In Exercises 33-36, find the arc length of the graph of the parametric equations on the given interval(s). 33. x = -3 sin(2t), y = 3 cos(2t) on [0, π]
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- x3 (b) Calculate the arc length of the curve y =' - from x = 1 and x = 2. + A storage tank is designed by rotating y = x² + 1; about the x- axis, y- axis, line x = 2, and revolves 180° where x and y are both measured in meters. Determine how many cubic meters the tank can hold. (c)Consider the following. - sin(-), y= co(e), X = y = cos (a) Eliminate the parameter to find a Cartesian equation of the curve.Find y' and y". . sin3y=x²+tany+1
- 2 a). Find y' if Sin(x+y)= y´ cos x sin(x+ y)= y° cos x 2 b). Sketch a graph of using geogebra or another software by c). Find an equation of the tangent line to the graph of sin(x+ y)= y² cos x, at (T, 0) and graph this tangent line in the graph in part b. d). Find an equation of the tangent line to the graph of sin(x + y)= y´ cos x at (",") and graph this 2'2 tangent line in the graph in part b.Find the length of the curve r = = cos(4) + sin(8), 0 < 0 < . %3DFind all points (if any) of horizontal and vertical tangency to the curve. x = 3 cos² (e), y = 8 sin(0) horizontal tangent (x, y) = = vertical tangent (x, y) =