1. Solve each linear congruence for all integers x so that 0 sx <m a) 11x...
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.
Prove Congruence Property 3 C3 If a=b (mod m) and c < 1, then ac = bc (mod mc)
4. Solve for x, 0 SX < 360° a) 2 sinx + 3 = 0 b) 7cosx + 2 = 0 c) 2sinx - sinx = 0 d) 2cos2x - cosx - 1 = 0
2. (5) Solve each of the following 2) (r+7)?(x-3); <0 b) 2x +3r-11x 26
Solve the following equation for all radian solutions and if 0 sx<27. Give all answ there is no solution, enter NO SOLUTION.) sin x 2 sin x cos x = 0 (a) all radian solutions (Let k be any integer.) 5n x= Tk, + 2nk, + 2tk rad 3 (b) Osx<22 at 57 X = X rad 3' 3 Need Help? Read It Talk to a Tutor 7. [1/2 Points] DETAILS PREVIOUS ANSWERS MCKTRIG8 6.1.043. Solve the following equation for...
Solve the equation for x If 0 sx < 21. Give your answer in radians using exa cos x + cos2x = 0 7C 3 X Need Help? Read It Talk to a Tutor 7. [1/1 Points] DETAILS PREVIOUS ANSWERS MCKTRIG8 6.2.02: Solve the equation for x if 0 sx < 22. Give your answer in radians using exact 2 sin2 x - 3cOS X - 3 = 0 21 411 . 33 Need Help? Read It Talk to a...
c(x + y2) for 0 SX S1 and 0 sys1 f(x,y) = 0 0.w. Find the conditional pdf of X given Y = y. (a) (b) Fim (r< 10-1)
8. Given integers m and 1<a<m, with am, prove that the equation ar = 1 (mod m) has no solution. (This means that here is no 1 appearing in the multiplication table mod m, in front of any of the divisors of m. That is, if m is composite, and a is a factor of m then a has no multiplicative inverse in mod m.)
Please solve the above 4 questions. 1. Using the extended Euclidean Algorithm, find all solutions of the linear congruence 217x 133 (mod 329), where 0 x < 329 (Eg. if 5n, n 0,. ,6) 24 + 5n, п %3D 0, 1, . .., 6, type 24 + x< 11 2. Find all solutions of the congruence 7x = 5 (mod 11) where 0 (Eg. if 4,7 10, 13, type 4,7,10,13, none. or if there are no solutions, type I 3....
0, x<-0.8 F(x)0.25x + 0.2. -0.8 sx<3.2 1, 3.2 sx ound your answers to 3 decimal places etermine the following: PX 1.8) T0.95