Find an equation of the surface of revolution generated by revolving the curve given below in the indicated coordinate plane about the given axis. $\begin{array}{|c|c|c|} \hline \text { Equation of Curve } & \text { Coordinate Plane } & \text { Axis of Revolution } \\ \hline z=5 x & x z \text {-plane } & z \text {-axis } \\ \hline \end{array}$

A) \[x ^ { 2 } + y ^ { 2 } = \frac { z } { 5 }\] B) \[x ^ { 2 } + z ^ { 2 } = \frac { y ^ { 2 } } { 25 }\] C) \[x ^ { 2 } + y ^ { 2 } = \frac { z ^ { 2 } } { 5 }\] D) \[x ^ { 2 } + y ^ { 2 } = \frac { z ^ { 2 } } { 25 }\] E) \[y ^ { 2 } + z ^ { 2 } = \frac { x ^ { 2 } } { 25 }\] A) \[x ^ { 2 } + y ^ { 2 } = \frac { z } { 5 }\] B) \[x ^ { 2 } + z ^ { 2 } = \frac { y ^ { 2 } } { 25 }\] C) \[x ^ { 2 } + y ^ { 2 } = \frac { z ^ { 2 } } { 5 }\] D) \[x ^ { 2 } + y ^ { 2 } = \frac { z ^ { 2 } } { 25 }\] E) \[y ^ { 2 } + z ^ { 2 } = \frac { x ^ { 2 } } { 25 }\]

Exam 11: Vectors in the Plane

$\text { Find the triple scalar product } ( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { w } \text {. }$ $\mathbf { u } = \{ - 6,7,4 \} , \mathbf { v } = \{ - 6,3 , - 2 \} , \mathbf { w } = \{ 3 , - 3,6 \}$

(Multiple Choice)

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Question 21

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

(Multiple Choice)

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Question 22

Find the length of the minor axis of the ellipse generated when the surface $z = \frac { x ^ { 2 } } { 5 } + \frac { y ^ { 2 } } { 25 }$ is intersected by the plane $z = 5$

(Multiple Choice)

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Question 23

Find an equation in rectangular coordinates for the equation given in spherical coordinates. $\rho = - 7 \csc \phi \sec \theta$

(Multiple Choice)

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Question 24

Find the direction angles of the vector u given below. Round your answer to one decimal place. $\mathbf { u } = ( 7,1 , - 3 \}$

(Multiple Choice)

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Question 25

$\text { Suppose a } 48000 \text {-pound truck is parked on a } 10 ^ { \circ } \text { slope as shown in the figure. }$ Assume the only force to overcome is that due to gravity. Find the force perpendicular to the hill. Round your answer to one decimal place. $\text { Suppose a } 48000 \text {-pound truck is parked on a } 10 ^ { \circ } \text { slope as shown in the figure. } Assume the only force to overcome is that due to gravity. Find the force perpendicular to the hill. Round your answer to one decimal place.$

(Multiple Choice)

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Question 26

A child applies the brakes on a bicycle by applying a downward force of 25 pounds on the pedal when the crank makes a $60 ^ { \circ }$ angle with the horizontal (see figure). The crank is 6 inches in length. Find the torque at $P$ . Round your answer to two decimal places. $A child applies the brakes on a bicycle by applying a downward force of 25 pounds on the pedal when the crank makes a 60 ^ { \circ } angle with the horizontal (see figure). The crank is 6 inches in length. Find the torque at P . Round your answer to two decimal places.$

(Multiple Choice)

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Question 27

Determine whether the following planes are parallel, orthogonal, or neither. If they are neither parallel nor orthogonal, find the angle of intersection. -2x-31y+5z+3=0 -3x+y+5z-4=0

(Multiple Choice)

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Question 28

To carry a 500-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 $20 ^ { \circ }$ angle away from the vertical and the other makes a $30 ^ { \circ }$ angle as shown in the figure below. Find the vertical component of each worker's force. Round your answer to two decimal places. $To carry a 500-pound cylindrical weight, two workers lift on the ends of short ropes tied to an eyelet on the top center of the cylinder. One rope makes a 20 ^ { \circ } angle away from the vertical and the other makes a 30 ^ { \circ } angle as shown in the figure below. Find the vertical component of each worker's force. Round your answer to two decimal places.$

(Multiple Choice)

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Question 29

$\text { Given } \mathbf { u } = ( - 1,6,4 ) \text { and } \mathbf { v } = \langle 0,1,0 \} \text {, find } \mathbf { u } \times \mathbf { v } \text {. }$

(Multiple Choice)

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Question 30

Find the magnitude of the vector given below. $\mathbf { v } = \langle - 5 , - 4 , - 3 \}$

(Multiple Choice)

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Question 31

Find the vector v whose initial and terminal points are given below. $( 5.5,2.1 ) , ( 9.5,6.1 )$

(Multiple Choice)

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Question 32

Find an equation of a plane passing through the given point and perpendicular to the given vector. Point: $( 3 , - 1 , - 3 ) \quad$ Vector: $\mathbf { v } = \{ 6,5,4 \}$

(Multiple Choice)

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Question 33

Identify the equation (written in terms of cylindrical or spherical coordinates) of the following graph.

(Multiple Choice)

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Question 34

Find a set of parametric equations of the line through the point $( - 7,5,4 ) \text { parallel to }$ the vector $\mathrm { v } = \{ 8,5,2 \}$ .

(Multiple Choice)

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Question 35

$\text { Given } \mathbf { u } = ( 4 , - 3 , - 4 ) \text { and } \mathbf { v } = ( 5,3,6 ) \text { find } \mathbf { v } \times \mathbf { u } \text {. }$

(Multiple Choice)

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Question 36

Identify the following quadric surface. $\frac { x ^ { 2 } } { 7 } + \frac { y ^ { 2 } } { 6 } + \frac { z ^ { 2 } } { 2 } = 1$

(Multiple Choice)

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Question 37

The top of a rubber bushing designed to absorb vibrations in an automobile is the surface of revolution generated by revolving the curve $z = \frac { 1 } { 5 } y ^ { 2 } + 3 , ( 0 \leq y \leq 5 ) \text { in the } y z \text {-plane }$ about the z-axis. The bushing has a hole of 4 centimeters in diameter through its center and parallel to the axis of revolution. All measurements are in centimeters and the bushing is set on the xy-plane. Find the volume of the rubber bushing. Round your answer to two decimal places.

(Multiple Choice)

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Question 38

Find an equation of the surface of revolution generated by revolving the curve given below in the indicated coordinate plane about the given axis. Equation of Curve Coordinate Plane Axis of Revolution z=5x xz -plane z -axis

(Multiple Choice)

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Question 39

Find vectors u and v whose initial and terminal points are given. Determine whether u and v are equivalent. $\mathbf { u } : ( 6,5 ) , ( 9,11 ) \quad \mathbf { v } : ( 3 , - 5 ) , \quad ( 6,1 )$

(Multiple Choice)

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Question 40

Showing 21 - 40 of 125

$\text { Find the triple scalar product } ( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { w } \text {. }$ $\mathbf { u } = \{ - 6,7,4 \} , \mathbf { v } = \{ - 6,3 , - 2 \} , \mathbf { w } = \{ 3 , - 3,6 \}$

Find the length of the minor axis of the ellipse generated when the surface $z = \frac { x ^ { 2 } } { 5 } + \frac { y ^ { 2 } } { 25 }$ is intersected by the plane $z = 5$

Find an equation in rectangular coordinates for the equation given in spherical coordinates. $\rho = - 7 \csc \phi \sec \theta$

Find the direction angles of the vector u given below. Round your answer to one decimal place. $\mathbf { u } = ( 7,1 , - 3 \}$

Determine whether the following planes are parallel, orthogonal, or neither. If they are neither parallel nor orthogonal, find the angle of intersection. -2x-31y+5z+3=0 -3x+y+5z-4=0

$\text { Given } \mathbf { u } = ( - 1,6,4 ) \text { and } \mathbf { v } = \langle 0,1,0 \} \text {, find } \mathbf { u } \times \mathbf { v } \text {. }$

Find the magnitude of the vector given below. $\mathbf { v } = \langle - 5 , - 4 , - 3 \}$

Find the vector v whose initial and terminal points are given below. $( 5.5,2.1 ) , ( 9.5,6.1 )$

Find an equation of a plane passing through the given point and perpendicular to the given vector. Point: $( 3 , - 1 , - 3 ) \quad$ Vector: $\mathbf { v } = \{ 6,5,4 \}$

Identify the equation (written in terms of cylindrical or spherical coordinates) of the following graph.

