4. Consider the subspace V of R' given by 1 3 V = span (a) Find an orthonormal basis for the orthogonal complement V-.

Q: 2. Find the volume of solid generated by revolving te area enclosed by: x=y2+1, x=0, y=0 and y=2…

A: The area enclosed by x=y2+1, x=0, y=0 and y=0 The shaded portion is the required region

Q: Compute f(10.25) for a given set of data below using: 1. Lagrange Interpolating Polynomial 2.…

A:

Q: Determine whether the following systems of differential equations are de- generate. In the…

A: Given,System of differential equations. We need to check in both the given cases whether they are…

Q: 3. Determine the convergence of the series: 8. Σ k=1(2k +1)! of

A:

Q: Q6) Find the approximate value of A and B in ya = x(1 – x)(A + Bx) where y + x² = 0 and y(0) = y(1)…

A: Given data A polynomial  ya=x(1-x)(A+Bx) A differential equation  y"+x2=0ord2ydx2+x2=0 Boundary…

Q: QUESTION 1 (a) Determine the Inverse Laplace transform of the following expressions: 1 (s-4)' (b)…

A: Solution

Q: Find the mass of a plate bounded by one arch of the curve y = sin x, and the x-axis, if the density…

A: A scalar function f(x,y) is a rule that is used to associate a number, or quantity with a particular…

Q: Find the general solution of dy/dx= e^3x+2y

A:

Q: Theorem 8. Let B = {u, u,., u,} be an orthonormal basis of an inner product space V. Then a linear…

A:

Q: b. e d

A:

Q: The two vector fields are F = -10ax + 840y and G = 192ax – 7ay + 8az. For the point P(8, 8, 6),…

A:

Q: Supply the missing integrand and the limits of integration x dx dy V4 + x² _dy %3D

A:

Q: Solve for the laplace transform of e^(at) cos bt using using the integral formula for laplace…

A: The solution is given as

Q: 2. Use membership tables to prove that A - (BnC) = (A – B) U (A – C).

A: To Prove: A-B∩C=A-B∪A-CUsing the membership table.

Q: 1 2 Q4) Find the maximum eigen value for the system A = 5 4 with initial vector x' (0) = (1 1)

A:

Q: What is the intercept for observations with X2 equal to 0? a. 2.121 b. 0.055 c. 1.343 d. -0.723

A: The intercept for observations with X2 equal to 0 is determined as shown below.

Q: Express the following complex number in its polar form. 2+5i 6.- -4-7i

A: Solution :-

Q: C. Use the Golden Section method to solve the minimum of f(x) = In(x²) + In (x³) + In(x*) using an…

A: Given: The function to be minimized is f(x)=ln(x2)+ln(x3)+ln(x4) xi=0.2xu=4

Q: If X x2(m, mµ²) find the corresponding (a) mgf; and (b) characteristic function.

A:

Q: 6. (a) Carefully sketch (and shade) the (finite) region R in the first quadrant which is bounded…

A:

Q: ESSAY WRITING 1. Site one real-life application for the topic Geometric Designs 2. Site one…

A: We will use the basic knowledge of applications of mathematics to answer this question.

Q: 0 0 0 1 0 0 0 1 0 ) Let A =

A:

Q: 1. If the statement "for some x, P(x)" is false, then the statement "for every x, P(x)" is false. 2.…

A: This is a problem of Logic.

Q: QUESTION 22 The following adjacency matrix corresponds to a directed graph. Determine if the…

A: We have to find the solution.

Q: Let G be a graph with vertex set V(G) = {v1, v2, v3, V4, V5, V6, V7} and edge set E(G) = {vrv2, vv3,…

A: Given that G is a graph with vertex set VG = v1, v2, v3, v4, v5, v6, v7 and edge set EG = v1v2,…

Q: The value of the triple integral (x² + y)dV where E is the E portion of x + y + z? = 4 with 0 < y,…

A: Solution:-

Q: prove it .The set of all optimum solution of the general convex programming problem is a convex

A: Proof

Q: 6. (a) Carefully sketch (and shade) the (finite) region R in the first quadrant which is bounded…

A: (b) To Set up: Integral for the region which is bounded above by the curve y(x)=x(10-x) and bounded…

Q: A motor and geartrain used in a servo system are operated with a steady voltage and the output of…

A:

Q: 1. Use an appropriate way to determine whether the following is convergent or divergent. k 'Ink i. Σ…

A:

Q: TRUE OR FALSE 10. Addition and Simplification can be applied to part of lines of proof. 11. If p, q,…

A:

Q: Let  V  and  W  be vector spaces over the field  F  and let  T  be a linear transformation from  V…

A:

Q: III. In a particular very small region, the consumer price index, C, depends on the current valuc of…

A: Given information C = 100 + e-EPF where, C = Consumer Price Index E = Gross Domestic Regional…

Q: V. Determine all the relative minimum and maximum values, and saddle points of the function h…

A: The given function is hx,y=x3-3x+3xy2...(1) To find: The maximum, minimum values and saddle points.

Q: 3(1+6) – log(5+ sin(VI+yi)) +4(z + 2)-3 Draw a parse tree for

A: Solution: To address this articulation we present three new unary administrators. The logarithm work…

Q: Let G be a graph with vertex set V(G) = {v1, v2, V3, V4, V5, V6, V7} and edge set E(G) = {v1v2,…

A:

Q: Express the following complex number in its polar form. 2+5i -4-7i

A:

Q: dz and ду Suppose z is a function of x and y, and tan Vy² + x² = 2*e6y. Solve for

A: This is a problem of partial differentiation.

Q: 2. Consider the initial value problem y' = 2x +1 Sy +1 y(2) = 1. a. Estimate y(3) using h = 0.5 with…

A: (a) Given the initial value problem y'=2x+15y4+1 with condition y2=1 i.e. x0=2, y0=1 To find y3 i.e.…

Q: The mathematics department of the College of Science consists of four people: Josie who is…

A: Using the logical assertions presented, we must derive the hobbies associated with the individuals.

Q: TRUE OR FALSE 16. The exclusive disjunction of -1 <1 and – 1+1 = 0 is true. 17. A conditional…

A:

Q: Read the following items carefully. Write-by-hand your solutions and/or proofs in short bond papers…

A:

Q: 5. (a) Let z = (a + ai)(b+ bv3i) where a and b are positive real numbers. Without using a…

A:

Q: 5.19 Consider the mapping T: L'(0,2) L'(0, 2), (Tf)(x):= f(t)dt. (i) Show that T indeed maps L'(0,…

A: We will use the basic knowledge of functional analysis to answer both the parts of this question…

Q: Solve the DE: dy + 2xy = 2x³y3. dx

A: The given problem is to solve the given differential equation. The given differential equation is of…

Q: 4. Let f:R→Rbe a function defined by f(x)=x for every xe X . Show that f is a continuous.

A:

Q: Let G, and G, be two groups. Let H and H, be normal subgroups of G G, respectively then @ H, x H, 4G…

A:

Q: 1. Which of the following permutations in S, is odd? (a) 53124 (b) 51423 (c) 51234 (ed) 54231

A:

Q: If A is an  m × n matrix with entries in the field F, then                   row rank (A) = column…

A:

Q: 1. Solve the linear system using Jacobi and Gauss-Seidel Method 2x – y = 2 3y + z = -2 - -x + y – 3z…

A: