Exam 10: Parametric Equations, Polar Coordinates, and Vectors

Suppose a plane flies at a constant groundspeed of 500 miles per hour due east and encounters a 50 mile-per-hour wind from the northwest.Both the airspeed and the compass direction must change to for the plane to maintain its groundspeed and eastward direction.Find the airspeed to maintain its groundspeed and eastward direction.Round your answer to two decimal places.

(Multiple Choice)

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Question 41

Find the vector v with the given magnitude ||v|| = 185 and the same direction as .

(Multiple Choice)

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Question 42

Classify the graph of the equation as a circle,a parabola,an ellipse,or a hyperbola.

(Multiple Choice)

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Question 43

Find the length of the curve over the given interval.

(Multiple Choice)

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Question 44

Classify the graph of the equation as a circle,a parabola,an ellipse,or a hyperbola.

(Multiple Choice)

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Question 45

Find the points of intersection of the graphs of the equations.

(Multiple Choice)

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Question 46

Use the result,"the set of parametric equations for the line passing through and is " to find a set of parametric equations for the line passing through and .

(Multiple Choice)

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Question 47

To carry a 100-pound cylindrical weight,two workers lift on the ends of short ropes tied to an eyelet on the top center of the cylinder.One rope makes a 20° angle away from the vertical and the other makes a 30° angle as shown in the figure below.Find each rope's tension if the resultant force is vertical.Round your answer to two decimal places.

(Multiple Choice)

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Question 48

Find the length of the curve over the interval .

(Multiple Choice)

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Question 49

Find the area of the surface generated by revolving the curve about the given axis. (i)x-axis; (ii)y-axis

(Multiple Choice)

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Question 50

Find given the following.

(Multiple Choice)

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Question 51

Find the center,foci,and vertices of the hyperbola.

(Multiple Choice)

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Question 52

Find the focus of the parabola given by .

(Multiple Choice)

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Question 53

Find an equation of the ellipse with vertices and eccentricity .

(Multiple Choice)

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Question 54

Identify any points at which the cycloid is not smooth.

(Multiple Choice)

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Question 55

Find given the following vector function.

(Multiple Choice)

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Question 56

A baseball,hit 9 feet above the ground,leaves the bat at an angle of and is caught by an outfielder 9 feet above the ground and 500 feet from home plate.What is the initial speed of the ball? Round your answer to two decimal places.

(Multiple Choice)

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Question 57

Suppose a plane is flying in the direction 302°.Its speed with respect to the air is 900 kilometers per hour.The wind at the plane's altitude is from the southwest at 100 kilometers per hour (see figure).What is the true direction of the plane? Round your answer to two decimal places.

(Multiple Choice)

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Question 58

Find the vectors r(t)and r' (t)for the following vector function.

(Multiple Choice)

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Question 59

Use the properties of the derivative to find given the following vector-valued functions.

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Question 60

Showing 41 - 60 of 173

Find the vector v with the given magnitude ||v|| = 185 and the same direction as .

Classify the graph of the equation as a circle,a parabola,an ellipse,or a hyperbola.

Find the length of the curve over the given interval.

Classify the graph of the equation as a circle,a parabola,an ellipse,or a hyperbola.

Find the points of intersection of the graphs of the equations.

Use the result,"the set of parametric equations for the line passing through and is " to find a set of parametric equations for the line passing through and .

Find the length of the curve over the interval .

Find the area of the surface generated by revolving the curve about the given axis. (i)x-axis; (ii)y-axis

Find given the following.

Find the center,foci,and vertices of the hyperbola.

Find the focus of the parabola given by .

Find an equation of the ellipse with vertices and eccentricity .

Identify any points at which the cycloid is not smooth.

Find given the following vector function.

A baseball,hit 9 feet above the ground,leaves the bat at an angle of and is caught by an outfielder 9 feet above the ground and 500 feet from home plate.What is the initial speed of the ball? Round your answer to two decimal places.

Suppose a plane is flying in the direction 302°.Its speed with respect to the air is 900 kilometers per hour.The wind at the plane's altitude is from the southwest at 100 kilometers per hour (see figure).What is the true direction of the plane? Round your answer to two decimal places.

Find the vectors r(t)and r' (t)for the following vector function.

Use the properties of the derivative to find given the following vector-valued functions.

Preparation for Calculus

Limits and Their Properties

Differentiation

Applications of Differentiation

Integration

Differential Equations

Applications of Integration

Integration Techniques, L'Hôpital's Rule, and Improper Integrals

Infinite Series

Mechanical Ventilation and Sedation: Assessment, Medications, and Complications

Filters

Exam 10: Parametric Equations, Polar Coordinates, and Vectors

Find the vector v with the given magnitude ||v|| = 185 and the same direction as . ​

Classify the graph of the equation as a circle,a parabola,an ellipse,or a hyperbola. ​ ​

Find the length of the curve over the given interval. ​ ​

Classify the graph of the equation as a circle,a parabola,an ellipse,or a hyperbola. ​ ​

Find the points of intersection of the graphs of the equations. ​ ​

Use the result,"the set of parametric equations for the line passing through and is " to find a set of parametric equations for the line passing through and . ​

Find the length of the curve over the interval . ​

Find the area of the surface generated by revolving the curve about the given axis. ​ ​ (i)x-axis; (ii)y-axis ​

Find given the following. ​ ​

Find the center,foci,and vertices of the hyperbola. ​ ​

Find the focus of the parabola given by . ​

Find an equation of the ellipse with vertices and eccentricity . ​

Identify any points at which the cycloid is not smooth. ​

Find given the following vector function. ​ ​

A baseball,hit 9 feet above the ground,leaves the bat at an angle of and is caught by an outfielder 9 feet above the ground and 500 feet from home plate.What is the initial speed of the ball? Round your answer to two decimal places. ​

Suppose a plane is flying in the direction 302°.Its speed with respect to the air is 900 kilometers per hour.The wind at the plane's altitude is from the southwest at 100 kilometers per hour (see figure).What is the true direction of the plane? Round your answer to two decimal places. ​ ​

Find the vectors r(t)and r' (t)for the following vector function. ​ ​

Use the properties of the derivative to find given the following vector-valued functions. ​​ ​

Preparation for Calculus

Limits and Their Properties

Differentiation

Applications of Differentiation

Integration

Differential Equations

Applications of Integration

Integration Techniques, L'Hôpital's Rule, and Improper Integrals

Infinite Series

Mechanical Ventilation and Sedation: Assessment, Medications, and Complications

Filters

Find the vector v with the given magnitude ||v|| = 185 and the same direction as .

Classify the graph of the equation as a circle,a parabola,an ellipse,or a hyperbola.

Find the length of the curve over the given interval.

Classify the graph of the equation as a circle,a parabola,an ellipse,or a hyperbola.

Find the points of intersection of the graphs of the equations.

Use the result,"the set of parametric equations for the line passing through and is " to find a set of parametric equations for the line passing through and .

Find the length of the curve over the interval .

Find the area of the surface generated by revolving the curve about the given axis. (i)x-axis; (ii)y-axis

Find given the following.

Find the center,foci,and vertices of the hyperbola.

Find the focus of the parabola given by .

Find an equation of the ellipse with vertices and eccentricity .

Identify any points at which the cycloid is not smooth.

Find given the following vector function.

A baseball,hit 9 feet above the ground,leaves the bat at an angle of and is caught by an outfielder 9 feet above the ground and 500 feet from home plate.What is the initial speed of the ball? Round your answer to two decimal places.

Suppose a plane is flying in the direction 302°.Its speed with respect to the air is 900 kilometers per hour.The wind at the plane's altitude is from the southwest at 100 kilometers per hour (see figure).What is the true direction of the plane? Round your answer to two decimal places.

Find the vectors r(t)and r' (t)for the following vector function.

Use the properties of the derivative to find given the following vector-valued functions.