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- Find the length of polar curve of r=θ^2 with θ less than or equal to 7π/4 and greater or equal to 0.Sketch the regions defined by the polar coordinate inequalities 0 ≤ r ≤ 6 cos θWhat are the coordinates of the vertices of △A′B′C′ after a reflection across a line through point P with a y-intercept at y=−2 followed by translation T3,3?
- What are the coordinates of the vertices of△A′B′C′after a reflection across a line through point P with a y-intercept at y=−2 followed by translation T3,3?An ant is walking on the xy-plane is such a way that its distance to the point (2, 4) is always the same as its distance to the x-axis. Find an equation for the path of the ant.Determine the family of curves of all parabola's with axis parallel to the x-axis and with distance from focus to vertex fixed as "a".
- A flashlight is shaped like a paraboloid and the light source is placed at the focus so that the light bounces off parallel to the axis of symmetry, this is done to maximize illumina- tion. a particular flashlight has its light source located 1 cm from the base and is 6 cm deep. what is the width of the flashlight's opening?determine the surface of revolution if it is revolved about x=-3Determine the DE of the family of curves. Sketch its representative members Parabolas with vertex and focus on the line y=3
- A lamp is placed three units to the right of the y-axis, and a shadow is cast by the elliptical region given by x2 + 4y2 = 5.If the point (−5, 0) is on the edge of the shadow, how far up is the lamp located? I.e. if the lamp is placed in point (3, Y), what is the value of Y?Verify that the two families of curves are orthogonal, where C and K are real numbers. Use a graphing utility to graph the two families for two values of C and two values of K. x2 + y2 = C2 , y = KxVerify that the two families of curves are orthogonal, where C and K are real numbers. Use a graphing utility to graph the two families for two values of C and two values of K. xy = C, x2 − y2 = K