The parametric equations where 0 tl describe the line segment that joins the points P1(x1, y and P2(x2, y2) Use a graphing device to draw the triangle with vertices A(1, 1), B(3, 4), C(1,7). Find the parametrization, including endpoints, and sketch to check. (Enter your answers as a comma- separated list of equations. Let x and y be in terms of t.) A to B B to C A to C The parametric equations where 0 tl describe the line...
The parametric equations below describe the line segment that joins the points P1(X1,Y1) and P2(x2,12). Consider the triangle A(1, 1), B(4,2), C(1, 4). Find the parametrization, including endpoints and sketch to check. X = X1 + (x2 - X1) y = V1 + (Y2 - Y1)t Ostsi (a) A to B x(t) = 1 + (2-1) y(t) = 1+(3-1) ostsi (b) B to C x(t) = (t) = Ostsi (c) A to C X(t) = y(t) = Ostsi
Select the first set of parametric equations, x = a cos(bt), y = c sin(dt). (a) Set the equations to x = 2 cos(t), y = 2 sin(t) using the sliders for a, b, c, and d. Describe the parametric curve. This answer has not been graded yet. What minimum parameter domain is required to draw the entire circle? Osts How many times is the circle traced out for Osts 4? Click the Animate button and observe the relationship between...
2) Find a rectangular equation for the curve with the given parametric equations. x = 2 sin(t).y = 2 cos(t);0 st <270 (b) x2 + y2 = 2 c) x2 + y2 = 4 (d) y = x2 - 4 (a) y2 - x2 = 2 (e) y = x2 - 2
Consider the parametric equations below. x = 2 + 4t y = 1-t2 (a) Sketch the curve by using the parametric equations to plot points. Indicate with an arrow the direction in which the curve is traced as t increases.(b) Eliminate the parameter to find a Cartesian equation of the curve. y = _______ Consider the parametric equations below. x = 3t - 5 y = 2t + 4 (a) Sketch the curve by using the parametric equations to plot points. Indicate with an arrow the...
1. A) Create a table of x- and y-values for the parametric equations, x = 3t - 2 and y = 7 - 4t using t= -2,-1,0,1, and 2, and 6 S 4 3 6 5 4 3 2 1 2 4 5 6 2 B) plot the points (x, y) generated in part (A) and sketch the graph of the parametric equations.
Find a vector equation and parametric equations for the line segment that joins P to Q. (D |-1+2-) 1 P(0, -1, 4) 4 -t.2 3 t. r(t) 4 vector equation X 7 4 t.2 3 1 - t. (x(t), y(t), z(t)) 4 X - parametric equations 2 If two objects travel through space along two different curves, it's often important to know whether they will collide. (Will a missile hit its moving target? Will two aircraft collide?) The curves might...
Find parametric equations for the path of a particle that moves around the given circle in the manner described. x2 + (y - 3)2 = 4 (a) Once around clockwise, starting at (2, 3). X(t) = y(t) = Osts 211 (b) Three times around counterclockwise, starting at (2, 3). X(t) = 2cos(t) y(t) = Osts (c) Halfway around counterclockwise, starting at (0,5). x(t) = y(t) = Osts
1. Find parametric equations and a parameter interval for the motion of the particle starting at the point (2,0) and tracing the top half of the circle x2 + y2 - 4 four times =1 2.Replace the cartesian equation with polar equation x2y 9 xy = 2 (x - 3)" + (y + 1)? - 4 3. Identify the symmetries of the curves. Then sketch the curves in the x-y plane a) = 2-2cost b)r? - sint 1. Give a...
Find parametric equations for the line described below. 30) The line through the points P(-1, -1, -1) and Q(7,-5,7) Find a parametrization for the line segment beginning at P1 and er 31) P1(3, 0, -2) and P2(0, 5, 0)