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Find r so that the line through (2; 6) and (- 4; r) is as follows:

ii. Perpendicular to x + 2y = 1


Find the section of the conicoid x^2/2-2y^2/3 = 2z by the plane x-2y+z = 1. What conic does this section represent? Justify your answer.
Find the equation of the line which passes through the point (1,√3) and makes an angle of 30◦ with the line x-√3y+√3 = 0.

12000 and grows 5% every year what will be the population after 12 years to the nearest whole number


Use traces to sketch and identify the surface x^2=y^2+4z^2


Find the equation of a circle with center at (-1,-3) passing through the intersection point of the two lines: 4x+y-4=0 and x-y-6=0


Two stations, located at M (−1.5, 0) and N (1.5, 0) (units are in km), simultaneously send sound signals to a ship, with the signal traveling at the speed of 0.33 km/s. If the signal from N was received by the ship four seconds before the signal it received from M, find the equation of the curve containing the possible location of the ship. 


Write the standard form of equation of parabola given the following properties: vertex (0,0); focus (0,-1); directrix line y=1; and axis of symmetry x=0.


Write the standard form of equation of parabola given the following properties: vertex (0,0); focus (0,-1); directrix line y=1; and axis of symmetry x=0. (use ^2 for "squared";


Write the standard form of equation of parabola given the following properties: vertex (0,0); focus (0,-1); directrix line y=1; and axis of symmetry x=0. (use ^2 for "squared";


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