Exam 30: Applications and Models

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A Global Positioning System satellite orbits a = 13,000 miles above Earth's surface (see figure).Find the angle of depression from the satellite to the horizon.Assume the radius of Earth is 4000 miles.Round your answer to two decimal places.

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Question 1

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If $a = 11$ and $c = 28$ ,determine the value of B.Round to two decimal places.

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Question 2

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A police department has set up a speed enforcement zone on a straight length of highway.A patrol car is parked parallel to the zone,a = 210 feet from one end and b = 130 feet from the other end (see figure). Find the length l of the zone.Round your answer to two decimal places.

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Question 3

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If the sides of a rectangular solid are as shown,and $s = 4$ ,determine the angle,?,between the diagonal of the base of the solid and the diagonal of the solid.Round answer to two decimal places.

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Question 4

A land developer wants to find the distance across a small lake in the middle of his proposed development.The bearing from A to B is $\mathrm { N } 31 ^ { \circ } \mathrm { W }$ .The developer leaves point A and travels 74 yards perpendicular to $\overline{A B}$ to point C.The bearing from C to point B is $\mathrm { N } ~59 ^ { \circ } \mathrm { W }$ .Determine the distance,AB,across the small lake.Round distance to nearest yard. $A land developer wants to find the distance across a small lake in the middle of his proposed development.The bearing from A to B is \mathrm { N } 31 ^ { \circ } \mathrm { W } .The developer leaves point A and travels 74 yards perpendicular to \overline{A B} to point C.The bearing from C to point B is \mathrm { N } ~59 ^ { \circ } \mathrm { W } .Determine the distance,AB,across the small lake.Round distance to nearest yard.$

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Question 5

The designers of a water park are creating a new slide and have sketched some preliminary drawings.The length of the ladder is a = 24 feet,and its angle of elevation is 60º (see figure). Find the height of the slide.Round your answer to two decimal places.

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Question 6

The sun is 20º above the horizon.Find the length of a shadow cast by a park statue that is 30 feet tall.Approximate the answer to two decimal places.

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Question 7

A cellular telephone tower that is 150 feet tall is placed on top of a mountain that is 1200 feet above sea level.What is the angle of depression from the top of the tower to a cell phone user who is 6 horizontal miles away and 400 feet above sea level? Round your answer to two decimal places.

(Multiple Choice)

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Question 8

A point on the end of a tuning fork moves in simple harmonic motion described by? $d = a \sin \omega t$ ? Find ? given that the tuning fork for middle C has a frequency 270 of vibrations per second. ?

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Question 9

Find the altitude of the isosceles triangle shown in the figure.Round your answer to two decimal places.? $Find the altitude of the isosceles triangle shown in the figure.Round your answer to two decimal places.? \theta = 45 ^ { \circ } , b = 11 ?$ $\theta = 45 ^ { \circ } , b = 11$ ?

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Question 10

Find the altitude of the isosceles triangle shown below if $\theta = 53 ^ { \circ }$ and $b = 25 \text { meters }$ .Round answer to two decimal places. $Find the altitude of the isosceles triangle shown below if \theta = 53 ^ { \circ } and b = 25 \text { meters } .Round answer to two decimal places.$

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Question 11

A ball that is bobbing up and down on the end of a spring has a maximum displacement of 3 inches.Its motion (in ideal conditions)is modeled by? $y = \frac { 1 } { 4 } \cos 18 t ( t > 0 )$ where y is measured in feet and t is the time in seconds. What is the period of the oscillations? ?

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Question 12

After leaving the runway,a plane's angle of ascent is 17^o and its speed is 278 feet per second.How many minutes will it take for the airplane to climb to a height of 11,500 feet? Round answer to two decimal places.

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Question 13

For the simple harmonic motion described by the trigonometric function,find the maximum displacement.? $d = \frac { 1 } { 2 } \sin 6 \pi t$ ?

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Question 14

The sun is 25º above the horizon.Find the length of a shadow cast by a building that is $\alpha = 130$ feet tall (see figure).Approximate the answer to two decimal places.? $The sun is 25º above the horizon.Find the length of a shadow cast by a building that is \alpha = 130 feet tall (see figure).Approximate the answer to two decimal places.? ?$ ?

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Question 15

Find a model for simple harmonic motion satisfying the specified conditions. ? Displacement (t = 0): 0 Amplitude: 5 centimeters Period: 2 seconds ?

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Question 16

For the simple harmonic motion described by the trigonometric function,find the least positive value of t for which d = 0. ?? $d = \frac { 1 } { 64 } \sin 794 \pi t$ ?

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Question 17

The height of an outdoor basketball backboard is $12 \frac { 1 } { 4 }$ feet,and the backboard casts a shadow $17 \frac { 1 } { 2 }$ feet long. Find the angle of elevation of the sun.Round your answer to one decimal place. ?

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Question 18

For the simple harmonic motion described by the trigonometric function,find the maximum displacement.? $d = \frac { 1 } { 4 } \cos 20 \pi t$ ?

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Question 19

For the simple harmonic motion described by the trigonometric function,find the maximumvalue of d when .? $d = 6 \cos \frac { 6 \pi } { 5 } t$ Round your answer to nearest whole number. ?

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Question 20

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Exam 30: Applications and Models

A Global Positioning System satellite orbits a = 13,000 miles above Earth's surface (see figure).Find the angle of depression from the satellite to the horizon.Assume the radius of Earth is 4000 miles.Round your answer to two decimal places.​ ​

If a=11a = 11a=11 and c=28c = 28c=28 ,determine the value of B.Round to two decimal places.

A police department has set up a speed enforcement zone on a straight length of highway.A patrol car is parked parallel to the zone,a = 210 feet from one end and b = 130 feet from the other end (see figure).​ ​ Find the length l of the zone.Round your answer to two decimal places. ​

If the sides of a rectangular solid are as shown,and s=4s = 4s=4 ,determine the angle,?,between the diagonal of the base of the solid and the diagonal of the solid.Round answer to two decimal places.

The designers of a water park are creating a new slide and have sketched some preliminary drawings.The length of the ladder is a = 24 feet,and its angle of elevation is 60º (see figure).​ ​ Find the height of the slide.Round your answer to two decimal places. ​

The sun is 20º above the horizon.Find the length of a shadow cast by a park statue that is 30 feet tall.Approximate the answer to two decimal places. ​

A cellular telephone tower that is 150 feet tall is placed on top of a mountain that is 1200 feet above sea level.What is the angle of depression from the top of the tower to a cell phone user who is 6 horizontal miles away and 400 feet above sea level? Round your answer to two decimal places. ​

A point on the end of a tuning fork moves in simple harmonic motion described by? d=asin⁡ωtd = a \sin \omega td=asinωt ? Find ? given that the tuning fork for middle C has a frequency 270 of vibrations per second. ?

Find the altitude of the isosceles triangle shown in the figure.Round your answer to two decimal places.? θ=45∘,b=11\theta = 45 ^ { \circ } , b = 11θ=45∘,b=11 ?

Find the altitude of the isosceles triangle shown below if θ=53∘\theta = 53 ^ { \circ }θ=53∘ and b=25 meters b = 25 \text { meters }b=25 meters .Round answer to two decimal places.

After leaving the runway,a plane's angle of ascent is 17o and its speed is 278 feet per second.How many minutes will it take for the airplane to climb to a height of 11,500 feet? Round answer to two decimal places.

For the simple harmonic motion described by the trigonometric function,find the maximum displacement.? d=12sin⁡6πtd = \frac { 1 } { 2 } \sin 6 \pi td=21​sin6πt ?

The sun is 25º above the horizon.Find the length of a shadow cast by a building that is α=130\alpha = 130α=130 feet tall (see figure).Approximate the answer to two decimal places.? ?

Find a model for simple harmonic motion satisfying the specified conditions. ? Displacement (t = 0): 0 Amplitude: 5 centimeters Period: 2 seconds ?

For the simple harmonic motion described by the trigonometric function,find the least positive value of t for which d = 0. ?? d=164sin⁡794πtd = \frac { 1 } { 64 } \sin 794 \pi td=641​sin794πt ?

The height of an outdoor basketball backboard is 121412 \frac { 1 } { 4 }1241​ feet,and the backboard casts a shadow 171217 \frac { 1 } { 2 }1721​ feet long. Find the angle of elevation of the sun.Round your answer to one decimal place. ?

For the simple harmonic motion described by the trigonometric function,find the maximum displacement.? d=14cos⁡20πtd = \frac { 1 } { 4 } \cos 20 \pi td=41​cos20πt ?

For the simple harmonic motion described by the trigonometric function,find the maximumvalue of d when .? d=6cos⁡6π5td = 6 \cos \frac { 6 \pi } { 5 } td=6cos56π​t Round your answer to nearest whole number. ?

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

A Global Positioning System satellite orbits a = 13,000 miles above Earth's surface (see figure).Find the angle of depression from the satellite to the horizon.Assume the radius of Earth is 4000 miles.Round your answer to two decimal places.

If $a = 11$ and $c = 28$ ,determine the value of B.Round to two decimal places.

A police department has set up a speed enforcement zone on a straight length of highway.A patrol car is parked parallel to the zone,a = 210 feet from one end and b = 130 feet from the other end (see figure). Find the length l of the zone.Round your answer to two decimal places.

If the sides of a rectangular solid are as shown,and $s = 4$ ,determine the angle,?,between the diagonal of the base of the solid and the diagonal of the solid.Round answer to two decimal places.

The designers of a water park are creating a new slide and have sketched some preliminary drawings.The length of the ladder is a = 24 feet,and its angle of elevation is 60º (see figure). Find the height of the slide.Round your answer to two decimal places.

The sun is 20º above the horizon.Find the length of a shadow cast by a park statue that is 30 feet tall.Approximate the answer to two decimal places.

A cellular telephone tower that is 150 feet tall is placed on top of a mountain that is 1200 feet above sea level.What is the angle of depression from the top of the tower to a cell phone user who is 6 horizontal miles away and 400 feet above sea level? Round your answer to two decimal places.

A point on the end of a tuning fork moves in simple harmonic motion described by? $d = a \sin \omega t$ ? Find ? given that the tuning fork for middle C has a frequency 270 of vibrations per second. ?

Find the altitude of the isosceles triangle shown in the figure.Round your answer to two decimal places.? $Find the altitude of the isosceles triangle shown in the figure.Round your answer to two decimal places.? \theta = 45 ^ { \circ } , b = 11 ?$ $\theta = 45 ^ { \circ } , b = 11$ ?

After leaving the runway,a plane's angle of ascent is 17^o and its speed is 278 feet per second.How many minutes will it take for the airplane to climb to a height of 11,500 feet? Round answer to two decimal places.

For the simple harmonic motion described by the trigonometric function,find the maximum displacement.? $d = \frac { 1 } { 2 } \sin 6 \pi t$ ?

For the simple harmonic motion described by the trigonometric function,find the least positive value of t for which d = 0. ?? $d = \frac { 1 } { 64 } \sin 794 \pi t$ ?

The height of an outdoor basketball backboard is $12 \frac { 1 } { 4 }$ feet,and the backboard casts a shadow $17 \frac { 1 } { 2 }$ feet long. Find the angle of elevation of the sun.Round your answer to one decimal place. ?

For the simple harmonic motion described by the trigonometric function,find the maximum displacement.? $d = \frac { 1 } { 4 } \cos 20 \pi t$ ?

For the simple harmonic motion described by the trigonometric function,find the maximumvalue of d when .? $d = 6 \cos \frac { 6 \pi } { 5 } t$ Round your answer to nearest whole number. ?