?


A) 45\frac { 4 } { 5 }
B) 8π5\frac { 8 \pi } { 5 }
C) 54\frac { 5 } { 4 }
D) 5π8\frac { 5 \pi } { 8 }
E) 58\frac { 5 } { 8 }

F) A) and B)
G) None of the above

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For the simple harmonic motion described by the trigonometric function,find the frequency per second.? d=116cos12πtd = \frac { 1 } { 16 } \cos 12 \pi t ?


A) 16 ?
B) ? ?
C) 12
D) 2?
E) 6

F) C) and E)
G) All of the above

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Find the length of the sides of a regular pentagon inscribed in a circle of radius 26 inches.Round your answer to one decimal place. ​


A) 31.6 in.
B) 33.6 in.
C) 30.6 in.
D) 32.6 in.
E) 34.6 in.

F) None of the above
G) C) and D)

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The length of a shadow of a tree is 120 feet when the angle of elevation of the sun is 33º.Approximate the height of the tree.Approximate the answer to one decimal place. ​


A) 77.9 ft
B) 81.9 ft
C) 79.9 ft
D) 78.9 ft
E) 80.9 ft

F) B) and C)
G) A) and E)

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An engineer erects a 111-foot cellular telephone tower.Find the angle of elevation to the top of the tower at a point on level ground 62 feet from its base.Round your answer to one decimal place. ​


A) 60.8º
B) 64.8º​
C) 63.8º
D) 61.8º
E) 62.8º

F) A) and B)
G) A) and E)

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For the simple harmonic motion described by the trigonometric function,find the least positive value of t for which d=0d = 0 ? d=6cos6π5td = 6 \cos \frac { 6 \pi } { 5 } t ?


A) 125\frac { 12 } { 5 }
B) 512\frac { 5 } { 12 }
C) 56\frac { 5 } { 6 }
D) 65\frac { 6 } { 5 }
E) 16\frac { 1 } { 6 }

F) C) and D)
G) D) and E)

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