2. Find the roots of the give vectors) in the plane; find c real parts and the imagina to (iii) and (iv). (i) cubic roots of -1

Q: Prove that 2^? +3^? is a multiple of 5 for all odd ?∈N.

A: We will solve this problem using principle of mathematical induction.

Q: Exercise 14.4.22. Let o be a permutation in S,. (a) Show that there exists an integer k > 1 such…

A: Given that α is a permutation in Sn.

Q: What times 0.1 equals 11

A:

Q: Find the area of the triangle using the following information, Round to the nearest hundredth, if…

A: Introduction: The formula of the area of the triangle is given by, Area=a×b×sin(C)2 Where a and b…

Q: Find T(t) and N(t) at the given point. r(t) = (t² – 8)i + tj; t= 8 %3D T(8) = N(8) =

A: Given that r(t)=(t2-8)i+tjTo find T(t) and N(t) at the point where t=8

Q: Maximize: F = 39x+17y Subject to: x+2y<8 x+y<6 x+4y<14 x, y 2 0

A:

Q: 2. Let f(z) = cos(rr/4), where r is in radian. Use the huadratic Lagrange interpo based on the…

A: Here given function fx=cosxπ4 and x0=0, x1=1, x2=2, x3=4

Q: Find all sixth roots of I, by solving the equation 1. [Hint: Find the zeros of the polynomial f(x) =…

A: Use the following formulae, to obtain the solution. a2-b2=a-ba+ba3-b3=a-ba2+ab+b2a3+b3=a+ba2-ab+b2

Q: Problem 5. A space has the line element, ds? =v°du? +u°dv² . Determine whether this space is flat or…

A: Given: Line element, ds2=v2du2+u2dv2. To find: Whether the space is flat or curved.

Q: numbers and Vị Suppose that . Let A be the 3x: eigen valesof

A:

Q: Determine whether the sequence is divergent or convergent. If it is convergent, evaluate its limit.…

A: We have given a sequence ,  xn = 31 + 19 arctann17n If we say that sequence xn is convergent , it…

Q: 5. Find the Laplace transform of the equation f" (t) + f(t) = sin bt where f(0) and f'(0) = 0 (a )…

A:

Q: 20 27 24 29 26 Consider the graph given above. Use the nearest neighbor algorithm to find the…

A: To find- Consider the graph given above. Use the nearest neighbor algorithm to find the Hamiltonian…

Q: The value of 'b' for which u(x, y) = ebx cos 5y is harmonic

A:

Q: 4. Use the Laplace transformation to solve the wave equation, ‚²u I > 0, t>0 subject to the initial…

A:

Q: Find the values of x1, x2, x3 in the system of Linear Equations 2x, – 6x, – x3 = -38 —3x, — х, + 7х,…

A: For easy understanding let x1 = ax2 = bx3 = c So the given equations are 2a-6b-c=-38  -3a-b+7c=-34…

Q: Given a surjective function ? ∶ [−1, 1] → [−1, 1], prove or disprove: ? −1 (? {0}) = {0}.

A:

Q: 2. Use mathematical induction to show that if a is an eigenvalue of an n × n matrix A, with x a…

A:

Q: Mapmakers in the fictional land of Euleria have drawn the borders of the various dukedoms of the…

A: Given- Mapmakers in the fictional land of Euleria have drawn the borders of the various dukedoms of…

Q: Find the matrix for T relative to the basis B, and use Theorem 8.5.2 to compute the matrix for T…

A:

Q: Suppose C is the curve from (0, 0) to (2, 0) to (2, 3) to (0, 3) to (0, 0). Find the work done by…

A:

Q: -5 Let M = 5 . Find cj and c2 such that 3 M² + c, M + c2I, = 0, where I2 is the identity 2 ×2…

A:

Q: 1 -2 6. 1 1 -3 Let A = -1 0 and P = 0. 0. 0 0 -1 1 Given that P diagonalizes A, then compute each of…

A: Hope you like it

Q: For the following logarithms, either write the correct value, or explain why the expression does not…

A:

Q: 5. Triangle ABC is a right triangle with an angles A = 90°, B = 36.86°, and C = 53.13°, If AC is…

A:

Q: Practice Exercise: Find the differential equations of the following by eliminating the arbitrary…

A:

Q: Use the shell method to find the volume of the solid generated by revolving the region x2 and…

A:

Q: The graph of a function f is shown in the figure above. Which of the following limf(x) = 1 %3D o lim…

A:

Q: An open map is a map f : X → Y such that for every open U C X, the set f(U) is open in Y. Prove that…

A:

Q: The value of 'b' for which u(x, y) = ebx cos 5y is harmonic

A:

Q: Sketch the region R of integration and switch the order of integration. 10 *In(y) f(x, y) dx dy Jo

A: To find- Sketch the region R of integration and switch the order of integration. ∫110∫0lnyfx, y dx…

Q: The function f(r) = sinh(r) is one-to-one and so is invertible. Using our rule / formula for…

A: When the inverse of a function y=fx is f-1x then the derivative of inverse is given by…

Q: The other type of question in chapter 7 is solving trigonometric equation. We will not be practicing…

A:

Q: exponential function rate of change   Consider a function P(x) = 5.4 (1.05)^x   a) explain what…

A: (a) Here, P(x) = 5.4 (1.05)^x represents a geometric series.   P(0) = 5.4 (1.05)^0 = 5.4 x 1 = 5.4…

Q: Find the solution of the equation = e cos y which tends to zero as x → 0o and has the value cos y…

A:

Q: Subtract the given number system. Show your complete and detailed solution. 24325 – 1345

A:

Q: Question 1 Let S be the surface that is the part of the plane x + y + z the first octant. Find a…

A: Given that S be the surface that is part of the plane  x+y+z=3       ...(1) lying in the first…

Q: Complete the proof of Property 4 of the following theorem by supplying the justification for each…

A: We have to prove that c0=0 L.H.S=c0 =c(0+0) ,                 ∴ 0+0=0 by additive identity property…

Q: A tin can has a base diameter of 10 cm and a height of 10 cm. The can is initially full, but a hole…

A: We have to find how fast is the water level falling?

Q: Find the eigenvalues 11 < 12 < 13 and corresponding eigenvectors of the matrix

A: Given,          A=-5-201400-130005

Q: Consider the following. y 24 y = f{x) 12 12 24 X (a) Use six rectangles to find estimates of each…

A:

Q: Let G be simple connected planar graph. If G has 8 vertices and 11 edges, in how many regions will…

A: Euler formula for planar graph: Let G be a connected planar graph, and let n, e and f denote,…

Q: Time left 2:05:38 dy sin x+2y = tan° dx 3 X Choose... Choose. Exact Differential Equation Separable…

A: sinxdydx+2y=tan3x2 is Linear differential equation as it has degree 1.

Q: Determine whether the series is convergent or divergent. n2 Σ n7 + n n = 1 O convergent O divergent

A: We have given a series , ∑n=1∞ n2n7 + n. We need to determine whether the given series is convergent…

Q: A flower garden is shaped like a circle. Its diameter is 28 yd. A ring-shaped path goes around the…

A:

Q: 3 -2 7. Let u , and y . Let W = Span{, . -1 2 3 13 (a) Verify that {u,, ư2} is an orthogonal set.…

A:

Q: Let 2 (-1)** 'ak be a convergent alternating series with terms that are nonincreasing in magnitude.…

A: We have to find the upper bound for  error.

Q: Let T and T' be topologies on a set X such that T' is strictly finer than T. If Y is a subset of X,…

A: The two topologies τ and τ' is defined on a set X. It is given that τ' is strictly finer than τ. By…

Q: QUESTION 5 a) What is the maximum possible order of an element in S,? Give an example of one of…

A: (a) any element in S7 is either a cycle or composition of disjoint cycles.     Now, maximum order of…

Q: Here we consider f(x) = Vx near x = 8. (a) Find T1(x) and T2(x) centered at r = 8. (b) Separately…

A: We are authorized to answer three subparts at a time, since you have not mentioned which part you…