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8th Edition

Charles P. McKeague + 1 other

Publisher: Cengage Learning

ISBN: 9781305652224

Chapter 3.5, Problem 62PS

Textbook Problem

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A two-stage gear train consists of four gears meshed together (Figure 10). The second and third gears are attached, so that they share the same angular velocity

To determine

Find a formula for the angular velocity of the fourth gear in terms of the angular velocity of the first gear and the values of

**Given information:**

Angular velocity of the first gear

Angular velocity of the second gear

Angular velocity of the third gear

Angular velocity of the fourth gear

**Formula used:**

The linear velocity

Consider the linear velocities of the first, second, third and fourth gears are

Also, consider the numbers of teeth of the first, second, third and fourth gears are

To find the formula for the angular velocity of the fourth gear

Substitute

Trigonometry (MindTap Course List)

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Ch. 3.1 - For Questions 1 through 3, fill in each blank with...Ch. 3.1 - For Questions 1 through 3, fill in each blank with...Ch. 3.1 - For Questions 1 through 3, fill in each blank with...Ch. 3.1 - Complete each statement regarding an angle and...Ch. 3.1 - Draw each of the following angles in standard...Ch. 3.1 - Draw each of the following angles in standard...Ch. 3.1 - Draw each of the following angles in standard...Ch. 3.1 - Draw each of the following angles in standard...Ch. 3.1 - Draw each of the following angles in standard...Ch. 3.1 - Draw each of the following angles in standard...

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Use the unit circle to find the six trigonometric...Ch. 3.3 - Use the unit circle to find the six trigonometric...Ch. 3.3 - Use the unit circle to find the six trigonometric...Ch. 3.3 - Use the unit circle to find the six trigonometric...Ch. 3.3 - Use the unit circle to find the six trigonometric...Ch. 3.3 - Use the unit circle to find the six trigonometric...Ch. 3.3 - Use the unit circle to find the six trigonometric...Ch. 3.3 - Use the unit circle to find the six trigonometric...Ch. 3.3 - Use the unit circle to find all values of between...Ch. 3.3 - Use the unit circle to find all values of between...Ch. 3.3 - Use the unit circle to find all values of between...Ch. 3.3 - Use the unit circle to find all values of between...Ch. 3.3 - Use the unit circle to find all values of between...Ch. 3.3 - Use the unit circle to find all values of between...Ch. 3.3 - Graph the unit circle using parametric equations...Ch. 3.3 - Graph the unit circle using parametric equations...Ch. 3.3 - Graph the unit circle using parametric equations...Ch. 3.3 - Graph the unit circle using parametric equations...Ch. 3.3 - Graph the unit circle using parametric equations...Ch. 3.3 - Graph the unit circle using parametric equations...Ch. 3.3 - Graph the unit circle using parametric equations...Ch. 3.3 - Graph the unit circle using parametric equations...Ch. 3.3 - Graph the unit circle using parametric equations...Ch. 3.3 - Graph the unit circle using parametric equations...Ch. 3.3 - Graph the unit circle using parametric equations...Ch. 3.3 - Graph the unit circle using parametric equations...Ch. 3.3 - Graph the unit circle using parametric equations...Ch. 3.3 - Graph the unit circle using parametric equations...Ch. 3.3 - Graph the unit circle using parametric equations...Ch. 3.3 - Graph the unit circle using parametric equations...Ch. 3.3 - For Problems 49 through 56, use Figure 14, which...Ch. 3.3 - For Problems 49 through 56, use Figure 14, which...Ch. 3.3 - For Problems 49 through 56, use Figure 14, which...Ch. 3.3 - For Problems 49 through 56, use Figure 14, which...Ch. 3.3 - For Problems 49 through 56, use Figure 14, which...Ch. 3.3 - For Problems 49 through 56, use Figure 14, which...Ch. 3.3 - For Problems 49 through 56, use Figure 14, which...Ch. 3.3 - For Problems 49 through 56, use Figure 14, which...Ch. 3.3 - If angle is in standard position and the terminal...Ch. 3.3 - If angle is in standard position and the terminal...Ch. 3.3 - If t is the distance from (1,0) to (0.5403,0.8415)...Ch. 3.3 - If t is the distance from (1,0) to (0.9422,0.3350)...Ch. 3.3 - Find the coordinates of the point on the unit...Ch. 3.3 - Find the coordinates of the point on the unit...Ch. 3.3 - Identify the argument of each function. tan5Ch. 3.3 - Identify the argument of each function. cosCh. 3.3 - Identify the argument of each function. sin2ACh. 3.3 - Identify the argument of each function. cos(A2)Ch. 3.3 - Identify the argument of each function. sin(x+2)Ch. 3.3 - Identify the argument of each function. tan(2x)Ch. 3.3 - Evaluate cos23. Identify the function, the...Ch. 3.3 - Evaluate sin116. Identify the function, the...Ch. 3.3 - Use a calculator to approximate each value to four...Ch. 3.3 - Use a calculator to approximate each value to four...Ch. 3.3 - Use a calculator to approximate each value to four...Ch. 3.3 - Use a calculator to approximate each value to four...Ch. 3.3 - Use a calculator to approximate each value to four...Ch. 3.3 - Use a calculator to approximate each value to four...Ch. 3.3 - If we start at the point (1,0) and travel once...Ch. 3.3 - If we start at the point (1,0) and travel once...Ch. 3.3 - If we start at the point (1,0) and travel once...Ch. 3.3 - If we start at the point (1,0) and travel once...Ch. 3.3 - Which of the six trigonometric functions are not...Ch. 3.3 - Which of the six trigonometric functions are not...Ch. 3.3 - For Problems 83 through 94, determine lithe...Ch. 3.3 - For Problems 83 through 94, determine lithe...Ch. 3.3 - For Problems 83 through 94, determine lithe...Ch. 3.3 - For Problems 83 through 94, determine lithe...Ch. 3.3 - For Problems 83 through 94, determine lithe...Ch. 3.3 - For Problems 83 through 94, determine lithe...Ch. 3.3 - For Problems 83 through 94, determine lithe...Ch. 3.3 - For Problems 83 through 94, determine lithe...Ch. 3.3 - For Problems 83 through 94, determine lithe...Ch. 3.3 - For Problems 83 through 94, determine lithe...Ch. 3.3 - For Problems 83 through 94, determine lithe...Ch. 3.3 - For Problems 83 through 94, determine lithe...Ch. 3.3 - Use the diagram shown in Figure 12 for the...Ch. 3.3 - Use the diagram shown in Figure 12 for the...Ch. 3.3 - Use the diagram