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- Solve: yv + 10yiv + 53y''' + 124y'' + 100y' = 0 a. y = C1e3xcos4x + C2e3xsin4x + C3e-2x + C4xe-2x + C5 b. y = C1e-3xcos4x + C2e-3xsin4x + C3e-2x + C4xe-2x + C5 c. y = C1e-3xcos4x + C2e-3xsin4x + C3e2x + C4xe2x + C5 d. y = C1e3xcos4x + C2e3xsin4x + C3e2x + C4xe2x + C5Find the set of values of 'a' if the points (1, 2) and (3, 4) lie to the same side of the straight line 3x -5y + a= 0.Y=a(x-1)^2+2 passes through the points (10,-160) A=
- Express u = (6,-2) as a linear combination of v = (1, 1) and w = (1,-1).Suppose you are climbing a hill whose shape is given by the equation z = 2000 - 0.005x² -0.01y2, where x, y, and z are measured in meters, and you are standing at a point with coordinates (60, 40, 1966). The positive x-axis points east and the positive y-axis points north. (a) If you walk due south, will you start to ascend or descend? ascend O descend At what rate? vertical meters per horizontal meter (b) If you walk northwest, will you start to ascend or descend? O ascend Odescend At what rate? (Round your answer to two decimal places.) vertical meters per horizontal meter (c) In which direction. the slope largest? What is the rate of ascent in that direction? vertical meters per horizontal meter At what angle above the horizontal does the path in that direction begin? (Round your answer to two decimal places.) 010х2 + 14х + 13 dx. J (2х + 1)(2к2 + 4х + 10)