I. Solve for z. All final answers must be in Zn where n is the modulus. (a) x = 3(15) +45 mod 18 (b) z-12 mod 13 (c) 6r mod 11 = 1 (d) x + 2 mod 9 = 0

Q: true or false  1..The GCD of -50, -100 and -125 is -25 2.If (a, b) = d and d│m, then (ax is…

A: Solution

Q: 1. Find A -4A5 for 1025 A = -2 3 -1 2

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Q: QUESTION 4 In a vector space V, prove that Ov=0 for all veV.

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Q: əz ax+by+sin(ax +by) show that b əx Q5-A) If z = (ax +by)² +e+by+sin( ax a Əz dy

A: The given problem is to show the following condition for the given multivariate function of z.

Q: dy = The image below is a slope field for the differential equation a(y - b), where dx a and b are…

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Q: The wave equation = may be studied by separation of variables: u(x, t) = X(x)T(t). If(x) = -k² X(x),…

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Q: emon-crusted salmon (L),

A: Given that,  L = Lemon Crusted Salmon C = Crab-stuffed Chicken G = Garlic prime rib W = Wasabi rolls

Q: If ÿ(t) = v₁ (t), ý(t) = v₂ (t) satisfy the system of differential equations: ÿ' (t) = Aÿ(t), then…

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Q: The sphere shown below has radius 12 meters. }x X We are trying to find the volume by making…

A: The radius of the sphere is given as 12 meters. The horizontal slices are made in the sphere x…

Q: What is the value of the summation? a.) 2 3 Σ Σ(i+j) i=1 j=1 b.) 8 Σ 3· 2 j=0 c.) 4 Σ (-2) j-0

A: a) ∑  i=12∑   j=13 (i+j) b)∑j=083·2j c)∑j=04-2j We have to find the value of the given summation .

Q: 10. Prove that w|+|2|="2² VWZ+ W+z +√WZ

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Q: TON (B) Discuss the convergence of the given sequence: a(n) = sin 2

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Q: b) We are interested in the oscillatory solution given by If the boundary conditions are Identify…

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Q: I. 2.) Simplify. Write "undefined" for expressions that are undefined. 2 6 5 3 1 2 11.0 -6 4 -6 2 20…

A: The given expression is  26-64·53-62+1220 simplify…

Q: Q2. Find the convergence interval and radius of the series: √n (2x+5)* nal

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Q: Determine the magnitude of the vector difference V' = V₂ - V₁ and the angle 0x which V' makes with…

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Q: 7 relatively prime uct and quotient of a

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Q: 15 20 22.5 362.78 517.35 602.97

A: The first order Lagrange polynomial is given as, fx=x-x1xo-x1fxo+x-xox1-xofx1

Q: 13. Show that the following functions are contin- uous but not differentiable: (a) z (b) |z²2 (c)…

A: 13) We need to show that given functions are continuous but not differentiable. We know that , a…

Q: A) B) T Solve the initial value problem Solve the differential equation y + 10y +34y = 0 e²x dy…

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Q: - 4. Let C = C₁ U C₂, where C₁ is the semicircle x = √√4y – y² traced from (0,4) to (0,0) while is…

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Q: Show that W = {(a,0, b)|a, b = R} is a subspace of R³.

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Q: please answer the same way above the former one. j) When is the particle speeding up? k) When is…

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Q: X-2 Evaluate the integral (t³ Inti+ 3t³ sin (t) j+ k) dt. x(x+1)

A: Given the integral ∫t3lnt i→+3t3sint4 j→+x-2xx+1 k→dt

Q: Find the cardinal number of each of the following sets. Assume the pattern continues in each part.…

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Q: The position of a particle moving along a straight line is given by the function S(t) = 2sint +…

A: Direction of particle depends on sign of its velocity

Q: Let A be an n x n diagonalizable matrix. Suppose T : R" → R" is transformation with the standard…

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Q: Sketch the solid whose volume is given by the following integral and evaluate the integral. S/2/4…

A: Note : φ= constant  , represents a cone  and ρ= constant  , represents a sphere .

Q: Let z = f(x, y) be a differentiable function defined for every point on the plane, and let u be a…

A: (a)Let the function f(x,y) be the height of a mountain range at each point X =(x,y). If you stand at…

Q: elatively prime integers that are NO

A: 11. Since a, b are not relatively prime, which means they have common factor let b=ka for some…

Q: PART#B Use the divergence theorem to calculate the flux of the vector field F(x, y, z)=…

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Q: 8. Mary Catacutan and Pedro Perez are considering the possibility of teaching swimming to kids…

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Q: Question 1: Doing 2 DFTs in one go Consider two length N vectors with real numbers in them-a, y ERN.…

A: Here, C,X and Y be the DFT of c,x, and y.

Q: 16 Solve for xá = 27×-6 x: 16 4 a. T b.-2014 c. 21 d. 2 e

A: Given  19=27x-6 rewrite the equation as  132=33x-6 3-2=33x-6 bases are same so powers  must be same…

Q: Find the Inverse Laplace Transforms of the following. 4 1) | S-3

A: We will use laplace transformation table to find inverse laplace transformation

Q: Use triple integration in Cartesian coordinates to find the volume of the region in the first octant…

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Q: 13. Evaluate [-72, 48] 24 O-24 - 144 144 14. If a = 5 and b = 7, what are the possible values of m…

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Q: Consider the recurrence relation an = -an-1 +12an-2 with first two terms ao = 1 and a₁ = 20. a.…

A: given an=-an-1+12an-2 and a0=1, a1=20…

Q: QUESTION 11 11.2 If A is an invertible matrix that is diagonalisable, prove that A¹ is…

A: We have given that , A is an invertible matrix which is diagonalizable. We need to show that , A-1…

Q: We have verified that x² and x³ are linearly independent solutions of the following second-order,…

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Q: Find the general and Singular Solution of the Following differential equation y²Lny = XyP+ P²

A: Let us start solving the problem step by step  Given differential equation is y^2ln y…

Q: 4. Find (a) Fourier Sine Series, and (b) Fourier Cosine series for the func- tion f(x) = sin(x),…

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Q: Determine the area of the shaded region in the graph below: y y=x²-1 d -1 X

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Q: 8. Mary Catacutan and Pedro Perez are considering the possibility of teaching swimming to kids…

A: Given- Mary Catacutan and Pedra Perez are considering the possibility of teaching swimming to kids…

Q: Find the derivative of the given function. 7⁰0 8 Y + 7 √√x (ln(7.7))" y' 7 = 4 3 X2 X

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Q: Find the volume of a parallelepiped if four of its eight vertices are A(0,0,0), B(1,5,0), C(0, –…

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Q: PART#C Use the divergence theorem to calculate the flux of the vector field P(x, y, a)-ar+…

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Q: Let C(x) be the statement "x has a cat." let D(x) be the statement "x has a dog," and let F(x) be…

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Q: 4. Given 25_3__8 what digits must be placed in the blank to make it divisible by 9? 10 and 8 6 and 3…

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Q: Karim wants to invest $100000 in two investments at 8% and 10%. How much should he invest in each if…

A: The formula is I = Prt, Where I = interest earned, P = principal, r = rate of interest, t = time.