Investigate the shape of the surface with parametric equations
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- Find parametric equations for the line formed by the intersection of planes x+y-z=3 and 3x-y+3z=5.arrow_forwardA plane directly above Denver, Colorado, (altitude 1650 meters) flies to Bismark, North Dakota (altitude 550 meters). It travels at 650 km/hour along a line at 8500 meters above the line joining Denver and Bismark. Bismark is about 850 km in the direction 60° north of east from Denver. Find parametric equations describing the plane's motion. Assume the origin is at sea level beneath Denver, that the x-axis points east and the y-axis points north, and that the earth is flat. Measure distances in kilometers and time in hours. F(t) = 10.15 k + tarrow_forwardA plane directly above Denver, Colorado, (altitude 1650 meters) flies to Bismark, North Dakota (altitude 550 meters). It travels at 650 km/hour along a line at 8500 meters above the line joining Denver and Bismark. Bismark is about 850 km in the direction 60° north of east from Denver. Find parametric equations describing the plane's motion. Assume the origin is at sea level beneath Denver, that the z-axis points east and the y-axis points north, and that the earth is flat. Measure distances in kilometers and time in hours. F(t) =arrow_forward
- Sketch the curve represented by the parametric equations (indicate the orientation of the curve), and write the corresponding rectangular equation by eliminating the parameter. x = t3, y = t^2/9arrow_forwardExplain how a pair of parametric equations generates a curve in the xy-plane.arrow_forwardWithout using a graphing utility, sketch the surface with equation x2 + y2 − z2 = 0.arrow_forward
- Find parametric equations for a circle of radius 2, centered at (3, 5).arrow_forwardEliminate the parameter in x = -t^2+9t and y = t-4 and then identify the parametric curve and sketch it's graph.arrow_forwardYou are watching your friend ride a Ferris wheel whose radius is 40 feet and center at (0,43). When you start watching your friend at t=0, they are at the highest point of the Ferris wheel. You notice the wheel is spinning clockwise at a rate of 120 seconds per revolution. Create a parametric equation that represents your friend's position at t seconds. DO NOT USE A CALCUATOR.arrow_forward
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