3. Show that if n = 3 mod 4, then n cannot be the sum of squares of two integers.(i.e there are no x, y EZ such that x² + y² = n.)

Q: * 2: The function f(x) = x² + 2x² + 3x² + 4x₁x₂ + 5x₂x3 + 6x1x3 can be written in the form f(X) =…

A:

Q: (b) Find the following integrals: i. f(4x³+ sin x) dx. ii. ₁²(x²+)dx.

A:

Q: Consider the differential equation dx t5 = dt t6 +3 (a) State the form of the differential equation…

A: There are many different methods that are used to solve a first order ordinary differential…

Q: 3x + 2y = 4 2x − y =-9 x + 3y = 13

A: We have: 3x+2y=42x-y=-9x+3y=13 This can be written as: 322-113xy=4-913 The augmented matrix is…

Q: 10. Using 5x5 grids, determine the equation for steady state temperature distribution at T21, T22…

A: Using calculator for solving of system of linear equations

Q: 1 Obtain a numerical solution of y-1 = using Euler's method with step size equal to (0.02) y and…

A:

Q: Problem 8 5 Let A= 2 Calculate the eigenvalues A₁ and A₂ of A, and the corresponding eigenvectors ₁…

A: Introduction: In linear algebra, eigenvalues are related to eigenvectors. In the analysis of linear…

Q: 7. By separating a) b) the variables convert the PDE into a system of ODES Sem азт а т + д?хду дхду…

A: By the seperation of variable we consider the unknown is the product of two functions one is the…

Q: Let f be a mapping from [1,+∞[ to [1,+∞[, defined by f(x)=x+1/x. Then f is continuous but it is not…

A: A function is homeomorphic when it follows the bijection. The bijective property is one of the…

Q: An investor has $683,000 to invest in bonds. Bond A yields an average of 6% and the bond B yields…

A:

Q: (c) Explain the Bisection Method to compute a real root of f(x) = 0 and find the condition of…

A:

Q: x³y" + xy' - y = 0 ; y=x

A:

Q: Consider polynomials with degree less than or equal to n. We can think that each polynomial…

A:

Q: Use transformations to sketch the function y=-3log10 (x-1) + 2 y = -310g 10 (x - 1) + 2 Parent…

A:

Q: 2. Using an appropriate method, compute the following integrals. dx x² + 3x + 2 (i) sin³x cos*x dx…

A: (i)

Q: 2. Find the root of the function/ (Take the tolerance as 0.01) 4 by using the Newton-Raphson Method.

A: The given problem is to find the approximate root of given function using the Newton raphson method…

Q: Investor Dan has $758,000 to invest in a CD and a mutual fund. The CD yields 4.2% and the mutual…

A:

Q: The multiplicative inverse of x²+x-1 in Z5 [x]/ is: O x^3 O x+1 O x^4 O None

A:

Q: (a) For each of the following linear transformations, write down its matrix and describe its type.…

A: (a) To find: the transformation matrices. Please post the multiple questions separately. Here I…

Q: oblem 5. Let P, be the vector space of all polynomials of degree 2 or less, and let ♬ be the…

A:

Q: Q1:/ Read the article below and answer the questions after. PM25 is the leading global environmental…

A: By using sentence mentioned in given paragraph i.e., PM2.5 is the leading global environmental…

Q: 11: Given the function f(x) = 8x² - 4x₁x₂ + 5x² and Xo = [5 2]. Then G¹g at Xo is equal (( G is the…

A:

Q: Iff: [a,b] R is bounded and has only a finit number of discontinuous points, then f is Riemann…

A:

Q: what is the difference between Binet's formula to its simplified version? Are there any rules on…

A:

Q: 0.7 0.6 H.w1: evaluate fofo ex siny dx dy i) using the trapizodial rule in both direction, Ax = Ay =…

A: To evaluate the definite integral ∫abfxdx, use the following formulae. Trapezoidal Rule:…

Q: 11. Explain what Average Rate of Change and Instantaneous Rate of Change are. Use graphical diagrams…

A:

Q: Calculate the distance from your house to the college in km. Determine the type of number whether…

A:

Q: Find the orthogonal projection of -10 14 11 V = 15 onto the subspace V of R4 spanned by -1 2 1 X1 =…

A:

Q: * Consider the following matrices /1 1 1/2 3 4) ^ - (-: 2) - - († ;) -- ( 7² :¦ ¦) -- () --(:::;) A…

A:

Q: . Use x,  y and z as variables to rewrite the following sentences to mathematical statements  A…

A:

Q: The angular position of a point on a rotating wheel is given by 0-4.65 +8.95t2 +4.09t³, where is in…

A: angular position of a point on a rotating wheel is given by θ=4.65+8.95t2+4.09t3 where θ is in…

Q: Q5) Use Euler's method with h-0.14 to obtain a numerical solution of y = 1+ (y-x)² subject to…

A:

Q: Choose the correct letter that corresponds to the exact answer. 1. Find the derivative of f(x) =…

A:

Q: Find the magnitude of the vectors represented 5 3 1 by (a) (b) |³| (c) 12 4 3 LO 5 1

A:

Q: Find the line that best fit the data 2 [8] [8] [3]- "

A:

Q: 5 the following Tuation Sutisfied Cauchy - Rieman. equation 4 W = Z Z" سر

A:

Q: x1 + x2 + x3 = 0 x4+x₂+2x3 = 0

A:

Q: L- s-1 (s²+9) Find laplace inverse

A:

Q: Let (-3, 8) be a point on the terminal side of 0. Find the exact values of sin 0, csc0, and cot 0.

A: Here we use basic trigonometry to solve this

Q: Graph the parametric equations below (x(t) = t - sint ly(t) = 1- cost

A: The given parametric equations are: xt=t-sin tyt=1-cos t Find the value of x and y for multiple…

Q: Question 1 Calculate the acceleration for t=7.3. Table 1: Velocity and time table Time 1 2 3.25 4.5…

A:

Q: A company wishes to produce two types of souvenirs: Type A and Type B. Each Type A souvenir will…

A:

Q: Find the area of the surface generated when the curve f(x) = 9 tanx on [] Area = (Type an integer or…

A:

Q: Find the value of the magnitude of the vector v. (a) v = -3i+ 10j (b) v=4i-6j (c) - 2i-3j.

A: if a vector v=ai+bj then its magnitude v=a2+b2

Q: 5 is to be apportioned among these states

A: Given as, Numbed of seat= 17 and total population= 20090.

Q: 4. Find the unique solution y(x) of the differential equation d²y = 1+e¯ª dx² for which y(0) = 0 and…

A:

Q: [2 1] -31 Let A = 1 1 and b = -9. The QR factorization of 2 1 the matrix A is given by: 1 1 = 3-√2 3…

A: Solution

Q: Explain why the integral is improper. 49 1 dx 1.6 1.4 1.2 Y 0.81 0.6 0.4 0.2 10 20 O At least one of…

A:

Q: Create a proof for the following argument 1. P v (Q⊃R)   2. (S v L) ⊃(Q * X)   3. Q ⊃~P   4. S…

A: We prove the given argument by using rules of inference.

Q: 2. Consider the plane z = 4 - x - 2y. (a) Please find the distance from (1,0, −2) to a point (x, y,…

A: The given plane is z=4-x-2y To find: (a) the distance from (1,0,-2) to the point (x,y,z) on the…