Suppose n E Z. Prove that if n² + 3 is even, then n is odd.

Q: Use Green's theorem to find the area integral if V(x.y) = (x²+y®)į+ (x²=y®\j¸ where C is a solid…

A: The given vector is Vx,y=x2+y2i+x2-y2 j and  The given parabola is y=2-x2. We know the Green's…

Q: Show that the subset of R2 given by {(x, y) E R² : xy = 1, x > 0} is closed.

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Q: Let M1 F → F be a transformation defined by M1(f) mation? Justify your answer. (1² + 1)ƒ(t). %3D

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Q: Find all the solutions r E Ziz to the equation r³ – 5x² – 7x = 0 mod 13.

A: First, solve in real number then ring down to the finite field.

Q: urvilinear inteorale. late Find yay (0,0) , (4,0) r where is the pen 4e.x the 1quan (1, a) ato here…

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Q: Graph the inequality on a plane. X+ys3

A: Graph in xy-plane

Q: 1/4 1. Find all the values of 3.

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Q: Solve the following differential equation using Laplace transformation y′′ +4y′ +20y = (greek…

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Q: Example 1.3.1 Check lim inf[0, n/(n +1)) = lim sup[0, n/(n +1)) = [0, 1). n-00 We can now give an…

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Q: For the following boundary value problem, use the collocation method to determine a solution of the…

A: Collocation method is used to find the numerical solution of the ordinary differential equation.…

Q: Let X = {1, 2, 3, 4, 5} and Y = {3, 4}. We define the relation R on the set P (X) by the formula (A…

A: Here, I have shown that the given relation is an equivalence relation and found out the equivalence…

Q: SET-UP the definite integral that will give the area of the region specified using (a) x as the…

A: We have to set up the definite integral for the given region of integration which is used to…

Q: urvilinear integral: Find de x dx + yay is the perimeter of the where (0.0), (4,0) ,(0,1), (4, d)…

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Q: Suppose A and B are non-empty bounded subsets of positive real numbers. Define A·B = {r •y:x € A, y…

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Q: If the Wronskian W of f and g is t'e", and if f(t) = t, find g(t). NOTE: Use c as an arbitrary…

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Q: Find all proper nontrivial subgroups of Z, x Z, x Z. Find all subgroups of Z; x Z4 of order 4.

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Q: Find the volume of the solid within the cylinder r2 + y? = 4 that is bounded below by the xy-plane…

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Q: H-solve log , (log, (log x)) = 1

A: Given: log3log2logx=1 Concept: logax=logbxlogba

Q: Define a sequence {E;} where En = r -,r| where n is positive integer. Find P({r}) for any r E [0,1]

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Q: Tank # 1 initially holds 50 gals of brine with a concentration of 1 lb/gal, while Tank # 2 initially…

A: Given: Tank1: The volume of tank 1=50 gals x1(t)= amount of salt at time tx1(0)=50 gals× 1…

Q: (2) Consider the power series f(x) = En=1 ngn (X – 2)" (a) Find the radius of convergence and…

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Q: 5- Graph the following function( Y=-1/4 log ,(3x-6)+1

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Q: This problem is related to core exercise 31 (module 5) in the textbook, and reguires you to do some…

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Q: 6. Determine whether P = and Q = 10,3,2 > are orthogonal vectors.

A: As per our guidelines we need to solve only one question. Please, repost the remaining questions as…

Q: find the coordinates of the centroid of the plane area bounded by the parabola y=4-x^2 and the…

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Q: 2. Given Ü = 7î – ĵ + k and W = -2î – 5ĵ + 6k , compute a) Proj w V and b) Proj y W

A: Ya

Q: et f(x) = |x| where xeR. Discuss the continuity and differentiability of f(x) at x = 0

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Q: For problems 1-2, find a general solution to the system x' = Ax where [6 1. A =

A: According to Bartleby guidelines, I am solving only the first question.Please resubmit the question…

Q: n topulogical manikuld - show that Mis locally compact 6

A: This is a problem of differential geometry.

Q: Solve using Laplace transform technique y"+ 4y = 9t, y(0) = 0, y(0) = 7 %3!

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Q: Consider the two matrices: 2 4 1 -5 A = B = 2 Compute A + 3 B. The result is equal to: Select one:…

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Q: Use Fermat's Little Theorem to find each value. Remember, x-1) =1 (mod p). Write your answer in…

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Q: Equation condition for three related markets is given by 10x1 + 3x2 + 6x3 = 76 4x1 +5x3 = 41 5x1…

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Q: Write the equation of the hyperbola in standard form. (-1,7) (-1,5)

A: Consider the given figure. We have to find the standard equation of hyperbola. The standard form of…

Q: Show that any compact set in R is closed and bounded.

A: Proof

Q: 12. The graph of f is shown below on the xy-plane. Explain why y = 0.8(x – 1) + 0.4(x – 1)² + 0.1(x…

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Q: Consider such a definition average distance, which is the average distance over all pairs of nodes…

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Q: Prove that if S is a bounded set then S is bounded.

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Q: Solve the following system of linear equations: 2x + 3y – 4z = 1, - 2w + x + y+ z = 0, w – x + y – z…

A: Given system of linear equations is w−2x+3y−4z=12w+x+y+z=0w−x+y−z=−1........1 We have to find the…

Q: Esther works at a clothing store which marks up its retail clothing by 40%. The store purchases…

A: Given, The store purchases pants for Php 500 The store purchases jackets for Php 400 The store…

Q: For each of the following equations, • find general solutions; • solve the initial value problem…

A: Since you have asked multiple questions, we will solve one question for you. If you want any…

Q: Evaluate the following limit using Taylor series. lim 3x X00 (.... Rewrite the given limit using a…

A: We will use taylor series of ex ex=1+x1!+x22!+x33!+......∞

Q: Q2) Using Graphical Method to determine the optimal value of X1 & X2 that maximize value of Z, Max.…

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Q: Find all proper nontrivial subgroups of Z; x Z, × Z;. Find all subgroups of Z; x Z4 of order 4.

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Q: Problem 5. Find all primes p such that 1+p: 2P is a perfect square.

A: We have to find all prime p such that 1 + p×2p is a perfect square.

Q: Given a scalar field f(x, y)= xy + x² and C is the curve defined by the equation y =-x². Calculate F…

A: Given scalar field  fx,y=xy+x2 and C is the curve defined by the equation y=-x2.

Q: f(t) = sin* 3t

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Q: 0くt 27. Express the answer using the symbols of unit step functions. (b) Express the answer obtained…

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Q: Using the theorem on determinants, show that 11 а а- А %3D |1 b b2| %3D (b — а)(с — а)(с - b) с с2

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Q: Find the Fourier series of f(x) = {1 2<x<4 and f(x) = f(x + 4), and calculate the partial sums…

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