how to use barcode in c#.net Enter the Cubic in Software

Creation QR Code ISO/IEC18004 in Software Enter the Cubic

Enter the Cubic
Generate QR Code In None
Using Barcode generation for Software Control to generate, create QR-Code image in Software applications.
Decode Quick Response Code In None
Using Barcode scanner for Software Control to read, scan read, scan image in Software applications.
Let s solve a two-by-two system in which one equation is linear and the other is cubic Consider these: x 3 + 6x 2 + 14x y = 7 and 6x + 2y = 2
Create QR Code In C#
Using Barcode drawer for .NET Control to generate, create QR Code JIS X 0510 image in .NET framework applications.
QR Code ISO/IEC18004 Maker In Visual Studio .NET
Using Barcode creation for ASP.NET Control to generate, create QR Code 2d barcode image in ASP.NET applications.
First, we morph Again, it appears as if we ought to let x be the independent variable, and then derive two functions of that variable In the first equation, we can add 7 to each side, getting
QR Code Creator In .NET Framework
Using Barcode generator for VS .NET Control to generate, create QR Code image in Visual Studio .NET applications.
Make QR Code ISO/IEC18004 In Visual Basic .NET
Using Barcode drawer for Visual Studio .NET Control to generate, create QR Code JIS X 0510 image in .NET framework applications.
x 3 + 6x 2 + 14x y + 7 = 0 Then we can add y to each side and transpose the equation left-to-right, obtaining y as a function of x : y = x 3 + 6x 2 + 14x + 7 In the second equation, we can divide through by 2 to obtain 3x y = 1 Adding 1 to each side gives us 3x y + 1 = 0
Drawing ANSI/AIM Code 39 In None
Using Barcode drawer for Software Control to generate, create Code 3 of 9 image in Software applications.
EAN / UCC - 13 Creation In None
Using Barcode drawer for Software Control to generate, create European Article Number 13 image in Software applications.
Enter the Cubic
Making EAN / UCC - 14 In None
Using Barcode creation for Software Control to generate, create EAN / UCC - 13 image in Software applications.
UCC - 12 Generation In None
Using Barcode creator for Software Control to generate, create Universal Product Code version A image in Software applications.
We can add y to each side and transpose the equation left-to-right, getting the function y = 3x + 1
Data Matrix Generator In None
Using Barcode maker for Software Control to generate, create Data Matrix image in Software applications.
Create USS Code 128 In None
Using Barcode printer for Software Control to generate, create ANSI/AIM Code 128 image in Software applications.
Next, we mix When we mix the independent-variable parts of the above functions, we obtain one equation in one variable:
Postnet 3 Of 5 Creation In None
Using Barcode creation for Software Control to generate, create Postnet 3 of 5 image in Software applications.
USS-128 Recognizer In Visual Basic .NET
Using Barcode decoder for .NET framework Control to read, scan read, scan image in Visual Studio .NET applications.
x 3 + 6x 2 + 14x + 7 = 3x + 1 If we subtract the quantity (3x + 1) from both sides, we get x 3 + 6x 2 + 11x + 6 = 0 This is a straightforward cubic equation in polynomial standard form The roots aren t obvious from casual inspection, but we can use the techniques from Chap 25 to solve it
Bar Code Recognizer In VS .NET
Using Barcode Control SDK for ASP.NET Control to generate, create, read, scan barcode image in ASP.NET applications.
Creating Bar Code In Visual Basic .NET
Using Barcode printer for .NET framework Control to generate, create bar code image in .NET applications.
Next, we solve Now that we have derived a cubic equation in one variable, our mission is to find its roots We can use synthetic division several times to obtain factors Ultimately, we find that the cubic factors into
EAN13 Drawer In Objective-C
Using Barcode encoder for iPhone Control to generate, create UPC - 13 image in iPhone applications.
Code 39 Extended Printer In None
Using Barcode creator for Online Control to generate, create ANSI/AIM Code 39 image in Online applications.
(x + 1)(x + 2)(x + 3) = 0 The roots can be found by solving the three equations we get when we set each binomial equal to 0 Those roots are x = 1, x = 2, and x = 3 The y-values can be found by plugging these roots into either of the original functions Let s use the linear one; it s the less messy of the two! For x = 1, we have y = 3x + 1 = 3 ( 1) + 1 = 3 + 1 = 2 Now we know that our first solution is (x, y) = ( 1, 2) When x = 2, we have y = 3x + 1 = 3 ( 2) + 1 = 6 + 1 = 5
Linear Generator In VB.NET
Using Barcode drawer for .NET Control to generate, create Linear Barcode image in .NET framework applications.
Generating UPC-A Supplement 5 In None
Using Barcode maker for Online Control to generate, create UPC A image in Online applications.
458 More Two-by-Two Systems
Our second solution is (x, y) = ( 2, 5) Plugging in x = 3, we have y = 3x + 1 = 3 ( 3) + 1 = 9 + 1 = 8 Our third solution is (x, y) = ( 3, 8)
Finally, we check There are six arithmetic exercises to do! It s tedious, but if we want to be sure our solutions are right, it s mandatory We d better be careful with the signs, using negative additions rather than subtractions as much as possible! We check ( 1, 2) in the first original equation:
x 3 + 6x 2 + 14x y = 7 ( 1)3 + 6 ( 1)2 + 14 ( 1) ( 2) = 7 1 + 6 1 + ( 14) + 2 = 7 1 + 6 + ( 14) + 2 = 7 7 = 7 Next, we check ( 2, 5) in the first original equation: x 3 + 6x 2 + 14x y = 7 ( 2)3 + 6 ( 2)2 + 14 ( 2) ( 5) = 7 8 + 6 4 + ( 28) + 5 = 7 8 + 24 + ( 28) + 5 = 7 7 = 7 Next, we check ( 3, 8) in the first original equation: x 3 + 6x 2 + 14x y = 7 ( 3)3 + 6 ( 3)2 + 14 ( 3) ( 8) = 7 27 + 6 9 + ( 42) + 8 = 7 27 + 54 + ( 42) + 8 = 7 7 = 7 That completes the check for the original cubic Now we plug ( 1, 2) into the second original equation: 6x + 2y = 2 6 ( 1) + 2 ( 2) = 2 6 + ( 4) = 2 2=2
Copyright © OnBarcode.com . All rights reserved.