Solution r(t) = 6 cos(t) i + 6 sin(t)j + 3tk. The parametric equations for this curve are x= y = 6 sin(t), z = Since x² + y² = + 36.sin²(t) = the curve must lie on the circular cylinder x² + y² = The point (x, y, z) lies directly above the point (x, y, 0), which moves counterclockwise around the circle x² + y2. in the xy-plane. (The projection of the curve onto the xy-plane has vector equation r(t) = (6 cos(t), 6 sin(t), 0). See this example.) Since z = 3t, the curve spirals upward around the cylinder as t increases. The curve, shown in the figure below, is called a helix.

Q: correct

A:

Q: The equation y =1-x² can be described parametricall by x = sin t, y = cos² t. %3D اختر احدى الدجابات…

A:

Q: (x(t) = sin t ly(t) = sin 2t

A:

Q: 1.) Given the parametric equations: x=t'- 1 and y=f+t, find the 1ª and 2nd derivatives.

A: We will find the derivatives.

Q: Select all parametric equations below, whose graph is the top part of the circle of radius 1. 0x =…

A: x=cos(t),y=sin(t) for t∈-π,0 This represents the half circle in the lower part. This is NOT the…

Q: 60 50 60 50 40 40 30 30 20 10 20 50 100 150 10 20 40 60 80 (d) Use a graphing utility to approximate…

A:

Q: 3. What is the parametric equation for the line through the point (1 ,2, 3) parallel to the x- axis?…

A:

Q: (a) Let f(x, y) = sin(y?). Compute fry and fyr and show that they are equal to each other. (b) Let…

A:

Q: Which is a parametric equation for the curve 25 = (x +7) + (y+ A. c(t) = (5 cos(t) – 5, 5 sin(t) –…

A:

Q: 1. Express the given parametric curve by an equation in x and (a) x = 8t²-5, y = 2t - 1, for t€…

A: