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- (2, 0) Convert to polar coordinates with r,≥0 and 0≤theta<2Find the area of the surface formed by revolving the polar equation over the given interval about the given line. Polar Equation Interval Axis of Revolution r = eaθ 0 ≤ θ ≤ π 2 θ = π 2A simplified model of the Earth-Mars system assumes that the orbits of Earth and Mars are circular with radii of 2 and 3 respectively, and that Earth completes a complete orbit in one year while Mars takes two years. The position of Mars as seen from Earth is given by the parametric equations x= (3−4 cosπt) cosπt+2,y= (3−4 cosπt) sinπt. a. Graph the parametric equations for 0≤t≤2. b. Letting r= 3−4 cosπt, explain why the path of Mars as seen from Earth is a limacon
- These questions deal with converting points and curves from one coordinate system to another. Transform the following point (x, y) = (−3,−3) from Cartesian coordinates to Polar Coordinates. Be sure to include a sketch of the point.Find the area of the surface formed by revolving the polar equation over the given interval about the given line. Polar Equation r = 2 sin θ Interval 0 ≤ θ ≤ π/2 Axis of Revolution θ = π/2Sketch the polar curve r = 2 − 2 cos(θ). can you please show how you found all the points necessary to sketch this curve
- Find the length of the curve over the given interval. Polar Equation r = 5 cos θ Interval [π/2, π]The curves C1 and C2 are both symmetric with respect to the polar axis. Each of these curves is traced counterclockwise as the value of θ increases on the interval [0, 2π]. Also, for each of these curves, r > 0 when θ ∈ [0, 2π]. 1) Let P be the point of intersection of C1 and C2 in the second quadrant. Find polar coordinates (r, θ) for the point P where r > 0 and θ ∈ [0, 2π].2) Let R be the region that is inside both C1 and C2. Set up, but do not evaluate, the integral or sum of integrals for the AREA and PERIMETER of R.Sketch the curve with polar equation r = cos(3θ), 0 ≤ 0 < 2π, plotting only the points with r≥ 0 and including explanations for your answer.