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a) Find a Cartesian equation relating and corresponding to the parametric equations: x=2sin(3t), y=9cos(3t). Write your answer in the form P(x,y)=0, where P(x,y) is a polynomial in x and y, such that the coefficient of y^2 is 4. b)Find the equation of the

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A plane curve can often be represented in Cartesian coordinates by an implicit equation of the form (,) = for some specific function f. If this equation can be solved explicitly for y or x – that is, rewritten as y = g ( x ) {\displaystyle y=g(x)} or x = h ( y ) {\displaystyle x=h(y)} for specific function g or h – then this provides an ...

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The Doppler angle value of a pixel identifies the surface of a cone of angle,(, from the antenna’s velocity vector that is defined by the Doppler cone equation or Doppler cone condition: Eq. 51 Where: VARP: ECEF coordinates of the sensor velocity vector, R: ECEF coordinates of the unknown ground point. RARP: ECEF coordinates of the sensor position

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Finally, setting = cdefines a cone at the origin as in the right figure below. In your worksheet, plot the coordinate surfaces = 4, = 1, and = 1 in spherical coordinates. The equation in Cartesian coordinates of the sphere of radius cis x2 + y2 + z2 = c2.

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The connection between polar and Cartesian coordinates is r cos9 r sin 9 Equation for O do not uniquely determine it when x and y are given. Therefore, in converting from Cartesian to polar coordinates, it is not good enough jwst to find r and 9 that satisfy equations. We must chocxse 9 so that the point (r, 9) lies in correct quadrant.

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The cone edge is defined by setting Y = 0, where the intensity approaches infinity . For a spatiotemporal Gaussian pulse excitation, the intensity distribution of the photonic Mach cone computed by Eq. 3 is shown in fig. S2B. We also numerically evaluated the photonic Mach cone using the time-resolved Monte Carlo method.

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