shown in Figure 12 for the...Ch. 3.3 - Use the diagram shown in Figure 12 for the...Ch. 3.3 - The diagram of the unit circle shown in Figure 15...Ch. 3.3 - The diagram of the unit circle shown in Figure 15...Ch. 3.3 - The diagram of the unit circle shown in Figure 15...Ch. 3.3 - The diagram of the unit circle shown in Figure 15...Ch. 3.3 - The diagram of the unit circle shown in Figure 15...Ch. 3.3 - The diagram of the unit circle shown in Figure 15...Ch. 3.3 - The diagram of the unit circle shown in Figure 15...Ch. 3.3 - The diagram of the unit circle shown in Figure 15...Ch. 3.3 - Problems 107 through 112 refer to right triangle...Ch. 3.3 - Problems 107 through 112 refer to right triangle...Ch. 3.3 - Problems 107 through 112 refer to right triangle...Ch. 3.3 - Problems 107 through 112 refer to right triangle...Ch. 3.3 - Problems 107 through 112 refer to right triangle...Ch. 3.3 - Problems 107 through 112 refer to right triangle...Ch. 3.3 - Use the unit circle in Figure 14 to approximate...Ch. 3.3 - If angle is in standard position and the terminal...Ch. 3.3 - Use a calculator to approximate sec4. -1.3213...Ch. 3.3 - Which statement is possible for some real number...Ch. 3.4 - For Questions 1 through 4, fill in each blank with...Ch. 3.4 - For Questions 1 through 4, fill in each blank with...Ch. 3.4 - For Questions 1 through 4, fill in each blank with...Ch. 3.4 - For Questions 1 through 4, fill in each blank with...Ch. 3.4 - For each of the following problems, is a central...Ch. 3.4 - For each of the following problems, is a central...Ch. 3.4 - For each of the following problems, is a central...Ch. 3.4 - For each of the following problems, is a central...Ch. 3.4 - For each of the following problems, is a central...Ch. 3.4 - For each of the following problems, is a central...Ch. 3.4 - For each of the following problems, is a central...Ch. 3.4 - For each of the following problems, is a central...Ch. 3.4 - For each of the following problems, is a central...Ch. 3.4 - For each of the following problems, is a central...Ch. 3.4 - Arc Length The minute hand of a clock is 1.2...Ch. 3.4 - Arc length The minute hand of a clock is 4.5...Ch. 3.4 - Arc Length A satellite 200 miles above the earth...Ch. 3.4 - Arc Length How long, in hours, does it take the...Ch. 3.4 - Arc Length The pendulum on a grandfather clock...Ch. 3.4 - Arc Length Find the total distance traveled in 1...Ch. 3.4 - Cable Car Drive System The current San Francisco...Ch. 3.4 - Cable Car Drive System The first cable railway to...Ch. 3.4 - Drum Brakes The Isuzu NPR 250 light truck with...Ch. 3.4 - Drum Brakes The Isuzu NPR 250 truck with automatic...Ch. 3.4 - Diameter of the Moon From the earth, the moon...Ch. 3.4 - Diameter of the Sun If the distance to the sun is...Ch. 3.4 - Repeat Example 2 from this section for the...Ch. 3.4 - Repeat Example 2 from this section for the...Ch. 3.4 - Repeat Example 2 from this section for the...Ch. 3.4 - Repeat Example 2 from this section for the...Ch. 3.4 - Ferris Wheel In Problem Set 2.3, we mentioned a...Ch. 3.4 - Ferris Wheel A Ferris Wheel called Colossus that...Ch. 3.4 - In each of the following problems, is a central...Ch. 3.4 - In each of the following problems, is a central...Ch. 3.4 - In each of the following problems, is a central...Ch. 3.4 - In each of the following problems, is a central...Ch. 3.4 - In each of the following problems, is a central...Ch. 3.4 - In each of the following problems, is a central...Ch. 3.4 - In each of the following problems, is a central...Ch. 3.4 - In each of the following problems, is a central...Ch. 3.4 - In each of the following problems, is a central...Ch. 3.4 - In each of the following problems, is a central...Ch. 3.4 - Find the area of the sector formed by the given...Ch. 3.4 - Find the area of the sector formed by the given...Ch. 3.4 - Find the area of the sector formed by the given...Ch. 3.4 - Find the area of the sector formed by the given...Ch. 3.4 - Find the area of the sector formed by the given...Ch. 3.4 - Find the area of the sector formed by the given...Ch. 3.4 - Find the area of the sector formed by the given...Ch. 3.4 - Find the area of the sector formed by the given...Ch. 3.4 - Area of a Sector An arc of length 3 feet is cut...Ch. 3.4 - Area of a Sector A central angle of 2 radians cuts...Ch. 3.4 - Radius of a Circle If the sector formed by a...Ch. 3.4 - Arc Length What is the length of the arc cut off...Ch. 3.4 - Radius of a Circle A sector of area 2/3 square...Ch. 3.4 - Radius of a Circle A sector of area 25 square...Ch. 3.4 - Lawn Sprinkler A lawn sprinkler is located at the...Ch. 3.4 - Windshield Wiper An automobile windshield wiper 10...Ch. 3.4 - Cycling The Campagnolo Hyperon Ultra Two carbon...Ch. 3.4 - Cycling The Reynolds RZR 46 carbon wheel, which...Ch. 3.4 - Pac-Man Figure 17 shows an image of Pac-Man from...Ch. 3.4 - Coffee Filter A conical coffee filter is made from...Ch. 3.4 - Apparent Diameter As we mentioned in this section,...Ch. 3.4 - Apparent Diameter As we mentioned in this section,...Ch. 3.4 - Apparent Diameter As we mentioned in this section,...Ch. 3.4 - Apparent Diameter As we mentioned in this section,...Ch. 3.4 - Angle of Elevation If a 75-foot flagpole casts a...Ch. 3.4 - Height of a Hill A road up a hill makes an angle...Ch. 3.4 - Angle of Depression A person standing 5.2 feet...Ch. 3.4 - Distance and Bearing A boat travels on a course of...Ch. 3.4 - Geometry The height of a right circular cone is...Ch. 3.4 - Height of a Tree Two people decide to find the...Ch. 3.4 - If =40 is a central angle in a circle of radius 9...Ch. 3.4 - If =40 is a central angle in a circle of radius 9...Ch. 3.4 - A curve along a highway is an arc of a circle with...Ch. 3.4 - A lawn sprinkler has been set to rotate through an...Ch. 3.5 - For Questions 1 through 4, fill in each blank with...Ch. 3.5 - For Questions 1 through 4, fill in each blank with...Ch. 3.5 - For Questions 1 through 4, fill in each blank with...Ch. 3.5 - For Questions 1 through 4, fill in each blank with...Ch. 3.5 - Find the linear velocity of a point moving with...Ch. 3.5 - Find the linear velocity of a point moving with...Ch. 3.5 - Find the linear velocity of a point moving with...Ch. 3.5 - Find the linear velocity of a point moving with...Ch. 3.5 - Find the linear velocity of a point moving with...Ch. 3.5 - Find the linear velocity of a point moving with...Ch. 3.5 - Find the distance s covered by a point moving with...Ch. 3.5 - Find the distance s covered by a point moving with...Ch. 3.5 - Find the distance s covered by a point moving with...Ch. 3.5 - Find the distance s covered by a point moving with...Ch. 3.5 - Find the distance s covered by a point moving with...Ch. 3.5 - Find the distance s covered by a point moving with...Ch. 3.5 - Point P sweeps out central angle as it rotates on...Ch. 3.5 - Point P sweeps out central angle as it rotates on...Ch. 3.5 - Point P sweeps out central angle as it rotates on...Ch. 3.5 - Point P sweeps out central angle as it rotates on...Ch. 3.5 - Point P sweeps out central angle as it rotates on...Ch. 3.5 - Point P sweeps out central angle as it rotates on...Ch. 3.5 - Rotating Light Figure 3 shows a lighthouse that is...Ch. 3.5 - Rotating Light Using the diagram in Figure 3, find...Ch. 3.5 - In the problems that follow, point P moves with...Ch. 3.5 - In the problems that follow, point P moves with...Ch. 3.5 - In the problems that follow, point P moves with...Ch. 3.5 - In the problems that follow, point P moves with...Ch. 3.5 - In the problems that follow, point P moves with...Ch. 3.5 - In the problems that follow, point P moves with...Ch. 3.5 - For each of the following problems, find the...Ch. 3.5 - For each of the following problems, find the...Ch. 3.5 - For each of the following problems, find the...Ch. 3.5 - For each of the following problems, find the...Ch. 3.5 - For each of the following problems, find the...Ch. 3.5 - For each of the following problems, find the...Ch. 3.5 - For each of the following problems, a point is...Ch. 3.5 - For each of the following problems, a point is...Ch. 3.5 - For each of the following problems, a point is...Ch. 3.5 - For each of the following problems, a point is...Ch. 3.5 - For each of the following problems, a point is...Ch. 3.5 - For each of the following problems, a point is...Ch. 3.5 - Velocity at the Equator The earth rotates through...Ch. 3.5 - Velocity at the Equator Assuming the radius of the...Ch. 3.5 - Velocity of a Miser Blade A mixing blade on a food...Ch. 3.5 - Velocity of a Lawnmower Blade A gasoline-driven...Ch. 3.5 - Cable Cars The San Francisco cable cars travel by...Ch. 3.5 - Cable Cars The Los Angeles Cable Railway was...Ch. 3.5 - Cable Cars The Cleveland City Cable Railway had a...Ch. 3.5 - Cable Cars The old Sutter Street cable car line in...Ch. 3.5 - Ski Lift A ski lift operates by driving a wire...Ch. 3.5 - Ski Lift An engineering firm is designing a ski...Ch. 3.5 - Velocity of a Ferris Wheel Figure 7 is a model of...Ch. 3.5 - Velocity of a Ferris Wheel Use Figure 7 as a model...Ch. 3.5 - Ferris Wheel For the Ferns wheel described in...Ch. 3.5 - Ferris Wheel For the Ferris wheeI described in...Ch. 3.5 - Velocity of a Bike Wheel A woman rides a bicycle...Ch. 3.5 - Velocity of a Bike Wheel Find the number of...Ch. 3.5 - Gear Trains Figure 8 shows a single-stage gear...Ch. 3.5 - Gear Trains Figure 8 shows a single-stage gear...Ch. 3.5 - A gear train consists of three gears