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Exam 12: Section 4: Vector-Valued Functions

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Because of a storm, ground controllers instruct the pilot of a plane flying at an altitude of 1.6 miles to make a Because of a storm, ground controllers instruct the pilot of a plane flying at an altitude of 1.6 miles to make a turn and climb to an altitude of 1.8 miles. The model for the path of the plane during this maneuver is where t is the time in hours and is the distance in miles. Determine the speed of the plane. Round your answer to the nearest integer. turn and climb to an altitude of 1.8 miles. The model for the path of the plane during this maneuver is Because of a storm, ground controllers instruct the pilot of a plane flying at an altitude of 1.6 miles to make a turn and climb to an altitude of 1.8 miles. The model for the path of the plane during this maneuver is where t is the time in hours and is the distance in miles. Determine the speed of the plane. Round your answer to the nearest integer. where t is the time in hours and Because of a storm, ground controllers instruct the pilot of a plane flying at an altitude of 1.6 miles to make a turn and climb to an altitude of 1.8 miles. The model for the path of the plane during this maneuver is where t is the time in hours and is the distance in miles. Determine the speed of the plane. Round your answer to the nearest integer. is the distance in miles. Determine the speed of the plane. Round your answer to the nearest integer.

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Question 1
Correct Answer:
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A

Find a set of parametric equations for the tangent line to the graph at Find a set of parametric equations for the tangent line to the graph at and use the equations for the line to approximate . and use the equations for the line to approximate Find a set of parametric equations for the tangent line to the graph at and use the equations for the line to approximate . . Find a set of parametric equations for the tangent line to the graph at and use the equations for the line to approximate .

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Question 2
Correct Answer:
Verified

A

Find the principle unit normal vector to the curve given below at the specified point. Find the principle unit normal vector to the curve given below at the specified point.

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Question 3
Correct Answer:
Verified

B

Verify that the space curves intersect at the given values of the parameter. Find the angle between the tangent vectors at the point of intersection. Verify that the space curves intersect at the given values of the parameter. Find the angle between the tangent vectors at the point of intersection. , , , Verify that the space curves intersect at the given values of the parameter. Find the angle between the tangent vectors at the point of intersection. , , Verify that the space curves intersect at the given values of the parameter. Find the angle between the tangent vectors at the point of intersection. , , , Verify that the space curves intersect at the given values of the parameter. Find the angle between the tangent vectors at the point of intersection. , ,

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Question 4

Find Find at time for the space curve . Round your answer to three decimal places. at time Find at time for the space curve . Round your answer to three decimal places. for the space curve Find at time for the space curve . Round your answer to three decimal places. . Round your answer to three decimal places.

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Question 5

Find Find at time for the plane curve . Round your answer to three decimal places. at time Find at time for the plane curve . Round your answer to three decimal places. for the plane curve Find at time for the plane curve . Round your answer to three decimal places. . Round your answer to three decimal places.

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Question 6

Find the unit tangent vector to the curve given below at the specified point. Find the unit tangent vector to the curve given below at the specified point.

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Question 7

Find Find at time for the space curve . at time Find at time for the space curve . for the space curve Find at time for the space curve . .

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Question 8

Find the unit tangent vector Find the unit tangent vector for the line tangent to the space curve at point . for the line tangent to the space curve Find the unit tangent vector for the line tangent to the space curve at point . at point Find the unit tangent vector for the line tangent to the space curve at point . .

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Question 9

Find the principle unit normal vector to the curve given below at the specified point. Find the principle unit normal vector to the curve given below at the specified point.

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Question 10

Use the result, "the tangential and normal components of acceleration for a projectile fired at an angle Use the result, the tangential and normal components of acceleration for a projectile fired at an angle with the horizontal at an initial speed of are and respectively., to find the tangential component of acceleration for a projectile fired at an angle of with the horizontal at an initial speed of 152 feet per second. What is the component when the projectile is at its maximum height? with the horizontal at an initial speed of Use the result, the tangential and normal components of acceleration for a projectile fired at an angle with the horizontal at an initial speed of are and respectively., to find the tangential component of acceleration for a projectile fired at an angle of with the horizontal at an initial speed of 152 feet per second. What is the component when the projectile is at its maximum height? are Use the result, the tangential and normal components of acceleration for a projectile fired at an angle with the horizontal at an initial speed of are and respectively., to find the tangential component of acceleration for a projectile fired at an angle of with the horizontal at an initial speed of 152 feet per second. What is the component when the projectile is at its maximum height? and Use the result, the tangential and normal components of acceleration for a projectile fired at an angle with the horizontal at an initial speed of are and respectively., to find the tangential component of acceleration for a projectile fired at an angle of with the horizontal at an initial speed of 152 feet per second. What is the component when the projectile is at its maximum height? respectively.", to find the tangential component of acceleration for a projectile fired at an angle of Use the result, the tangential and normal components of acceleration for a projectile fired at an angle with the horizontal at an initial speed of are and respectively., to find the tangential component of acceleration for a projectile fired at an angle of with the horizontal at an initial speed of 152 feet per second. What is the component when the projectile is at its maximum height? with the horizontal at an initial speed of 152 feet per second. What is the component when the projectile is at its maximum height?

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Question 11

Find Find at time for the plane curve . Round your answer to three decimal places. at time Find at time for the plane curve . Round your answer to three decimal places. for the plane curve Find at time for the plane curve . Round your answer to three decimal places. . Round your answer to three decimal places.

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Question 12

Find Find at time for the space curve . Round your answer to three decimal places. at time Find at time for the space curve . Round your answer to three decimal places. for the space curve Find at time for the space curve . Round your answer to three decimal places. . Round your answer to three decimal places.

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Question 13

Find the principle unit normal vector to the curve given below at the specified point. Find the principle unit normal vector to the curve given below at the specified point.

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Question 14

Find Find at time for the plane curve . Round your answer to three decimal places. at time Find at time for the plane curve . Round your answer to three decimal places. for the plane curve Find at time for the plane curve . Round your answer to three decimal places. . Round your answer to three decimal places.

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Question 15

Use the result, "the tangential and normal components of acceleration for a projectile fired at an angle Use the result, the tangential and normal components of acceleration for a projectile fired at an angle with the horizontal at an initial speed of are and respectively., to find the normal component of acceleration for a projectile fired at an angle of with the horizontal at an initial speed of 148 feet per second. What is the component when the projectile is at its maximum height? with the horizontal at an initial speed of Use the result, the tangential and normal components of acceleration for a projectile fired at an angle with the horizontal at an initial speed of are and respectively., to find the normal component of acceleration for a projectile fired at an angle of with the horizontal at an initial speed of 148 feet per second. What is the component when the projectile is at its maximum height? are Use the result, the tangential and normal components of acceleration for a projectile fired at an angle with the horizontal at an initial speed of are and respectively., to find the normal component of acceleration for a projectile fired at an angle of with the horizontal at an initial speed of 148 feet per second. What is the component when the projectile is at its maximum height? and Use the result, the tangential and normal components of acceleration for a projectile fired at an angle with the horizontal at an initial speed of are and respectively., to find the normal component of acceleration for a projectile fired at an angle of with the horizontal at an initial speed of 148 feet per second. What is the component when the projectile is at its maximum height? respectively.", to find the normal component of acceleration for a projectile fired at an angle of Use the result, the tangential and normal components of acceleration for a projectile fired at an angle with the horizontal at an initial speed of are and respectively., to find the normal component of acceleration for a projectile fired at an angle of with the horizontal at an initial speed of 148 feet per second. What is the component when the projectile is at its maximum height? with the horizontal at an initial speed of 148 feet per second. What is the component when the projectile is at its maximum height?

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Question 16

Find the unit tangent vector T(t) and then use it to find a set of parametric equations for the line tangent to the space curve given below at the given point. Find the unit tangent vector T(t) and then use it to find a set of parametric equations for the line tangent to the space curve given below at the given point.

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Question 17

Find Find at time for the plane curve . Round your answer to three decimal places. at time Find at time for the plane curve . Round your answer to three decimal places. for the plane curve Find at time for the plane curve . Round your answer to three decimal places. . Round your answer to three decimal places.

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Question 18

Find the unit tangent vector to the curve given below at the specified point. Find the unit tangent vector to the curve given below at the specified point.

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Question 19

Find Find at time for the space curve . Round your answer to three decimal places. at time Find at time for the space curve . Round your answer to three decimal places. for the space curve Find at time for the space curve . Round your answer to three decimal places. . Round your answer to three decimal places.

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Question 20
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