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- Rotate the xy-axes in the plane counterclockwise through an angle θ= 135° to obtain new x' y' -axes. Use the methods of this section to find (a) the x' y'-coordinates of the point whose xy-coordinates are (3, 2) and (b) the xy-coordinates of the point whose x'y' -coordinates are (4, -4)Triangle MNP with vertices M(-2,0),N(0,-1),P(-3,-2) a)90 degrees counterclockwise rotation about the origin b)dilation with scale factor of 3,centered at the origin What's the mirror image?A figure is located at (0,0) (-3,-4) and (-3,0) on a coordinate plane. What kind of 3-D shape would be created of the figure was rotated around the x-axis. Show your work
- Find parametric equations for the path of a particle that moves along the circle described by x2 + (y − 2)2 = 16 in the manner described. (Enter your answer as a comma-separated list of equations. Let x and y be in terms of t.) (a) Once around clockwise, starting at (4, 2). 0 ≤ t ≤ 2?. (b) Two times around counterclockwise, starting at (4, 2). 0 ≤ t ≤ 4?. (c) Halfway around counterclockwise, starting at (0, 6). 0 ≤ t ≤ ?.Find parametric equations for the path of a particle that moves along the circle x2 + (y − 3)2 = 16 in the manner described. (Enter your answer as a comma-separated list of equations. Let x and y be in terms of t.) (a) Once around clockwise, starting at (4, 3). 0 ≤ t ≤ 2π. (b) Three times around counterclockwise, starting at (4, 3). 0 ≤ t ≤ 6π. (c) Halfway around counterclockwise, starting at (0, 7). 0 ≤ t ≤ π.Find parametric equations and a parameter interval for the motion of a particle that moves along the graph of y = x2 in the following way: Beginning at (0, 0) it moves to (3, 9), and then travels back and forth from (3, 9) to (-3, 9) infinitely many times.
- Find parametric equations and a parameter interval for the motion of a particle starting at the point (3,0) and tracing the top half of the circle x2+ y2 = 9 eight times. Find parametric equations for the particle's motion. Let the parameter interval for the motion of the particle be 0 ≤ t ≤ 8π. x = y = (Type expressions using t as the variable.)An arctic village maintains a circular cross-country ski trail that has a radius of 2.3 kilometers. A skier started skiing from the position (0.163, 2.294), measured in kilometers, and skied counter-clockwise for 0.92 kilometers, where he paused for a brief rest. (Consider the circle to be centered at the origin). Determine the ordered pair (in both kilometers and radii) on the coordinate axes that identifies the location where the skier rested. (Hint: Start by drawing a diagram to represent this situation.)A figure is located at (0, 0), (−3, −4), and (−3, 0) on a coordinate plane. What kind of 3-D shape would be created if the figure was rotated around the x-axis? Provide an explanation and proof of your answer to receive full credit. Include the dimensions of the 3-D shape in your explanation.
- Find parametric equations for the path of a particle tht moves along the circle x2+ (y-3)2 = 16 in the manner described. Enter your answer as a comma-separated list of equations. Let x and y be in terms of t. a) Once around clockwise, starting at (4, 3). 0 ≤ t ≤ 2?. b) Four times around counterclockwise, starting at (4, 3). 0 ≤ t ≤ 8?. c) Halfway around counterclockwise, starting at (0, 7). 0 ≤ t ≤ ?.xgraph and label 13 and 14 and their given rotation about the origin. Give the coordinates of the images.trapezoid K’L’M’N’ is rotated image of trapezoid MLMN after which of the following rotation?