meshed...Ch. 3.5 - A two-stage gear train consists of four gears...Ch. 3.5 - Cycling When a cyclist pedals. he turns a gear,...Ch. 3.5 - Cycling When a cyclist pedals. he turns a gear,...Ch. 3.5 - Cycling When a cyclist pedals. he turns a gear,...Ch. 3.5 - Cycling When a cyclist pedals. he turns a gear,...Ch. 3.5 - Cycling When a cyclist pedals. he turns a gear,...Ch. 3.5 - Alcohol Dragster On board most alcohol dragsters...Ch. 3.5 - Magnitude of a Vector Find the magnitudes of the...Ch. 3.5 - Magnitude of a Vector The magnitude of the...Ch. 3.5 - Distance and Bearing A ship sails for 85.5 miles...Ch. 3.5 - Distance and Bearing A plane flying with a...Ch. 3.5 - +Find the linear velocity of a point moving with...Ch. 3.5 - Find the angular velocity of a point moving with...Ch. 3.5 - Find the linear velocity of a point rotating at 30...Ch. 3.5 - A pulley is driven by a belt moving at a speed of...Ch. 3 - Draw each of the following angles in standard...Ch. 3 - Draw each of the following angles in standard...Ch. 3 - Use a calculator to find each of the following...Ch. 3 - Use a calculator to find each of the following...Ch. 3 - Use a calculator to find each of the following...Ch. 3 - Use a calculator to find , to the nearest tenth of...Ch. 3 - Use a calculator to find , to the nearest tenth of...Ch. 3 - Give the exact value of each of the following:...Ch. 3 - Give the exact value of each of the following:...Ch. 3 - Give the exact value of each of the following:...Ch. 3 - Give the exact value of each of the following:...Ch. 3 - Give the exact value of each of the following:...Ch. 3 - Give the exact value of each of the following:...Ch. 3 - Give the exact value of each of the following: If...Ch. 3 - Give the exact value of each of the following:...Ch. 3 - Give the exact value of each of the following: Use...Ch. 3 - Determine if the statement sinz=2 is possible for...Ch. 3 - Evaluate 2cos(3x2) when x is 4.Ch. 3 - If =60o is a central angle in a circle of radius 6...Ch. 3 - If =5 is a central angle that cuts off an arc...Ch. 3 - Find the area of the sector formed by central...Ch. 3 - Distance A boy is twirling a model airplane on a...Ch. 3 - Area of a Sector A central angle of 4 radians cuts...Ch. 3 - Point P moves with angular velocity =4 radians per...Ch. 3 - For each of the following problems, a points is...Ch. 3 - For each of the following problems, a point is...Ch. 3 - Angular Velocity A belt connects a pulley of...Ch. 3 - Linear Velocity A propeller with radius 3.50 feet...Ch. 3 - Cable Cars If a 14 -foot-diameter sheave is used...Ch. 3 - Cycling A pro cyclist is riding in the Vuelta a...Ch. 3 - Determine the lengths of MO, OP, and MG. Figure 2...Ch. 3 - Find angle QOP in terms of and .Ch. 3 - Use right triangle trigonometry to find lengths a...Ch. 3 - We know that the angular velocity of the arm is 3...Ch. 3 - We know that the angular velocity of the arm is 3...Ch. 3 - Graph this function with your graphing calculator....Ch. 3 - We mentioned in Chapter 2 that the Ferris wheel...Ch. 3 - Use the information given in Figure 1 to find x,...Ch. 3 - Geometry Find the measure of one of the interior...Ch. 3 - Find the distance from the origin to the point...Ch. 3 - Find all angles that are coterminal with 150.Ch. 3 - In which quadrant will lie if sin0 and cos0?Ch. 3 - Find all six trigonometric functions for if the...Ch. 3 - Find the remaining trigonometric functions of if...Ch. 3 - If sec=4, find cos.Ch. 3 - Multiply (sin+3)(sin7).Ch. 3 - Prove that sin(csc+cot)=1+cos is an identity by...Ch. 3 - Find sinA , cosA, tanA, and sinB , cosB, and tanB...Ch. 3 - Fill in the blank to make the statement true: sec...Ch. 3 - Subtract 1532 from 2515.Ch. 3 - Use a calculator to find to the nearest tenth of...Ch. 3 - Give the number of significant digits in each...Ch. 3 - If triangle ABC is a right triangle with B=48o,...Ch. 3 - Distance and Bearing A ship leaves the harbour...Ch. 3 - Angle of Depression A man standing on the roof a...Ch. 3 - Vector Magnitude If vector V has magnitude 5.0 and...Ch. 3 - Static Equilibrium David and his sister Jessica...Ch. 3 - Draw 117.8o in standard position and then name the...Ch. 3 - Use a calculator to find , to the nearest tenth of...Ch. 3 - Convert 390o to radian measure. Write your answer...Ch. 3 - Give the exact value of sin53.Ch. 3 - Use the unit circle to find all values of between...Ch. 3 - Use the unit circle to explain how the value of...Ch. 3 - If =6 is a central angle in a circle of radius 12...Ch. 3 - Find the area of the sector formed by central...Ch. 3 - Point P moves with angular velocity 34 radians per...Ch. 3 - Velocity of a DVD A DVD, when placed in a DVD...

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