4. Evaluate loga(-3), when loga(VT) = 0.2. 13 marks) 5. The function z is given as: z=f(x,y) = 2x2y - 5xy - y sin (xy) Show that a2z дхду az àyox (8 marks]
Given the function f : {w, x, y, z} 5 with ordering w < x < y < z and f = (4, 3, 5, 4). i. Identify each of the following: domain, codomain or range, image ii. Is f one-to-one? Explain. 1 iii. Is f onto? Explain.
I. a) (4 points) For a given function F(x, y, z) = xz + (y + z)(x + z) Draw the logic circuit diagram of the function: b) Using Boolean Algebra to simply the above function c) Use Demorgan's Theorem to find out the complement of the above function F(x,y,z)xz+ + 2)(x +z)
1) Prove that if loga x = y, then lo8b x = (loga x)(logb a). Plot loga n for 1 S ns 100 when a 2, e and 10.(10-points) 2) Prove that (b) Ση-112-n(n+ 1 )(2n+ 1 )/6 k+1) (1-x) if X Hint: Induction - Discrete Math (15-points) 3) Consider two balanced dices with each of the six faces marked 1 to 6. In one single throw of these two dice, list all the possible outcomes. Compute the average value...
8.) (10 Points) Given the contour diagram z = f(x,y). 2 1 2 3 4 -2 R a. Find i. f(-1,1) 11. a value of x for which f(x, 1) = 3 iii. a value of y for which f(0,y) = -2 b. The given graph has a local maximum value. At which point (x,y) does this occur? c. Determine the sign (positive or negative) of the following partial derivatives. i. (1,0) ii. fy(0,1)
(a) Given the (z, y) values (1, 2), (2, 4), (3, 10), (5,8) write in matrix form the linear system to solve for the b, coelicients in the interpolating cubic spline with natural boundary conditions. (b) If an interpolating cubic spline is as given below, find (1) what points it interpolates and (2) its value at z= 0. -1.27(r +1)3 + 6.54(r + 1) – 2 for -1 <r<1 9.15(r - 1)3 - 7.57(r - 1)? - 8.59( - 1)...
8. A 4-vector < x,y, z,t > describes the position of an object at a given time, using < x,y,z > for its coordinates at t for the time. Suppose s-scale (for s a Real number) is the operation of moving < x, y, z > to< sx, sy, sz > in a single time step. Which of the following is true? OA. The process of computing the new vector can be achieved by using a 3 x 3-matrix. OB....
Use a Venn Diagram. Let P(Z)=0.47, P(Y)=0.24, and P(Z ∪ Y)=0.56. Find each probability. (a) P(Z′ ∩ Y′) (b) P(Z′ ∪ Y′) (c) P(Z′ ∪ Y') (d) P(Z ∩ Y') Complete the Venn diagram below using the given probabilities. I can't figure out how to find the circled answer! Please and thank you!
2. You are given the following multivariate PDF 3 (x, y, z) else s fxx.2(z, y, z)- I, 0 where S-((z, y,2)lr'ザ+8-1) (a) (5 points) Let T be the set of all points that lie inside the largest cylinder by volume that can be inscribed in the region of S. Similarly let U be the set of all points that lie inside the largest cube that can be inscribed in the region of S. What would the probabilities P(X,Y, Z)...
5] (2) GIVEN: a> 0,0# {(x, y, z) z a"-x'-y") W is the solid region of R' that is below 2 and above the xy- plane. W has constant density,8 and the mass of W is M, m(W) M FIND: The moment of inertia, I, of W with respect to the z- axis, express 2 I in terms of M and a without 8