Elementary Technical Mathematics
12th Edition
ISBN: 9781337630580
Author: Dale Ewen
Publisher: Cengage Learning
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Chapter 4, Problem 7R
To determine
To calculate: The number of digits which are significant or the accuracy of the measurement
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4. Consider Chebychev's equation
(1 - x²)y" - xy + λy = 0
with boundary conditions y(-1) = 0 and y(1) = 0, where X is a constant.
(a) Show that Chebychev's equation can be expressed in Sturm-Liouville form
d
· (py') + qy + Ary = 0,
dx
y(1) = 0, y(-1) = 0,
where p(x) = (1 = x²) 1/2, q(x) = 0 and r(x) = (1 − x²)-1/2
(b) Show that the eigenfunctions of the Sturm-Liouville equation are extremals of the
functional A[y], where
A[y]
=
I[y]
J[y]'
and I[y] and [y] are defined by
-
I [y] = √, (my² — qy²) dx
and
J[y] = [[", ry² dx.
Explain briefly how to use this to obtain estimates of the smallest eigenvalue >1.
1
(c) Let k > be a parameter. Explain why the functions y(x) = (1-x²) are suitable
4
trial functions for estimating the smallest eigenvalue. Show that the value of A[y]
for these trial functions is
4k2
A[y] =
=
4k - 1'
and use this to estimate the smallest eigenvalue \1.
Hint:
L₁ x²(1 − ²)³¹ dr =
1
(1 - x²)³ dx
(ẞ > 0).
2ẞ
2. If loga b + log, a = √√29, find all possible values of loga blog, a
I need some assistance solving Part B of this question. Refer to the excel data in the image provided to answer Part B. SoftBus Company sells PC equipment and customized software to small companies to help them manage their day-to-day business activities. Although SoftBus spends time with all customers to understand their needs, the customers are eventually on their own to use the equipment and software intelligently. To understand its customers better, SoftBus recently sent questionnaires to a large number of prospective customers. Key personnel—those who would be using the software—were asked to fill out the questionnaire. SoftBus received 82 usable responses, as shown in the file. You can assume that these employees represent a random sample of all of SoftBus's prospective customers. SoftBus believes it can afford to spend much less time with customers who own PCs and score at least 4 on PC Knowledge. Let's call these the "PC-savvy" customers. On the other hand, SoftBus believes it…
Chapter 4 Solutions
Elementary Technical Mathematics
Ch. 4.1 - Determine the accuracy of each measurement; that...Ch. 4.1 - Determine the accuracy of each measurement; that...Ch. 4.1 - Determine the accuracy of each measurement; that...Ch. 4.1 - Determine the accuracy of each measurement; that...Ch. 4.1 - Determine the accuracy of each measurement; that...Ch. 4.1 - Determine the accuracy of each measurement; that...Ch. 4.1 - Determine the accuracy of each measurement; that...Ch. 4.1 - Determine the accuracy of each measurement; that...Ch. 4.1 - Determine the accuracy of each measurement; that...Ch. 4.1 - Determine the accuracy of each measurement; that...
Ch. 4.1 - Determine the accuracy of each measurement; that...Ch. 4.1 - Determine the accuracy of each measurement; that...Ch. 4.1 - Determine the accuracy of each measurement; that...Ch. 4.1 - Determine the accuracy of each measurement; that...Ch. 4.1 - Determine the accuracy of each measurement; that...Ch. 4.1 - Determine the accuracy of each measurement; that...Ch. 4.1 - Determine the accuracy of each measurement; that...Ch. 4.1 - Determine the accuracy of each measurement; that...Ch. 4.1 - Determine the accuracy of each measurement; that...Ch. 4.1 - Determine the accuracy of each measurement; that...Ch. 4.1 - Determine the accuracy of each measurement; that...Ch. 4.1 - Determine the accuracy of each measurement; that...Ch. 4.1 - Determine the accuracy of each measurement; that...Ch. 4.1 - Prob. 24ECh. 4.1 - Determine the accuracy of each measurement; that...Ch. 4.1 - Prob. 26ECh. 4.1 - Determine the accuracy of each measurement; that...Ch. 4.1 - Determine the accuracy of each measurement; that...Ch. 4.1 - Determine the accuracy of each measurement; that...Ch. 4.1 - Prob. 30ECh. 4.1 - Determine the accuracy of each measurement; that...Ch. 4.1 - Determine the accuracy of each measurement; that...Ch. 4.1 - Determine the accuracy of each measurement; that...Ch. 4.1 - Determine the accuracy of each measurement; that...Ch. 4.1 - Determine the accuracy of each measurement; that...Ch. 4.1 - Prob. 36ECh. 4.2 - Find a. the precision and b. the greatest possible...Ch. 4.2 - Find a. the precision and b. the greatest possible...Ch. 4.2 - Find a. the precision and b. the greatest possible...Ch. 4.2 - Find a. the precision and b. the greatest possible...Ch. 4.2 - Find a. the precision and b. the greatest possible...Ch. 4.2 - Find a. the precision and b. the greatest possible...Ch. 4.2 - Find a. the precision and b. the greatest possible...Ch. 4.2 - Find a. the precision and b. the greatest possible...Ch. 4.2 - Find a. the precision and b. the greatest possible...Ch. 4.2 - Find a. the precision and b. the greatest possible...Ch. 4.2 - Find a. the precision and b. the greatest possible...Ch. 4.2 - Find a. the precision and b. the greatest possible...Ch. 4.2 - Find a. the precision and b. the greatest possible...Ch. 4.2 - Find a. the precision and b. the greatest possible...Ch. 4.2 - Find a. the precision and b. the greatest possible...Ch. 4.2 - Find a. the precision and b. the greatest possible...Ch. 4.2 - Find a. the precision and b. the greatest possible...Ch. 4.2 - Find a. the precision and b. the greatest possible...Ch. 4.2 - Find a. the precision and b. the greatest possible...Ch. 4.2 - Find a. the precision and b. the greatest possible...Ch. 4.2 - Find a. the precision and b. the greatest possible...Ch. 4.2 - Find a. the precision and b. the greatest possible...Ch. 4.2 - Find a. the precision and b. the greatest possible...Ch. 4.2 - Find a. the precision and b. the greatest possible...Ch. 4.2 - Find a. the precision and b. the greatest possible...Ch. 4.2 - Find a. the precision and b. the greatest possible...Ch. 4.2 - Find a. the precision and b. the greatest possible...Ch. 4.2 - Find a. the precision and b. the greatest possible...Ch. 4.2 - Find a. the precision and b. the greatest possible...Ch. 4.2 - Find a. the precision and b. the greatest possible...Ch. 4.3A - Read the measurement in millimeters shown on each...Ch. 4.3A - Read the measurement in millimeters shown on each...Ch. 4.3A - Read the measurement in millimeters shown on each...Ch. 4.3A - Read the measurement in millimeters shown on each...Ch. 4.3A - Read the measurement in millimeters shown on each...Ch. 4.3A - Read the measurement in millimeters shown on each...Ch. 4.3A - Read the measurement in millimeters shown on each...Ch. 4.3A - Read the measurement in millimeters shown on each...Ch. 4.3A - Read the measurement in millimeters shown on each...Ch. 4.3A - Prob. 10ECh. 4.3A - Prob. 11ECh. 4.3A - Prob. 12ECh. 4.3B - Read the measurement in inches shown on each...Ch. 4.3B - Read the measurement in inches shown on each...Ch. 4.3B - Read the measurement in inches shown on each...Ch. 4.3B - Prob. 4ECh. 4.3B - Prob. 5ECh. 4.3B - Read the measurement in inches shown on each...Ch. 4.3B - Prob. 7ECh. 4.3B - Prob. 8ECh. 4.3B - Prob. 9ECh. 4.3B - Read the measurement in inches shown on each...Ch. 4.3B - Prob. 11ECh. 4.3B - Read the measurement in inches shown on each...Ch. 4.4A - Read the measurement shown on each metric...Ch. 4.4A - Read the measurement shown on each metric...Ch. 4.4A - Read the measurement shown on each metric...Ch. 4.4A - Prob. 4ECh. 4.4A - Prob. 5ECh. 4.4A - Prob. 6ECh. 4.4A - Prob. 7ECh. 4.4A - Prob. 8ECh. 4.4A - Prob. 9ECh. 4.4A - Prob. 10ECh. 4.4A - Read the measurement shown on each metric...Ch. 4.4A - Prob. 12ECh. 4.4A - Read the measurement shown on each metric...Ch. 4.4A - Prob. 14ECh. 4.4A - Prob. 15ECh. 4.4A - Prob. 16ECh. 4.4A - Prob. 17ECh. 4.4A - Prob. 18ECh. 4.4A - Prob. 19ECh. 4.4A - Read the measurement shown on each metric...Ch. 4.4B - Read the measurement shown on each U.S....Ch. 4.4B - Prob. 2ECh. 4.4B - Prob. 3ECh. 4.4B - Prob. 4ECh. 4.4B - Prob. 5ECh. 4.4B - Prob. 6ECh. 4.4B - Read the measurement shown on each U.S....Ch. 4.4B - Read the measurement shown on each U.S....Ch. 4.4B - Prob. 9ECh. 4.4B - Prob. 10ECh. 4.4B - Prob. 11ECh. 4.4B - Prob. 12ECh. 4.4B - Prob. 13ECh. 4.4B - Prob. 14ECh. 4.4B - Prob. 15ECh. 4.4B - Prob. 16ECh. 4.4B - Prob. 17ECh. 4.4B - Prob. 18ECh. 4.4B - Prob. 19ECh. 4.4B - Prob. 20ECh. 4.5 - In each set of measurements, find the measurement...Ch. 4.5 - In each set of measurements, find the measurement...Ch. 4.5 - In each set of measurements, find the measurement...Ch. 4.5 - In each set of measurements, find the measurement...Ch. 4.5 - In each set of measurements, find the measurement...Ch. 4.5 - Prob. 6ECh. 4.5 - Prob. 7ECh. 4.5 - In each set of measurements, find the measurement...Ch. 4.5 - In each set of measurements, find the measurement...Ch. 4.5 - Prob. 10ECh. 4.5 - Prob. 11ECh. 4.5 - In each set of measurements, find the measurement...Ch. 4.5 - In each set of measurements, find the measurement...Ch. 4.5 - In each set of measurements, find the measurement...Ch. 4.5 - Prob. 15ECh. 4.5 - Prob. 16ECh. 4.5 - In each set of measurements, find the measurement...Ch. 4.5 - Prob. 18ECh. 4.5 - Prob. 19ECh. 4.5 - Prob. 20ECh. 4.5 - Use the rules for addition of measurements to find...Ch. 4.5 - Use the rules for addition of measurements to find...Ch. 4.5 - Use the rules for addition of measurements to find...Ch. 4.5 - Use the rules for addition of measurements to find...Ch. 4.5 - Use the rules for addition of measurements to find...Ch. 4.5 - Prob. 26ECh. 4.5 - Use the rules for addition of measurements to find...Ch. 4.5 - Use the rules for addition of measurements to find...Ch. 4.5 - Use the rules for addition of measurements to find...Ch. 4.5 - Prob. 30ECh. 4.5 - Prob. 31ECh. 4.5 - Use the rules for addition of measurements to find...Ch. 4.5 - Use the rules for subtraction of measurements to...Ch. 4.5 - Use the rules for subtraction of measurements to...Ch. 4.5 - Prob. 35ECh. 4.5 - Use the rules for subtraction of measurements to...Ch. 4.5 - Use the rules for subtraction of measurements to...Ch. 4.5 - Use the rules for subtraction of measurements to...Ch. 4.5 - Prob. 39ECh. 4.5 - Prob. 40ECh. 4.5 - Use the rules for subtraction of measurements to...Ch. 4.5 - If you bolt four pieces of metal with thicknesses...Ch. 4.5 - Prob. 43ECh. 4.5 - Prob. 44ECh. 4.5 - A welder cuts several pieces of steel angle of...Ch. 4.5 - Prob. 46ECh. 4.5 - Prob. 47ECh. 4.5 - Prob. 48ECh. 4.5 - An automobile cooling system is leaking. One day...Ch. 4.5 - Prob. 50ECh. 4.5 - Prob. 51ECh. 4.5 - A 6-room building has the following supply air...Ch. 4.5 - Prob. 53ECh. 4.5 - Prob. 54ECh. 4.5 - Prob. 55ECh. 4.6 - Use the rules for multiplication and/or division...Ch. 4.6 - Use the rules for multiplication and/or division...Ch. 4.6 - Use the rules for multiplication and/or division...Ch. 4.6 - Use the rules for multiplication and/or division...Ch. 4.6 - Use the rules for multiplication and/or division...Ch. 4.6 - Use the rules for multiplication and/or division...Ch. 4.6 - Use the rules for multiplication and/or division...Ch. 4.6 - Prob. 8ECh. 4.6 - Use the rules for multiplication and/or division...Ch. 4.6 - Use the rules for multiplication and/or division...Ch. 4.6 - Use the rules for multiplication and/or division...Ch. 4.6 - Prob. 12ECh. 4.6 - Use the rules for multiplication and/or division...Ch. 4.6 - Use the rules for multiplication and/or division...Ch. 4.6 - Use the rules for multiplication and/or division...Ch. 4.6 - Use the rules for multiplication and/or division...Ch. 4.6 - Use the rules for multiplication and/or division...Ch. 4.6 - Use the rules for multiplication and/or division...Ch. 4.6 - Use the rules for multiplication and/or division...Ch. 4.6 - Prob. 20ECh. 4.6 - Use the rules for multiplication and/or division...Ch. 4.6 - Use the rules for multiplication and/or division...Ch. 4.6 - Use the rules for multiplication and/or division...Ch. 4.6 - Use the rules for multiplication and/or division...Ch. 4.6 - Use the rules for multiplication and/or division...Ch. 4.6 - Prob. 26ECh. 4.6 - V=lwh is the formula for the volume of a...Ch. 4.6 - Find the volume of a cube measuring 8.10 cm on...Ch. 4.6 - The formula s=4.90t2 gives the distances, s in...Ch. 4.6 - Given K.E.=12mv2,m=2.87106kg,andv=13.4m/s. Find...Ch. 4.6 - A formula for determining the theoretical...Ch. 4.6 - Six pieces of metal, each 2.48 mm in thickness,...Ch. 4.6 - Find the volume of a storage bin cylinder with...Ch. 4.6 - In 2010, the United States harvested 12.4 billion...Ch. 4.6 - Prob. 35ECh. 4.6 - Prob. 36ECh. 4.6 - Prob. 37ECh. 4.6 - Prob. 38ECh. 4.6 - Prob. 39ECh. 4.6 - Prob. 40ECh. 4.6 - Prob. 41ECh. 4.6 - Prob. 42ECh. 4.6 - Prob. 43ECh. 4.6 - Prob. 44ECh. 4.6 - Prob. 45ECh. 4.6 - The weather forecast for tonight calls for about 1...Ch. 4.6 - Prob. 47ECh. 4.6 - According to the Environmental Protection Agency,...Ch. 4.6 - There is so much water in the world that we...Ch. 4.7 - For each measurement, find the precision, the...Ch. 4.7 - For each measurement, find the precision, the...Ch. 4.7 - For each measurement, find the precision, the...Ch. 4.7 - For each measurement, find the precision, the...Ch. 4.7 - For each measurement, find the precision, the...Ch. 4.7 - For each measurement, find the precision, the...Ch. 4.7 - For each measurement, find the precision, the...Ch. 4.7 - For each measurement, find the precision, the...Ch. 4.7 - For each measurement, find the precision, the...Ch. 4.7 - For each measurement, find the precision, the...Ch. 4.7 - For each measurement, find the precision, the...Ch. 4.7 - For each measurement, find the precision, the...Ch. 4.7 - For each measurement, find the precision, the...Ch. 4.7 - For each measurement, find the precision, the...Ch. 4.7 - For each measurement, find the precision, the...Ch. 4.7 - For each measurement, find the precision, the...Ch. 4.7 - For each measurement, find the precision, the...Ch. 4.7 - Prob. 18ECh. 4.7 - Prob. 19ECh. 4.7 - Prob. 20ECh. 4.7 - Compare each set of measurements by indicating...Ch. 4.7 - Compare each set of measurements by indicating...Ch. 4.7 - Complete the table: Given measurement Tolerance...Ch. 4.7 - Complete the table: Given measurement Tolerance...Ch. 4.7 - Complete the table: Given measurement Tolerance...Ch. 4.7 - Complete the table: Given measurement Tolerance...Ch. 4.7 - Complete the table: Given measurement Tolerance...Ch. 4.7 - Complete the table: Given measurement Tolerance...Ch. 4.7 - Complete the table: Given measurement Tolerance...Ch. 4.7 - Complete the table: Given measurement Tolerance...Ch. 4.7 - Complete the table: Given measurement Tolerance...Ch. 4.7 - Complete the table: Given measurement Tolerance...Ch. 4.7 - Complete the table: Given measurement Tolerance...Ch. 4.7 - Prob. 34ECh. 4.7 - Prob. 35ECh. 4.7 - Complete the table: Given measurement Tolerance...Ch. 4.7 - Complete the table: Given measurement Tolerance...Ch. 4.7 - Prob. 38ECh. 4.7 - Complete the table: Architects estimate Maximum...Ch. 4.7 - Complete the table: Architects estimate Maximum...Ch. 4.7 - Complete the table: Architects estimate Maximum...Ch. 4.7 - Complete the table: Architects estimate Maximum...Ch. 4.8 - For each resistor shown, find the resistance and...Ch. 4.8 - For each resistor shown, find the resistance and...Ch. 4.8 - Prob. 3ECh. 4.8 - For each resistor shown, find the resistance and...Ch. 4.8 - Prob. 5ECh. 4.8 - For each resistor shown, find the resistance and...Ch. 4.8 - For each resistor shown, find the resistance and...Ch. 4.8 - For each resistor shown, find the resistance and...Ch. 4.8 - Prob. 9ECh. 4.8 - For each resistor shown, find the resistance and...Ch. 4.8 - For each resistor shown, find the resistance and...Ch. 4.8 - For each resistor shown, find the resistance and...Ch. 4.8 - Prob. 13ECh. 4.8 - Prob. 14ECh. 4.8 - Prob. 15ECh. 4.8 - What color code on the first three bands is needed...Ch. 4.8 - What color code on the first three bands is needed...Ch. 4.8 - Prob. 18ECh. 4.8 - Prob. 19ECh. 4.8 - Prob. 20ECh. 4.8 - Prob. 21ECh. 4.8 - Prob. 22ECh. 4.8 - Prob. 23ECh. 4.8 - What color code on the first three bands is needed...Ch. 4.8 - Prob. 25ECh. 4.8 - Find a. the tolerance in ohms, b. the upper...Ch. 4.8 - Prob. 27ECh. 4.8 - Prob. 28ECh. 4.8 - Prob. 29ECh. 4.8 - Find a. the tolerance in ohms, b. the upper...Ch. 4.9 - Read each scale:Ch. 4.9 - Prob. 2ECh. 4.9 - Prob. 3ECh. 4.9 - Prob. 4ECh. 4.9 - Prob. 5ECh. 4.9 - Prob. 6ECh. 4.9 - Prob. 7ECh. 4.9 - Prob. 8ECh. 4.9 - Prob. 9ECh. 4.9 - Prob. 10ECh. 4.9 - Prob. 11ECh. 4.9 - Prob. 12ECh. 4.9 - Read each scale:Ch. 4.9 - Prob. 14ECh. 4.9 - Read each scale:Ch. 4.9 - Prob. 16ECh. 4.9 - Prob. 17ECh. 4.9 - Prob. 18ECh. 4.9 - Read each scale:Ch. 4.9 - Prob. 20ECh. 4.9 - Prob. 21ECh. 4.9 - Prob. 22ECh. 4 - Give the number of significant digits (the...Ch. 4 - Give the number of significant digits (the...Ch. 4 - Prob. 3RCh. 4 - Prob. 4RCh. 4 - Prob. 5RCh. 4 - Prob. 6RCh. 4 - Prob. 7RCh. 4 - Prob. 8RCh. 4 - Find a. the precision and b. and greatest possible...Ch. 4 - Prob. 10RCh. 4 - Prob. 11RCh. 4 - Prob. 12RCh. 4 - Prob. 13RCh. 4 - Prob. 14RCh. 4 - Prob. 15RCh. 4 - Prob. 16RCh. 4 - Read the measurement shown on the vernier caliper...Ch. 4 - Prob. 18RCh. 4 - Prob. 19RCh. 4 - Read the measurement shown on the U.S. micrometer...Ch. 4 - Find the measurement that is a. the most accurate...Ch. 4 - Prob. 22RCh. 4 - Prob. 23RCh. 4 - Prob. 24RCh. 4 - Prob. 25RCh. 4 - Prob. 26RCh. 4 - Prob. 27RCh. 4 - Prob. 28RCh. 4 - Prob. 29RCh. 4 - Prob. 30RCh. 4 - Prob. 31RCh. 4 - Prob. 32RCh. 4 - Prob. 33RCh. 4 - For each resistor find its resistance and its...Ch. 4 - Prob. 35RCh. 4 - Prob. 36RCh. 4 - Give the number of significant digits in each...Ch. 4 - Give the number of significant digits in each...Ch. 4 - Prob. 3TCh. 4 - Find a. the precision and b. the greatest possible...Ch. 4 - Prob. 5TCh. 4 - Find a. the precision and b. the greatest possible...Ch. 4 - Prob. 7TCh. 4 - Read the measurement shown on the vernier caliper...Ch. 4 - Prob. 9TCh. 4 - Read the measurement shown on the U.S. micrometer...Ch. 4 - Prob. 11TCh. 4 - Find the measurement that is a. the most accurate,...Ch. 4 - Use the rules of measurement to multiply:...Ch. 4 - Use the rules of rules of measurement to add:...Ch. 4 - Prob. 15TCh. 4 - Use the rules of measurement to divide: 6.28m225mCh. 4 - Prob. 17TCh. 4 - Find a. the relative error and b. the percent of...Ch. 4 - Prob. 19TCh. 4 - Read each scale:Ch. 4 - Prob. 1CRCh. 4 - Round 32,518.612 to nearest a. ten b. hundredth.Ch. 4 - Prob. 3CRCh. 4 - Prob. 4CRCh. 4 - Prob. 5CRCh. 4 - Prob. 6CRCh. 4 - Prob. 7CRCh. 4 - Prob. 8CRCh. 4 - Prob. 9CRCh. 4 - Prob. 10CRCh. 4 - Prob. 11CRCh. 4 - Prob. 12CRCh. 4 - Prob. 13CRCh. 4 - Prob. 14CRCh. 4 - Prob. 15CRCh. 4 - Prob. 16CRCh. 4 - Prob. 17CRCh. 4 - Prob. 18CRCh. 4 - Prob. 19CRCh. 4 - Prob. 20CRCh. 4 - Given the number of significant digits in each...Ch. 4 - Find a. the precision and b. the greatest possible...Ch. 4 - Find a. the precision and b. the greatest possible...Ch. 4 - Prob. 24CRCh. 4 - Prob. 25CRCh. 4 - Prob. 26CRCh. 4 - Prob. 27CRCh. 4 - Prob. 28CRCh. 4 - Prob. 29CRCh. 4 - Prob. 30CRCh. 4 - Prob. 31CRCh. 4 - Prob. 32CRCh. 4 - Prob. 33CRCh. 4 - Read each scale:
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