Let a and b be integers, such that: a + 5b and: 5a - b, are both divisible by 2002. Try that; a² is also divisible by 2002.

Q: Solve the given initial-value problem. =-11x-y = - 25x-y x(x) y(t) de de x(1) = 0, y(1) = 1

A:

Q: '0 8 3 تر محمد (1 + x)5 dx

A: According to guideline we need to solve one question. Rest of the questions should be reposted.

Q: Let B = {B₁ = [], B₂ = 1²²= 1·²=6 D be a basis of M2x2 (R). Suppose that T: M₂×2 (R) → P₂(R) is a…

A:

Q: IF AN ITEM IS VALID (V), THEN SHOW THAT IT IS VIA PROOF OF VALIDITY (S); BUT IF IT IS NOT VALID.…

A:

Q: Prove that every positive integer n can be written as the sum of distinct powers of 2. E.g. 1 = 2º,…

A: To show that every positive integer n can be written as the sum of distinct powers of 2. We will use…

Q: The sum of two numbers is sixty-two. The difference between their squares is nine hundred…

A:

Q: 2. Let ABC be a triangle with AB = 3, BC = √3 and CA = √√3. Let XYZ be a triangle with XY = 3√3, ZX…

A:

Q: ] [Backwards difference approximation of first derivative] Using Taylor's theorem, in lecture we…

A:

Q: 2. Suppose ƒ'(x) = (x − 1)¹⁰ (x + 2)⁹999 (x + 3)(x + 5)³(x − 2)¹2000. Find all values of x for which…

A:

Q: [e²t + e-4t] e2t - e e-4t Find a planar linear system X' = AX to which X(t) is a solution. X(t) = =

A:

Q: In a game, two people take ball(s) from 56 balls alternatively. Every time each person can take at…

A: To get hold of the 56th ball it's important to get hold of the 52nd ball and so on. This is the key…

Q: a. Prove that √6 is irrational. b. There exist no integers a and b for which 21a+30b=1. c. If a and…

A:

Q: Find the right match for the following ODEs out of: 1st Order Linear ODE 1st Order Non Linear ODE…

A:

Q: Solve the system of linear equations, using the Gauss-Jordan elimination method. (If there is no…

A:

Q: IF AN ITEM IS VALID (V), THEN SHOW THAT IT IS VIA PROOF OF VALIDITY (S); BUT IF IT IS NOT VALID.…

A:

Q: Let / denote the line in R with equation y = = 3x - 2. Let Q = (2, -1). (a) Write the line / in…

A:

Q: The fuel tanks for airplanes are in the wings, cross section below. The tank must hold 5400 lb of…

A: Given that the fuel for airplanes are in the wings, the cross-section is below. The tank must hold…

Q: 7. Construct the truth table for the following propositions: a. (~pvq) →~q b. (p^~q) →r c. (p^~q) →…

A: 7. The given propositions, a) ~p∨q→~q b) p∧~q→r c) p∧~q↔q∨r  d) ~p∨q→r e) p∨q∨~p∧q→r We have to find…

Q: Examine each of the following relations given below and state in each case, giving reasons whether…

A: (i) Since 4, 5, 6 are the elements of domain of R having their unique images, this relation R is a…

Q: kp - x² + 5x²+4x = 12+ + 30e to) = (0) (250)P x(0)=1, x'(0)=3 Solve the above IvP and then find OH…

A:

Q: (a) 24091335 24091335 mod 19 ® ê (b) 742806 mod 349

A:

Q: 1. Chapter 14 Review 43: Let g(u,v) = f(u³ - v3, v³ - u3). Prove that g д + u2 ди ди 2 = = 0.

A:

Q: ve That The Scaling nmutative.

A:

Q: a) For each sequence, give an example of a monotone subsequence. (b) For each sequence, give its…

A: This is the question of sequence and limit.

Q: . Let S be a bounded set on R. Let f SR be uniformly continuous on S. Prove that f must be bounded…

A: We use Heine Hotel Theorem.

Q: Use the graph of f'to (a) identify the critical numbers of f, and (b) determine whether f has a…

A: We know that,  1. Critical number= x- coordinate at which f' is zero 2. relative minimum is present…

Q: Solve the given linear programming problems without graphing NOTE: USE BASIC SOLUTIONS 2. 9X1 +7X₂ ≤…

A:

Q: Prove by induction that, for every n\geq2 n+1 (1-2)(1-¹)(1-(1-1/2) = ² 2n

A: To Prove: We have to prove by induction that for every n≥2, we have:…

Q: 12. Prove using both the pick a point method and the algebraic method For each set, A, B, and C, (A^…

A:

Q: Two cards are drawn without replacement from a standard deck of 52 playing cards. What is the…

A:

Q: 1. Let A a, b, c, d. Consider the following relation on A: (a) Draw a diagram of R R-(b, b), (b, d),…

A:

Q: Find the standard matrix for the linear transformation T: R² 3 and then reflects about the line y…

A:

Q: mnps.schoology.com to search An inequality is solved as shown below. Between which two steps is an…

A: There is an error Between step 1 and step 2   so option (b) is true

Q: (a) Consider the following phase line, where c is a positive constant. y=c y=0 i. Write down a…

A: The differential equation for this phase line

Q: 2. Let V be the set of all ordered pairs of real numbers, and consider the following addition and…

A:

Q: Evaluate the expression. 19P3 3! 19 C3 19P3 3! 19 C3 (Type an in

A:

Q: Let S be a bounded set. Prove there is an increasing sequence (sn) of points in S such that lim sn =…

A:

Q: A fixed point of a function f is somer where f(x) = x. Suppose that f: [a, b] → R is differentiable…

A:

Q: 3. Which of the intervals (0, 5), (0, 5], [0, 5), [0, 5], (1, 4], [2, 3], (2, 3) contains a) 0? c)…

A: Given (0,5),(0,5],[0,5),[0,5],(1,4],[2,3],(2,3)  we know that the interval notation information open…

Q: s.t. maxr₁ +372 ZER² z+az² = 10

A:

Q: An office building is installing eight Wi-Fi transmitting stations.  Any stations within 200 feet of…

A:

Q: Prove by induction that, for every n ≥ 1, 72 Σ(-1)² = (-1) n(n+1) 2 i=1

A: Note : Since you have posted multiple questions , we will provide the solution only to the first…

Q: In a machine company, at least 45% of the machines produced per month do not pass the finish test…

A:

Q: Question 1 Prove: Vn> 1 € Z, 1+6+11+16 + · +(5n-4)= = n(5n-3) 2

A: The given problem is to prove that sum of series of 1+6+11+16+.....+(5n-4) =n(5n-3)/2.

Q: Find g'(x) for the given function. Then find g'(-4), g'(0), and g'(2). g(x)=√15x

A:

Q: 2. A function f A → R is Lip- schitz if there exists an M> 0 so that for all x, y E A with x y we…

A:

Q: 4. This diagram represents 3 batches of light yellow paint. Draw a diagram that represents 1 batch…

A:

Q: Find a particular solution and the general solution of the nonhomogeneous DE's: A) y'' + y = e^t B)…

A:

Q: uts) Do the following for the set X = {1,2,3,4,5). 7. (a) Give an example of a relation on X that is…

A:

Q: 12 (e). Find a QR-decomposition of (i). A= 1 1 1 ( 031

A: