explain why there are no integers x and y such that 25x+30y=1
Question 1 9y" + 30y' + 25y = 0 O y = (C1 + c2x)e-5x/3 O y = (c1 + c2x)25x/3 O y=ce-5x/3 Oy- cze-5x/3 + c2
TiMX 2+ 2x-3 X²-2x+1 8 90x = y 25x to continuous at in {+ x +3 forxay x=3? Why 37-5, for 74 continuous atx4 ? why?
34.2. For each of the following equations, either find a solution (x, y) in positive integers or explain why no such solution can exist. (a) r2 - 1ly27 (b) 2 11y2 433 34.2. For each of the following equations, either find a solution (x, y) in positive integers or explain why no such solution can exist. (a) r2 - 1ly27 (b) 2 11y2 433
Consider the differential equation 2y"' + 167" + 30y' = tan(x) Note that y = 1, y = e-3x, and y = e-5x are solutions of the complementary equation. Now consider using variation of parameters. Set up the expression for u,' in determinant form.
Find all integers x, y, 0 < x, y < n, that satisfy each of the following pairs of congruences. If no solutions exist, explain why. (a) x + 5y = 3(mod n), and 4x + y = 1(mod n), for n = 8. (b) 7x + 2y = 3(mod n), and 9x + 4y = 6(mod n), for n=5.
Find the partial fraction decomposition for the rational expression. x + 7 3 25x - 16x x² + 7 3 25x-16x (Simplify your answer. Use integers or fractions for any numbers in the expre
Copy of R - 25x<2, -2sys 2 Consider the functions f(x,y)= 3 - 3 xy - x - y and the region (Then during the investigation of Absolute Extrema, we have to investigate(chose all possible options for values at all four intersection points to Investigate for Internal critical points and (-1,-1) is an internal critical point lla for Internal critical points and (1,1) is an internal critical point.Illa for critical points on four boundary.IVO critical points on three boundary VO
1. Answer the following questions. If they cannot be answered, explain why. (a) Solve the following problem with the Laplace transform method. Identify the free, forced, steady state and transient responses. #+25x 100, x(0) = 10, (0) 4 (b) Take the Laplace transform of y+ 0, y(0) =-3
Variation of parameters y'' - 10y' + 30y = 2e3x + 3e2x
x<--2 F(x)= {0.25x + 0.5 -25x<2 25x Determine the following: (a) P(X<1.8) (b) P(x>-1.5) (c) P(X<-2) (d) P(-1< X <I)