Question

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Parametric equations and a parameter interval for the motion of a particle in the xy-plane are given. Identify the particle's path by finding a Cartesian equation for it. Graph the Cartesian equation by hand Indicate the portion of the graph traced by the particle and the direstion of motion- 43 2 -1 2) 2) Flnd all points of horizontal and vertical tangency to the curve 3) 3) Find the are length of the curve with the given interval. x» 6t2 , y : 2t3 interval: 1 s t s 4 (Leave your answer in exact form in terms of radical)

Plot the point whose polar coordinates are given. 4) (2, -5rt/4) 4) Convert the polar equation to Cartesian equation. 5) Find the slope of the polar curve at the indicated point. 6) 6) r-1-sin θ, θ:0 7) Find the length of the curve over the given interval r e30 on the interval 0s0s2. 7)

Show transcribed image text Parametric equations and a parameter interval for the motion of a particle in the xy-plane are given. Identify the particle's path by finding a Cartesian equation for it. Graph the Cartesian equation by hand Indicate the portion of the graph traced by the particle and the direstion of motion- 43 2 -1 2) 2) Flnd all points of horizontal and vertical tangency to the curve 3) 3) Find the are length of the curve with the given interval. x» 6t2 , y : 2t3 interval: 1 s t s 4 (Leave your answer in exact form in terms of radical)
Plot the point whose polar coordinates are given. 4) (2, -5rt/4) 4) Convert the polar equation to Cartesian equation. 5) Find the slope of the polar curve at the indicated point. 6) 6) r-1-sin θ, θ:0 7) Find the length of the curve over the given interval r e30 on the interval 0s0s2. 7)