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Show That in spherical coordinates a curve given by the parametric equation
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- Sketch the curve represented by each set of equations by eliminating the parameter. a. x=5cos and y=3sin,02 b. x=1+tan and y=2+2sec,/23/2arrow_forwardA gear train consists of three gears meshed together (Figure 9). The middle gear is known as an idler. Show that the angular velocity of the third gear does not depend on the number of teeth of the idler gear (Gear 2).arrow_forwardSketch and describe the orientation of the curve given by the parametric equations x=2tandy=4t2+2,2t2.arrow_forward
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- Sketch the curve given by the pair of parametric equations over the given interval. x = 4 cost, y = 2 sin t A C B D Submit Answer A) B) 6 D) ↑ L El 13 B2 73 +49 " 5 л 4 3x 4 5x 4 7x 300 -8--6 12 16 тул E 3 2 +00 TOR 4 4 л 42 3x HI+ 7x 1 42arrow_forwardUse the parametric equations shown below to answer the following. x = t?V3 and 1,3 y = 3t - (a) Use a graphing utility to graph the curve on the interval -3 sts 3. y y 아 6 4 4 2 10 -10 -5 -2 -4 y 6 4 2 2 4 6 8 10 20 30 -2 -4 (b) Find dy/dx and d?y/dx². dx dy dx2 (c) Find the equation of the tangent line at the point (V3, ). y = (d) Find the length of the curve on the interval -3 st 3. |(e) Find the surface area generated by revolving the curve about the x-axis.arrow_forwardUnder what conditions can you find the length of a curver = ƒ(θ), a ≤ θ ≤ b, in the polar coordinate plane? Give an exampleof a typical calculation.arrow_forward
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