Let I and J be ideals of R. Prove that if I ∩ J = {0}, then rs = 0 for r e I and s e J.

Q: The value X2 .2 ... -2 x1 + 6 x2 + x3 = 9 - X1 + x2 + 7 x3 4x1 – x2 – x3 = 3 = -6

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Q: 6. Find the Inverse Transform of F(s) S-8 3 A f(1) =6+e¬8 – 4e B f(1) =6-e"+ 4e* © s(1) = - 6+ e +…

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Q: Jse Gauss-Jordan Elimination to solve the following system. Identify the Gaussian Matrix and the…

A: Convert the given system of equation in the matrix form. 3-0.1-0.20.17-0.30.3-0.210xyz=7.85-19.371.4…

Q: Card 1 Card 2 16 17 18 19 20 21 22 23 4 5 6 7 12 13 14 15 24 25 26 27 28 29 30 20 21 22 23 28 29 30…

A: In a card trick, a number between 1 and 63 is chosen from the cards. The chosen number lies on cards…

Q: Find the solution. (D2+2D-3)y = 0 A y = B y = c,e- +cge²2 D

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Q: Yumi wants to buy a volleyball. Its original price is ₱965 and is on sale at 25% discount. How much…

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Q: gcd(334'517º, 210579l1312). Determine the value of æ. Let x O 5 O 180 O 20 O 60 O 220 O none of the…

A: The given problem is to find the gcd of the given two numbers in the exponent form. Given…

Q: Compute the following limits using L'Hospital's rule if appropriate. Use INF to denote oo and MINF…

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Q: Tx/2+sin(ix) f(x) = V2r then = (x).

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Q: f(t) = 2t² + 4t – 3 4+2s-3s? А. c 4+4s-3s? С. s3 2+2s-3s2 В. 2+4s-3s2 D. s3

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Q: Use Gauss-Jordan Elimination to solve the following system. Identify the Gaussian Matrix and the…

A: We use Gauss-Jordan Elimination method to solve the given matrix.

Q: Given the following matrices, perform the indicated matrix operation. 8 1 [5 1 -2 -3 -4 0 -9 3 1 7 2…

A: We can solve this question using given information , first we multiply 4 into matrix B next we…

Q: w the depth first traversal of the following graph. Start at vertex 1. Ties are resolved in…

A: Here I run a python script and see the result.

Q: Find the D.E. for each of the curves determined by the condition that at each point (x, y) ,   The…

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Q: 8) Use the Gauss-Jordan method to find the inverse of the matrix A %3D 23

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Q: Ax) = Ln=0 n! e Show that: GAx)dx = En=1 n(n+1) (–2)"-1 (n +2)! ||

A: Here we use integration and series theorems to find the solution.

Q: what IS the absolute value 7 -2 +i ? a. -J5 C. I b. J5

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Q: what Is the conjugate of Js -J2i ? a. Jo -Joi d. -i b.Ja -ぶ

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Q: -x², 5х - 4, 4x* - 3х, 1<x<2 X <0 0 <x<1 If f(x) = then f(x) is discontinuous at x = Зх + 4, x 2 2…

A: f(x) is discontinuous at x if left hand limit not equal to right hand limit

Q: Problem 3: Given the nth-term formula below, compute the first five terms of the sequence: an n=…

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Q: 5. Determine the Fourier cosine series of f(x) = n²– x² 0<x<1

A: We have ,  f(x) = π2 - x2 We need to find Fourier Cosine series of f(x). We know that , Fourier…

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: Match the theorem or rule for what it justi 25 One pair of consecutive sides are congruent It has…

A: Given: One pair of consecutive sides are congruent:  It has been proven to be a mombus and a…

Q: f(t) = sin* 3t

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Q: Find the Laplace Transform of f(t) = cos? 3t A F(s) = -+ s2+36 B F(s) = 2s?+36 s²+36 , © ru) - :)…

A: We have to find the Laplace transform of f(t)=cos23t .

Q: Find the solution. (D + 602 + 110 + 6)y = 0 A y = c,e-2«, +c,e y = c,e '+c,e -3x c) y = c ,xe" + c,e…

A: Consider y=emx be the solution of the given differential equation. Differentiate the equation y=emx…

Q: -1 3. ( 2B + A')

A: We have to find inverse using adjoin matrix method.

Q: Use Forward and Backward differentiation to f' (1) calculate as accurately as you can. Let h = 0.08…

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Q: In calm waters, the oil spilling from the ruptured hull of a grounded tanker spreads in all…

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Q: Verify Green's theorem in plane for (x - 2xy)dx + (xy+ 3)dy where c is the boundary of the region…

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Q: . Is sin y x² dx + ydy = 0 a linear?  2. Is y' = y+x / x a homogeneous Equation?

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Q: Use the incomplete partial fraction method to solve the DE y′′+ 2y′+ 2y = e^(t)cos t.

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Q: f(t) = sin* 3t A.G 12 24 + s2 +36 8 (s2 +144 B. 8 \s2+144 . (t 4s + s2 +36 c. * ) D.(14 12 24 С. 8…

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Q: A house and lot with the original price of ₱2,300,000 was sold at a discount price of ₱2,150,000.…

A: The formula to calculate the discount rate is Discount %=discountoriginal price×100%.

Q: Define analytically the periodic functions shown. 1 f(x) 2 2 4 6 8 -1

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Q: Learning Competency: Determine the relationship between differentiability and continuity of a…

A: Option C claim ,evidence and reason

Q: fj+1 - fj-1 2Ax Assuming a uniform grid spacing of Ax, derive a finite difference approximation to…

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Q: The equatiokn  Y = (x,y)T  is given as a vectorfunction with 2 components and A = table below 3 2 2…

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Q: a Prove that I = { : a,b,c,d are even integers} is an ideal of M2(Z). d

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Q: Determine one real root of f (z) = 8 (sin z) e- lafter two iterations of the Newton-Raphson Method…

A: The equation in the form f(x)=0 is called a transcendental equation. The solution of the equation is…

Q: 3s - 2 Find the Inverse Laplace Transform of G (s) = 2s² – 6s – 2 A 8(1) = 3e 2 sinh cosh 13 B 8 (1)…

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Q: Sketch the region bounded by the given curves, then find the centroid of its area. 1. у%3D х*,…

A: (5) From Symmetry we can see that centroid of the bounded region is at (0, 0)

Q: 10. Which of the vectors U =, V = and W = are in the same plane?

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Q: f(t) = t sinh 5t 5s 5s С. (s2+25)2 А. (s2-25)2 10s 10s В. (s2-25)2 D.- (s2+25)2

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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: . Use Taylor's neries, to prove that ein z tan (x+ h)3tan" % + (h sin z). sin 3z sin 2z + (h sin zj…

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Q: 8 3 Find the Inverse Laplace Transform of 35²+12 2- 49 3 - sin7t+ -cosh (2t) 7 4 A. 4 - sin2t +-sinh…

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Q: Solve the dy *+g+ 3 differential %3D equation.

A: The given problem is to solve the given differential equation. Given differential equation dy/dx…