Mathematics: A Practical Odyssey
8th Edition
ISBN: 9781305104174
Author: David B. Johnson, Thomas A. Mowry
Publisher: Cengage Learning
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Chapter 8.2, Problem 39E
To determine
To find:
The surface area of cube in square units.
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2. Show that
8
xa
S
-dx
(b² + 12) dr = 2 cos(π2)
пра-1
a, b real and
-1 0
Your solution should clearly explain the closed contour you are using, and state clearly any
vanishing properties of integrals over contours that are being used. You are free to quote
from the lectures, the appropriate results on such vanishing properties, without deriving
these properties. Any residue calculations involved should be explained clearly.
Could you please answer this question using excel.Thanks
1. Calculate the integral
500
x sin x
(a² +x2)20
dx
by using the residue theorem. You may assume that a is real and a > 0. Your solution should
clearly explain the closed contour you are using, and state clearly any vanishing properties
of integrals over contours that are being used.
Chapter 8 Solutions
Mathematics: A Practical Odyssey
Ch. 8.1 - When necessary, round off answers to one decimal...Ch. 8.1 - When necessary, round off answers to one decimal...Ch. 8.1 - When necessary, round off answers to one decimal...Ch. 8.1 - Prob. 4ECh. 8.1 - When necessary, round off answers to one decimal...Ch. 8.1 - When necessary, round off answers to one decimal...Ch. 8.1 - When necessary, round off answers to one decimal...Ch. 8.1 - When necessary, round off answers to one decimal...Ch. 8.1 - In Exercise 9 and 10, find a the area and b the...Ch. 8.1 - Prob. 10E
Ch. 8.1 - Prob. 11ECh. 8.1 - In Exercises 1120, find (a) the area and (b) the...Ch. 8.1 - In Exercises 1120, find (a) the area and (b) the...Ch. 8.1 - In Exercises 1120 find(a) the area and (b) the...Ch. 8.1 - In Exercises 1120, find (a) the area and (b) the...Ch. 8.1 - In Exercises 1120, find (a) the area and (b) the...Ch. 8.1 - Prob. 17ECh. 8.1 - In Exercises 1120 find a the area and b the...Ch. 8.1 - In Exercises 1120 find a the area and b the...Ch. 8.1 - In Exercises 1120 find a the area and b the...Ch. 8.1 - In Exercises 21 and 22, find (a) the area and (b)...Ch. 8.1 - Prob. 22ECh. 8.1 - A circular swimming pool has diameter 50ft and is...Ch. 8.1 - A rectangular swimming pool 30feet by 15feet is...Ch. 8.1 - Prob. 25ECh. 8.1 - Prob. 26ECh. 8.1 - Prob. 27ECh. 8.1 - Prob. 28ECh. 8.1 - You jog 34 mile due north, then 112 miles due...Ch. 8.1 - You walk 100 yards due south, then 120 yards due...Ch. 8.1 - A 10-foot ladder leans against a wall. If the base...Ch. 8.1 - Prob. 32ECh. 8.1 - Prob. 33ECh. 8.1 - Prob. 34ECh. 8.1 - The length of the edges of a triangular canvas are...Ch. 8.1 - Jim Mulios wants to fertilize his backyard. The...Ch. 8.1 - Reddies Pizza Bash is famous for its Loads-o-Meat...Ch. 8.1 - Prob. 38ECh. 8.1 - Prob. 39ECh. 8.1 - Prob. 40ECh. 8.1 - Prob. 41ECh. 8.1 - In Exercise3944, use the following information: in...Ch. 8.1 - Prob. 43ECh. 8.1 - Prob. 44ECh. 8.1 - Prob. 45ECh. 8.1 - Prob. 46ECh. 8.1 - Prob. 47ECh. 8.1 - Prob. 48ECh. 8.1 - Prob. 49ECh. 8.1 - Prob. 50ECh. 8.1 - Prob. 51ECh. 8.1 - Prob. 52ECh. 8.1 - Prob. 53ECh. 8.1 - Prob. 54ECh. 8.1 - Prob. 55ECh. 8.1 - Prob. 56ECh. 8.1 - Prob. 57ECh. 8.1 - Prob. 58ECh. 8.1 - Prob. 59ECh. 8.2 - When necessary, round off answers to two decimal...Ch. 8.2 - When necessary, round off answers to two decimal...Ch. 8.2 - When necessary, round off answers to two decimal...Ch. 8.2 - When necessary, round off answers to two decimal...Ch. 8.2 - Prob. 5ECh. 8.2 - When necessary, round off answers to two decimal...Ch. 8.2 - Prob. 7ECh. 8.2 - In Exercises714, find the volume of each figure....Ch. 8.2 - In Exercises714, find the volume of each figure....Ch. 8.2 - In Exercises714, find the volume of each figure....Ch. 8.2 - In Exercises714, find the volume of each figure....Ch. 8.2 - In Exercises714, find the volume of each figure....Ch. 8.2 - Prob. 13ECh. 8.2 - Prob. 14ECh. 8.2 - From a 10-inch-by-16-inch piece of cardboard,...Ch. 8.2 - From a 24-inch-square piece of cardboard, square...Ch. 8.2 - A grain silo consists of a cylinder with a...Ch. 8.2 - A propane gas tank consists of a cylinder with a...Ch. 8.2 - A regulation baseball hardball has a circumference...Ch. 8.2 - A regulation tennis ball has a diameter of 212...Ch. 8.2 - The diameter of the earth is approximately 7, 920...Ch. 8.2 - The diameter of the earth is approximately 7, 920...Ch. 8.2 - Prob. 23ECh. 8.2 - Prob. 24ECh. 8.2 - In Exercises 25 and 26, use the following...Ch. 8.2 - Prob. 26ECh. 8.2 - Prob. 27ECh. 8.2 - Golf balls are packaged three to a rectangular...Ch. 8.2 - Prob. 29ECh. 8.2 - Marcus Robinson bought an older house and wants to...Ch. 8.2 - Prob. 31ECh. 8.2 - The student union at the University of Utopia U2...Ch. 8.2 - A water storage tank is an upside-down cone, as...Ch. 8.2 - The diameter of a conical paper cup is 3.5inches....Ch. 8.2 - Prob. 35ECh. 8.2 - Prob. 36ECh. 8.2 - Prob. 37ECh. 8.2 - Prob. 38ECh. 8.2 - Prob. 39ECh. 8.2 - Prob. 40ECh. 8.2 - Prob. 41ECh. 8.2 - Prob. 42ECh. 8.2 - Prob. 43ECh. 8.3 - In Exercises 1-4. determine whether each...Ch. 8.3 - Prob. 2ECh. 8.3 - Prob. 3ECh. 8.3 - Prob. 4ECh. 8.3 - Prob. 5ECh. 8.3 - Prob. 6ECh. 8.3 - Prob. 7ECh. 8.3 - Prob. 8ECh. 8.3 - Following the method of Problem 48 of the Rhind...Ch. 8.3 - Prob. 10ECh. 8.3 - Prob. 