5. Suppose n > 0 Show that if ā is the (multiplicative) inverse of a modulo n then erpn(а)-erph (a). (Hint. Consider ākak-Ga)k-1k-1 (mod n))
5. Suppose n > 0 Show that if ā is the (multiplicative) inverse of a modulo n then erpn(а)-erph (a). (Hint. Consider ākak-Ga)k-1k-1 (mod n))
Problem 6. (15 pts.) Project the vector b = (1, 2,5) onto the line spanned by the vector (2,3,4). Use the linear algebra viewpoint and notation, NOT the multi- dimensional calculus one. Show work to justify your answers to the following: (a) Find the projection vector p. (b) Find the projection matrix P. (c) Find the error vector e.
(40 pts) 2a. Show that u(z) is the solution to the problem where k(x)-1 for x < 1/2 and k = 2 for x > 1 /2. 2b. Set up the weak form for the differential equation above and the resulting element stiffness and element load vector and calculate the element stiffness matrix and load vector for 4 quadratic elements by using the Gaussian quadrature that is going to exactly calculate the integrals Then set up the global K and...
Question 48 5 pts What is the pH of a 2.2 M solution of HOBr (K, - 2.0 x 10°)? Report your answer to the nearest whole number.
Thank you
4. (15 pts) a) Show that the Taylor series method, 2 is second-order accurate. b) (10 pts) For f(t, y) y2, write out one step of this mlethod
4. (15 pts) a) Show that the Taylor series method, 2 is second-order accurate. b) (10 pts) For f(t, y) y2, write out one step of this mlethod
2) [5 pts] Sketch the vector model for l = 3 and for every vector show the L, value.
5. Let K be a subfield of a field L. Show that L is a vector space over K In particular, C and R are vector spaces over Q.
vector Problem #5: Use the divergence theorem to find the outward fly SfF:nds of the field F = tan-1(10y + 3z) i + e sxj + 1x2 + y2 + z2 k, where S is the surface of the region bounded by the graphs of z = Vx2 + y2 and x2 + y2 + z2 = 49. ,z2 + 3 cos x + Problem #5: Enter your answer symbolically, as in these examples
Question 5. (15 pts) Find the maximum and minimum of S(,y) 22 + y2 = 1. on the circle
#4 please
3. (12 pts). (a) (8 pts) Directly compute the flux Ф of the vector field F-(x + y)1+ yj + zk over the closed surface S given by z 36-x2-y2 and z - 0. Keep in mind that N is the outward normal to the surface. Do not use the Divergence Theorem. Hint: Don't forget the bottom! (b) (4 pts) Sketch the surface. ts). Use the Divergence Theorem to compute the flux Ф of Problem 3. Hint: The...