Question 1

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. o B) 30o C) 31o D) 32o E) 33o" class="answers-bank-image d-inline" rel="preload" >

Accepted Answer

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

Question 2

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.
?

Accepted Answer

A)    h2+34h+17,189\sqrt { h ^ { 2 } + 34 h + 17,189 }h2+34h+17,189c34,79.3,68.167,158.7,102.5,238c34.3,79.3,51.8,119.3,52.5,120c340,-704.7,510.7,-1060.3,512,-1067l0 -0c4.7,-7.3,11,-11,19,-11H40000v40H1012.3s-271.3,567,-271.3,567c-38.7,80.7,-84,175,-136,283c-52,108,-89.167,185.3,-111.5,232c-22.3,46.7,-33.8,70.3,-34.5,71c-4.7,4.7,-12.3,7,-23,7s-12,-1,-12,-1s-109,-253,-109,-253c-72.7,-168,-109.3,-252,-110,-252c-10.7,8,-22,16.7,-34,26c-22,17.3,-33.3,26,-34,26s-26,-26,-26,-26s76,-59,76,-59s76,-60,76,-60zM1001 80h400000v40h-400000z'/>​ 
B)    h2+17h+17,189\sqrt { h ^ { 2 } + 17 h + 17,189 }h2+17h+17,189c34,79.3,68.167,158.7,102.5,238c34.3,79.3,51.8,119.3,52.5,120c340,-704.7,510.7,-1060.3,512,-1067l0 -0c4.7,-7.3,11,-11,19,-11H40000v40H1012.3s-271.3,567,-271.3,567c-38.7,80.7,-84,175,-136,283c-52,108,-89.167,185.3,-111.5,232c-22.3,46.7,-33.8,70.3,-34.5,71c-4.7,4.7,-12.3,7,-23,7s-12,-1,-12,-1s-109,-253,-109,-253c-72.7,-168,-109.3,-252,-110,-252c-10.7,8,-22,16.7,-34,26c-22,17.3,-33.3,26,-34,26s-26,-26,-26,-26s76,-59,76,-59s76,-60,76,-60zM1001 80h400000v40h-400000z'/>​  ?
C)    h2+20h+689\sqrt { h ^ { 2 } + 20 h + 689 }h2+20h+689c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​ 
D)    h2+40h+689\sqrt { h ^ { 2 } + 40 h + 689 }h2+40h+689c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​  ?
E)    h2+34h+289\sqrt { h ^ { 2 } + 34 h + 289 }h2+34h+289c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​F) C) and D)
G) A) and E)

Question 3

For the simple harmonic motion described by the trigonometric function,find the least positive value of t for which  d=0d = 0d=0  ?  d=6cos⁡6π5td = 6 \cos \frac { 6 \pi } { 5 } td=6cos56π​t  ?

Accepted Answer

A)    125\frac { 12 } { 5 }512​ 
B)    512\frac { 5 } { 12 }125​ 
C)    56\frac { 5 } { 6 }65​ 
D)    65\frac { 6 } { 5 }56​ 
E)    16\frac { 1 } { 6 }61​F) A) and B)
G) A) and C)

Question 4

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. ​

Accepted Answer

A)  31.6 in.
B)  33.6 in.
C)  30.6 in.
D)  32.6 in.
E)  34.6 in.F) All of the above
G) A) and B)

Question 5

For the simple harmonic motion described by the trigonometric function,find the least positive value of t for which d = 0.?  d=112sin⁡14πtd = \frac { 1 } { 12 } \sin 14 \pi td=121​sin14πt  ?

Accepted Answer

A)    114\frac { 1 } { 14 }141​ 
B)    112\frac { 1 } { 12 }121​ 
C)    121212 
D)    16\frac { 1 } { 6 }61​ 
E)    141414F) C) and D)
G) D) and E)

Question 6

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. ​

Accepted Answer

A)  60.8º
B)  64.8º​
C)  63.8º
D)  61.8º
E)  62.8ºF) A) and D)
G) None of the above

Question 7

Determine the angle between the diagonal of a cube and its edge,as shown in the figure,where  a=12a = 12a=12  .Round your answer to one decimal place.? o B) 57.7o C) 55.7o D) 54.7o E) 58.7o ? " class="answers-bank-image d-inline" rel="preload" > ?

Accepted Answer

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

Question 8

For the simple harmonic motion described by the trigonometric function,find the maximum displacement.?  d=8cos⁡6π5td = 8 \cos \frac { 6 \pi } { 5 } td=8cos56π​t  ?

Accepted Answer

A)    555  ?
B)    65\frac { 6 } { 5 }56​ 
C)   8
D)    18\frac { 1 } { 8 }81​ 
E)    56\frac { 5 } { 6 }65​F) All of the above
G) A) and D)

Question 9

For the simple harmonic motion described by the trigonometric function,find the frequency per second.?  d=14sin⁡6πtd = \frac { 1 } { 4 } \sin 6 \pi td=41​sin6πt  ?

Accepted Answer

A)    333 
B)    666 
C)    3π3 \pi3π 
D)    6π6 \pi6π 
E)    2π2 \pi2πF) C) and D)
G) B) and E)

Question 10

Solve the right triangle shown in the figure for all unknown sides and angles.Round your answers to two decimal places.?  ??  A=30∘,b=12A = 30 ^ { \circ } , b = 12A=30∘,b=12  ?

Accepted Answer

A)    a≈13.86,c≈6.93,B=60∘a \approx 13.86 , c \approx 6.93 , B = 60 ^ { \circ }a≈13.86,c≈6.93,B=60∘ 
B)    a≈0.59,c≈1.16,B=60∘a \approx 0.59 , c \approx 1.16 , B = 60 ^ { \circ }a≈0.59,c≈1.16,B=60∘  ?
C)    a≈6.93,c≈13.86,B=60∘a \approx 6.93 , c \approx 13.86 , B = 60 ^ { \circ }a≈6.93,c≈13.86,B=60∘ 
D)    a≈6.93,c≈13.86,B=45∘a \approx 6.93 , c \approx 13.86 , B = 45 ^ { \circ }a≈6.93,c≈13.86,B=45∘ 
E)    a≈6.93,c≈13.86,B=30∘a \approx 6.93 , c \approx 13.86 , B = 30 ^ { \circ }a≈6.93,c≈13.86,B=30∘F) All of the above
G) B) and D)

Question 11

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

Accepted Answer

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

Question 12

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. ​

Accepted Answer

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

Question 13

For the simple harmonic motion described by the trigonometric function,find the frequency per second.?  d=116cos⁡12πtd = \frac { 1 } { 16 } \cos 12 \pi td=161​cos12πt  ?

Accepted Answer

A)  16 ?
B)  ? ?
C)  12
D)  2?
E)  6 F) A) and D)
G) A) and B)

Question 14

Find the altitude of the isosceles triangle shown below if  θ=38∘	heta = 38 ^ { \circ }θ=38∘  and  b=8 centimeters b = 8 	ext { centimeters }b=8 centimeters   .Round your answer to two decimal places.

Accepted Answer

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

Question 15

Find the angle  α\alphaα  between two nonvertical lines  L1L _ { 1 }L1​  and  L2L _ { 2 }L2​  .The angle  α\alphaα  satisfies the equation?  tan⁡α=∣m2−m11+m2m1∣	an \alpha = \left| \frac { m _ { 2 } - m _ { 1 } } { 1 + m _ { 2 } m _ { 1 } } ight|tanα=​1+m2​m1​m2​−m1​​​  ? where  m1m _ { 1 }m1​  and  m2m _ { 2 }m2​  are slopes of  L1L _ { 1 }L1​  and  L2L _ { 2 }L2​  ,respectively.
(Assume that  m1m2≠1m _ { 1 } m _ { 2 } 
eq 1m1​m2​=1  . ) 
??  L1:2x−y=8L _ { 1 } : 2 x - y = 8L1​:2x−y=8   L2:x−5y=−4L _ { 2 } : x - 5 y = - 4L2​:x−5y=−4  ?
Round your answer to one decimal place.
?

Accepted Answer

A)  54.1o
B)  ?53.1o
C)  55.1o
D)  52.1o
E)  56.1o F) None of the above
G) A) and B)

Question 16

Find the lengths of all the unknown members of the truss. Round your answer to one decimal place.?  ?  A=30A = 30A=30  ?

Accepted Answer

A)    b≈22.0,a≈37.6b \approx 22.0 , a \approx 37.6b≈22.0,a≈37.6 
B)    b≈21.0,a≈36.6b \approx 21.0 , a \approx 36.6b≈21.0,a≈36.6 
C)    b≈24.0,a≈39.6b \approx 24.0 , a \approx 39.6b≈24.0,a≈39.6 
D)    b≈36.6,a≈21.0b \approx 36.6 , a \approx 21.0b≈36.6,a≈21.0 
E)    b≈23.0,a≈38.6b \approx 23.0 , a \approx 38.6b≈23.0,a≈38.6F) C) and D)
G) B) and E)

Question 17

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.
?

Accepted Answer

A)    θ=arccos⁡(130l) 	heta = \arccos \left( \frac { 130 } { l } ight) θ=arccos(l130​)  
B)    θ=arccos⁡(l130) 	heta = \arccos \left( \frac { l } { 130 } ight) θ=arccos(130l​)  
C)    θ=arcsin⁡(lh+17) 	heta = \arcsin \left( \frac { l } { h + 17 } ight) θ=arcsin(h+17l​)  
D)    θ=arcsin⁡(h+20l) 	heta = \arcsin \left( \frac { h + 20 } { l } ight) θ=arcsin(lh+20​)  
E)    θ=arctan⁡(130h+20) 	heta = \arctan \left( \frac { 130 } { h + 20 } ight) θ=arctan(h+20130​) F) C) and D)
G) A) and B)

Question 18

For the simple harmonic motion described by the trigonometric function,find the frequency per second.?  d=9cos⁡8π5td = 9 \cos \frac { 8 \pi } { 5 } td=9cos58π​t  ?