11ECh. 8.3 - Prob. 12ECh. 8.3 - Prob. 13ECh. 8.3 - Prob. 14ECh. 8.3 - Prob. 15ECh. 8.3 - Prob. 16ECh. 8.3 - Find the perimeter of a triangle having sides with...Ch. 8.3 - Prob. 18ECh. 8.3 - Prob. 19ECh. 8.3 - Prob. 20ECh. 8.3 - Prob. 21ECh. 8.3 - Prob. 22ECh. 8.3 - Prob. 23ECh. 8.3 - Prob. 24ECh. 8.3 - Problem 41 of the Rhind Papyrus pertains to...Ch. 8.3 - Prob. 26ECh. 8.3 - Prob. 27ECh. 8.3 - Prob. 28ECh. 8.3 - Prob. 29ECh. 8.3 - Prob. 30ECh. 8.4 - In Exercises 1-4, the given triangles are similar....Ch. 8.4 - In Exercises 1-4, the given triangles are similar....Ch. 8.4 - In Exercises 1-4, the given triangles are similar....Ch. 8.4 - In Exercises 1-4, the given triangles are similar....Ch. 8.4 - A 6-foot-tall man casts a shadow of 3.5 feet at...Ch. 8.4 - Prob. 6ECh. 8.4 - Prob. 7ECh. 8.4 - Use Figure 8.67 and the method of rearrangement to...Ch. 8.4 - Find the length of the longest object that will...Ch. 8.4 - Find the length of the longest object that will...Ch. 8.4 - Find the length of the longest object that will...Ch. 8.4 - Find the length of the longest object that will...Ch. 8.4 - Prob. 13ECh. 8.4 - Prob. 14ECh. 8.4 - In Exercises 1318, use the two column method to...Ch. 8.4 - Prob. 16ECh. 8.4 - Prob. 17ECh. 8.4 - Prob. 18ECh. 8.4 - Prob. 19ECh. 8.4 - Prob. 20ECh. 8.4 - Prob. 21ECh. 8.4 - Prob. 22ECh. 8.4 - If a sphere is inscribed in a cylinder, the...Ch. 8.4 - Prob. 24ECh. 8.4 - Prob. 25ECh. 8.4 - Prob. 26ECh. 8.4 - Prob. 27ECh. 8.4 - Prob. 28ECh. 8.4 - Prob. 29ECh. 8.4 - The purpose of this project is to calculate the...Ch. 8.4 - Prob. 31ECh. 8.4 - Prob. 32ECh. 8.5 - In Exercises 18, use trigonometric ratios to find...Ch. 8.5 - In Exercises 18, use trigonometric ratios to find...Ch. 8.5 - In Exercises 18, use trigonometric ratios to find...Ch. 8.5 - In Exercises 18, use trigonometric ratios to find...Ch. 8.5 - In Exercises 18, use trigonometric ratios to find...Ch. 8.5 - In Exercises 18, use trigonometric ratios to find...Ch. 8.5 - In Exercises 18, use trigonometric ratios to find...Ch. 8.5 - Prob. 8ECh. 8.5 - In Exercises 926. use the given information to...Ch. 8.5 - Prob. 10ECh. 8.5 - Prob. 11ECh. 8.5 - Prob. 12ECh. 8.5 - Prob. 13ECh. 8.5 - Prob. 14ECh. 8.5 - Prob. 15ECh. 8.5 - Prob. 16ECh. 8.5 - Prob. 17ECh. 8.5 - Prob. 18ECh. 8.5 - Prob. 19ECh. 8.5 - Prob. 20ECh. 8.5 - Prob. 21ECh. 8.5 - Prob. 22ECh. 8.5 - Prob. 23ECh. 8.5 - Prob. 24ECh. 8.5 - Prob. 25ECh. 8.5 - Prob. 26ECh. 8.5 - A cable runs from the top of a building to a point...Ch. 8.5 - A support cable runs from the top of a telephone...Ch. 8.5 - Prob. 29ECh. 8.5 - Prob. 30ECh. 8.5 - Prob. 31ECh. 8.5 - Prob. 32ECh. 8.5 - Prob. 33ECh. 8.5 - Prob. 34ECh. 8.5 - A billboard is on top of a building. You are 125.0...Ch. 8.5 - Prob. 36ECh. 8.5 - You are hiking along a river and see a tall tree...Ch. 8.5 - Prob. 38ECh. 8.5 - Prob. 39ECh. 8.5 - Prob. 40ECh. 8.5 - Prob. 41ECh. 8.5 - Prob. 42ECh. 8.5 - Prob. 43ECh. 8.5 - Two observers are 500feet apart. Each measures the...Ch. 8.5 - Prob. 45ECh. 8.5 - Prob. 46ECh. 8.5 - Prob. 47ECh. 8.5 - Prob. 48ECh. 8.5 - Prob. 49ECh. 8.5 - Prob. 50ECh. 8.5 - Prob. 51ECh. 8.5 - Prob. 52ECh. 8.5 - Prob. 53ECh. 8.6 - Prob. 1ECh. 8.6 - Prob. 2ECh. 8.6 - Prob. 3ECh. 8.6 - In Exercise 1-4, answer the following questions....Ch. 8.6 - Prob. 5ECh. 8.6 - Prob. 6ECh. 8.6 - Prob. 7ECh. 8.6 - Prob. 8ECh. 8.6 - Prob. 9ECh. 8.6 - Prob. 10ECh. 8.6 - In Exercises 11-20, answer the following...Ch. 8.6 - Prob. 12ECh. 8.6 - Prob. 13ECh. 8.6 - Prob. 14ECh. 8.6 - Prob. 15ECh. 8.6 - Prob. 16ECh. 8.6 - Prob. 17ECh. 8.6 - Prob. 18ECh. 8.6 - Prob. 19ECh. 8.6 - In Exercises 11-20, answer the following...Ch. 8.6 - Prob. 21ECh. 8.6 - Prob. 22ECh. 8.6 - Prob. 23ECh. 8.6 - Prob. 24ECh. 8.6 - Prob. 25ECh. 8.7 - Prob. 1ECh. 8.7 - Prob. 2ECh. 8.7 - Prob. 3ECh. 8.7 - Prob. 4ECh. 8.7 - Prob. 5ECh. 8.7 - Prob. 6ECh. 8.7 - Prob. 7ECh. 8.7 - Prob. 8ECh. 8.7 - Prob. 9ECh. 8.7 - Prob. 10ECh. 8.7 - Prob. 11ECh. 8.7 - Prob. 12ECh. 8.7 - Prob. 13ECh. 8.7 - A satellite dish antenna has a parabolic reflector...Ch. 8.7 - Prob. 15ECh. 8.7 - Prob. 16ECh. 8.7 - Prob. 17ECh. 8.7 - In Exercises 17-24, sketch the graph and find the...Ch. 8.7 - Prob. 19ECh. 8.7 - Prob. 20ECh. 8.7 - Prob. 21ECh. 8.7 - Prob. 22ECh. 8.7 - Prob. 23ECh. 8.7 - Prob. 24ECh. 8.7 - Prob. 25ECh. 8.7 - Prob. 26ECh. 8.7 - Prob. 27ECh. 8.7 - Prob. 28ECh. 8.7 - Prob. 29ECh. 8.7 - In Exercises 29-36, sketch the graph and find the...Ch. 8.7 - Prob. 31ECh. 8.7 - Prob. 32ECh. 8.7 - Prob. 33ECh. 8.7 - Prob. 34ECh. 8.7 - Prob. 35ECh. 8.7 - Prob. 36ECh. 8.7 - Prob. 37ECh. 8.7 - Prob. 38ECh. 8.8 - Prob. 1ECh. 8.8 - Prob. 2ECh. 8.8 - Prob. 3ECh. 8.8 - Prob. 4ECh. 8.8 - Prob. 5ECh. 8.8 - Prob. 6ECh. 8.8 - Prob. 7ECh. 8.8 - Prob. 8ECh. 8.8 - In Exercises 7-12, answer the questions for the...Ch. 8.8 - Prob. 10ECh. 8.8 - Prob. 11ECh. 8.8 - Prob. 12ECh. 8.8 - Prob. 13ECh. 8.8 - Prob. 14ECh. 8.8 - Prob. 15ECh. 8.8 - Prob. 16ECh. 8.8 - Prob. 17ECh. 8.8 - Prob. 18ECh. 8.8 - Prob. 19ECh. 8.8 - What was the scandal of elementary geometry?Ch. 8.8 - Prob. 21ECh. 8.8 - Who was the first mathematician to affirm the...Ch. 8.8 - Prob. 23ECh. 8.8 - Prob. 24ECh. 8.8 - Prob. 25ECh. 8.8 - Prob. 26ECh. 8.8 - Prob. 27ECh. 8.9 - HANDS ON The Sierpinski gasket Using a...Ch. 8.9 - The Sierpinski carpet. The Sierpinski carpet is...Ch. 8.9 - The Mitsubishi gasket. Carefully and accurately...Ch. 8.9 - The square snowflake. Carefully and accurately...Ch. 8.9 - Prob. 5ECh. 8.9 - Prob. 6ECh. 8.9 - Prob. 7ECh. 8.9 - Prob. 8ECh. 8.9 - Prob. 9ECh. 8.9 - Find the approximate dimension of the Sierpinski...Ch. 8.9 - Find the approximate dimension of the Mitsubishi...Ch. 8.9 - Prob. 12ECh. 8.9 - Find the approximate dimension of the square...Ch. 8.9 - Prob. 14ECh. 8.9 - Prob. 15ECh. 8.9 - Prob. 16ECh. 8.9 - Prob. 17ECh. 8.9 - Prob. 18ECh. 8.9 - Prob. 19ECh. 8.9 - Prob. 20ECh. 8.9 - Prob. 21ECh. 8.9 - 22. Describe the self-similarity of the given...Ch. 8.9 - Prob. 23ECh. 8.9 - Prob. 24ECh. 8.9 - Prob. 25ECh. 8.9 - Name three naturally occurring objects other than...Ch. 8.9 - Prob. 27ECh. 8.9 - Prob. 28ECh. 8.9 - Prob. 29ECh. 8.9 - Prob. 30ECh. 8.9 - Prob. 31ECh. 8.9 - Prob. 32ECh. 8.9 - Prob. 33ECh. 8.9 - Prob. 35ECh. 8.9 - Prob. 36ECh. 8.10 - Prob. 1ECh. 8.10 - Prob. 2ECh. 8.10 - Finding the perimeter of a Sierpinski carpet. See...Ch. 8.10 - Finding the area of a Sierpinski carpet. See...Ch. 8.10 - Prob. 5ECh. 8.10 - A square snowflake. See Exercise 4 in Section 8.9...Ch. 8.10 - Prob. 7ECh. 8.10 - Prob. 8ECh. 8.10 - Describe an application of fractal area,...Ch. 8.10 - Design your own fractal. Discuss its...Ch. 8.CR - Prob. 1CRCh. 8.CR - Prob. 2CRCh. 8.CR - Prob. 3CRCh. 8.CR - Prob. 4CRCh. 8.CR - Prob. 5CRCh. 8.CR - Saturn the ringed planet revolves around the sun...Ch. 8.CR - Prob. 7CRCh. 8.CR - Prob. 8CRCh. 8.CR - Prob. 9CRCh. 8.CR - Prob. 10CRCh. 8.CR - Find the volume and surface area of Figure 8.194.Ch. 8.CR - Prob. 12CRCh. 8.CR - Prob. 13CRCh. 8.CR - An oval athletic field is the combination of a...Ch. 8.CR - From a 12inch-by-18inch piece of cardboard,...Ch. 8.CR - A regulation baseball hardball has a circumference...Ch. 8.CR - Prob. 17CRCh. 8.CR - Prob. 18CRCh. 8.CR - Prob. 19CRCh. 8.CR - Prob. 20CRCh. 8.CR - Prob. 21CRCh. 8.CR - Prob. 22CRCh. 8.CR - Prob. 23CRCh. 8.CR - Find the length of the longest object that will...Ch. 8.CR - Prob. 25CRCh. 8.CR - Prob. 26CRCh. 8.CR - In Exercise 26 and 27, use the two-column method...Ch. 8.CR - Prob. 28CRCh. 8.CR - A regular dodecagon 12-sided polygon is inscribed...Ch. 8.CR - Prob. 30CRCh. 8.CR - Prob. 31CRCh. 8.CR - Prob. 32CRCh. 8.CR - Prob. 33CRCh. 8.CR - Prob. 34CRCh. 8.CR - Prob. 35CRCh. 8.CR - Prob. 36CRCh. 8.CR - Prob. 37CRCh. 8.CR - Prob. 38CRCh. 8.CR - Prob. 39CRCh. 8.CR - Prob. 40CRCh. 8.CR - Prob. 41CRCh. 8.CR - Prob. 42CRCh. 8.CR - Prob. 43CRCh. 8.CR - Prob. 44CRCh. 8.CR - The box fractal. To create this shape, use the...Ch. 8.CR - Prob. 46CRCh. 8.CR - Prob. 47CRCh. 8.CR - Prob. 48CRCh. 8.CR - Draw a building in two-point perspective. viewed...Ch. 8.CR - Prob. 50CRCh. 8.CR - Prob. 51CRCh. 8.CR - Prob. 52CRCh. 8.CR - Prob. 53CR
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