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Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
Publisher: Cengage Learning
ISBN: 9781337275347

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Section
BuyFindarrow_forward

Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
Publisher: Cengage Learning
ISBN: 9781337275347
Chapter 11.7, Problem 82E
Textbook Problem
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Converting a Rectangular EquationIn Exercises 79–86, convert the rectangular equation to an equation in (a) cylindrical coordinates and (b) spherical coordinates.

x 2 + y 2 = z

(a)

To determine

To calculate: Rectangular and Cylindrical coordinates are given. Calculate equation in cylindrical coordinatesfor the surface represented by the rectangular equation x2+y2=z.

Explanation of Solution

Given:

The rectangular equation is:

x2+y2=z

Formula used:

Conversion formula is:

x2+y2=r2z=z

Calculation:

Rectangular coordinates to cylindrical coordinates,

x2+y2=

(b)

To determine

To calculate: Spherical and Cylindrical coordinates are given. Calculate the equation in sphericalcoordinates for the surface represented by the rectangular equation x2+y2=z.

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Chapter 11 Solutions

Calculus (MindTap Course List)
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Ch. 11.1 - Writing a Vector in Different Forms In Exercises...Ch. 11.1 - Writing a Vector in Different Forms to Exercises...Ch. 11.1 - Writing a Vector in Different Forms to Exercises...Ch. 11.1 - Writing a Vector in Different Forms to Exercises...Ch. 11.1 - Writing a Vector in Different Forms In Exercises...Ch. 11.1 - Writing a Vector in Different Forms In Exercises...Ch. 11.1 - Finding a Terminal Point In Exercise 17 and 18,...Ch. 11.1 - Finding a Terminal Point In Exercise 17 and 18,...Ch. 11.1 - Finding a Magnitude of a Vector In Exercises...Ch. 11.1 - Finding a Magnitude of a Vector In Exercises...Ch. 11.1 - Finding a Magnitude of a Vector In Exercises...Ch. 11.1 - Finding a Magnitude of a VectorIn Exercises 1924,...Ch. 11.1 - Finding a Magnitude of a VectorIn Exercises 1924,...Ch. 11.1 - Finding a Magnitude of a VectorIn Exercises 1924,...Ch. 11.1 - Sketching Scalar MultipliesIn Exercises 25 and 26,...Ch. 11.1 - Sketching Scalar MultipliesIn Exercises 25 and 26,...Ch. 11.1 - Using Vector Operations In Exercise 27 and 28, And...Ch. 11.1 - Using Vector Operations In Exercise 27 and 28, And...Ch. 11.1 - Sketching a Vector In Exercises 29-34, use the...Ch. 11.1 - Sketching a Vector In Exercises 29-34, use the...Ch. 11.1 - Sketching a Vector In Exercises 29-34, use the...Ch. 11.1 - Sketching a Vector In Exercises 29-34, use the...Ch. 11.1 - Sketching a Vector In Exercises 29-34, use the...Ch. 11.1 - Sketching a Vector In Exercises 29-34, use the...Ch. 11.1 - Finding a Unit Vector In Exercises 35-38, find the...Ch. 11.1 - Finding a Unit Vector In Exercises 35-38, find the...Ch. 11.1 - Finding a Unit Vector In Exercises 35-38, find the...Ch. 11.1 - Finding a Unit Vector In Exercises 35-38, find the...Ch. 11.1 - Finding MagnitudesIn Exercises 3942, find the...Ch. 11.1 - Finding Magnitudes In Exercises 39-42, find the...Ch. 11.1 - Finding MagnitudesIn Exercises 3942, find the...Ch. 11.1 - Finding MagnitudesIn Exercises 3942, find the...Ch. 11.1 - Using the Triangle Inequality In Exercises 43 und...Ch. 11.1 - Using the Triangle Inequality In Exercises 43 und...Ch. 11.1 - Finding a Vector In Exercises 45-48, find the...Ch. 11.1 - Finding a Vector In Exercises 45-48, find the...Ch. 11.1 - Finding a Vector In Exercises 45-48, find the...Ch. 11.1 - Finding a Vector In Exercises 45-48, find the...Ch. 11.1 - Finding a VectorIn Exercises 4952, find the...Ch. 11.1 - Finding a Vector In Exercises 49-52, find the...Ch. 11.1 - Finding a Vector In Exercises 49-52, find the...Ch. 11.1 - Finding a VectorIn Exercises 4952, find the...Ch. 11.1 - Finding a Vector In Exercises 53-56, find the...Ch. 11.1 - Finding a Vector In Exercises 53-56, find the...Ch. 11.1 - Finding a Vector In Exercises 53-56, find the...Ch. 11.1 - Finding a Vector In Exercises 53-56, find the...Ch. 11.1 - EXPLORING CONCEPTS Think About ItIn Exercises 57...Ch. 11.1 - EXPLORING CONCEPTS Think About ItIn Exercises 57...Ch. 11.1 - EXPLORING CONCEPTS Triangle Consider a triangle...Ch. 11.1 - HOW DO YOU SEE IT? 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What is known about , the angle...Ch. 11.3 - Revenue The vector u= 3240,1450,2235 gives the...Ch. 11.3 - RevenueRepeat Exercises 49 after decreasing the...Ch. 11.3 - Orthogonal Vectors In Exercises 51-54, find two...Ch. 11.3 - Orthogonal Vectors In Exercises 51-54, find two...Ch. 11.3 - Orthogonal Vectors In Exercises 5154, find two...Ch. 11.3 - Orthogonal Vectors In Exercises 5154, find two...Ch. 11.3 - Finding an Angle Find the angle between a cubes...Ch. 11.3 - Finding an Angle Find the angle between the...Ch. 11.3 - Braking Load A 48,000-pound truck is parked on a...Ch. 11.3 - Braking LoadA 5400-pound sport utility vehicle is...Ch. 11.3 - Work An object is pulled 10 feet across a floor...Ch. 11.3 - WorkA wagon is pulled by exerting a force of 65...Ch. 11.3 - Work A car is towed using a force of 1600 newtons....Ch. 11.3 - Work A pallet truck is pulled by exerting a force...Ch. 11.3 - True or False? In Exercises 63 and 64, determine...Ch. 11.3 - True or False? 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The vertices of a triangle in...Ch. 11.4 - True or False? In Exercises 43-46, determine...Ch. 11.4 - True or False? In Exercises 43-46, determine...Ch. 11.4 - True or False? In Exercises 43-46, determine...Ch. 11.4 - True or False? In Exercises 4346, determine...Ch. 11.4 - Proof In Exercises 47-52, prove the property of...Ch. 11.4 - ProofIn Exercises 4752, prove the poverty of the...Ch. 11.4 - Proof In Exercises 47-52, prove the property of...Ch. 11.4 - ProofIn Exercises 4752, prove the poverty of the...Ch. 11.4 - Proof In Exercises 47-52, prove the property of...Ch. 11.4 - ProofIn Exercises 4752, prove the poverty of the...Ch. 11.4 - Proof Prove that uv=uv if u and v are orthogonal.Ch. 11.4 - Proof Prove that u(vw)=(uw)v(uv)w.Ch. 11.4 - Proof Prove Theorem 11.9.Ch. 11.5 - CONCEPT CHECK Parametric and Symmetric...Ch. 11.5 - CONCEPT CHECK Normal Vector The equation of a...Ch. 11.5 - CONCEPT CHECK PlaneWrite an equation of a plane in...Ch. 11.5 - CONCEPT CHECK Parallel Planes Explain how to find...Ch. 11.5 - Checking Points on a Line In Exercises 5 and 6,...Ch. 11.5 - Checking Points on a Line In Exercises 5 and 6,...Ch. 11.5 - Finding Parametric and Symmetric EquationsIn...Ch. 11.5 - Finding Parametric and Symmetric EquationsIn...Ch. 11.5 - Finding Parametric and Symmetric EquationsIn...Ch. 11.5 - Finding Parametric and Symmetric Equations In...Ch. 11.5 - Finding Parametric and Symmetric EquationsIn...Ch. 11.5 - Finding Parametric and Symmetric EquationsIn...Ch. 11.5 - Finding Parametric and Symmetric EquationsIn...Ch. 11.5 - Finding Parametric and Symmetric EquationsIn...Ch. 11.5 - Finding Parametric and Symmetric Equations In...Ch. 11.5 - Finding Parametric and Symmetric Equations In...Ch. 11.5 - Finding Parametric EquationsIn Exercises 1724,...Ch. 11.5 - Finding Parametric EquationsIn Exercises 1724,...Ch. 11.5 - Finding Parametric EquationsIn Exercises 1724,...Ch. 11.5 - Finding Parametric EquationsIn Exercises 1724,...Ch. 11.5 - Finding Parametric EquationsIn Exercises 1724,...Ch. 11.5 - Finding Parametric EquationsIn Exercises 1724,...Ch. 11.5 - Finding Parametric EquationsIn Exercises 1724,...Ch. 11.5 - Finding Parametric EquationsIn Exercises 1724,...Ch. 11.5 - Using Parametric and Symmetric EquationsIn...Ch. 11.5 - Using Parametric and Symmetric EquationsIn...Ch. 11.5 - Using Parametric and Symmetric EquationsIn...Ch. 11.5 - Using Parametric and Symmetric EquationsIn...Ch. 11.5 - Determining Parallel Lines In Exercises 29-32,...Ch. 11.5 - Determining Parallel Lines In Exercises 29-32,...Ch. 11.5 - Determining Parallel Lines In Exercises 29-32,...Ch. 11.5 - Determining Parallel Lines In Exercises 29-32,...Ch. 11.5 - Finding a Point of IntersectionIn Exercises 3336,...Ch. 11.5 - Finding a Point of IntersectionIn Exercises 3336,...Ch. 11.5 - Finding a Point of IntersectionIn Exercises 3336,...Ch. 11.5 - Finding a Point of IntersectionIn Exercises 3336,...Ch. 11.5 - Checking Points in a Plane In Exercises 37 and 38,...Ch. 11.5 - Checking Points in a Plane In Exercises 37 and 38,...Ch. 11.5 - Finding an Equation of a PlaneIn Exercises 3944,...Ch. 11.5 - Finding an Equation of a PlaneIn Exercises 3944,...Ch. 11.5 - Finding an Equation of a PlaneIn Exercises 3944,...Ch. 11.5 - Finding an Equation of a PlaneIn Exercises 3944,...Ch. 11.5 - Finding an Equation of a PlaneIn Exercises 3944,...Ch. 11.5 - Finding an Equation of a PlaneIn Exercises 3944,...Ch. 11.5 - Finding an Equation of a PlaneIn Exercises 4556,...Ch. 11.5 - Finding an Equation of a PlaneIn Exercises 4556,...Ch. 11.5 - Finding an Equation of a PlaneIn Exercises 4556,...Ch. 11.5 - Finding an Equation of a PlaneIn Exercises 4556,...Ch. 11.5 - Finding an Equation of a PlaneIn Exercises 4556,...Ch. 11.5 - Finding an Equation of a PlaneIn Exercises 4556,...Ch. 11.5 - Finding an Equation of a PlaneIn Exercises 4556,...Ch. 11.5 - Finding an Equation of a PlaneIn Exercises 4556,...Ch. 11.5 - Finding an Equation of a PlaneIn Exercises 4556,...Ch. 11.5 - Finding an Equation of a PlaneIn Exercises 4556,...Ch. 11.5 - Finding an Equation of a PlaneIn Exercises 4556,...Ch. 11.5 - Finding an Equation of a PlaneIn Exercises 4556,...Ch. 11.5 - Finding an Equation of a PlaneIn Exercises 5760,...Ch. 11.5 - Finding an Equation of a PlaneIn Exercises 5760,...Ch. 11.5 - Finding an Equation of a PlaneIn Exercises 5760,...Ch. 11.5 - Finding an Equation of a PlaneIn Exercises 5760,...Ch. 11.5 - Parallel PlanesIn Exercises 6164, determine...Ch. 11.5 - Parallel PlanesIn Exercises 6164, determine...Ch. 11.5 - Parallel PlanesIn Exercises 6164, determine...Ch. 11.5 - Parallel PlanesIn Exercises 6164, determine...Ch. 11.5 - Intersection of PlanesIn Exercises 6568, (a) find...Ch. 11.5 - Intersection of PlanesIn Exercises 6568, (a) find...Ch. 11.5 - Intersection of PlanesIn Exercises 6568, (a) find...Ch. 11.5 - Intersection of PlanesIn Exercises 6568, (a) find...Ch. 11.5 - Comparing PlanesIn Exercises 6974, determine...Ch. 11.5 - Comparing PlanesIn Exercises 6974, determine...Ch. 11.5 - Comparing PlanesIn Exercises 6974, determine...Ch. 11.5 - Comparing PlanesIn Exercises 6974, determine...Ch. 11.5 - Comparing PlanesIn Exercises 6974, determine...Ch. 11.5 - Comparing PlanesIn Exercises 6974, determine...Ch. 11.5 - Sketching a Graph of a PlaneIn Exercises 7582,...Ch. 11.5 - Sketching a Graph of a PlaneIn Exercises 7582,...Ch. 11.5 - Sketching a Graph of a PlaneIn Exercises 7582,...Ch. 11.5 - Sketching a Graph of a PlaneIn Exercises 7582,...Ch. 11.5 - Sketching a Graph of a PlaneIn Exercises 7582,...Ch. 11.5 - Sketching a Graph of a PlaneIn Exercises 7582,...Ch. 11.5 - Sketching a Graph of a PlaneIn Exercises 7582,...Ch. 11.5 - Sketching a Graph of a PlaneIn Exercises 7582,...Ch. 11.5 - Intersection of a Plane and a LineIn Exercises...Ch. 11.5 - Intersection of a Plane and a LineIn Exercises...Ch. 11.5 - Intersection of a Plane and a LineIn Exercises...Ch. 11.5 - Intersection of a Plane and a LineIn Exercises...Ch. 11.5 - Finding the Distance Between a Point and a PlaneIn...Ch. 11.5 - Finding the Distance Between a Point and a PlaneIn...Ch. 11.5 - Finding the Distance Between a Point and a PlaneIn...Ch. 11.5 - Finding the Distance Between a Point and a PlaneIn...Ch. 11.5 - Finding the Distance Between Two Parallel PlanesIn...Ch. 11.5 - Finding the Distance Between Two Parallel PlanesIn...Ch. 11.5 - Finding the Distance Between Two Parallel PlanesIn...Ch. 11.5 - Finding the Distance Between Two Parallel PlanesIn...Ch. 11.5 - Finding the Distance Between a Point and a LineIn...Ch. 11.5 - Finding the Distance Between a Point and a LineIn...Ch. 11.5 - Finding the Distance Between a Point and a LineIn...Ch. 11.5 - Finding the Distance Between a Point and a LineIn...Ch. 11.5 - Finding the Distance Between Two Parallel Lines In...Ch. 11.5 - Finding the Distance Between Two Parallel LinesIn...Ch. 11.5 - EXPLORING CONCEPTS PlanesConsider a line and a...Ch. 11.5 - EXPLORING CONCEPTS PlanesHow many planes are...Ch. 11.5 - EXPLORING CONCEPTS Think About ItDo two distinct...Ch. 11.5 - HOW DO YOU SEE IT? Match the general equation with...Ch. 11.5 - Modeling Data Personal consumption expenditures...Ch. 11.5 - Mechanical Design The figure shows a chute at the...Ch. 11.5 - DistanceTwo insects are crawling along different...Ch. 11.5 - Finding an Equation of a SphereFind the standard...Ch. 11.5 - Finding a Point of IntersectionFind the point of...Ch. 11.5 - Finding the Distance Between a Plane and a...Ch. 11.5 - Finding Parametric EquationsFind a set of...Ch. 11.5 - Finding Parametric EquationsFind a set of...Ch. 11.5 - True or False? In Exercises 113118, determine...Ch. 11.5 - True or False? In Exercises 113118, determine...Ch. 11.5 - True or False? In Exercises 113118, determine...Ch. 11.5 - True or False? In Exercises 113118, determine...Ch. 11.5 - True or False? In Exercises 113-118, determine...Ch. 11.5 - True or False? In Exercises 113118, determine...Ch. 11.6 - CONCEPT CHECK Quadric Surfaces How are quadric...Ch. 11.6 - CONCEPT CHECK Classifying an Equation What does...Ch. 11.6 - CONCEPT CHECK Trace of a Surface What is meant by...Ch. 11.6 - CONCEPT CHECK Think About It Does every...Ch. 11.6 - Matching In Exercises 5-10, match the equation...Ch. 11.6 - Matching In Exercises 5-10, match the equation...Ch. 11.6 - Matching In Exercises 5-10, match the equation...Ch. 11.6 - Matching In Exercises 5-10, match the equation...Ch. 11.6 - Matching In Exercises 5-10, match the equation...Ch. 11.6 - Matching In Exercises 5-10, match the equation...Ch. 11.6 - Sketching a Surface in SpaceIn Exercises 1114,...Ch. 11.6 - Sketching a Surface in SpaceIn Exercises 1114,...Ch. 11.6 - Sketching a Surface in SpaceIn Exercises 1114,...Ch. 11.6 - Sketching a Surface in SpaceIn Exercises 1114,...Ch. 11.6 - Sketching a Quadric SurfaceIn Exercises 1526,...Ch. 11.6 - Sketching a Quadric SurfaceIn Exercises 1526,...Ch. 11.6 - Sketching a Quadric SurfaceIn Exercises 1526,...Ch. 11.6 - Sketching a Quadric SurfaceIn Exercises 1526,...Ch. 11.6 - Sketching a Quadric SurfaceIn Exercises 1526,...Ch. 11.6 - Sketching a Quadric SurfaceIn Exercises 1526,...Ch. 11.6 - Sketching a Quadric SurfaceIn Exercises 1526,...Ch. 11.6 - Sketching a Quadric SurfaceIn Exercises 1526,...Ch. 11.6 - Sketching a Quadric SurfaceIn Exercises 1526,...Ch. 11.6 - Sketching a Quadric SurfaceIn Exercises 1526,...Ch. 11.6 - Sketching a Quadric SurfaceIn Exercises 1526,...Ch. 11.6 - Sketching a Quadric SurfaceIn Exercises 1526,...Ch. 11.6 - EXPLORING CONCEPTS HyperboloidExplain how to...Ch. 11.6 - EXPLORING CONCEPTS EllipsoidIs every trace of an...Ch. 11.6 - EXPLORING CONCEPTS Quadric SurfaceIs there a...Ch. 11.6 - HOW DO YOU SEE IT? 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GeographyBecause of the forces caused by its...Ch. 11.6 - Machine Design The top of a rubber bushing...Ch. 11.6 - Using a Hyperbolic ParaboloidDetermine the...Ch. 11.6 - Intersection of SurfacesExplain why the curve of...Ch. 11.6 - Think About ItThree types of classic topological...Ch. 11.7 - CONCEPT CHECK Cylindrical CoordinatesDescribe the...Ch. 11.7 - CONCEPT CHECK Spherical CoordinatesDescribe the...Ch. 11.7 - Cylindrical-to-Rectangular ConversionIn Exercises...Ch. 11.7 - Cylindrical-to-Rectangular ConversionIn Exercises...Ch. 11.7 - Cylindrical-to-Rectangular ConversionIn Exercises...Ch. 11.7 - Cylindrical-to-Rectangular ConversionIn Exercises...Ch. 11.7 - Cylindrical-to-Rectangular ConversionIn Exercises...Ch. 11.7 - Cylindrical-to-Rectangular ConversionIn Exercises...Ch. 11.7 - Rectangular-to-Cylindrical ConversionIn Exercises...Ch. 11.7 - Rectangular-to-Cylindrical ConversionIn Exercises...Ch. 11.7 - Rectangular-to-Cylindrical ConversionIn Exercises...Ch. 11.7 - Rectangular-to-Cylindrical ConversionIn Exercises...Ch. 11.7 - 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In Exercises 101 and 102, determine...Ch. 11.7 - True or False? In Exercises 101 and 102, determine...Ch. 11.7 - Intersection of SurfaceIdentify the curve of...Ch. 11.7 - Intersection of Surface Identify the curve of...Ch. 11 - Writing Vectors in Different Forms In Exercises 1...Ch. 11 - Writing Vectors in Different FormsIn Exercises 1...Ch. 11 - Finding a Vector In Exercises 3 and 4, find the...Ch. 11 - Finding a Vector In Exercises 3 and 4, find the...Ch. 11 - Finding Coordinates of a PointFind the coordinates...Ch. 11 - Using the Three-Dimensional Coordinate...Ch. 11 - Finding the Distance Between Two Points in SpaceIn...Ch. 11 - Finding the Distance Between Two Points in SpaceIn...Ch. 11 - Finding the Equation of a SphereIn Exercises 9 and...Ch. 11 - Finding the Equation of a SphereIn Exercises 9 and...Ch. 11 - Finding the Equation of a SphereIn Exercises 11...Ch. 11 - Finding the Equation of a SphereIn Exercises 11...Ch. 11 - Writing a Vector in Different Forms In Exercises...Ch. 11 - Writing a Vector in Different Forms In Exercises...Ch. 11 - Finding a VectorIn Exercises 15 and 16, find the...Ch. 11 - Finding a VectorIn Exercises 15 and 16, find the...Ch. 11 - Using Vectors to Determine Collinear PointsIn...Ch. 11 - Using Vectors to Determine Collinear PointsIn...Ch. 11 - Finding a Unit VectorFind a unit vector in the...Ch. 11 - Finding a VectorFind the vector v of magnitude 8...Ch. 11 - Finding Dot ProductsIn Exercises 21 and 22, let...Ch. 11 - Finding Dot ProductsIn Exercises 21 and 22, let...Ch. 11 - Finding the Angle Between Two Vectors In Exercises...Ch. 11 - Finding the Angle Between Two Vectors In Exercises...Ch. 11 - Comparing VectorsIn Exercises 25 and 26, determine...Ch. 11 - Comparing VectorsIn Exercises 25 and 26, determine...Ch. 11 - Finding the Projection of u onto v In Exercises 27...Ch. 11 - Finding the Projection of u onto v In Exercises 27...Ch. 11 - Orthogonal VectorsFind two vectors in opposite...Ch. 11 - WorkAn object is pulled 8 feet across a floor...Ch. 11 - Finding Cross Products In Exercises 31 and 32,...Ch. 11 - Finding Cross ProductsIn Exercises 31 and 32, find...Ch. 11 - Finding a Unit VectorFind a unit vector that is...Ch. 11 - AreaFind the area of the parallelogram that has...Ch. 11 - Torque A vertical force of 40 pounds acts on a...Ch. 11 - VolumeUse the triple scalar product to find the...Ch. 11 - Finding Parametric and Symmetric Equations In...Ch. 11 - Finding Parametric and Symmetric Equations In...Ch. 11 - Finding Parametric EquationsIn Exercises 39 and...Ch. 11 - Finding Parametric EquationsIn Exercises 39 and...Ch. 11 - Finding an Equation of a PlaneIn Exercises 4144,...Ch. 11 - Finding an Equation of a PlaneIn Exercises 4144,...Ch. 11 - Finding an Equation of a Plane In Exercises 41-44,...Ch. 11 - Finding an Equation of a PlaneIn Exercises 4144,...Ch. 11 - Distance Find the distance between the point...Ch. 11 - Distance Find the distance between the point...Ch. 11 - Distance Find the distance between the planes...Ch. 11 - Distance Find the distance between the point...Ch. 11 - Sketching a Surface in Space In Exercises 49-58,...Ch. 11 - Sketching a Surface in Space In Exercises 49-58,...Ch. 11 - Sketching a Surface in Space In Exercises 49-58,...Ch. 11 - Sketching a Surface in SpaceIn Exercises 4958,...Ch. 11 - Sketching a Surface in Space In Exercises 49-58,...Ch. 11 - Sketching a Surface in SpaceIn Exercises 4958,...Ch. 11 - Sketching a Surface in Space In Exercises 49-58,...Ch. 11 - Sketching a Surface in SpaceIn Exercises 4958,...Ch. 11 - Sketching a Surface in Space In Exercises describe...Ch. 11 - Sketching a Surface in SpaceIn Exercises 4958,...Ch. 11 - Surface of RevolutionFind an equation for the...Ch. 11 - Surface of RevolutionFind an equation for the...Ch. 11 - Converting Rectangular CoordinatesIn Exercises 61...Ch. 11 - Converting Rectangular CoordinatesIn Exercises 61...Ch. 11 - Cylindrical-to-Rectangular ConversionIn Exercises...Ch. 11 - Cylindrical-to-Rectangular ConversionIn Exercises...Ch. 11 - Spherical-to-Rectangular ConversionIn Exercises 65...Ch. 11 - Spherical-to-Rectangular ConversionIn Exercises 65...Ch. 11 - Converting a Rectangular EquationIn Exercises 67...Ch. 11 - Converting a Rectangular Equation In Exercises 67...Ch. 11 - Cylindrical-to-Rectangular Conversion In Exercises...Ch. 11 - Cylindrical-to- Rectangular ConversionIn Exercises...Ch. 11 - Spherical-to-Rectangular Conversion In Exercises...Ch. 11 - Spherical-to-Rectangular Conversion In Exercises...Ch. 11 - ProofUsing vectors, prove the Law of Sines: If a,...Ch. 11 - Using an Equation Consider the function...Ch. 11 - Proof Using vectors, prove that the line segments...Ch. 11 - Proof Using vectors, prove that the diagonals of a...Ch. 11 - Distance (a) Find the shortest distance between...Ch. 11 - Orthogonal Vectors Let P0 be a point in the plane...Ch. 11 - Volume (a) Find the volume of the solid bounded...Ch. 11 - Volume (a) Use the disk method to find the volume...Ch. 11 - ProofProve the following property of the cross...Ch. 11 - Using Parametric Equations Consider the line given...Ch. 11 - Sketching Graphs Sketch the graph of each equation...Ch. 11 - Sketching GraphsSketch the graph of each equation...Ch. 11 - Tetherball A tetherball weighing 1 pound is pulled...Ch. 11 - Towing A loaded barge is being towed by two...Ch. 11 - ProofConsider the vectors u=cos,sin,0 and...Ch. 11 - Latitude-Longitude SystemLos Angeles is located at...Ch. 11 - Distance Between a Point and a PlaneConsider the...Ch. 11 - Distance Between Parallel PlanesShow that the...Ch. 11 - Intersection of PlanesShow that the curve of...

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