EBK MULTIVARIABLE CALCULUS
11th Edition
ISBN: 8220103600781
Author: Edwards
Publisher: YUZU
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Question
Chapter 11.3, Problem 54E
To determine
To calculate: The two
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3.12 (B). A horizontal beam AB is 4 m
long and of constant flexural rigidity. It is
rigidly built-in at the left-hand end A and simply supported on a non-yielding support
at the right-hand end B. The beam carries Uniformly distributed vertical loading of
18 kN/m over its whole length, together with a vertical downward load of 10KN at
2.5 m from the end A. Sketch the S.F. and B.M. diagrams for the beam, indicating
all main values. Cl. Struct. E.] CS.F. 45,10,376 KN, B.M. 186, +36.15 kNm.7
Qize
f(x)
=
x + 2x2 - 2
x² + 4x²² -
Solve the equation using Newton
Raphson
-b±√√b2-4ac
2a
@4x²-12x+9=0
27 de febrero de 2025
-b±√√b2-4ac
2a
⑥2x²-4x-1=0
a = 4 b=-12
c=9
a = 2
b = 9
c = \
x=-42±√(2-4 (4) (9)
2(4))
X =
(12) ±√44)-(360)
2(108)
x = ±√
X = =±√√²-4(2) (1)
2()
X = ±√
+
X =
X =
+
X₁ =
=
X₁ =
X₁ =
+
X₁ =
=
=
Chapter 11 Solutions
EBK MULTIVARIABLE CALCULUS
Ch. 11.1 - CONCEPT CHECK Scalar and Vector Describe the...Ch. 11.1 - CONCEPT CHECK Vector Two points and a vector are...Ch. 11.1 - Sketching a Vector In Exercises 3 and 4, (a) find...Ch. 11.1 - Prob. 4ECh. 11.1 - Equivalent Vectors In Bunches 5-8, find the...Ch. 11.1 - Equivalent Vectors In Bunches 5-8, find the...Ch. 11.1 - Equivalent Vectors In Bunches 5-8, find the...Ch. 11.1 - Equivalent Vectors In Bunches 5-8, find the...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 - Writing a Vector in Different Forms In Exercises...Ch. 11.1 - Writing a Vector in Different Forms to Exercises...Ch. 11.1 - Prob. 13ECh. 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 - Prob. 19ECh. 11.1 - Prob. 20ECh. 11.1 - Prob. 21ECh. 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 - Prob. 30ECh. 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 - Prob. 34ECh. 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 - Prob. 40ECh. 11.1 - Finding MagnitudesIn Exercises 3942, find the...Ch. 11.1 - Prob. 42ECh. 11.1 - Using the Triangle Inequality In Exercises 43 und...Ch. 11.1 - Prob. 44ECh. 11.1 - Prob. 45ECh. 11.1 - Finding a Vector In Exercises 45-48, find the...Ch. 11.1 - Prob. 47ECh. 11.1 - Prob. 48ECh. 11.1 - Prob. 49ECh. 11.1 - Prob. 50ECh. 11.1 - Prob. 51ECh. 11.1 - Prob. 52ECh. 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 - Prob. 57ECh. 11.1 - Prob. 58ECh. 11.1 - Prob. 59ECh. 11.1 - HOW DO YOU SEE IT? Use the figure to determine...Ch. 11.1 - Finding Values In Exercises 61-66, And a and b...Ch. 11.1 - Prob. 62ECh. 11.1 - Prob. 63ECh. 11.1 - Prob. 64ECh. 11.1 - Prob. 65ECh. 11.1 - Prob. 66ECh. 11.1 - Finding Unit VectorsIn Exercises 6772, find a unit...Ch. 11.1 - Prob. 68ECh. 11.1 - Prob. 69ECh. 11.1 - Prob. 70ECh. 11.1 - Finding Unit Vectors In Exercises 67-72, find a...Ch. 11.1 - Prob. 72ECh. 11.1 - Prob. 73ECh. 11.1 - Prob. 74ECh. 11.1 - Prob. 75ECh. 11.1 - Numerical and Graphical Analysis Forces with...Ch. 11.1 - Prob. 77ECh. 11.1 - Prob. 78ECh. 11.1 - Cable Tension In Exercises 79 and 80, determine...Ch. 11.1 - Cable TensionIn Exercises 79 and 80, determine the...Ch. 11.1 - Projectile Motion A gun with a muzzle velocity of...Ch. 11.1 - Prob. 82ECh. 11.1 - Navigation A plane is flying with a bearing of...Ch. 11.1 - NavigationA plane flies at a constant groundspeed...Ch. 11.1 - Prob. 85ECh. 11.1 - Prob. 86ECh. 11.1 - Prob. 87ECh. 11.1 - Prob. 88ECh. 11.1 - Prob. 89ECh. 11.1 - True or False? In Exercises 85-94, determine...Ch. 11.1 - Prob. 91ECh. 11.1 - True or False? In Exercises 8594, determine...Ch. 11.1 - Prob. 93ECh. 11.1 - Prob. 94ECh. 11.1 - Prob. 95ECh. 11.1 - Prob. 96ECh. 11.1 - Prob. 97ECh. 11.1 - Proof Prove that the vector w=uv+vu bisects the...Ch. 11.1 - Prob. 99ECh. 11.1 - PUTNAM EXAM CHALLENGE A coast artillery gun can...Ch. 11.2 - CONCEPT CHECK Describing Coordinates A point in...Ch. 11.2 - Prob. 2ECh. 11.2 - CONCEPT CHECK Comparing Graphs Describe the graph...Ch. 11.2 - Prob. 4ECh. 11.2 - Plotting Points In Exercises 5-8. plot the points...Ch. 11.2 - Prob. 6ECh. 11.2 - Prob. 7ECh. 11.2 - Prob. 8ECh. 11.2 - Finding Coordinates of a Point In Exercises 9-12,...Ch. 11.2 - Finding Coordinates of a PointIn Exercises 912,...Ch. 11.2 - Finding Coordinates of a PointIn Exercises 912,...Ch. 11.2 - Prob. 12ECh. 11.2 - Using the Three-Dimensional Coordinate System In...Ch. 11.2 - Prob. 14ECh. 11.2 - Using the Three-Dimensional Coordinate System In...Ch. 11.2 - Prob. 16ECh. 11.2 - Using the Three-Dimensional Coordinate System In...Ch. 11.2 - Prob. 18ECh. 11.2 - Using the Three-Dimensional Coordinate System In...Ch. 11.2 - Using the Three-Dimensional Coordinate System In...Ch. 11.2 - Using the Three-Dimensional Coordinate System In...Ch. 11.2 - Prob. 22ECh. 11.2 - Using the Three-Dimensional Coordinate System In...Ch. 11.2 - Prob. 24ECh. 11.2 - Prob. 25ECh. 11.2 - Prob. 26ECh. 11.2 - Prob. 27ECh. 11.2 - Prob. 28ECh. 11.2 - Classifying a TriangleIn Exercises 2932, find the...Ch. 11.2 - Classifying a TriangleIn Exercises 2932, find the...Ch. 11.2 - Classifying a TriangleIn Exercises 2932, find the...Ch. 11.2 - Prob. 32ECh. 11.2 - Prob. 33ECh. 11.2 - Prob. 34ECh. 11.2 - Prob. 35ECh. 11.2 - Prob. 36ECh. 11.2 - Finding the Equation of a Sphere In Exercises...Ch. 11.2 - Prob. 38ECh. 11.2 - Finding the Equation of a SphereIn Exercises 3742,...Ch. 11.2 - Prob. 40ECh. 11.2 - Prob. 41ECh. 11.2 - Prob. 42ECh. 11.2 - Prob. 43ECh. 11.2 - Prob. 44ECh. 11.2 - Prob. 45ECh. 11.2 - Prob. 46ECh. 11.2 - Prob. 47ECh. 11.2 - Prob. 48ECh. 11.2 - Prob. 49ECh. 11.2 - Prob. 50ECh. 11.2 - Prob. 51ECh. 11.2 - Prob. 52ECh. 11.2 - Prob. 53ECh. 11.2 - Prob. 54ECh. 11.2 - Prob. 55ECh. 11.2 - Prob. 56ECh. 11.2 - Prob. 57ECh. 11.2 - Prob. 58ECh. 11.2 - Prob. 59ECh. 11.2 - Prob. 60ECh. 11.2 - Prob. 61ECh. 11.2 - Finding a Vector In Exercises 59-62, rind the...Ch. 11.2 - Prob. 63ECh. 11.2 - Parallel Vectors In Exercises 63-66, determine...Ch. 11.2 - Prob. 65ECh. 11.2 - Parallel Vectors In Exercises 63-66, determine...Ch. 11.2 - Prob. 67ECh. 11.2 - Prob. 68ECh. 11.2 - Prob. 69ECh. 11.2 - Prob. 70ECh. 11.2 - Prob. 