Accepted Answer

A)    45\frac { 4 } { 5 }54​ 
B)    8π5\frac { 8 \pi } { 5 }58π​ 
C)    54\frac { 5 } { 4 }45​ 
D)    5π8\frac { 5 \pi } { 8 }85π​ 
E)    58\frac { 5 } { 8 }85​F) A) and E)
G) None of the above

Question 19

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

Accepted Answer

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

Question 20

Find the angle ? between two nonvertical lines  L1L _ { 1 }L1​  and  L2L _ { 2 }L2​  .The angle ? satisfies the equation?  tan⁡α=∣m2−m11+m2m1∣	an \alpha = \left| \frac { m _ { 2 } - m _ { 1 } } { 1 + m _ { 2 } m _ { 1 } } ight|tanα=​1+m2​m1​m2​−m1​​​  ? where  m1m _ { 1 }m1​  and  m2m _ { 2 }m2​  are slopes of  L1L _ { 1 }L1​  and  L2L _ { 2 }L2​  ,respectively.
(Assume that  m1m2≠1m _ { 1 } m _ { 2 } 
eq 1m1​m2​=1  . ) ?  L1L _ { 1 }L1​  : 5x - 4y = 5  L2L _ { 2 }L2​  : x + y = 1
?
Round your answer to one decimal place.
?

Accepted Answer

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

Exam 30: Applications and Models

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

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

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

Correct Answer
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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 ?

Correct Answer
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Correct Answer
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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.? ?

Correct Answer
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Correct Answer
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Correct Answer
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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.? $d = \frac { 1 } { 12 } \sin 14 \pi t$ ?

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

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

Correct Answer
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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.

Correct Answer
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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.

Correct Answer
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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.

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

Correct Answer
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Exam 30: Applications and Models

For the simple harmonic motion described by the trigonometric function,find the maximum displacement.? d=8cos⁡6π5td = 8 \cos \frac { 6 \pi } { 5 } td=8cos56π​t ?

Correct AnswerverifiedShow Answer

For the simple harmonic motion described by the trigonometric function,find the frequency per second.? d=14sin⁡6πtd = \frac { 1 } { 4 } \sin 6 \pi td=41​sin6πt ?

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Find the altitude of the isosceles triangle shown below if θ=38∘\theta = 38 ^ { \circ }θ=38∘ and b=8 centimeters b = 8 \text { centimeters }b=8 centimeters .Round your answer to two decimal places.

Correct AnswerverifiedShow Answer

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

Correct AnswerverifiedShow Answer

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

Correct AnswerverifiedShow Answer

Find the lengths of all the unknown members of the truss. Round your answer to one decimal place.? ? A=30A = 30A=30 ?

Correct AnswerverifiedShow Answer

Determine the angle between the diagonal of a cube and its edge,as shown in the figure,where a=12a = 12a=12 .Round your answer to one decimal place.? ?

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

For the simple harmonic motion described by the trigonometric function,find the least positive value of t for which d = 0.? d=112sin⁡14πtd = \frac { 1 } { 12 } \sin 14 \pi td=121​sin14πt ?

Correct AnswerverifiedShow Answer

Solve the right triangle shown in the figure for all unknown sides and angles.Round your answers to two decimal places.? ?? A=30∘,b=12A = 30 ^ { \circ } , b = 12A=30∘,b=12 ?

Correct AnswerverifiedShow Answer

For the simple harmonic motion described by the trigonometric function,find the frequency per second.? d=9cos⁡8π5td = 9 \cos \frac { 8 \pi } { 5 } td=9cos58π​t ?

Correct AnswerverifiedShow Answer

For the simple harmonic motion described by the trigonometric function,find the frequency per second.? d=116cos⁡12πtd = \frac { 1 } { 16 } \cos 12 \pi td=161​cos12πt ?

Correct AnswerverifiedShow Answer

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. ​

Correct AnswerverifiedShow Answer

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. ​

Correct AnswerverifiedShow Answer

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. ​

Correct AnswerverifiedShow Answer

For the simple harmonic motion described by the trigonometric function,find the least positive value of t for which d=0d = 0d=0 ? d=6cos⁡6π5td = 6 \cos \frac { 6 \pi } { 5 } td=6cos56π​t ?

Correct AnswerverifiedShow Answer

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

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

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

Correct Answer
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Correct Answer
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Correct Answer
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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.? ?

Correct Answer
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Correct Answer
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Correct Answer
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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.? $d = \frac { 1 } { 12 } \sin 14 \pi t$ ?

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

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

Correct Answer
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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.

Correct Answer
verified

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.

Correct Answer
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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.

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

Correct Answer
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