scribe the motion of a particle with position (x, y) as t varies in the given interva Et≤ 2n.
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- Write parametric equations for a cycloid traced by a point P on a circle of radius a as the circle rolls along the x -axis given that P is at a maximum when x=0.Starting from the point (3,−4,−2) reparametrize the curve r(t)=(3+1t)i+(−4−3t)j+(−2−3t)k in terms of arclength. HINT. Your result should be the position of the "particle", which moves along the curve, after traveling distance s from the initial point.Find a parametrization of the right branch (x > 0) of the hyperbola(x/a)2−*(y/b)2= 1 using cosh t and sinh t. How can you parametrize the branch x < 0?
- Parametrize a circular spiral centered at the z-axis, starting at (0,2,0) and ending at (0,2,12) after four turns counterclockwise for 0 <= t <= 1 and find its length.Obtain the center of gravity of the skin of the rotating object that occurs if the arc y = √9 - x2; (0≤x≤3) is rotated on the x-axis△ABC is rotated around the line x=0 to produce a solid. What describes the shape of the solid?
- Let C be the boundary of the region in the first quadrant bounded by the x-axis, a quarter-circle with radius 9, and the y-axis, oriented counterclockwise starting from the origin. Label the edges of the boundary as C1,C2,C3 starting from the bottom edge going counterclockwise. Give each edge a constant speed parametrization with domain 0≤t≤1 How can I solve the blanks in the attached picture? Thank youFind parametrizations The portion of the hemisphere x2 + y2 + z2 = 10, y>= 0, in the first octantFind the curved surface area of the solid generated by revolving the part of the curve y=x² from (0,0) to (√6,6) about the y-axis.