- 11-3.Q1: What is the volume of a cone inscribed in a 6-cm3 cylinder?
- 11-3.Q2: What is the volume of a paraboloid inscribed in a 6-cm3 cylinder?
- 11-3.Q3: Sketch the graph: y = sin x
- 11-3.Q4: Sketch the graph: y = ln x
- 11-3.Q5: Sketch the graph: y = 2x
- 11-3.Q6: Sketch the graph: y = x2
- 11-3.Q7: Density = (?)/(?)
- 11-3.Q8: Work = (?)(?)
- 11-3.Q9: If y = sin1 x, then = ?.
- 11-3.Q10: y varies linearly with x. If x = 0, y = 12 and if x = 2, y = 20. If...
- 11-3.1: The region bounded by the graph of y = ln x, the x-axis, and the li...
- 11-3.2: The region bounded by the graph of y = sin x and the x-axis, betwee...
- 11-3.3: The region under the graph of y = 9 x2 is rotated about the y-axis ...
- 11-3.4: The region bounded by the graphs of y = and y = 0.5x is rotated abo...
- 11-3.5: Two Cone Problem: Two cones have the same sizebase radius 3 in. and...
- 11-3.6: Two Cylinder Problem: Two cylinders have the same shape3-in. radius...
- 11-3.7: The region bounded by the graphs of y = 4 2x2, y = 3 x2, and x = 0 ...
- 11-3.8: The region in (Figure 11-3f) is rotated about the y-axis to form a ...
- 11-3.9: Uranium Fuel Pellet Problem: Uranium oxide is used as a fuel in nuc...
- 11-3.10: The triangular region in the first quadrant,bounded by the graphs o...
- 11-3.11: Find the mass of a sphere of radius r if a. The density varies dire...
- 11-3.12: Mass of Earth Problem: The density of Earth is about 12 g/cm3 at it...
- 11-3.13: The region under the graph of y = ex from x = 0 to x = /2 is rotate...
- 11-3.14: Buckminsters Elliptical Dome Problem: Architect Buckminster Fuller ...
Solutions for Chapter 11-3: Mass of a Variable-Density Object
Full solutions for Calculus: Concepts and Applications | 2nd Edition
Boxplot (or box-and-whisker plot)
A graph that displays a five-number summary
See Compounded k times per year.
Variable representing the domain value of a function (usually x).
The difference between the third quartile and the first quartile.
Law of cosines
a2 = b2 + c2 - 2bc cos A, b2 = a2 + c2 - 2ac cos B, c2 = a2 + b2 - 2ab cos C
Linear factorization theorem
A polynomial ƒ(x) of degree n > 0 has the factorization ƒ(x) = a(x1 - z1) 1x - i z 22 Á 1x - z n where the z1 are the zeros of ƒ
Linear programming problem
A method of solving certain problems involving maximizing or minimizing a function of two variables (called an objective function) subject to restrictions (called constraints)
See Absolute value of a complex number.
An interval that does not include its endpoints.
Data items more than 1.5 times the IQR below the first quartile or above the third quartile.
Power rule of logarithms
logb Rc = c logb R, R 7 0.
A function that can be written in the form ƒ(x) = ax 2 + bx + c, where a, b, and c are real numbers, and a ? 0.
Rational zeros theorem
A procedure for finding the possible rational zeros of a polynomial.
Reflection through the origin
x, y and (-x,-y) are reflections of each other through the origin.
A triangle with a 90° angle.
symmetric about the x-axis
A graph in which (x, -y) is on the graph whenever (x, y) is; or a graph in which (r, -?) or (-r, ?, -?) is on the graph whenever (r, ?) is
A function that maps real numbers to real numbers.
The product of a force applied to an object over a given distance W = ƒFƒ ƒAB!ƒ.
Zero factor property
If ab = 0 , then either a = 0 or b = 0.