Prove that an angle of θ radians is constructible if and only if the real number cosθ(sinθ) constructible.

Q: The weights of 40 pupils are shown below 35 43 52 39 62 54 58 37 44 62 43 48 53 42 55 37 45 50 40 46…

A: Making use of Tally method.

Q: Determine whether the following series is convergent or divergent. If it converges, find its value.…

A:

Q: 2. Give an example of a graph with at least four vertices, or prove that none exists, such that: (a)…

A: Graph theory, construct a graph

Q: Let A be a non-empty set of positive numbers, which is bounded above and let B = {x e R: 1/x e A}. 1…

A:

Q: y = 5/(sin3x +cos3x)

A:

Q: Differentiate the following using (a) forward difference method; (b) backward difference method; (c)…

A: We are given the following function.      f(x)=12 sinh(x) at x=1 Note: We will be taking the step…

Q: 1 -1 (c) Let A : -1 1 1 and define LA : Rª → R³ by %3D -1 1 1 LA: 12 H A. Find the kernel of LA.…

A:

Q: Using Variation of Parameters, the particular solution y, of the non-homogeneous differential…

A:

Q: From the particular solution of the DE y" + 2y' + y = x at x = 0, y = - 2,  y' = 2, obtain the value…

A:

Q: II. Consider the function g defined by 1 g(x, y) = cos (TLV) + logg(r – y)" Do as indicated. g 1.…

A:

Q: 5. (a) Let V = R* and let (·, ·) be the standard dot product on V. (i) Calculate (e, +€3; €2 + €4).…

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

Q: Use the following methods to solve for the root of the equation f (x) = xe* – sin?x

A: The False Position (also known as Regula Falsi) method uses the formula:…

Q: Determine whether the following series converges or diverges: Vn5+8 Input C for convergence and D…

A:

Q: 2 - Given matrix A = -5 applying 3. 1 -3) 31 row operation it become -5 what row operation used? a.…

A:

Q: Give the adjacency matrix of the graph below.

A: The entries of the matrix are the number of edges from a vertex to another vertex.

Q: 6. Let 15 2 8 B= |-3 4 1 L4 -4 5. e) Find odj a Compute det (B) E Show that the B (Adj B) = (odj 8)…

A:

Q: Let Lin{u} =U, Lin{w} = W, where %3D %3D 3 u = w = Mark only correct statements. O a. The matrix of…

A:

Q: Find an equation of the tangent plane to the given parametric surface at the specified point. x = u?…

A: Solution:-

Q: 3. Let A : →P be given by I1 12 0, 2' 22 In A(T1,..., In, ...) = In,...) 2n a) Prove that A is…

A: Please find the answer in next step

Q: How many 10-bit strings are there when a. there is no restrictions as to the format? b. The string…

A: Solution :-

Q: 3. Using both Simpson 1/3 and 3/8 rules compare the Error of the equation. -dy 1+cosy

A:

Q: Consider the function g defined by g(r, y) = cos (Tx V) + COS log3(r – y) Do as indicated. 1.…

A: Instantaneous rate of change of a function g in the direction of the vector v is given by ∇g.u where…

Q: x = 0 x # 0 Let g(x) = {sin Find all values of h for which h satisfy the following conditions on I =…

A: We will use the basic knowledge of set theory and functions to answer this question completely and…

Q: 8. Construct the graph of the following Matrices: Adjacency Matrix 1 2 3 4 Adjacency Matrix 1 2 3 4…

A:

Q: For the differential equation (x2 – 4)y" + (x - 2)y' + 2y = 0, a regular singular point is:

A:

Q: Determine all of the equilibrium solutions of the autonomous differential equation dy = 2 (y- 8) (y…

A:

Q: The indicial equation of the differential equation x2y" – x²y' + (1 +x)y-0 is: O r(r-2)=0 O…

A: Here we use basic formula of indicial equation

Q: Solve the system of differential equations Sx1' = 331x1 + 420x2 | x2' = – 264xı – 335x2 21(0) = 27,…

A: We can write the given system of differential equation in the matrix form as below:…

Q: 5. Write each symbolic statement as an English sentence. Use p, q, r, s, and t as defined below. p:…

A:

Q: Find a series solution about the ordinary point 0 of the differential equation y" +8xy-4y= 0 O None…

A: To obtain the power series solution of the second order differential equation, use the following…

Q: Which of the following is the correct form of the partial fraction decomposition of 1 x3 + 2x2 + x…

A: Here denominator is  x3 + 2x2 + x = x × (x2 + 2x + 1) = x × (x + 1)2  Thus,  x3 + 2x2 + x factored…

Q: a, A function, f(t), with period 2n is given as f(t)= +E[a, cos(nt)+b, sin(nt)]. n-l The term [az…

A:

Q: Use the root test to determine whether the series 8n° – n – 2 converges or diverges. 2n2 +n+ 2 n=1…

A:

Q: Using the method of undetermined coefficients, the form of y, of the differential equation: y4) -…

A:

Q: The one dimensional wave equation describes how waves of speed c propogate along a taught string. It…

A:

Q: 8. 9. 1. Let A -6 -7 3 -1 (a) Doing all the computations by hand, find the characteristic polynomial…

A:

Q: We consider the linear transformation T : R3 ------R 3 T(x,y,z) = ( x+2y-z, -x+y+2z, 3z) 1. Give the…

A:

Q: Evaluate the following integral equation as indicated per item. Indicate the identity used for each…

A: Introduction: Differentiation and integration are the two most important operations in Calculus. We…

Q: az az and dy IV. Suppose z is a function of r and y, and tan y² + x² Solve for

A: Given    tanx2+y2  =zxe6y

Q: 1-12 For each of the following power series, find the interval of convergence and radius of conver-…

A:

Q: Measure of minor arc SH= _____?

A: This is a problem related to circle. Let us find the measure of the minor arc SH in the next steps.

Q: 3. Find the moving trihedral and the curvature at any point of R(t) = (ln(6t), e²¬t,5t).

A: Given R⇀(t) = ln(6t),e1-t,5t …………………………(1) The moving trihedral of R⇀(t)  at point t=1 (as in…

Q: 1. Find the smallest distance from the point (0, c, 0) to the surface y = x? + z?.

A:

Q: Which one of the terms below best describes the data above Category • Numerical Qualitative

A: Let us solve the problem in the next step.

Q: 628 + j5z4 + 6 = 0 3.

A:

Q: (5) For the given impedances, z, = 10 + jo N, z, = 0 – j10 N and z, = 10 + j1o N, Determine, z- =…

A: Consider the given impedances, z1=10+j0z2=0-j10z3=10+j10 here, we need to find to find the value of,…

Q: Determine if the matrix is nonsingular. Explain. [1 3 21 1 4 l1 -7 21

A:

Q: Solve the following surface integral (use definition): F = [322 6 6rz] with parabolic cylinder…

A: To calculate the surface integral of the vector field F across the surface S, use the following…

Q: Solve the following differential equation with the method of undetermined coefficients y" + y' – 6y…

A:

Q: 1. Consider the following intervals on R: A = (0,1); B = (1,2); and C = [2,3). For each pair of…

A: