workshop6

# workshop6 - P where the parameter is the angle that the ray...

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Workshop 6 1) Suppose R is the region in the plane enclosed by y = x 2 and y = 4. a) Compute the perimeter P and area A of R , and then compute the ratio Q = A/P 2 . Note By squaring the perimeter the ratio becomes independent of the units chosen to measure the region. b) Compute this ratio Q = A/P 2 for these four regions: the region R , a square, a circle, and an equilateral triangle. Draw the ﬁgures in increasing order of Q . 2) The point P travels on the parabola y = x 2 . a) Give parametric formulas for the location of P where the parameter is the ﬁrst coordinate of the point P . b) Give parametric formulas for the location of P where the parameter is the second coordinate of the point P . The parametric formulas will have to be given “piecewise”. c) Give parametric formulas for the location of
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Unformatted text preview: P where the parameter is the angle that the ray from the origin to P makes with the positive x-axis. d) Give parametric formulas for the location of P where the parameter is the angle that the ray from the point (0 , 1) to P makes with the ray from (0 , 1) to the origin. e) Give parametric formulas for the location of P where the parameter is the distance from the origin to P . The parametric formulas again will have to be given “piecewise”. 3) Sketch the cardioid r = 1-sin θ . What percentage of its enclosed area is above the x-axis? What percentage of its enclosed area is inside a circle of radius 1 centered at the origin?...
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