Use Laplace transform to solve the partial differential equation: d²u du du(x,0) = , t> 0, 0

Q: Hiwo- solve the hyperblic partial differential equation numericaly where d²u d²u dx² = with initial…

A: Given  ∂2u∂x2=∂2u∂t2 The wave equation is ∂2u∂t2=c2∂2u∂x2 So c2=1 The difference for the given…

Q: For an arbitrary function f: XY, prove that the following relations hold: a) f(Uier Ai) = Uiel…

A:

Q: In Exercises 15 to 22, (a) determine whether the graph is Eulerian. If it is, find an Euler circuit.…

A:

Q: 1. Show, by drawing, that the following graphs are planar: (11) the graph of the octahedron.

A: Solution :-

Q: How many 7-letter words contain exactly 2 vowels? (For example, an 8-letter word with 5 vowels is…

A: To find the number of words contain exactly two vowels :-

Q: In Exercises 15 to 22, (a) determine whether the graph is Eulerian. If it is, find an Euler circuit.…

A: A connected graph G is said to be Eulerian if the graph G has a Euler circuit. A graph has an Euler…

Q: Be sure to show all work and all problem solving strategies. Give complete explanations for each…

A: Solution : a) X1 matrix is product of A and X where, X1(i,1)=Ai1X0(11)+Ai2X0(21)+Ai3X0(31) where,…

Q: 6. Suppose A = (3, -2, 4), B = (-5, 7, 2) and C = (4, 6, -1), find A × B.A+B-C.

A:

Q: 2. The personnel department of a particular company has observed that 20% of the people the company…

A:

Q: Let A be an n x n matrix. Assume that the inverse matrix of A exists. The inverse matrix can be…

A:

Q: (1) Using Legendre polynomials, find linear least-squares approximation to f(x) = In|xl.

A:

Q: Directions: Briefly answer the reflection questions below. 1. Why do we need not to include the…

A: Indefinite integration is denoted as ∫f(x)dx=F(x)+C Where C is constant of integration  and F(x) is…

Q: 0: PC (q)

A:

Q: If u = x² tan equal to (a) (c) x - y x + y - 2 x² + -1X 2² μ is - then 9 Әхду y -1 ½ - y² tan X (b)…

A:

Q: Mrs. Pack wants to teach her children responsibility and how to work while helping them earn money…

A: We can use calculus to maximize area  For relative maximum or minimum To maximize or minimize  a…

Q: If ƒ (0) = 1, ƒ (1) = 2, ƒ(2) = 33, f(3) = 244. Find a cubic spline approximation, assuming S" (0) =…

A:

Q: For a matrix A, define the eigen-vector as a non-zero column matrix X and eigen-value a scalar ›…

A:

Q: ý t + 45 зух P(x) = = 2x Q(x) = 2х 2

A:

Q: A major oil company wants to build a refinery that will be supplied from three port cities. Port B…

A: The objective is tantamount to minimizing the sum of distances between the refinery and  the three…

Q: If ƒ (0) = 1, ƒ (1) = 2, ƒ(2) = 33, f(3) = 244. Find a cubic spline approximation, assuming S" (0) =…

A:

Q: Homework: a. Use the Gauss-Seidel method to obtain the solution of the system until the percent…

A:

Q: M be a point on the circle circum ove the following: If n is even,

A:

Q: 7. Evaluate sizda by r (a) manipulating the integrand. (b) making a substitution. 88

A:

Q: Show that the fractional parts of a given sequence {annz1 is uniformly distributed if and only if 1…

A:

Q: ng Task 4: Given the equation x² + y² = 9. Differentiate using implicit differentiation. Express y…

A:

Q: PROBLEM Carry out the substitution in the improper integral 2 cos 0 = ei + e-i /2 Sh log (2 cos 0)…

A:

Q: Find the least squares quadratic which best fits the curve Y= ex interval •< X<I ao+aix +azx over…

A:

Q: 2. If f(x, y) = log (x² + y²), then ƒ + fyy is equal to 1 (a) x² + 2 (b) 0 + y 2 x² - y² y²-x² (c)…

A: We need to find the partial derivatives fxx , fyy  of the function f(x, y)=log(x2+y2) to find fxx +…

Q: 3 (a) So 4√3x dx √3x-x² 2

A:

Q: Use separation of variables method to solve: ди ổn ôn + =u where u(0, y) = 0 and ду Əx² du(x,0) ду =…

A:

Q: 4 Prove Borel Cantelli theorem (lecture notes p.16) i.e. Let (2, F, P) be a probability space and…

A: (a).Since         lim sup Ei C ∪k=m∞Ei⇒P lim sup Ei≤P∩(m≥1)∪(j≥m)Ej⇒limm→∞P∪(j≥m)EjUse…

Q: x(n)= a"u(k − n) for k>0

A: Introduction: The Z-transform translates a discrete-time signal, which is a sequence of real or…

Q: Given the following 2√2 h3(n): (²1³) " (n)u(m) 3 2.1 Determine the system function H(z). Simplify…

A:

Q: x Which of the following statements is/are true about the graph of R(x) = x² 4 - A. As the value of…

A: Introduction: For a rational function, vertical asymptote is quite natural. The points where the…

Q: The radius of a circle which circumscribes a regular n-si (a) Find the sum of the squares of all the…

A:

Q: 3+3=

A: Solution

Q: In Exercises 9 to 12, determine whether the two graph are equivalent. 9. B C C A D B

A: given two graphs

Q: Minimize C=3L-4K subject to 120=3K⁰.7L0.3. Find L*, K*, A*, C*. Now, Use Bordered Hessian to verify.

A: z =xy subject to x + 2y = 2lagrange function:L =U(x,y) +λ (M-p1x-p2y)

Q: 5. If u = f (y + ax) + ( (y - ax), then to อิน น อน (a) ay (b} 2 ay (c) −a? (d) a สิน 2 ay? 2 a อน…

A:

Q: Q5) Using graphical method to solve the following matrix game B1 B2 B3 A1 1 3 12 A2 8 6 2

A: This method can only be used in games with no saddle point, and having a pay-off matrix of type n×2…

Q: Use Laplace transform to solve the partial differential equation: o'y dy = ox² dt +xt where y(x,0) =…

A: Solution

Q: I. Evaluate each of the following iterated integrals. 1. Jo” Jovix dxdy R/2 (siny Inx 2. ²x…

A:

Q: NEED ASAP!! Find a root greater than zero of f(x)=e^x−2x−5 using the Fixed-Point Iteration Method…

A:

Q: radius of convergence is not 1/3. It says 1/3 is incorrect.

A: given series ∑n=1∞2+-1n·x+4n-1 radius of convergence is defined as R=limn→∞12+-1n1n

Q: For a data set of size 10, the highest order of a polynomial that could be fitted using Least…

A: Inbtroduction: The least square approach involves minimising the sum of the squares of the points'…

Q: In Exercises 29 and 30, a floor plan of a museum is shown. Draw a graph that represents the floor…

A: No it is not possible to walk through the museum and pass through each doorway without going through…

Q: 10- تقرير رياضيات on Mo Tu We Th Fr Sa Su X Memo No. Date 1 Inx X log x e X sin (X) cos (x) Tan ( X…

A:

Q: Use the Crank-Nicolson method with h = 0.1 and k = 0.01 to approximate the solution to the problem…

A:

Q: 1) Solve by using Laplace transform the partial differential equation 2² 8² dt2 =9. y(0,t) = 0,…

A: Solution

Q: Learning Task 5: Solve the following problems involving optimization. Do this in your notebook. 1. A…

A: