Problem 1: Determine the solution of the given system of linear equation: X2 + 2r, + 2x,+ 6x, = 3x, - 2x, + 4x, + 4x, + 12x, = -3 14 3x, 2x, - 2x, + 4x3 + 5x, + 15x5 2x, + 4x, + 4x, + 13x, |3D 10 2x 13

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Q: Prove that if a = b mod n and c= d mod n, then ac bd mod n.

A: Given if a≡bmodn and c≡dmodn We have to show that ac≡bdmodn. Now, a≡bmodn ⇒n/a−b⇒a−b=nq1,q1∈Z⇒a=nq1+...

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A: The general form of a vector-valued function in three dimensions is given by F=F1,F2,F3, where F1, F...

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A: Solution:-

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Q: dy, ycos x+sin y + y Solve dx sin x+x cos y+x Solve (1+xy) ydx +1(1-xy)xdy = 0 %3D

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Q: 3. Find the solution of the given initial value problem using MVP: 4y(2) – 8y(1) – 5y = x*e2* – 8x y...

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Q: (3){1,3}= {3,1} (4) Ø = {Ø}

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Q: Evaluate the iterated integral by converting to polar coordinates. V2 - y 6(x + y) dx dy

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Q: The Laplace inverse is 3 3! 2 1 t 2 3

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Q: Given system of linear equations: х +у—3z %3D 4 2х + 4y — 4z %3D 5 —х + у + 4z %3D —3

A: Given equations are x + y - 3z = 4      → (1)2x + 4y - 4z = 5  → (2)-x + y + 4z = -3  →(3)

Q: Consider the functions f and g, defined on R. Use set notation to represent the domain of h(x) : S(x...

A: The given problem is related to function and its domain. We need to understand the concept of domain...

Q: 2. Find the maximum and minimum of the function f(x,y) 1 subject to the = x² +2y² constraint x + 2x?...

A: Substituting.

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Q: 29. You have been given an order to prepare 14 progesterone capsules for a patient in your pharmacy....

A: The most appropriate capsule size is 1 as per the given Table and hence option c. is correct.

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A: Given: The plots depicting particular aspects of the system modelling an interaction between the pop...

Q: B: Find the area of the shaded region show y y =1+x X=-1- y=-1 Fig(1)

A: According to the given below figure:  area of the shaded region is  ∫y=-11∫x=-1y2dxdy+∫y=12∫x=-1y-1...

Q: 2(x + y)dx – x(x + 2y – 2)dy = 0 ? cos y et 1+x² O D y2 e`y O A B

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Q: Evaluate 1 dA x² + y² +1 where R is region in the first quadrant bounded by y = 0, y = x and x² + y²...

A: We have to evaluate ∬1x2+y2+1dA The region R is in the first quadrant bounded by y=0, y=x and x2+y2=...

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Q: 2. Find the solution of the given initial value problem using MUC: 2y(3) – y(2) – 2y(1) + y = 4x3 – ...

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Q: 2. Find the maximum and minimum of the function f(x,y) subject to the x² +2y² constraint x* +2x²y² +...

A: This is a problem of multi variable calculus.

Q: I. Represent the following equations in R by a vector-valued/parametric equations: 4. 4r - 32y? + 4r...

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Q: y' = x1 - y2

A: Introduction  A differential equation has a general solution and a singular solution. The general so...

Q: 1. Find the general solution of the given differential equation using MUC: y() – 4y(3) – 21y(2) + 10...

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Q: 0 0 0 A =3 3 0 3 3 0 has two real eigenvalues, one of algebraic multiplicity 1 and one of algebraic ...

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Q: 5. (a) Suppose f: N→ Z is a one-to-one onto function. Prove that the function g: N × N → N x Z defin...

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Q: Find all the roots of z for the following equation (2 - j6) z2 + (3 + j5) z – 5 +j= 0 When a value i...

A: Using factorisation

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Q: i Apply Green's theorem to eve luate S [rex=y)dx +Cx+g)dy], where C is the bocundaug qxis aiad the u...

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Q: Eleven members of the executive committee of the Student Senate must vote for a student representati...

A: Option D is correct answer

Q: 2. 3- va(c + ian ) - va(0+ in ) Z1 = + i sin + i sin COs 22 = cos

A: This is the problem of complex analysis.

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Q: Can you help me find the correct solution for this problem? 1. Find and classify any stationary poin...

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Q: a11 a12 a21 022 a2n Question 2(a): If A = and c = then express the product Ac as linear am2 Cn combi...

A: We have an m×n matrix A and n×1 vector c. We have to write the matrix Ac as the linear combination o...

Q: Let t(2 – t) if 0 2. Solve the initial-value problem y" + 2y' + 2y = g, y(0) = 0, y'(0) = 0. You ma...

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Q: Use a double integral in polar coordinates to find the area of the region bounded on the inside by t...

A: Solution:-

Q: Simplify down to a single integral in terms of . .3 /9-x² 63–42²–4z² Volume = 1 dy dz dx = Σ da. V9-...

A: ∫-33∫-9-x29-x2y3x2+3z263-4x2-4z2dzdx

Q: Which of the following is the general solution to the differential equation y(2xy + 1)dx – xdy x (ху...

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Q: Which of the following differential equation has a solution of y = e"(c, cos 2x + c, sin 2x) ?

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