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qr code vb.net y 6 4 t=1 t=0 2 x 6 2 t = 1 4 t = 2 2 4 6 t=2 in .NET
y 6 4 t=1 t=0 2 x 6 2 t = 1 4 t = 2 2 4 6 t=2 Code 39 Scanner In .NET Framework Using Barcode Control SDK for Visual Studio .NET Control to generate, create, read, scan barcode image in .NET applications. Code39 Printer In .NET Using Barcode encoder for .NET Control to generate, create Code39 image in .NET applications. Figure 161 Code39 Decoder In .NET Framework Using Barcode reader for .NET Control to read, scan read, scan image in .NET framework applications. Bar Code Creator In .NET Using Barcode generator for VS .NET Control to generate, create bar code image in VS .NET applications. Cartesiancoordinate graph of the parametric equations x = 2t and y = 3t
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Are you confused
If you re having trouble understanding the concept of a parameter, imagine the passage of time In science and engineering, elapsed time t is the parameter on which many things depend In the Cartesian situation described above, as time flows from the past (t < 0) through the present moment (t = 0) and into the future (t > 0), a point moves along the line in Fig 161, going from the third quadrant (lower left, in the past) through the origin (right now) and into the first quadrant (upper right, in the future) In the polar case, as time flows from the present (t = 0) into the future (t > 0), a point travels along the spiral in Fig 162, starting at the center (right now) and going counterclockwise, arriving at the outer end when t = p (a little while from now) Here s a challenge! Find a pair of parametric equations that represent the line shown in Fig 163 Solution
We re given two points on the line One of them, (0,3), tells us that the yintercept is 3 We can deduce the slope from the coordinates of the other point When we move 4 units to the right from (0,3), we must go downward by 3 units (or upward by 3 units) to reach (4,0) The rise over run ratio is 3 to 4, so the slope is 3/4 The slopeintercept form of the equation for our line is y = ( 3/4)x + 3 y 6 (0, 3) 4 2 (4, 0) x 6 4 2 2 4 6 2 4 6
Figure 163 How can we represent this line as a pair of parametric equations
Parametric Equations in TwoSpace
We can let x vary directly with the parameter t We describe that relation simply as x=t That s one of our two parametric equations We can substitute t for x into the pointslope equation to get y = ( 3/4)t + 3 That s the other parametric equation Here s an experiment! Do you suspect that the pair of equations x=t and y = ( 3/4)t + 3 isn t the only parametric way we can represent the line in Fig 163 If so, maybe you re right Let x = 2t, or x = t + 1, or x = 2t + 1, and see what happens when you generate the equation for y in terms of t on that basis When you put the two parametric equations together, do you get the same line as the one shown in Fig 163

