Question 1

Find a vector-valued function, using the given parameter, to represent the intersection of the surfaces given below. Surfaces
Parameter

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Question 2

Suppose the two particles travel along the space curves  and  . A collision will occur at the point of intersection P if both particles are at P at the same time. Find the point of collision.

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Question 3

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

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Question 4

Find the point on the curve given below at which the curvature K is zero.

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Question 5

Represent the following curve by a vector-valued function.

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Question 6

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

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Question 7

A baseball is hit 5 feet above the ground at 80 feet per second and at an angle of  with respect to the ground. Find the arc length of the trajectory. Round your answer to one decimal place. ​

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Question 8

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

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Question 9

The quarterback of a football team releases a pass at a height of 6 feet above the playing field, and the football is caught by a receiver 78 yards directly downfield at a height of 4 feet. The pass is released at an angle of  with the horizontal. Find the time in seconds the receiver has to reach the proper position after the quarterback releases the football. Round your answer to one decimal place.

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Question 10

Find the domain of the vector-valued function given below.  where

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Question 11

Find the vectors  and  for the following vector function. ​  ​

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Question 12

Find the indefinite integral below.  Do not include an arbitrary constant vector.

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Question 13

Find the length of the space curve given below.

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Question 14

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

Accepted Answer

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Question 15

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

Accepted Answer

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Question 16

Determine the range of a projectile fired at a height of 3 feet above the ground with an initial velocity of 500 feet per second and at an angle of  above the horizontal. Use the model for projectile motion, assuming there is no air resistance. Round your answer to three decimal places.

Accepted Answer

The answer of Determine the range of a projectile fired...

Question 17

Suppose the outer edge of a playground slide is in the shape of a helix of radius 8 meters. The slide has a height of 2 meters and makes one complete revolution from top to bottom. Find a vector-valued function for the helix.

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Question 18

A 5800-pound vehicle is driven at a speed of 25 miles per hour on a circular interchange of radius 90 feet. To keep the vehicle from skidding off course, what frictional force must the road surface exert on the tires? Round your answer to one decimal place.

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Question 19

Sketch the curve represented by the vector-valued function  and give the orientation of the curve.

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Question 20

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

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Quiz 12: Vector-Valued Functions

Find a vector-valued function, using the given parameter, to represent the intersection of the surfaces given below. Surfaces Parameter

Suppose the two particles travel along the space curves and . A collision will occur at the point of intersection P if both particles are at P at the same time. Find the point of collision.

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

Find the point on the curve given below at which the curvature K is zero.

Represent the following curve by a vector-valued function.

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

A baseball is hit 5 feet above the ground at 80 feet per second and at an angle of with respect to the ground. Find the arc length of the trajectory. Round your answer to one decimal place. ​

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

Find the domain of the vector-valued function given below. where

Find the vectors and for the following vector function. ​ ​

Find the indefinite integral below. Do not include an arbitrary constant vector.

Find the length of the space curve given below.

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

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

Determine the range of a projectile fired at a height of 3 feet above the ground with an initial velocity of 500 feet per second and at an angle of above the horizontal. Use the model for projectile motion, assuming there is no air resistance. Round your answer to three decimal places.

Suppose the outer edge of a playground slide is in the shape of a helix of radius 8 meters. The slide has a height of 2 meters and makes one complete revolution from top to bottom. Find a vector-valued function for the helix.

A 5800-pound vehicle is driven at a speed of 25 miles per hour on a circular interchange of radius 90 feet. To keep the vehicle from skidding off course, what frictional force must the road surface exert on the tires? Round your answer to one decimal place.

Sketch the curve represented by the vector-valued function and give the orientation of the curve.

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

A baseball is hit 5 feet above the ground at 80 feet per second and at an angle of with respect to the ground. Find the arc length of the trajectory. Round your answer to one decimal place.

Find the vectors and for the following vector function.