P Preliminary Concepts 1 Line And Angle Relationships 2 Parallel Lines 3 Triangles 4 Quadrilaterals 5 Similar Triangles 6 Circles 7 Locus And Concurrence 8 Areas Of Polygons And Circles 9 Surfaces And Solids 10 Analytic Geometry 11 Introduction To Trigonometry A Appendix Chapter10: Analytic Geometry
10.1 The Rectangular Coordinate System 10.2 Graphs Of Linear Equations And Slope 10.3 Preparing To Do Analytic Proofs 10.4 Analytic Proofs 10.5 Equations Of Lines 10.6 The Three-dimensional Coordinate System 10.CR Review Exercises 10.CT Test Section10.1: The Rectangular Coordinate System
Problem 1E: Plot and then label the points A0,-3, B3,-4, C5, 6, D-2,-5, and E-3, 5. Problem 2E: Give the coordinates of each point A, B, C, D, and E. Also name the quadrant in which each point... Problem 3E: Find the distance between each pair of points: a 5,-3 and 5, 1 c 0, 2 and 0,-3 b -3, 4 and 5, 4 d... Problem 4E: If the distance between -2, 3 and -2,a is 5 units, find all possible values of a. Problem 5E: If the distance between b,3 and 7, 3 is 3.5 units, find all possible values of b. Problem 6E Problem 7E: Find the distance between each pair of points: a 0,-3 and 4, 0 c 3, 2 and 5,-2 b -2, 5 and 4,-3 d... Problem 8E: Find the distance between each pair of points: a -3,-7 and 2, 5 c -a,-b and a,b b 0, 0 and -2, 6 d... Problem 9E: Find the midpoint of the line segment that joins each pair of points: a 0,-3 and 4, 0 c 3, 2 and... Problem 10E Problem 11E: Points A and B have symmetry with respect to the origin O. Find the coordinates of B if A is the... Problem 12E: Points A and B have symmetry with respect to point C 2,3. Find the coordinates of B if A is the... Problem 13E: Points A and B have symmetry with respect to point C. Find the coordinates of C given the point: a A... Problem 14E: Points A and B have symmetry with respect to the x-axis. Find the coordinates of B if A is the... Problem 15E Problem 16E: Points A and B have symmetry with respect to the vertical line where x=2. Find the coordinates of A... Problem 17E: Points A and B have symmetry with respect to the y-axis. Find the coordinates of A if B is the... Problem 18E Problem 19E: Points A and B have symmetry with respect to a vertical line x=a or a horizontal line y=b. Give an... Problem 20E: In Exercises 20 to 22, apply the Midpoint Formula. M 3,-4is the midpoint of AB-, in which A is the... Problem 21E Problem 22E Problem 23E: A rectangle ABCD has three of its vertices at A2,-1,B6,-1, and C6,3. Find the fourth vertex and the... Problem 24E: A rectangle MNPQ has three of its vertices at M0, 0,Na,0, and Q0,b. Find the fourth vertex P and the... Problem 25E: Use the Distance Formula to determine the type of triangle that has these vertices: a A0, 0,B4,0,... Problem 26E: Use the method of Example 4 to find the equation of the line that describes all points equidistant... Problem 27E: Use the method of Example 4 to find the equation of the line that describes all points equidistant... Problem 28E: For coplanar points A,B, and C, suppose that you have used the Distance Formula to show that... Problem 29E Problem 30E Problem 31E Problem 32E: There are two points on the x-axis that are located a distance of 6 units from the points 3,1.... Problem 33E: The triangle that has vertices at M-4,0,N3,-1,andQ2,4 has been boxed in, as shown. Find the area of... Problem 34E: Use the boxing method as suggested in Exercise 33, to find the area RST, with R-2,4,S-1,-2,andT6,5.... Problem 35E: Determine the area of ABC if A=2,1,B=5,3,andC is the reflection of the B across the x-axis. Problem 36E: Find the area of ABC In Exercise 35, but assume that C is the reflection of B across the y-axis. Problem 37E: Find the exact volume of the solid that results when the triangular region with vertices at 0, 0, 5,... Problem 38E: Find the exact volume of the solid that results when the triangular region with vertices at 0, 0, 6,... Problem 39E: Find the exact volume of the solid that results when the rectangular region with vertices at 0, 0,... Problem 40E: Find the exact volume of the solid that results when the region bounded in quadrant I by the axes... Problem 41E: Find the exact lateral area of each solid in Exercise 40. Find the exact volume of the solid formed... Problem 42E: Find the volume of the solid formed when the triangular region having vertices at 2, 0, 4, 0, and 2,... Problem 43E: By definition, an ellipse is the locus of points whose sum of distances from two fixed points F1 and... Problem 44E: By definition, a hyperbola is the locus of points whose positive difference of distances from two... Problem 45E Problem 46E: Use the Distance Formula to show that the equation of the parabola with focus F0,2 and directrix... Problem 47E: Following a 90 counterclockwise rotation about the origin, the image of A3, 1 is point B-1, 3. What... Problem 48E: Consider the point Ca,b. What is the image of C after a counterclockwise rotation of a 90 about the... Problem 49E Problem 50E: The graphs of the parabolas eith equations y=x2 and the line y=18-x2 intersect at two points. Find... Problem 51E Problem 36E: Find the area of ABC In Exercise 35, but assume that C is the reflection of B across the y-axis.
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12.Vector analysis (calculus 4)
Transcribed Image Text: Find the center of mass of an object that occupies
the upper hemisphere of x2 + y² + z² = 1
and has density x2 + y2
Select one:
a. (0,0,5/8)
b. (0,0,1/8)
c. Non of them
d. (0,0,3/8)
e. (0,0,7/8)
Calculus that deals with differentiation and integration of the vector field in three-dimensional Euclidean space. It deals with quantities that have both magnitude and direction.
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