![]() ![]() Im currently doing a year 12 pre uni course in pure maths. "Each of the profile segments (AB, BC and CD), are parabolic. The gradient of the profiles at points B and C where the segments join, are the same to ensure the track is smooth. Numerically solve and graphically display. Graph Cartesian functions, relations, and inequalities, plus polar, parametric, and ordinary differential equations. At point A the track is 30m above the ground and inclined at 100 below the horizontal. Graphmatica 2.1 Download Now Direct link a powerful, easy-to-use, equation plotter with numerical and calculus features. ![]() Point B is 10m above the ground level and 8 m horizontally across from A. Graphmatica is a powerful, easy-to-use equation plotter for high school algebra through college calc Graphmatica. Point C is at same height as B and 11m horizontally from A. ![]() YOUR TASK: Determine the height of the track above the ground at point D and devise a method of estimating the length of the track with a view to estimating the cost of the repairs at $165/m." At D, 22m horizontally from A the track has a slope of zero. Im completely stumped on how to start this question. I have spent the last 5 hours plotting points in Graphmatica trying to come up with 3 functions that meet the needs of the question.Īny tips on where to begin with a question such as this? GRAPHMATICA 2.0 E HOW TO Let's represent the three parabolas as symbolic quadratic functions for now. y1 will be the function that joins A and B, y2 joins B and C, and 圓 joins C and D. We know that the slope of y1 is -10 at x=0. So if we plug in x=0 into y1', the answer will be -10. So finally, y1, which is a parabola that passes through (0,30) and (8,10) and has a slope of -100 at x=0, is: Now lets look back at what we know of y1. NEXT: Let's work with y2, the parabola joining B and C: Let's find the gradient of y1 at B (8,10) or x=8, since we know it will be the same as the gradient of y2 at B. We know y2'=5 at x=8 (same as y1' at x=8 to make the track smooth). Chuang dolma facebook sign, Arnold remix 2.0, E dry geldern muttizettel. We also can find out the slope of y2 at another point. Facebook ipad update profile picture, Software graphmatica downloads. We see that y2 is the same height off the ground at both B (8,10) and C (11,10). Since parabolas can only be at the same height at points symmetric around their vertex, the vertex of the parabola must be halfway between x=8 and x=11: at x=9.5. Graphmatica is a powerful, easy-to-use, equation plotter with numerical and calculus features: - Graph Cartesian functions, relations, and inequalities, plus polar, parametric, and ordinary differential equations. Using these two points, we can solve for d and e.Ġ = 2*d*9.5 + e = 19d + e Now subtract one equation from the other to cancel the e'sĥ = -3d -> d = -5/3 Now plug d into either one of the two equations we started with to get e We know the slope at the vertex is horizontal or 0. So finally, y2, which is a parabola that passes through (8,10) and (11,10) has a slope of 95 at x=8, is: We know it passes through point B (8,10). ![]()
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