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4.Spiral- The spiral is a curve that has a varying radius. It is used on railroads and most modern highways. It provides a transition from the tangent to a simple curve or between simple curves in a compound curve (Figure 3-2, View D). 1.2.0 Elements of a Horizontal Curve The elements of a circular curve are shown in Figure 3-3.
The curve C has equation y x= − −9 2( )2. a) Describe geometrically the three transformations that map the graph of y x= 2 onto the graph of C. b) Hence, sketch the graph of C. The sketch must include the coordinates of • … all the points where the curve meets the coordinate axes. • … the maximum point of the curve.
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The horizontal curves are, by definition, circular curves of radius R. The elements of a horizontal curve are shown in Figure 7.9 and summarized (with units) in Table 7.2. The equations 7.8 through 7.13 that apply to the analysis of the curve are given below. A 7-degree horizontal curve covers an angle of 63o15’34”.
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Check your answer using simple geometry. Exercise 6: Find the area enclosed between the curves y = 4x + 5 , y = 5x + 4 and the x-axis. Exercise 7: Find the area between y = sin x and y = cos x between two successive points where the curves intersect. Exercise 7: This area = /4 7 /4 [sin x − cos x] dx
1) The diagram shows intemally tangent circles, where the inside circle passes through the center of the large circle. What is the area of the shaded region?
(b) The constant ais a lineardistortion of the curve. (c) If b=25=24 the curve is calledthe electricmotor curve. Calculus Questions: (a) Find the area of one loop. (b) Find the points on the curve where the tangent line is vertical. (c) Find the length of the inner curve. (d) Find the area between the inner and outer curves (and between y=§c).
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of a general curve can be characterized by two numbers, the curvature and the torsion. The required textbook sections are: 2.1, 2.3. The examples in this note are mostly di erent from examples in the textbook. Please read the textbook carefully and try your hands on the exercises. During this please don't
