number 9 9) Let C be the arc of the circle: x +y-9 from (3.0) to a) Find a parametric equation of a circle of radius r 3 that starts at (3,0) and has a counterclockwise orientation b) Find the int...
Give parametric equations that describe a full circle of radius R, centered at the origin with clockwise orientation, where the parameter t varies over the interval [0,22]. Assume that the circle starts at the point (R,0) along the x-axis. Consider the following parametric equations, x=−t+7, y=−3t−3; minus−5less than or equals≤tless than or equals≤5. Complete parts (a) through (d) below. Consider the following parametric equation. a.Eliminate the parameter to obtain an equation in x and y. b.Describe the curve and indicate...
Find the parametric equation of a circle of radius R, centered at (x = a; y = b), using the arc length as a parameter.
Let the curve C in the (x, y)-plane be given by the parametric equations x = e + 2, y = e2-1, tER. (a) Show that the point (3,0) belongs to the curve C. To which value of the parameter t does the point (3,0) correspond? (b) Find an expression for dy (dy/dt) without eliminating the parameter t, i.e., using de = (da/dt) (c) Using your result from part (b), find the value of at the point (3,0). (d) From...
3. Graph the region bounded by the parametric curve x cost and y = et where 0 t Find the length of the curve. b. Find the surface area of revolution when the region is revolved around the y -axis. a. 3. Graph the region bounded by the parametric curve x cost and y = et where 0 t Find the length of the curve. b. Find the surface area of revolution when the region is revolved around the y...
1 3. Let f(x) = 22(2-2)(2 - 4) and C a circle of radius 2k - 1 about the origin with counterclockwise orientation. (1) Find (2) Find 50, 5(=dz. Je_1(a) dz. 5. 1(a) dz. (3) Find
14 1. (10 marks) Let C be the curve 27x - y = 0 between y=0 and y=4. Sketch the graph of this curve. In each part, set up, but do not ovaluate, an integral or a sum of integrals that solves the problem. (a) Find the area of the surface generated by revolving C about the x-axis by integrating with respect to x (6) Find the area of the surface generated by revolving C about the y-axis by integrating...
answer all parts please except A if you cannot (6) Consider the vector field F(x,y)-《22, 3y). A path is closed if it ends whiere it starts Consider the 3 closed paths starting and ending at (3,0): C1 the circle of radius 3 centered at the origin, C2 the ellipse with equation 2 +3y2-9, and Cs the flat linear path going to -3 and then going straight back. (a) Use GeoGebra to plot the vector field F (b) For each, parametrize...
Let C be the curve (x - 3)2 + 9(y – 1)2 = 36, x +2y + z = 4, oriented counterclockwise when viewed from high on the z-axis. Let F be as shown below. Evaluate $.F. F.dr. F= (32² + 3y² + sin x? )i + (6xy + 3z)j + (x2 + 2yz)k $. F. dr= (Type an exact answer.) с
Please help me on the following homework problems, thank you! 1. Let C be the parametric curve given by (x(t), y(t)), whose graphs are shown below. Both consis t entirely of quarter-circles and line segments. The domain of this curve is [0,10] x(t) y(t) 4 4 0 1 2 3 4 5 6 7 89 10 t 0 1 2 3 4 5 6 789 10 t (a) Find the area of the region in the xy plane bounded by...
Please help!! Thanks 1. Consider the function f(x) e a) Find the length of the curve given by the equation y - f(x), -1 3x<1. b) Let R be the region bounded by the graph of f(x) and the lines 1,1 and y-0. Find the area of R. c) Find the coordinates of the center of mass of R. d) Consider the solid obtained by rotation of R about the r-axis. Find its volume and surface area. 1. Consider the...