- (5 points) Find all the solutions in Z5 of the equation 3 – T –ī=.
find all associates of 2x^5-x+1∈Z5[x]
Find all of the solutions to the equation cos(t) = a) t = 4 + ka or t= 7* + ka, kez b) t = 8 + 2kr or t = 7* + 2ka, ke Z c) t = 8 + ka or t = 3* + ka, kez d) t = 1 + 2kr or t = 3 + 2ka, ke Z e) t = 31 + 2kt or t = 5x + 2ka, kez
7.(16 points) Consider the curve F(t) = 4 cos(t)ī + 4 sin(t); +3tk. (a) Find the unit tangent vector T(t) and the unit normal vector function Ñ (t) at the point (-4,0,37). (b) Compute the curvature k at the point (-4,0,31).
4 Consider the autonomous differential equation y f(v) a) (3 points) Find all the equilibrium solutions (critical points). b) (3 points) Use the sign of y f(z) to determine where solutions are increasing / decreasing. Sketch several solution curves in each region determined by the critical points in c) (3 points) the ty-plane. d) (3 points) Classify each equilibrium point as asymptotically stable, unstable, or semi-stable and draw the corresponding phase line.
4 Consider the autonomous differential equation y f(v)...
Consider the autonomous differential equation y = f(y) = y4-4 уг = y"(y-2) (y+2). a) (3 points) Find all the equilibrium solutions (critical points). f(y) to determine where solutions are increasing / decreasing. Use the sign of y' e) (3 points) Sketch several solution curves in each region determined by the critical poins in the ty-plane
Consider the autonomous differential equation y = f(y) = y4-4 уг = y"(y-2) (y+2). a) (3 points) Find all the equilibrium solutions (critical points)....
#5 cryptography
5) Find all solutions to x3 + x2 + 2:-3 in F5 6) Find a solution to the equation 13-5 in Z/30Z
(a). (3 points) Suppose the solutions of differential equation xy'''−y'' = 0 are in the form of xr where r is some number. Find three solutions in the form of xr. (b). (5 points) Find the general solution of xy'''−y'' = 6x^3
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1.11. Find all polynomial solutions p(t, x) of the wave equation u (a) degp 2, (b) degp 3. up with
Find all solutions of the given equation 2- 6x3 + 3 = 0
Find all solutions of the equation. Express the solutions in radians in the form a + 2nx, where a is in 10,2x) cos K42 The solutions of the equation cos x = 5 are of the form x=OR (Type an expression using n as the variable Type an exact answer, using x as needed. Use integers or fractions for any numbers in the expression. Use a