Find a set of parametric equations of the line through the point $( - 7,5,4 ) \text { parallel to }$ the vector $\mathrm { v } = \{ 8,5,2 \}$ .

$\text { Given } \mathbf { u } = ( 4 , - 3 , - 4 ) \text { and } \mathbf { v } = ( 5,3,6 ) \text { find } \mathbf { v } \times \mathbf { u } \text {. }$

Identify the following quadric surface. $\frac { x ^ { 2 } } { 7 } + \frac { y ^ { 2 } } { 6 } + \frac { z ^ { 2 } } { 2 } = 1$

Find an equation of the surface of revolution generated by revolving the curve given below in the indicated coordinate plane about the given axis. Equation of Curve Coordinate Plane Axis of Revolution z=5x xz -plane z -axis

Find vectors u and v whose initial and terminal points are given. Determine whether u and v are equivalent. $\mathbf { u } : ( 6,5 ) , ( 9,11 ) \quad \mathbf { v } : ( 3 , - 5 ) , \quad ( 6,1 )$

Graphs and Models

A Preview of Calculus

The Derivative and the Tangent Line Problem

Extrema on an Interval

Antiderivatives and Indefinite Integration

Slope Fields and Eulers Method

Area of a Region Between Two Curves

Basic Integration Rules

Sequences

Conics and Calculus

Vector-Valued Functions

Introduction to Functions of Several Variables

Iterated Integrals and Area in the Plane

Vector Fields

Exact First-Order Equations

Filters

Exam 11: Vectors in the Plane

Find the length of the minor axis of the ellipse generated when the surface z=x25+y225z = \frac { x ^ { 2 } } { 5 } + \frac { y ^ { 2 } } { 25 }z=5x2​+25y2​ is intersected by the plane z=5z = 5z=5

Find an equation in rectangular coordinates for the equation given in spherical coordinates. ρ=−7csc⁡ϕsec⁡θ\rho = - 7 \csc \phi \sec \thetaρ=−7cscϕsecθ

Find the direction angles of the vector u given below. Round your answer to one decimal place. u=(7,1,−3}\mathbf { u } = ( 7,1 , - 3 \}u=(7,1,−3}

A child applies the brakes on a bicycle by applying a downward force of 25 pounds on the pedal when the crank makes a 60∘60 ^ { \circ }60∘ angle with the horizontal (see figure). The crank is 6 inches in length. Find the torque at PPP . Round your answer to two decimal places.

Determine whether the following planes are parallel, orthogonal, or neither. If they are neither parallel nor orthogonal, find the angle of intersection. -2x-31y+5z+3=0 -3x+y+5z-4=0

Given u=(−1,6,4) and v=⟨0,1,0}, find u×v. \text { Given } \mathbf { u } = ( - 1,6,4 ) \text { and } \mathbf { v } = \langle 0,1,0 \} \text {, find } \mathbf { u } \times \mathbf { v } \text {. } Given u=(−1,6,4) and v=⟨0,1,0}, find u×v.

Find the magnitude of the vector given below. v=⟨−5,−4,−3}\mathbf { v } = \langle - 5 , - 4 , - 3 \}v=⟨−5,−4,−3}

Find the vector v whose initial and terminal points are given below. (5.5,2.1),(9.5,6.1)( 5.5,2.1 ) , ( 9.5,6.1 )(5.5,2.1),(9.5,6.1)

Find an equation of a plane passing through the given point and perpendicular to the given vector. Point: (3,−1,−3)( 3 , - 1 , - 3 ) \quad(3,−1,−3) Vector: v={6,5,4}\mathbf { v } = \{ 6,5,4 \}v={6,5,4}

Identify the equation (written in terms of cylindrical or spherical coordinates) of the following graph.

Find a set of parametric equations of the line through the point (−7,5,4) parallel to ( - 7,5,4 ) \text { parallel to }(−7,5,4) parallel to the vector v={8,5,2}\mathrm { v } = \{ 8,5,2 \}v={8,5,2} .

Given u=(4,−3,−4) and v=(5,3,6) find v×u. \text { Given } \mathbf { u } = ( 4 , - 3 , - 4 ) \text { and } \mathbf { v } = ( 5,3,6 ) \text { find } \mathbf { v } \times \mathbf { u } \text {. } Given u=(4,−3,−4) and v=(5,3,6) find v×u.

Identify the following quadric surface. x27+y26+z22=1\frac { x ^ { 2 } } { 7 } + \frac { y ^ { 2 } } { 6 } + \frac { z ^ { 2 } } { 2 } = 17x2​+6y2​+2z2​=1

Find an equation of the surface of revolution generated by revolving the curve given below in the indicated coordinate plane about the given axis. Equation of Curve Coordinate Plane Axis of Revolution z=5x xz -plane z -axis

Find vectors u and v whose initial and terminal points are given. Determine whether u and v are equivalent. u:(6,5),(9,11)v:(3,−5),(6,1)\mathbf { u } : ( 6,5 ) , ( 9,11 ) \quad \mathbf { v } : ( 3 , - 5 ) , \quad ( 6,1 )u:(6,5),(9,11)v:(3,−5),(6,1)

Graphs and Models

A Preview of Calculus

The Derivative and the Tangent Line Problem

Extrema on an Interval

Antiderivatives and Indefinite Integration

Slope Fields and Eulers Method

Area of a Region Between Two Curves

Basic Integration Rules

Sequences

Conics and Calculus

Vector-Valued Functions

Introduction to Functions of Several Variables

Iterated Integrals and Area in the Plane

Vector Fields

Exact First-Order Equations

Filters

Find the length of the minor axis of the ellipse generated when the surface $z = \frac { x ^ { 2 } } { 5 } + \frac { y ^ { 2 } } { 25 }$ is intersected by the plane $z = 5$

Find an equation in rectangular coordinates for the equation given in spherical coordinates. $\rho = - 7 \csc \phi \sec \theta$

Find the direction angles of the vector u given below. Round your answer to one decimal place. $\mathbf { u } = ( 7,1 , - 3 \}$

$\text { Given } \mathbf { u } = ( - 1,6,4 ) \text { and } \mathbf { v } = \langle 0,1,0 \} \text {, find } \mathbf { u } \times \mathbf { v } \text {. }$

Find the magnitude of the vector given below. $\mathbf { v } = \langle - 5 , - 4 , - 3 \}$

Find the vector v whose initial and terminal points are given below. $( 5.5,2.1 ) , ( 9.5,6.1 )$

Find an equation of a plane passing through the given point and perpendicular to the given vector. Point: $( 3 , - 1 , - 3 ) \quad$ Vector: $\mathbf { v } = \{ 6,5,4 \}$

Find a set of parametric equations of the line through the point $( - 7,5,4 ) \text { parallel to }$ the vector $\mathrm { v } = \{ 8,5,2 \}$ .

$\text { Given } \mathbf { u } = ( 4 , - 3 , - 4 ) \text { and } \mathbf { v } = ( 5,3,6 ) \text { find } \mathbf { v } \times \mathbf { u } \text {. }$

Identify the following quadric surface. $\frac { x ^ { 2 } } { 7 } + \frac { y ^ { 2 } } { 6 } + \frac { z ^ { 2 } } { 2 } = 1$

Find vectors u and v whose initial and terminal points are given. Determine whether u and v are equivalent. $\mathbf { u } : ( 6,5 ) , ( 9,11 ) \quad \mathbf { v } : ( 3 , - 5 ) , \quad ( 6,1 )$