Explanation To draw a diagram from the given data which is shown in fig.1. Figure 1 Let height h , Slant height s and Radius r of the Cone. Using Pythagoras Theorem, ( s ) 2 = ( r ) 2 + ( h ) 2 Substituting, s = 4 in ( s ) 2 = ( r ) 2 + ( h ) 2 ( s ) 2 = ( r ) 2 + ( h ) 2 ( 4 ) 2 = ( r ) 2 + ( h ) 2 16 = r 2 + h 2 Solving for h , 16 = r 2 + h 2 h 2 = 16 − r 2 h = 16 − r 2 The volume of Cone is: V = 1 3 π r 2 h Substitute, h = 16 − r 2 , in V = 1 3 π r 2 h . V = 1 3 π r 2 h V = 1 3 π r 2 ( 16 − r 2 ) Differentiate V with respect to r . d V d r = d d r [ 1 3 π r 2 ( 16 − r 2 ) ] = 1 3 π r 2 ( 16 − r 2 ) = 1 3 π [ 2 r ( 16 − r 2 ) + r 2 ( − 2 r ) 2 16 − r 2 ] = 1 3 π [ 2 r ( 16 − r 2 ) − r 3 16 − r 2

Basic Technical Mathematics with Calculus (11th Edition)

11th Edition

ISBN: 9780134437736

Author: Allyn J. Washington, Richard Evans

Publisher: PEARSON

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Cylinders

A cylinder is a three-dimensional solid shape with two parallel and congruent circular bases, joined by a curved surface at a fixed distance. A cylinder has an infinite curvilinear surface.

Cones

A cone is a three-dimensional solid shape having a flat base and a pointed edge at the top. The flat base of the cone tapers smoothly to form the pointed edge known as the apex. The flat base of the cone can either be circular or elliptical. A cone is dr…

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Chapter 24.7, Problem 28E

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The maximum volume of liquid that the funnel will be able to hold by using the given data.

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Chapter 24.7, Problem 27E

Chapter 24.7, Problem 29E

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(b) Prove that if ACBC (A), then (A)=(B).

4. (a) Define the a-field generated by a class A of subsets of 2.

Chapter 24 Solutions

Basic Technical Mathematics with Calculus (11th Edition)

Ch. 24.1 - For the parabola y = 4 − x2, at the point (3, −5)...Ch. 24.1 - Prob. 2PE Ch. 24.1 - Prob. 1E Ch. 24.1 - Prob. 2E Ch. 24.1 - Prob. 3E Ch. 24.1 - Prob. 4E Ch. 24.1 - Prob. 5E Ch. 24.1 - Prob. 6E Ch. 24.1 - Prob. 7E Ch. 24.1 - Prob. 8E

Ch. 24.1 - Prob. 9E Ch. 24.1 - Prob. 10E Ch. 24.1 - Prob. 11E Ch. 24.1 - Prob. 12E Ch. 24.1 - In Exercises 11–14, find the equations of the...Ch. 24.1 - Prob. 14E Ch. 24.1 - Prob. 15E Ch. 24.1 - Prob. 16E Ch. 24.1 - Prob. 17E Ch. 24.1 - Prob. 18E Ch. 24.1 - Prob. 19E Ch. 24.1 - Prob. 20E Ch. 24.1 - Prob. 21E Ch. 24.1 - Where does the normal line to the parabola y = x —...Ch. 24.1 - Prob. 23E Ch. 24.1 - Prob. 24E Ch. 24.1 - A certain suspension cable with supports on the...Ch. 24.1 - Prob. 26E Ch. 24.1 - Prob. 27E Ch. 24.1 - Prob. 28E Ch. 24.1 - Prob. 29E Ch. 24.1 - Prob. 30E Ch. 24.2 - In Example 1, let x1 = 0.3, and find x2. EXAMPLE...Ch. 24.2 - Prob. 1E Ch. 24.2 - Prob. 2E Ch. 24.2 - Prob. 3E Ch. 24.2 - Prob. 4E Ch. 24.2 - Prob. 5E Ch. 24.2 - Prob. 6E Ch. 24.2 - Prob. 7E Ch. 24.2 - Prob. 8E Ch. 24.2 - Prob. 9E Ch. 24.2 - Prob. 10E Ch. 24.2 - Prob. 11E Ch. 24.2 - Prob. 12E Ch. 24.2 - Prob. 13E Ch. 24.2 - Prob. 14E Ch. 24.2 - Prob. 15E Ch. 24.2 - Prob. 16E Ch. 24.2 - Prob. 17E Ch. 24.2 - Prob. 18E Ch. 24.2 - Prob. 19E Ch. 24.2 - Prob. 20E Ch. 24.2 - Prob. 21E Ch. 24.2 - Prob. 23E Ch. 24.2 - Prob. 24E Ch. 24.2 - Prob. 25E Ch. 24.2 - Prob. 27E Ch. 24.2 - Prob. 28E Ch. 24.2 - Prob. 29E Ch. 24.2 - Prob. 30E Ch. 24.3 - Prob. 1PE Ch. 24.3 - Prob. 1E Ch. 24.3 - Prob. 2E Ch. 24.3 - Prob. 3E Ch. 24.3 - Prob. 4E Ch. 24.3 - Prob. 5E Ch. 24.3 - Prob. 6E Ch. 24.3 - Prob. 7E Ch. 24.3 - Prob. 8E Ch. 24.3 - Prob. 9E Ch. 24.3 - Prob. 10E Ch. 24.3 - Prob. 11E Ch. 24.3 - Prob. 12E Ch. 24.3 - Prob. 13E Ch. 24.3 - Prob. 14E Ch. 24.3 - Prob. 15E Ch. 24.3 - Prob. 16E Ch. 24.3 - In Exercises 11–30, find the indicated velocities...Ch. 24.3 - 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Prob. 20E Ch. 24.4 - Prob. 21E Ch. 24.4 - Prob. 22E Ch. 24.4 - Prob. 23E Ch. 24.4 - Prob. 24E Ch. 24.4 - Prob. 25E Ch. 24.4 - Prob. 26E Ch. 24.4 - Prob. 27E Ch. 24.4 - In Exercises 7–42, solve the problems in related...Ch. 24.4 - In Exercises 7–42, solve the problems in related...Ch. 24.4 - In Exercises 7–42, solve the problems in related...Ch. 24.4 - Prob. 31E Ch. 24.4 - Prob. 32E Ch. 24.4 - Prob. 33E Ch. 24.4 - Prob. 34E Ch. 24.4 - Prob. 35E Ch. 24.4 - Prob. 36E Ch. 24.4 - In Exercises 7–42, solve the problems in related...Ch. 24.4 - Prob. 38E Ch. 24.4 - Prob. 39E Ch. 24.4 - Prob. 40E Ch. 24.4 - Prob. 41E Ch. 24.4 - Prob. 42E Ch. 24.5 - Prob. 1PE Ch. 24.5 - Prob. 2PE Ch. 24.5 - Prob. 1E Ch. 24.5 - Prob. 2E Ch. 24.5 - Prob. 3E Ch. 24.5 - Prob. 4E Ch. 24.5 - Prob. 5E Ch. 24.5 - Prob. 6E Ch. 24.5 - Prob. 7E Ch. 24.5 - Prob. 8E Ch. 24.5 - Prob. 9E Ch. 24.5 - Prob. 10E Ch. 24.5 - Prob. 11E Ch. 24.5 - Prob. 12E Ch. 24.5 - Prob. 13E Ch. 24.5 - Prob. 14E Ch. 24.5 - Prob. 15E Ch. 24.5 - Prob. 16E Ch. 24.5 - 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A microprocessor chip is being designed with a...Ch. 24.7 - Prob. 18E Ch. 24.7 - What are the dimensions of the largest rectangular...Ch. 24.7 - A rectangular storage area is to be constructed...Ch. 24.7 - Prob. 21E Ch. 24.7 - Prob. 22E Ch. 24.7 - Prob. 23E Ch. 24.7 - Prob. 24E Ch. 24.7 - Prob. 25E Ch. 24.7 - Prob. 26E Ch. 24.7 - Prob. 27E Ch. 24.7 - Prob. 28E Ch. 24.7 - Prob. 29E Ch. 24.7 - Prob. 30E Ch. 24.7 - Prob. 31E Ch. 24.7 - Prob. 32E Ch. 24.7 - Prob. 33E Ch. 24.7 - What is the minimum slope of the curve y = x5 −...Ch. 24.7 - Prob. 35E Ch. 24.7 - Prob. 36E Ch. 24.7 - Prob. 37E Ch. 24.7 - Prob. 38E Ch. 24.7 - Prob. 39E Ch. 24.7 - Prob. 40E Ch. 24.7 - Prob. 41E Ch. 24.7 - Computer simulation shows that the drag F (in N)...Ch. 24.7 - Prob. 43E Ch. 24.7 - The potential energy E of an electric charge q due...Ch. 24.7 - An open box is to be made from a square piece of...Ch. 24.7 - Prob. 46E Ch. 24.7 - Prob. 47E Ch. 24.7 - Prob. 48E Ch. 24.7 - An oil pipeline is to be built from a refinery to...Ch. 24.7 - 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Prob. 43E Ch. 24.8 - Prob. 44E Ch. 24 - Prob. 1RE Ch. 24 - Prob. 2RE Ch. 24 - Prob. 3RE Ch. 24 - Prob. 4RE Ch. 24 - Prob. 5RE Ch. 24 - Prob. 6RE Ch. 24 - Prob. 7RE Ch. 24 - Prob. 8RE Ch. 24 - Prob. 9RE Ch. 24 - Prob. 10RE Ch. 24 - Prob. 11RE Ch. 24 - Prob. 12RE Ch. 24 - Prob. 13RE Ch. 24 - Prob. 14RE Ch. 24 - Prob. 15RE Ch. 24 - Prob. 16RE Ch. 24 - Prob. 17RE Ch. 24 - Prob. 18RE Ch. 24 - Prob. 19RE Ch. 24 - Prob. 20RE Ch. 24 - Prob. 21RE Ch. 24 - Prob. 22RE Ch. 24 - Prob. 23RE Ch. 24 - Prob. 24RE Ch. 24 - Prob. 25RE Ch. 24 - Prob. 26RE Ch. 24 - Prob. 27RE Ch. 24 - In Exercises 25–32, sketch the graphs of the given...Ch. 24 - Prob. 29RE Ch. 24 - Prob. 30RE Ch. 24 - Prob. 31RE Ch. 24 - Prob. 32RE Ch. 24 - Prob. 33RE Ch. 24 - Prob. 34RE Ch. 24 - Prob. 35RE Ch. 24 - Prob. 36RE Ch. 24 - Prob. 37RE Ch. 24 - Prob. 38RE Ch. 24 - Prob. 39RE Ch. 24 - Prob. 40RE Ch. 24 - Prob. 41RE Ch. 24 - Prob. 42RE Ch. 24 - Prob. 43RE Ch. 24 - Prob. 44RE Ch. 24 - Prob. 45RE Ch. 24 - Prob. 46RE Ch. 24 - Prob. 47RE Ch. 24 - Prob. 48RE Ch. 24 - Prob. 49RE Ch. 24 - Prob. 50RE Ch. 24 - Prob. 51RE Ch. 24 - Prob. 52RE Ch. 24 - In Exercises 49–94, solve the given problems. 53....Ch. 24 - Prob. 54RE Ch. 24 - Prob. 55RE Ch. 24 - Prob. 56RE Ch. 24 - The deflection y (in m) of a beam at a horizontal...Ch. 24 - Prob. 58RE Ch. 24 - Prob. 59RE Ch. 24 - Prob. 60RE Ch. 24 - Prob. 61RE Ch. 24 - Prob. 62RE Ch. 24 - In Fig. 24.75, the tension T supports the 40.0-N...Ch. 24 - Prob. 64RE Ch. 24 - Prob. 65RE Ch. 24 - Prob. 66RE Ch. 24 - An analysis of the power output P (in kW/m3) of a...Ch. 24 - The altitude h (in ft) of a certain rocket as a...Ch. 24 - Prob. 69RE Ch. 24 - Prob. 70RE Ch. 24 - Prob. 71RE Ch. 24 - Prob. 72RE Ch. 24 - Prob. 73RE Ch. 24 - A special insulation strip is to be sealed...Ch. 24 - Prob. 75RE Ch. 24 - Prob. 76RE Ch. 24 - Prob. 77RE Ch. 24 - Prob. 78RE Ch. 24 - Prob. 79RE Ch. 24 - Prob. 80RE Ch. 24 - Prob. 81RE Ch. 24 - Prob. 82RE Ch. 24 - Prob. 83RE Ch. 24 - Prob. 84RE Ch. 24 - Prob. 85RE Ch. 24 - Prob. 86RE Ch. 24 - 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