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sql server reporting services barcode font Ordinary Differential Equations in Software
Ordinary Differential Equations QR Code JIS X 0510 Reader In None Using Barcode Control SDK for Software Control to generate, create, read, scan barcode image in Software applications. Encode QR In None Using Barcode generator for Software Control to generate, create QR Code ISO/IEC18004 image in Software applications. with initial conditions as in (a). m = 5; g = 32.16; solution = DSolve[{m h''[t] m g h'[t], h'[0] 0, h[0] 1000}, h[t], t]; height2[t_]= solution[[1, 1, 2]] Scanning QR In None Using Barcode decoder for Software Control to read, scan read, scan image in Software applications. Paint QR Code ISO/IEC18004 In C# Using Barcode generation for .NET Control to generate, create QR Code 2d barcode image in VS .NET applications. 0.2 t( 804. + 1804. 0.2 t 160.8 0.2 t t) Paint QR Code In Visual Studio .NET Using Barcode generator for ASP.NET Control to generate, create QR image in ASP.NET applications. Denso QR Bar Code Generator In .NET Framework Using Barcode drawer for .NET Control to generate, create Denso QR Bar Code image in Visual Studio .NET applications. FindRoot[height2[t] 0, {t, 10}] {t 10.6213} It now takes 10.6213 sec to reach the ground. PlotLegends` Quick Response Code Creation In Visual Basic .NET Using Barcode maker for .NET framework Control to generate, create Denso QR Bar Code image in VS .NET applications. Barcode Printer In None Using Barcode encoder for Software Control to generate, create barcode image in Software applications. Plot[{height1[t], height2[t]}, {t, 0, 11}, PlotStyle {Thick,Thin}, PlotRange {0,1000}, AxesLabel {"Time","Height"}, PlotLegend {"Without air resistance","Air resistance included"}, LegendSize {1, .5}] Print Code128 In None Using Barcode encoder for Software Control to generate, create ANSI/AIM Code 128 image in Software applications. EAN / UCC  13 Drawer In None Using Barcode printer for Software Control to generate, create EAN13 Supplement 5 image in Software applications. Height 1000 800 600 400 200 Without air resistance 0 Air resistance included 2 4 6 8 10 Time
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Scanning UPC Symbol In C#.NET Using Barcode decoder for .NET framework Control to read, scan read, scan image in .NET framework applications. Print UPCA Supplement 5 In ObjectiveC Using Barcode creator for iPad Control to generate, create Universal Product Code version A image in iPad applications. g = 32.16; h = 3; = 30 Degree; v0 = 100; solution = DSolve[{x''[t] 0, y''[t] g, x'[0] v0 Cos[ ], y'[0] v0 Sin[ ], x[0] 0, y[0] h}, {x[t], y[t]}, t]; xsolution[t_]= solution[[1, 1, 2]] 50 3 t ysolution[t_]= solution[[1, 2, 2]] 3 + 50 t 16.08 t2 ParametricPlot[{xsolution[t], ysolution[t]}, {t, 0, 3.2}, AxesLabel {"x", "y"}] Bar Code Printer In Java Using Barcode generation for Eclipse BIRT Control to generate, create barcode image in BIRT applications. Generating GS1 128 In Java Using Barcode maker for Android Control to generate, create USS128 image in Android applications. y 40 30 20 10 50 100 150 200 250 x
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From the graph it is questionable whether y 35 when x = 200, so we compute precisely when the ball reaches the fence and then calculate its height at that instant. Solve[xsolution[t] 200] t 4 3 ysolution[t] /.% {32.7101} Since the height of the ball is less than 35 ft, the ball will not clear the fence. 11.8 At what angle should the ball in the previous problem be hit so that it goes over the fence
SOLUTION
First we want to get a relationship between y and q. Clear[ ] g = 32; h = 3; v0 = 100; solution = DSolve[{x''[t] 0, y''[t] g, x'[0] v0 Cos[ ], y'[0] v0 Sin[ ], x[0] 0, y[0] h}, {x[t], y[t]}, t] {{x[t] 100 t Cos[ ],y[t] 3 16 t
horiz[t_]= solution[[1, 1, 2]]; vert[t_]= solution[[1, 2, 2]] 3 16 t2 + 100 t Sin[ ] temp = Solve[horiz[t] 200, t] {{t 2 Sec[ ]}} + 100 t Sin[ ] } } Solve for t as a function of q. Define a function representing the height as a function of . Find which gives a height of 35 ft. The value of is expressed in degrees. height[p_]= vert[t] /. temp
64 Sec[ ] + 200
Tan[ ]} NSolve[height[ Degree] 35, p] Solve ifun : Inverse functions are being used by Solve, so some solutions may not be found; use Reduce for complete solution information. This warning may be safely disregarded. {{ 149.216}, { 111.694}, { 30.7838}, { 68.3065}} The negative values of may be disregarded. The ball will go over the fence if lies between 30.6357 and 68.4546 . We conclude by sketching these two trajectories. The vertical line represents the 35ft fence located 200 ft from home plate. = 30.6357 Degree; horiz[t_]= solution[[1, 1, 2]]; vert[t_]= solution[[1, 2, 2]]; graph1 = ParametricPlot[{horiz[t], vert[t]}, {t, 0, 6}] ; = 68.4546 Degree; horiz[t_]= solution[[1, 1, 2]]; vert[t_]= solution[[1, 2, 2]]; graph2 = ParametricPlot[{horiz[t], vert[t]}, {t, 0, 6}] ; graph3 = Graphics[Line[{{200, 0}, {200, 35}}]] ; Ordinary Differential Equations
Show[graph1, graph2, graph3, PlotRange { 50, 150}, AxesLabel {"x", "y"}] y 150 50 50 11.9 A culture of microorganisms grows at a rate proportional to the amount present at any given time. If there are 500 bacteria present after one day and 1200 after two days, how many bacteria will be present after four days SOLUTION
The differential equation described by this situation is dN = kN , where N is the number of bacteria present dt in the culture and k is a constant to be determined by the given information. The initial condition is N = 500 when t = 1. solution = DSolve[{n'[t] k n[t], n[1] 500}, n[t], t] {{n[t] 500 k+kt
population[t_]= solution[[1, 1, 2]]; Solve[population[2] 1200, k] Solve ifun : Inverse functions are being used by Solve, so some solutions may not be found; use Reduce for complete solution information.

