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

Aword processing program requires a 7- digit registration code made up of the digits 1,2,4,5,6,7 and 9 each number has to be used and no number can be used mor than once how many codes are possible

For the quadratic function [tex]y=(x+4)^2-1[/tex] , do the following: a) rewrite the function in the standard form, b) rewrite the function in intercept form, c) find the vertex, d) find the y-intercept, e) find the x-intercepts.

Astudent draws two parabolas on graph paper. both parabolas cross the x-axis at (–4, 0) and (6, 0). the y-intercept of the first parabola is (0, –12). the y-intercept of the second parabola is (0, –24). what is the positive difference between the a values for the two functions that describe the parabolas? write your answer as a decimal rounded to the nearest tenth