Question 1

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

Question 2

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

Accepted Answer

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

Question 3

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

Question 4

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

Question 5

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.

Accepted Answer

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

Question 6

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

Accepted Answer

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)  $b \approx 22.0 , a \approx 37.6$ 
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)  $b \approx 23.0 , a \approx 38.6$

Question 7

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

Accepted Answer

A)  $\frac { 4 } { 5 }$ 
B)  $\frac { 8 \pi } { 5 }$ 
C)  $\frac { 5 } { 4 }$ 
D)  $\frac { 5 \pi } { 8 }$ 
E)  $\frac { 5 } { 8 }$ 
A)  $\frac { 4 } { 5 }$ 
B)  $\frac { 8 \pi } { 5 }$ 
C)  $\frac { 5 } { 4 }$ 
D)  $\frac { 5 \pi } { 8 }$ 
E)  $\frac { 5 } { 8 }$

Question 8

Find the angle $\alpha$ between two nonvertical lines $L _ { 1 }$ and $L _ { 2 }$ .The angle $\alpha$ satisfies the equation? $\tan \alpha = \left| \frac { m _ { 2 } - m _ { 1 } } { 1 + m _ { 2 } m _ { 1 } } \right|$ ? where $m _ { 1 }$ and $$m _ { 2 }$$ are slopes of $L _ { 1 }$ and $L _ { 2 }$ ,respectively.
(Assume that $$m _ { 1 } m _ { 2 } \neq 1$$ . )
?? $L _ { 1 } : 2 x - y = 8$ $L _ { 2 } : x - 5 y = - 4$ ?
Round your answer to one decimal place.
?

Accepted Answer

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

Question 9

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

Accepted Answer

A)  $5$ ? 
B)  $\frac { 6 } { 5 }$ 
C)  8 
D)  $\frac { 1 } { 8 }$ 
E)  $\frac { 5 } { 6 }$ 
A)  $5$ ? 
B)  $\frac { 6 } { 5 }$ 
C)  8 
D)  $\frac { 1 } { 8 }$ 
E)  $\frac { 5 } { 6 }$

Question 10

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.

Accepted Answer

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

Question 11

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

Accepted Answer

A)  $\frac { 1 } { 14 }$ 
B)  $\frac { 1 } { 12 }$ 
C)  $12$ 
D)  $\frac { 1 } { 6 }$ 
E)  $14$ 
A)  $\frac { 1 } { 14 }$ 
B)  $\frac { 1 } { 12 }$ 
C)  $12$ 
D)  $\frac { 1 } { 6 }$ 
E)  $14$

Question 12

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

Accepted Answer

A)  $\frac { 12 } { 5 }$ 
B)  $\frac { 5 } { 12 }$ 
C)  $\frac { 5 } { 6 }$ 
D)  $\frac { 6 } { 5 }$ 
E)  $\frac { 1 } { 6 }$ 
A)  $\frac { 12 } { 5 }$ 
B)  $\frac { 5 } { 12 }$ 
C)  $\frac { 5 } { 6 }$ 
D)  $\frac { 6 } { 5 }$ 
E)  $\frac { 1 } { 6 }$

Question 13

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

Accepted Answer

A)  $3$ 
B)  $6$ 
C)  $3 \pi$ 
D)  $6 \pi$ 
E)  $2 \pi$ 
A)  $3$ 
B)  $6$ 
C)  $3 \pi$ 
D)  $6 \pi$ 
E)  $2 \pi$

Question 14

Find the angle ? between two nonvertical lines $$L _ { 1 }$$ and $L _ { 2 }$ .The angle ? satisfies the equation? $$\tan \alpha = \left| \frac { m _ { 2 } - m _ { 1 } } { 1 + m _ { 2 } m _ { 1 } } \right|$$ ? where $m _ { 1 }$ and $m _ { 2 }$ are slopes of $L _ { 1 }$ and $L _ { 2 }$ ,respectively.
(Assume that $m _ { 1 } m _ { 2 } \neq 1$ . )? $L _ { 1 }$ : 5x - 4y = 5 $L _ { 2 }$ : 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 
A) 83.7º 
B) 84.7º 
C) 85.7º 
D) 86.7º 
E) 87.7º

Question 15

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.?   ?

Accepted Answer

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

Question 16

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

Accepted Answer

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)  $a \approx 13.86 , c \approx 6.93 , B = 60 ^ { \circ }$ 
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)  $a \approx 6.93 , c \approx 13.86 , B = 30 ^ { \circ }$

Question 17

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

Question 18

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)  $\theta = \arccos \left( \frac { 130 } { l } \right)$ 
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)  $\theta = \arctan \left( \frac { 130 } { h + 20 } \right)$ 
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)  $\theta = \arctan \left( \frac { 130 } { h + 20 } \right)$

Question 19

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

Question 20

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

Accepted Answer

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

Exam 30: Applications and Models

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. ​

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

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. ​

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

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

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 ?

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 ?

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.

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 ?

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 ?

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 ?

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.? ?

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 ?

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. ​

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 ?

Rectangular Coordinates

Graphs of Equations

Linear Equations in Two Variables

Functions

Analyzing Graphs of Functions

A Library of Parent Functions

Transformations of Functions

Combinations of Functions Composite Functions

Inverse Functions

Mathematical Modeling and Variation

Quadratic Functions and Models

Polynomial Functions of Higher Degree

Polynomial and Synthetic Division

Complex Numbers

Zeros of Polynomial Functions

Rational Functions

Nonlinear Inequalities

Exponential Functions and Their Graphs

Logarithmic Functions and Their Graphs

Properties of Logarithms

Exponential and Logarithmic Equations

Exponential and Logarithmic Models

Radian and Degree Measure

Trigonometric Functions The Unit Circle

Right Triangle Trigonometry

Trigonometric Functions of Any Angle

Graphs of Sine and Cosine Functions

Graphs of Other Trigonometric Functions

Inverse Trigonometric Functions

Using Fundamental Identities

Verifying Trigonometric Equations

Solving Trigonometric Equations

Sum and Difference Formulas

Multiple Angle and Product to Sum Formulas

Law of Sines

Law of Cosines

Vectors in the Plane

Vectors and Dot Products

Trigonometric Form of a Complex Number

Linear and Nonlinear Systems of Equations

Two Variable Linear Systems

Multivariable Linear Systems

Partial Fractions

Systems of Inequalities

Linear Programming

Matrices and Systems of Equations

Operations With Matrices

The Inverse of a Square Matrix

The Determinant of a Square Matrix

Applications of Matrices and Determinants

Sequences and Series

Arithmetic Sequences and Partial Sums

Geometric Sequences and Series

Mathematical Induction

The Binomial Theorem

Counting Principles

Probability

Lines

Introduction to Conics Parabolas

Ellipses

Hyperbolas

Rotation of Conics

Parametric Equations

Polar Coordinates

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.

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.

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

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

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

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

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

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

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

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.? ?

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.

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