Show that for r=1x1 XER³, > A( 7 ) = 0 we have when 1x1=1 #0

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

A: First find the degree of all the vertex.  The degree of vertex  V of a graph is the number of edges…

Q: A disk is shaped a flat circular plate it's radius is 4.25inches to the nearest hundredth what is…

A: Solution

Q: (iii) (1) Find the x-intercepts of the parabola. Give your answers in decimal form, correct to two…

A:

Q: problem: Using the Laplace transform, solve the following initial value y" + 4y + 3y = e, y(0) = 1,…

A:

Q: You have 14 presents to give to your 3 kids. How many ways can this be done if: a. The presents are…

A:

Q: 7 8 3 2 9 6 4 10 5

A:

Q: 6. Let f(n)= o(n)/n. (a) Show that if p is prime, then f(p) = f(p). (b) Find all n such that f(n) =…

A: Introduction: Euler's Totient function is a mathematical multiplicative function that counts the…

Q: In Exercises 9 to 12, determine whether the two graphs are equivalent. 12. B D B D с F E A A F E

A:

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

A:

Q: 10. Prove that T/2 75/2. sin e cos (cos a cosec 0) de 10 T 2 (1-cos a).

A:

Q: Give an example of a non-planar graph that is not homeomorphic to K5or K3,3.

A: We can solve this using definition of planar graph.

Q: Q1/ From the following table of values, find the approximate value of f'(1.5) ? 1.2 1.7 1.5 0.4055…

A: Given:− To find: f'(1.5)

Q: GROUP holds four properties simultaneously: i) Closure, ii) Associative, iii) Identity element; and…

A:

Q: Determine whether a triangle with the given vertices is a scalene, isosceles, or equilateral…

A:

Q: Q3: Solve (x + y)dx - x dy = 0

A:

Q: If y = a e/, then radius of curvature p = a sec² 0 cosec 0, if (a) 0 = tan-12 (b) 0 = tan¨! a (c) 0…

A: The given equation of curve is y=aex/a

Q: ● Evaluate the following integrals: 4 Convert this Cartesian equation (x² + y²)²_9(x² - y²) = 0 to…

A:

Q: 1. 3) Suppose A = 4i-6j, B = i + 7j and C = 9i - 5j. Find (a) ||5B-3C|| (b) unit vector having the…

A:

Q: Use Picard's method to solve dx - Find y3(1)? -xy, y (0) = 1

A: Solution :-

Q: Use substitution to find the Taylor series at x = 0 of the function In 1 + 4x8 What is the general…

A: We have to find Taylor series for function in 1+4x8

Q: 2. If a is an involution, then Baß is an involution for any transformation B.

A: It is given that α is an involution. So, we can say that α2=I.

Q: Prove that given any constants a > 1 and b > 0, nº € o(a"). This shows that any exponential function…

A:

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

A: Let the rooms be a,b,c,d,e,f,g The floor plan can be made as follows.

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

A:

Q: Find the first five nonzero terms of the power series solution of the initial value problem: y + 4xy…

A: To find the first five nonzero terms of the power series solution of the below initial value…

Q: 0 Q4)(a) Find the maximum eigen value for the system A = x (0)=(0.02991) with initial vector

A: Let us find the maximum  eigenvalue of A using Power Method.

Q: Q2/ The region bounded by the curve y = x² and the line y = 3x, in the first quadrant is revolved…

A:

Q: Let , ² be the complex cube roots of unity. Let z₁, z₂, z, be complex numbers such that z₁+z₂+z3 = A…

A: We will use properties of cube root of unity  ω3=1  and  1 + ω + ω2 =0

Q: Find the Laplace transform of 1. f(t) = ½ [1 − u₂π(t)](2 sin t — sin 2t)

A:

Q: A function u = f(x, y) with continuous second partial derivatives satisfying Laplace's equation…

A: Solution

Q: Graph the following Equations: x+3 5. y²: 2x²+3x+2 6. r = sin + 2cos²0 7. r² = sin 20-3cos

A: We can solve this using given information

Q: Show that if 4, and A, are two events, then P(A₂)+P(A₂)−1≤P(44₂).

A:

Q: Show that if 4, and A, are two events, then P(A₂)+P(A₂)−1≤P(44₂).

A: First we will write Inclusion-exclusion principle for two sets.

Q: 12 f(x) = X ¹²³ + x² + x² + x² Show that whether f(x) is irreducible or not

A:

Q: Find the Laplace transform of 1. f(t) = [1 − u₂n(t)](2 sin t - sin 2t) - 2

A: Properties of the Laplace transform Laf(t)+bg(t)=aF(s)+bG(s)Lsinat=as2+a2Luc(t)sinat=e-css2+a2

Q: b if it Se was Where a + 2b = 3 find the Value (2x + 3) dx a, b E R

A:

Q: 2. If the population is infinite or the population is finite in which sampling is with replacement,…

A:

Q: The point of inflexion of the curve r = b0" are given by {a} r = b[¬n(n+1)]"¹² (b) r= b[n(n+1) ² (c)…

A:

Q: Use Laplace transform to solve the partial differential equation: d²u du du(x,0) t> 0, 0<x<1, u(x,0)…

A: Solution

Q: D B C E F

A:

Q: ermine the constant a so that the vector V = (x+3y)i + (y-2z)j + (x+az)k is solenoidal

A:

Q: Test the convergence of the following: n 3η +1 1- 4, n 3n-1 2- - Στη n=1 = 1) n Inle+ n+l

A:

Q: Show if x, is convergent or divergent T.3 'n sin(x) dx 1+x S'

A: Introduction: The convergence or divergence of an infinite series depends upon the sum of the…

Q: Can the graph G be orientable ? G:

A: We will use the definition of orientable Graph.  A graph G is said to be orientable if there exists…

Q: (ylny - e¯xy)dx + ( + x lny) dy = 0

A: The differential equation Mdx+Ndy=0 is said to be exact differential equation. If it satisfies the…

Q: Q4) Find the largest eigen value for the matrix A- [1 2] A= with x (0)=(7/17 1) 54

A:

Q: Find the maximum and minimum values of x^2 + y^2 − 2x − 2y on the disk of radius √ 8 centered at the…

A: Given function is  fx,y=x2+y2-2x-2y where bounded region is  x2+y2≤8.

Q: ) Solve by using Laplace transform the partial differential equation a²y 8² 9. dt2 Ox² y(0,t)= 0,…

A: Solution :-

Q: Using the parity theorem and contradiction, prove that for any odd positive integer p,√2p is…

A:

Q: You are given and Find the value of S₁=1+q+q²+...+ 1+ ( 9 + ¹) + (ª +1 = "Y

A: