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Practice Exercises Generating Denso QR Bar Code In None Using Barcode printer for Software Control to generate, create QR Code ISO/IEC18004 image in Software applications. QR Code 2d Barcode Decoder In None Using Barcode decoder for Software Control to read, scan read, scan image in Software applications. This is an openbook quiz You may (and should) refer to the text as you solve these problems Don t hurry! You ll find workedout answers in App C The solutions in the appendix may not represent the only way a problem can be figured out If you think you can solve a particular problem in a quicker or better way than you see there, by all means try it! Print QR Code ISO/IEC18004 In C#.NET Using Barcode drawer for Visual Studio .NET Control to generate, create QR Code 2d barcode image in .NET framework applications. QR Creation In Visual Studio .NET Using Barcode maker for ASP.NET Control to generate, create Quick Response Code image in ASP.NET applications. Practice Exercises
QR Code Creator In .NET Framework Using Barcode drawer for VS .NET Control to generate, create QR Code JIS X 0510 image in .NET framework applications. Paint QR Code ISO/IEC18004 In VB.NET Using Barcode encoder for .NET framework Control to generate, create QR image in VS .NET applications. 1 Let x = 23713018568 and y = 0902780337 Find xy to three decimal places using common logarithms 2 Approximate the product xy from Prob 1 using natural logarithms Show that the result is the same as that obtained with common logs when rounded off to three decimal places 3 The power gain of an electronic circuit, in units called decibels (abbreviated dB), can be calculated according to this formula: G = 10 log (Pout/Pin) where G is the gain, Pout is the output signal power, and Pin is the input signal power, both specified in watts Suppose the audio input to the left channel of highfidelity amplifier is 0535 watts, and the output is 237 watts What is the power gain of this circuit in decibels Round off the answer to the nearest tenth of a decibel 4 Suppose the audio output signal in the scenario of Prob 3 is run through a long length of speaker wire, so instead of the 237 watts that appears at the leftchannel amplifier output, the speaker only gets 193 watts What is the power gain of the length of speaker wire, in decibels Round off the answer to three decimal places 5 If a positive real number increases by a factor of exactly 10, how does its common (base10) logarithm change 6 Show that the solution to Prob 5 is valid for all positive real numbers 7 If a positive real number decreases by a factor of exactly 100 (becomes 1/100 as great), how does its common logarithm change 8 Show that the solution to Prob 7 is valid for all positive real numbers 9 If a positive real number is divided by a factor of 357, how does its natural (basee) logarithm change Express the answer to two decimal places 10 Show that the solution to Prob 9 is valid for all positive real numbers GTIN  13 Generation In None Using Barcode encoder for Software Control to generate, create EAN 13 image in Software applications. Generating Bar Code In None Using Barcode printer for Software Control to generate, create barcode image in Software applications. CHAPTER
Painting Data Matrix 2d Barcode In None Using Barcode encoder for Software Control to generate, create DataMatrix image in Software applications. Paint Code 128 Code Set A In None Using Barcode printer for Software Control to generate, create USS Code 128 image in Software applications. Review Questions and Answers
Generating Code39 In None Using Barcode generation for Software Control to generate, create Code 39 image in Software applications. UCC  12 Printer In None Using Barcode generator for Software Control to generate, create UCC128 image in Software applications. Part Three
Create Identcode In None Using Barcode maker for Software Control to generate, create Identcode image in Software applications. Barcode Recognizer In None Using Barcode decoder for Software Control to read, scan read, scan image in Software applications. This is not a test! It s a review of important general concepts you learned in the previous nine chapters Read it though slowly and let it sink in If you re confused about anything here, or about anything in the section you ve just finished, go back and study that material some more Generating Bar Code In .NET Framework Using Barcode generation for ASP.NET Control to generate, create bar code image in ASP.NET applications. UCC128 Generation In .NET Using Barcode generator for Visual Studio .NET Control to generate, create UCC  12 image in .NET framework applications. 21
Creating USS Code 39 In ObjectiveC Using Barcode maker for iPhone Control to generate, create Code39 image in iPhone applications. Creating UPC A In Visual C# Using Barcode printer for .NET framework Control to generate, create UPC Symbol image in Visual Studio .NET applications. Question 211 Drawing Barcode In Java Using Barcode printer for BIRT reports Control to generate, create bar code image in Eclipse BIRT applications. Draw Barcode In Java Using Barcode drawer for Android Control to generate, create barcode image in Android applications. There are two distinct numbers that, when squared, produce 1 What are those two numbers
Answer 211 One of them is the unit imaginary number, which we call j That s the engineer s and applied mathematician s notation Many mathematics texts use the letter i to represent it The other is the negative of the unit imaginary number, j Question 212 How can we show that squaring j produces the same result as squaring j
Answer 212 By definition, we know that j 2 = 1 We can multiply the left side of this equation by ( 1)2 without having any effect on its value, because ( 1)2 = 1 When we do that, we get ( 1)2j 2 = 1 Copyright 2008 by The McGrawHill Companies, Inc Click here for terms of use
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The power of product rule allows us to rewrite the left side of this equation, so it becomes [( 1)j ]2 = 1 But ( 1)j is the same thing as j, so we can simplify further to get ( j)2 = 1 This is the same result as we obtain by squaring j Question 213 How is an imaginary number put together
Answer 213 An imaginary number is the product of j and a real number Suppose we call the real number b If b is positive, then we write the product of j and b as jb If b is negative, we write the product as jb (We always put the minus sign first) If b = 0, then we can write the product as j0 But because j0 = 0, we would more likely write j0 simply as 0 Question 214 How can we show that j3 + j7 is the same as j7 + j3, assuming that the familiar distributive law of arithmetic works with the unit imaginary number Answer 214 When we apply the distributive law for multiplication over addition backward to the first expression, we get j3 + j7 = j(3 + 7) The commutative law for addition tells us that 3 + 7 = 7 + 3 By substitution on the right side, we get j3 + j7 = j(7 + 3) Applying the distributive law forward on the right side, we get j3 + j7 = j7 + j3 Question 215 How can we show, again assuming that the distributive law works with the unit imaginary number, that if a and b are any two real numbers, then ja + jb is the same as jb + ja Answer 215 We can use the same proof procedure as we did in Answer 214, using letter constants instead of numbers! The distributive law tells us that ja + jb = j(a + b)

