2. For each of the following, find all integers a with 0 S < n, satisfying the following congruences modulo n. (a) 3x5 (mod 7) (b) 3x 5(mod 6) (c) 3x 3(mod 7) (d) 3 3 (mod 6) (e) 2x 3(mod 50) (f) 22r 15(mod 67) (g) 79x 12 (mod 523)
2. For each of the following, find all integers a with 0 S
8 Minimize z= x + 3y 9 + 22 54 + 4yΣ Subject to 2y + 2 > ΛΙ ΛΙ ΛΙΛΙ ΛΙ 14 O Σ Ο Minimum is Maximize z = 4x + 2y 32 + 4y < < 32 5x + 5y < Subject to 0 VI VI ALAI y 0 Maximum is
Find all the integers x which are the solutions to the following congruences. x^2 is equivalent to 2 mod 17
1. Solve each linear congruence for all integers x so that 0 sx <m a) 11x 8 (mod 57) b) 14x 3 (mod 231)
Let F(x,y,z) = <7x, 5y, 2z > be a vector field. Find the flux of F through surface S. Surface S is that portion of 3x + 5y + 72 = 9 in the first octant. Answer: Finish attempt
Suppose that f (x II 2y), 0 < x < 1,0 < y < 1. Find EX + Y).
1.3.101 Find two values of θ, 0 θ < 2%, that satisfy the following equation. cos θ= 2 (Simplify your answer Type an exact answer, using π as needed. Use integers or fractions needed.)
(3 points) Maximize the function P = 7x – 8y subject to x > y > 6x + 5y = ( 10x + 2y > ΛΙ ΛΙ V 0 0 30 20 What are the corner points of the feasible set? The maximum value is and it occurs at . Type "None" in the blanks provided if the maximum does not exist.
Find the x-coordinate of all points on the curve y= 8x cos (7x) – 28/3x² - 41, <x< where the tangent line passes through the point P(0, -41) ( not on the curve). There are two value X1, X2 where xy < X2 : x1 = 0 . x2=0 Type an exact answer using n as needed.
Let F(x,y,z) = <7x, 5y, 2z> be a vector field. Find the flux of F through surface S. Surface S is that portion of 3x + 5y + 7z = 8 in the first octant. Answer: