- 11-4.Q1: Evaluate x2 if x is 5.
- 11-4.Q2: Evaluate x2 if x is 11.
- 11-4.Q3: Write sin 2x in terms of functions of x.
- 11-4.Q4: Write cos2 x in terms of cos 2x.
- 11-4.Q5: Resolve into partial fractions: 1/[(x 2)(x 5)]
- 11-4.Q6: Integrate: dx/[(x 2)(x 5)]
- 11-4.Q7: Differentiate: y = 1 / [(x 2)(x 5)]
- 11-4.Q8: Write the definition of indefinite integral.
- 11-4.Q9: Is f(x) = x3 7x increasing or decreasing at x = 2?
- 11-4.Q10: Which of these hypotheses of Rolles theorem is not a hypothesis of ...
- 11-4.1: Paraboloid Problem: The region in Quadrant I under the graph of y =...
- 11-4.2: Ellipsoid Problem: A half-ellipsoid (Figure 11-4g) is formed by rot...
- 11-4.3: Paraboloid Mass Problem: The paraboloid in has density, in grams pe...
- 11-4.4: Ellipsoid Mass Problem: The half-ellipsoid in has a weight density,...
- 11-4.5: Exponential Region and Solid Problem: Let R be the region under the...
- 11-4.6: Secant Curve Region Problem: Let R be the region under the graph of...
- 11-4.7: Centroid of a Triangle Experiment: Prove that the centroid of a tri...
- 11-4.8: Centroid Cut-Out Experiment: Let R be the region under the graph of...
- 11-4.9: Second Moment of Area Problem: Let R be the region under the graph ...
- 11-4.10: Second Moments for Plane Regions Problem: Find the second moment of...
- 11-4.11: Second Moments for Solid Figures: Find the second moment of volume ...
- 11-4.12: Rotation of Solids Problem: You can measure the amount of resistanc...
- 11-4.13: Beam Moment Problem: The stiffness of a beam is directly proportion...
- 11-4.14: Introduction to the Theorem of Pappus: The region R under the graph...
- 11-4.15: Theorem of Pappus Problem: Pappus was a Greek mathematician who liv...
- 11-4.16: Theorem of Pappus Proof: Prove the theorem of Pappus for volumes.
Solutions for Chapter 11-4: Moments, Centroids, Center of Mass,and the Theorem of Pappus
Full solutions for Calculus: Concepts and Applications | 2nd Edition
Solutions for Chapter 11-4: Moments, Centroids, Center of Mass,and the Theorem of PappusGet Full Solutions
A triangle in which all angles measure less than 90°
Addition property of equality
If u = v and w = z , then u + w = v + z
Additive identity for the complex numbers
0 + 0i is the complex number zero
A combination of variables and constants involving addition, subtraction, multiplication, division, powers, and roots
Arc length formula
The length of an arc in a circle of radius r intercepted by a central angle of u radians is s = r u.
An experiment in which subjects do not know if they have been given an active treatment or a placebo
Graph of a relation
The set of all points in the coordinate plane corresponding to the ordered pairs of the relation.
Graph of an equation in x and y
The set of all points in the coordinate plane corresponding to the pairs x, y that are solutions of the equation.
Irreducible quadratic over the reals
A quadratic polynomial with real coefficients that cannot be factored using real coefficients.
Law of sines
sin A a = sin B b = sin C c
A graph of a polar equation of the form r2 = a2 sin 2u or r 2 = a2 cos 2u.
Mode of a data set
The category or number that occurs most frequently in the set.
A logarithm with base e.
In an experimental study, an inactive treatment that is equivalent to the active treatment in every respect except for the factor about which an inference is to be made. Subjects in a blind experiment do not know if they have been given the active treatment or the placebo.
Principal nth root
If bn = a, then b is an nth root of a. If bn = a and a and b have the same sign, b is the principal nth root of a (see Radical), p. 508.
Theorem In a right triangle with sides a and b and hypotenuse c, c2 = a2 + b2
For an angle ? in standard position, a reference triangle is a triangle formed by the terminal side of angle ?, the x-axis, and a perpendicular dropped from a point on the terminal side to the x-axis. The angle in a reference triangle at the origin is the reference angle
Stemplot (or stem-and-leaf plot)
An arrangement of a numerical data set into a specific tabular format.
A special form for a system of linear equations that facilitates finding the solution.
The line x = a is a vertical asymptote of the graph of the function ƒ if limx:a+ ƒ1x2 = q or lim x:a- ƒ1x2 = q.