71ECh. 11.2 - Prob. 72ECh. 11.2 - Prob. 73ECh. 11.2 - Prob. 74ECh. 11.2 - Prob. 75ECh. 11.2 - Prob. 76ECh. 11.2 - Prob. 77ECh. 11.2 - Prob. 78ECh. 11.2 - Finding Unit Vectors In Exercises 79-82, find a...Ch. 11.2 - Prob. 80ECh. 11.2 - Prob. 81ECh. 11.2 - Prob. 82ECh. 11.2 - Prob. 83ECh. 11.2 - Prob. 84ECh. 11.2 - Prob. 85ECh. 11.2 - Prob. 86ECh. 11.2 - Prob. 87ECh. 11.2 - Sketching a Vector In Exercises 87 und 88, sketch...Ch. 11.2 - Prob. 89ECh. 11.2 - Prob. 90ECh. 11.2 - Prob. 91ECh. 11.2 - Prob. 92ECh. 11.2 - Prob. 93ECh. 11.2 - Prob. 94ECh. 11.2 - Prob. 95ECh. 11.2 - Prob. 96ECh. 11.2 - Prob. 97ECh. 11.2 - Tower Guy Wire The guy wire supporting a 100-foot...Ch. 11.2 - Auditorium Lights The lights in an auditorium are...Ch. 11.2 - Prob. 100ECh. 11.2 - Load Supports Find the tension in each of the...Ch. 11.2 - Prob. 102ECh. 11.2 - Prob. 103ECh. 11.3 - Prob. 1ECh. 11.3 - Direction Cosines Consider the vector v=v1,v2,v3....Ch. 11.3 - Prob. 3ECh. 11.3 - Prob. 4ECh. 11.3 - Prob. 5ECh. 11.3 - Prob. 6ECh. 11.3 - Prob. 7ECh. 11.3 - Prob. 8ECh. 11.3 - Prob. 9ECh. 11.3 - Prob. 10ECh. 11.3 - Finding the Angle Between Two Vectors In Exercises...Ch. 11.3 - Prob. 12ECh. 11.3 - Finding the Angle Between Two Vectors In Exercises...Ch. 11.3 - Prob. 14ECh. 11.3 - Prob. 15ECh. 11.3 - Prob. 16ECh. 11.3 - Prob. 17ECh. 11.3 - Prob. 18ECh. 11.3 - Alternative Form of Dot Product In Exercises 19...Ch. 11.3 - Prob. 20ECh. 11.3 - Prob. 21ECh. 11.3 - Prob. 22ECh. 11.3 - Prob. 23ECh. 11.3 - Prob. 24ECh. 11.3 - Prob. 25ECh. 11.3 - Prob. 26ECh. 11.3 - Classifying a TriangleIn Exercises 2730, the...Ch. 11.3 - Classifying a TriangleIn Exercises 2730, the...Ch. 11.3 - Classifying a TriangleIn Exercises 2730, the...Ch. 11.3 - Prob. 30ECh. 11.3 - Prob. 31ECh. 11.3 - Prob. 32ECh. 11.3 - Prob. 33ECh. 11.3 - Prob. 34ECh. 11.3 - Prob. 35ECh. 11.3 - Prob. 36ECh. 11.3 - Prob. 37ECh. 11.3 - Prob. 38ECh. 11.3 - Prob. 39ECh. 11.3 - Finding the Projection of u onto v In Exercises...Ch. 11.3 - Prob. 41ECh. 11.3 - Prob. 42ECh. 11.3 - Finding the Projection of u onto v In Exercises...Ch. 11.3 - Prob. 44ECh. 11.3 - Prob. 45ECh. 11.3 - Projection What can be said about the vectors u...Ch. 11.3 - Prob. 47ECh. 11.3 - Prob. 48ECh. 11.3 - Prob. 49ECh. 11.3 - RevenueRepeat Exercises 49 after decreasing the...Ch. 11.3 - Prob. 51ECh. 11.3 - Prob. 52ECh. 11.3 - Prob. 53ECh. 11.3 - Prob. 54ECh. 11.3 - Prob. 55ECh. 11.3 - Prob. 56ECh. 11.3 - Prob. 57ECh. 11.3 - Prob. 58ECh. 11.3 - Prob. 59ECh. 11.3 - Prob. 60ECh. 11.3 - Prob. 61ECh. 11.3 - Prob. 62ECh. 11.3 - Prob. 63ECh. 11.3 - Prob. 64ECh. 11.3 - Prob. 65ECh. 11.3 - Prob. 66ECh. 11.3 - Prob. 67ECh. 11.3 - Prob. 68ECh. 11.3 - Prob. 69ECh. 11.3 - Prob. 70ECh. 11.3 - Bond AngleConsider a regular tetrahedron with...Ch. 11.3 - Prob. 72ECh. 11.3 - Prob. 73ECh. 11.3 - Prob. 74ECh. 11.3 - Prob. 75ECh. 11.4 - CONCEPT CHECK Vectors Explain what uv represents...Ch. 11.4 - CONCEPT CHECK Area Explain how to find the area of...Ch. 11.4 - Prob. 3ECh. 11.4 - Cross Product of Unit VectorsIn Exercises 36, find...Ch. 11.4 - Cross Product of Unit Vectors In Exercises 3-6,...Ch. 11.4 - Prob. 6ECh. 11.4 - Prob. 7ECh. 11.4 - Prob. 8ECh. 11.4 - Finding Cross Products in Exercises 7-10, find (a)...Ch. 11.4 - Prob. 10ECh. 11.4 - Prob. 11ECh. 11.4 - Prob. 12ECh. 11.4 - Prob. 13ECh. 11.4 - Prob. 14ECh. 11.4 - Prob. 15ECh. 11.4 - Prob. 16ECh. 11.4 - Prob. 17ECh. 11.4 - Prob. 18ECh. 11.4 - Prob. 19ECh. 11.4 - Prob. 20ECh. 11.4 - Prob. 21ECh. 11.4 - Prob. 22ECh. 11.4 - Prob. 23ECh. 11.4 - Prob. 24ECh. 11.4 - Prob. 25ECh. 11.4 - Prob. 26ECh. 11.4 - Torque The brakes on a bicycle are applied using a...Ch. 11.4 - Prob. 28ECh. 11.4 - Prob. 29ECh. 11.4 - Prob. 30ECh. 11.4 - Finding a Triple Scalar Product In Exercises...Ch. 11.4 - Prob. 32ECh. 11.4 - Prob. 33ECh. 11.4 - Prob. 34ECh. 11.4 - Volume In Exercises 35 and 36, use t triple scalar...Ch. 11.4 - Prob. 36ECh. 11.4 - Volume In Exercises 37 and 38, find the volume of...Ch. 11.4 - Prob. 38ECh. 11.4 - EXPLORING CONCEPTS Comparing Dot Products Identify...Ch. 11.4 - Prob. 40ECh. 11.4 - EXPLORING CONCEPTS Cross ProductTwo nonzero...Ch. 11.4 - Prob. 42ECh. 11.4 - Prob. 43ECh. 11.4 - Prob. 44ECh. 11.4 - Prob. 45ECh. 11.4 - Prob. 46ECh. 11.4 - Prob. 47ECh. 11.4 - Prob. 48ECh. 11.4 - Prob. 49ECh. 11.4 - Prob. 50ECh. 11.4 - Prob. 51ECh. 11.4 - Prob. 52ECh. 11.4 - Prob. 53ECh. 11.4 - Proof Prove that u(vw)=(uw)v(uv)w.Ch. 11.4 - Prob. 55ECh. 11.5 - CONCEPT CHECK Parametric and Symmetric...Ch. 11.5 - Prob. 2ECh. 11.5 - Prob. 3ECh. 11.5 - Prob. 4ECh. 11.5 - Checking Points on a Line In Exercises 5 and 6,...Ch. 11.5 - Prob. 6ECh. 11.5 - Prob. 7ECh. 11.5 - Prob. 8ECh. 11.5 - Prob. 9ECh. 11.5 - Prob. 10ECh. 11.5 - Prob. 11ECh. 11.5 - Finding Parametric and Symmetric EquationsIn...Ch. 11.5 - Finding Parametric and Symmetric EquationsIn...Ch. 11.5 - Prob. 14ECh. 11.5 - Prob. 15ECh. 11.5 - Finding Parametric and Symmetric Equations In...Ch. 11.5 - Prob. 17ECh. 11.5 - Prob. 18ECh. 11.5 - Prob. 19ECh. 11.5 - Prob. 20ECh. 11.5 - Prob. 21ECh. 11.5 - Prob. 22ECh. 11.5 - Prob. 23ECh. 11.5 - Prob. 24ECh. 11.5 - Prob. 25ECh. 11.5 - Prob. 26ECh. 11.5 - Prob. 27ECh. 11.5 - Using Parametric and Symmetric EquationsIn...Ch. 11.5 - Prob. 29ECh. 11.5 - Prob. 30ECh. 11.5 - Prob. 31ECh. 11.5 - Prob. 32ECh. 11.5 - Finding a Point of IntersectionIn Exercises 3336,...Ch. 11.5 - Prob. 34ECh. 11.5 - Finding a Point of IntersectionIn Exercises 3336,...Ch. 11.5 - Prob. 36ECh. 11.5 - Prob. 37ECh. 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 - Prob. 40ECh. 11.5 - Prob. 41ECh. 11.5 - Prob. 42ECh. 11.5 - Finding an Equation of a PlaneIn Exercises 3944,...Ch. 11.5 - Prob. 44ECh. 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 - Prob. 50ECh. 11.5 - Finding an Equation of a PlaneIn Exercises 4556,...Ch. 11.5 - Prob. 52ECh. 11.5 - Finding an Equation of a PlaneIn Exercises 4556,...Ch. 11.5 - Prob. 54ECh. 11.5 - Prob. 55ECh. 11.5 - Prob. 56ECh. 11.5 - Prob. 57ECh. 11.5 - Prob. 58ECh. 11.5 - Finding an Equation of a PlaneIn Exercises 5760,...Ch. 11.5 - Prob. 60ECh. 11.5 - Parallel PlanesIn Exercises 6164, determine...Ch. 11.5 - Prob. 62ECh. 11.5 - Prob. 63ECh. 11.5 - Prob. 64ECh. 11.5 - Intersection of PlanesIn