Verify that the given functions y1 and y2 satisfy the corresponding homogeneous equation; then find a particular solution of the given nonhomogeneous equation. t2y'' − 2y = 5t2 − 1, t > 0, y1(t) = t2, y2(t) = t−1

Find the area of the triangle formed by the origin and the points of intersection of parabolas y=−3x^2+20 and y=x^2−16.

In each of the cases that follow, the magnitude of a vector is given along with the counterclockwise angle it makes with the +x axis. use trigonometry to find the x and y components of the vector. also, sketch each vector approximately to scale to see if your calculated answers seem reasonable. (a) 50.0 n at 60.0°, (b) 75 m/ s at 5π/ 6 rad, (c) 254 lb at 325°, (d) 69 km at 1.1π rad.

Officer brimberry wrote 32 tickets for traffic violations last week, but only 4 tickets this week. what is the percent decrease? give your answer to the nearest tenth of a percent.