Exercises 6568, (a) find...Ch. 11.5 - Prob. 66ECh. 11.5 - Prob. 67ECh. 11.5 - Prob. 68ECh. 11.5 - Comparing PlanesIn Exercises 6974, determine...Ch. 11.5 - Prob. 70ECh. 11.5 - Prob. 71ECh. 11.5 - Prob. 72ECh. 11.5 - Prob. 73ECh. 11.5 - Prob. 74ECh. 11.5 - Prob. 75ECh. 11.5 - Prob. 76ECh. 11.5 - Prob. 77ECh. 11.5 - Prob. 78ECh. 11.5 - Prob. 79ECh. 11.5 - Prob. 80ECh. 11.5 - Prob. 81ECh. 11.5 - Prob. 82ECh. 11.5 - Intersection of a Plane and a LineIn Exercises...Ch. 11.5 - Prob. 84ECh. 11.5 - Intersection of a Plane and a LineIn Exercises...Ch. 11.5 - Prob. 86ECh. 11.5 - Prob. 87ECh. 11.5 - Prob. 88ECh. 11.5 - Prob. 89ECh. 11.5 - Prob. 90ECh. 11.5 - Prob. 91ECh. 11.5 - Prob. 92ECh. 11.5 - Prob. 93ECh. 11.5 - Prob. 94ECh. 11.5 - Prob. 95ECh. 11.5 - Prob. 96ECh. 11.5 - Prob. 97ECh. 11.5 - Prob. 98ECh. 11.5 - Prob. 99ECh. 11.5 - Prob. 100ECh. 11.5 - Prob. 101ECh. 11.5 - Prob. 102ECh. 11.5 - Prob. 103ECh. 11.5 - Prob. 104ECh. 11.5 - Prob. 105ECh. 11.5 - Prob. 106ECh. 11.5 - Prob. 107ECh. 11.5 - Prob. 108ECh. 11.5 - Prob. 109ECh. 11.5 - Prob. 110ECh. 11.5 - Prob. 111ECh. 11.5 - Prob. 112ECh. 11.5 - Prob. 113ECh. 11.5 - True or False? In Exercises 113118, determine...Ch. 11.5 - Prob. 115ECh. 11.5 - Prob. 116ECh. 11.5 - Prob. 117ECh. 11.5 - Prob. 118ECh. 11.6 - CONCEPT CHECK Quadric Surfaces How are quadric...Ch. 11.6 - Prob. 2ECh. 11.6 - Prob. 3ECh. 11.6 - CONCEPT CHECK Think About It Does every...Ch. 11.6 - Prob. 5ECh. 11.6 - Matching In Exercises 5-10, match the equation...Ch. 11.6 - Prob. 7ECh. 11.6 - Matching In Exercises 5-10, match the equation...Ch. 11.6 - Prob. 9ECh. 11.6 - Matching In Exercises 5-10, match the equation...Ch. 11.6 - Sketching a Surface in SpaceIn Exercises 1114,...Ch. 11.6 - Prob. 12ECh. 11.6 - Prob. 13ECh. 11.6 - Prob. 14ECh. 11.6 - Prob. 15ECh. 11.6 - Prob. 16ECh. 11.6 - Prob. 17ECh. 11.6 - Prob. 18ECh. 11.6 - Prob. 19ECh. 11.6 - Prob. 20ECh. 11.6 - Prob. 21ECh. 11.6 - Prob. 22ECh. 11.6 - Prob. 23ECh. 11.6 - Prob. 24ECh. 11.6 - Prob. 25ECh. 11.6 - Prob. 26ECh. 11.6 - Prob. 27ECh. 11.6 - Prob. 28ECh. 11.6 - Prob. 29ECh. 11.6 - Prob. 30ECh. 11.6 - Prob. 31ECh. 11.6 - Finding an Equation for a Surface of RevolutionIn...Ch. 11.6 - Prob. 33ECh. 11.6 - Prob. 34ECh. 11.6 - Prob. 35ECh. 11.6 - Prob. 36ECh. 11.6 - Finding a Generating CurveIn Exercises 3740, find...Ch. 11.6 - Prob. 38ECh. 11.6 - Prob. 39ECh. 11.6 - Prob. 40ECh. 11.6 - Prob. 41ECh. 11.6 - Prob. 42ECh. 11.6 - Prob. 43ECh. 11.6 - Analyzing a TraceIn Exercises 43 and 44, analyze...Ch. 11.6 - Prob. 45ECh. 11.6 - Prob. 46ECh. 11.6 - Prob. 47ECh. 11.6 - Prob. 48ECh. 11.6 - Using a Hyperbolic ParaboloidDetermine the...Ch. 11.6 - Prob. 50ECh. 11.6 - Prob. 51ECh. 11.7 - CONCEPT CHECK Cylindrical CoordinatesDescribe the...Ch. 11.7 - Prob. 2ECh. 11.7 - Prob. 3ECh. 11.7 - Prob. 4ECh. 11.7 - Prob. 5ECh. 11.7 - Prob. 6ECh. 11.7 - Prob. 7ECh. 11.7 - Prob. 8ECh. 11.7 - Prob. 9ECh. 11.7 - Prob. 10ECh. 11.7 - Prob. 11ECh. 11.7 - Prob. 12ECh. 11.7 - Prob. 13ECh. 11.7 - Prob. 14ECh. 11.7 - Rectangular-to-Cylindrical ConversionIn Exercises...Ch. 11.7 - Prob. 16ECh. 11.7 - Prob. 17ECh. 11.7 - Prob. 18ECh. 11.7 - Rectangular-to-Cylindrical ConversionIn Exercises...Ch. 11.7 - Prob. 20ECh. 11.7 - Prob. 21ECh. 11.7 - Prob. 22ECh. 11.7 - Prob. 23ECh. 11.7 - Prob. 24ECh. 11.7 - Prob. 25ECh. 11.7 - Prob. 26ECh. 11.7 - Prob. 27ECh. 11.7 - Prob. 28ECh. 11.7 - Prob. 29ECh. 11.7 - Prob. 30ECh. 11.7 - Prob. 31ECh. 11.7 - Prob. 32ECh. 11.7 - Prob. 33ECh. 11.7 - Prob. 34ECh. 11.7 - Prob. 35ECh. 11.7 - Prob. 36ECh. 11.7 - Prob. 37ECh. 11.7 - Prob. 38ECh. 11.7 - Prob. 39ECh. 11.7 - Prob. 40ECh. 11.7 - Prob. 41ECh. 11.7 - Prob. 42ECh. 11.7 - Rectangular-to-Spherical ConversionIn Exercises...Ch. 11.7 - Prob. 44ECh. 11.7 - Prob. 45ECh. 11.7 - Prob. 46ECh. 11.7 - Prob. 47ECh. 11.7 - Prob. 48ECh. 11.7 - Prob. 49ECh. 11.7 - Prob. 50ECh. 11.7 - Spherical-to-Rectangular Conversion In Exercises...Ch. 11.7 - Prob. 52ECh. 11.7 - Prob. 53ECh. 11.7 - Prob. 54ECh. 11.7 - Spherical-to-Rectangular Conversion In Exercises...Ch. 11.7 - Prob. 56ECh. 11.7 - Spherical-to-Rectangular Conversion In Exercises...Ch. 11.7 - Prob. 58ECh. 11.7 - Prob. 59ECh. 11.7 - Prob. 60ECh. 11.7 - Prob. 61ECh. 11.7 - Prob. 62ECh. 11.7 - Prob. 63ECh. 11.7 - Prob. 64ECh. 11.7 - Prob. 65ECh. 11.7 - Prob. 66ECh. 11.7 - Prob. 67ECh. 11.7 - Prob. 68ECh. 11.7 - Prob. 69ECh. 11.7 - Prob. 70ECh. 11.7 - Prob. 71ECh. 11.7 - Prob. 72ECh. 11.7 - Prob. 73ECh. 11.7 - MatchingIn Exercises 7176, match the equation...Ch. 11.7 - MatchingIn Exercises 7176, match the equation...Ch. 11.7 - Prob. 76ECh. 11.7 - Prob. 77ECh. 11.7 - Prob. 78ECh. 11.7 - Prob. 79ECh. 11.7 - Prob. 80ECh. 11.7 - Prob. 81ECh. 11.7 - Prob. 82ECh. 11.7 - Converting a Rectangular EquationIn Exercises...Ch. 11.7 - Prob. 84ECh. 11.7 - Prob. 85ECh. 11.7 - Prob. 86ECh. 11.7 - Sketching a Solid In Exercises 8790, sketch the...Ch. 11.7 - Prob. 88ECh. 11.7 - Sketching a SolidIn Exercises 8790, sketch the...Ch. 11.7 - Prob. 90ECh. 11.7 - Prob. 91ECh. 11.7 - Prob. 92ECh. 11.7 - Prob. 93ECh. 11.7 - Prob. 94ECh. 11.7 - Prob. 95ECh. 11.7 - Prob. 96ECh. 11.7 - Prob. 97ECh. 11.7 - Prob. 98ECh. 11.7 - Prob. 99ECh. 11.7 - Prob. 100ECh. 11.7 - Prob. 101ECh. 11.7 - Prob. 102ECh. 11.7 - Intersection of SurfaceIdentify the curve of...Ch. 11.7 - Prob. 104ECh. 11 - Writing Vectors in Different Forms In Exercises 1...Ch. 11 - Prob. 2RECh. 11 - Prob. 3RECh. 11 - Prob. 4RECh. 11 - Prob. 5RECh. 11 - Prob. 6RECh. 11 - Prob. 7RECh. 11 - Prob. 8RECh. 11 - Prob. 9RECh. 11 - Prob. 10RECh. 11 - Prob. 11RECh. 11 - Prob. 12RECh. 11 - Prob. 13RECh. 11 - Prob. 14RECh. 11 - Prob. 15RECh. 11 - Prob. 16RECh. 11 - Prob. 17RECh. 11 - Prob. 18RECh. 11 - Prob. 19RECh. 11 - Prob. 20RECh. 11 - Prob. 21RECh. 11 - Prob. 22RECh. 11 - Prob. 23RECh. 11 - Finding the Angle Between Two Vectors In Exercises...Ch. 11 - Prob. 25RECh. 11 - Prob. 26RECh. 11 - Prob. 27RECh. 11 - Finding the Projection of u onto v In Exercises 27...Ch. 11 - Prob. 29RECh. 11 - Prob. 30RECh. 11 - Prob. 31RECh. 11 - Prob. 32RECh. 11 - Finding a Unit VectorFind a unit vector that is...Ch. 11 - AreaFind the area of the parallelogram that has...Ch. 11 - Prob. 35RECh. 11 - VolumeUse the triple scalar product to find the...Ch. 11 - Finding Parametric and Symmetric Equations In...Ch. 11 - Prob. 38RECh. 11 - Prob. 39RECh. 11 - Prob. 40RECh. 11 - Prob. 41RECh. 11 - Prob. 42RECh. 11 - Finding an Equation of a Plane In Exercises 41-44,...Ch. 11 - Prob. 44RECh. 11 - Prob. 45RECh. 11 - Prob. 46RECh. 11 - Distance Find the distance between the planes...Ch. 11 - Distance Find the distance between the point...Ch. 11 - Prob. 49RECh. 11 - Prob. 50RECh. 11 - Prob. 51RECh. 11 - Prob. 52RECh. 11 - Prob. 53RECh. 11 - Prob. 54RECh. 11 - Prob. 55RECh. 11 - Prob. 56RECh. 11 - Prob. 57RECh. 11 - Prob. 58RECh. 11 - Prob. 59RECh. 11 - Prob. 60RECh. 11 - Prob. 61RECh. 11 - Prob. 62RECh. 11 - Prob. 63RECh. 11 - Cylindrical-to-Rectangular ConversionIn Exercises...Ch. 11 - Prob. 65RECh. 11 - Spherical-to-Rectangular ConversionIn Exercises 65...Ch. 11 - Converting a Rectangular EquationIn Exercises 67...Ch. 11 - Prob. 68RECh. 11 - Cylindrical-to-Rectangular Conversion In Exercises...Ch. 11 - Cylindrical-to- Rectangular ConversionIn Exercises...Ch. 11 - Prob. 71RECh. 11 - Spherical-to-Rectangular Conversion In Exercises...Ch. 11 - ProofUsing vectors, prove the Law of Sines: If a,...Ch. 11 - Prob. 2PSCh. 11 - Prob. 3PSCh. 11 - Proof Using vectors, prove that the diagonals of a...Ch. 11 - Distance (a) Find the shortest distance between...Ch. 11 - Prob. 6PSCh. 11 - Volume (a) Find the volume of the solid bounded...Ch. 11 - Prob. 8PSCh. 11 - Prob. 9PSCh. 11 - Prob. 10PSCh. 11 - Prob. 11PSCh. 11 - Prob. 12PSCh. 11 - Prob. 13PSCh. 11 - Prob. 14PSCh. 11 - Prob. 15PSCh. 11 - Prob. 16PSCh. 11 - Distance Between a Point and a PlaneConsider the...Ch. 11 - Prob. 18PSCh. 11 - Prob. 19PS
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- 3.9 (A/B). A beam ABCDE, with A on the left, is 7 m long and is simply supported at Band E. The lengths of the various portions are AB 1-5m, BC = 1-5m, CD = 1 m and DE : 3 m. There is a uniformly distributed load of 15kN/m between B and a point 2m to the right of B and concentrated loads of 20 KN act at 4 and 0 with one of 50 KN at C. (a) Draw the S.F. diagrams and hence determine the position from A at which the S.F. is zero. (b) Determine the value of the B.M. at this point. (c) Sketch the B.M. diagram approximately to scale, quoting the principal values. [3.32 m, 69.8 KNm, 0, 30, 69.1, 68.1, 0 kNm.]arrow_forward4. Verify that V X (aẢ) = (Va) XẢ + aV X Ả where Ả = xyz(x + y + 2) A and a = 3xy + 4zx by carrying out the detailed differentiations.arrow_forward3. For each of the arrow or quiver graphs shown below, determine analytically V°C and V X Č. From these analytical solutions, identify the extrema (+/-) and plot these points on the arrow graph. (a) C = −✰CosxSiny + ŷSinxCosy -π<ׂу<π Ty (b) C = −xSin2y + ŷCos2y x, y<π -π< (c) C = −xCosx + ŷSiny -π< x, y < πarrow_forward
- 7.10 (B/C). A circular flat plate of diameter 305 mm and thickness 6.35 mm is clamped at the edges and subjected to a Uniform lateral pressure of 345 kN/m². Evaluate: (a) the central deflection, (b) the position and magnitude of the maximum radial stress. C6.1 x 10 m; 149.2 MN/m².] 100 200arrow_forward3.15 (B). A beam ABCD is simply supported at B and C with ABCD=2m; BC 4 m. It carries a point load of 60 KN at the free end A, a Uniformly distributed load of 60 KN/m between B and C and an anticlockwise moment of 80 KN m in the plane of the beam applied at the free end D. Sketch and dimension the S.F. and B.M. diagrams, and determine the position and magnitude of the maximum bending moment. CEL.E.] CS.F. 60, 170, 70KN, B.M. 120, +120.1, +80 kNm, 120.1 kNm at 2.83 m to right of 8.7arrow_forward7.1 (A/B). A Uniform I-section beam has flanges 150 mm wide by 8 mm thick and a web 180 mm wide and 8 mm thick. At a certain section there is a shearing force of 120 KN. Draw a diagram to illustrate the distribution of shear stress across the section as a result of bending. What is the maximum shear stress? [86.7 MN/m².arrow_forward
- 1. Let Ả = −2x + 3y+42, B = - - 7x +lý +22, and C = −1x + 2y + 42. Find (a) Ả X B (b) ẢX B°C c) →→ Ả B X C d) ẢB°C e) ẢX B XC.arrow_forward3.13 (B). A beam ABC, 6 m long, is simply-supported at the left-hand end A and at B I'm from the right-hand end C. The beam is of weight 100 N/metre run. (a) Determine the reactions at A and B. (b) Construct to scales of 20 mm = 1 m and 20 mm = 100 N, the shearing-force diagram for the beam, indicating thereon the principal values. (c) Determine the magnitude and position of the maximum bending moment. (You may, if you so wish, deduce the answers from the shearing force diagram without constructing a full or partial bending-moment diagram.) [C.G.] C240 N, 360 N, 288 Nm, 2.4 m from A.]arrow_forward5. Using parentheses make sense of the expression V · VXVV · Å where Ả = Ã(x, y, z). Is the result a vector or a scaler?arrow_forward
- 3.10 (A/B). A beam ABCDE is simply supported at A and D. It carries the following loading: a distributed load of 30 kN/m between A and B, a concentrated load of 20 KN at B, a concentrated load of 20 KN at C, a concentrated load of 10 KN at E; a distributed load of 60 kN/m between 0 and E. Span AB = 1.5 BC = CD = DE 1 m. Calculate the value of the reactions at A and D and hence draw the S.F. and B.M. diagrams. What are the magnitude and position of the maximum B.M. on the beam? [41.1, 113.9 KN, 28.15 kNm; 1.37 m from A.J m,arrow_forward3.14 (B). A beam ABCD, 6 m long, is simply-supported at the right-hand end and at a point B Im from the left-hand end A. It carries a vertical load of 10 KN at A, a second concentrated load of 20 KN at C, 3 m from D, and a uniformly distributed load of 10 kN/m between C and D. Determine: (a) the values of the reactions at B and 0, (6) the position and magnitude of the maximum bending moment. [33 KN, 27 KN, 2.7 m from D, 36.45k Nm.]arrow_forward3.17 (B). A simply supported beam has a span of 6 m and carries a distributed load which varies in a linea manner from 30 kN/m at one support to 90 kN/m at the other support. Locate the point of maximum bendin moment and calculate the value of this maximum. Sketch the S.F. and B.M. diagrams. [U.L.] [3.25 m from l.h. end; 272 KN m 30. 90arrow_forward
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