Discrete math Let S = Z × Z and define the relation R as follows (a, b)R(c, d) ⇔ ad = bc. Show that R is an equivalence relation and find the corresponding equivalence classes.

Q: For the given rational function f(x)=20−4x2           x2−9​ ​(A) Find x and y intercepts for the…

A: Given that f(x)=20−4x2x2-9 (a) For x-intercepts f(x)=0 ⇒20-4x2=0⇒x=±5 therefore, x-intercept is ±5,0…

Q: Question 7. Shandy is a popular drink for young people in England. It is a mixture of beer and…

A: The owner likes to serve the mixture with 60% lemonade and 40% beer The bartender mixes 4 pints of…

Q: Therefore | (A')"| = |S¯¹ A"S| |(A')"| = |S¯¹ ||S||A"|. |(A')"| = |I||A", where I is the identity…

A: Problem is to rearrange the given logic.

Q: y = x²e-x + 4e*

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Q: Problem 4 Suppose the function f has n + 1 derivatives at the point xo, and let = xo + 0x (x − xo)…

A: As per the question we are given a function f(x) which has (n+1) derivatives at the point x0 And ξ =…

Q: Find the particular solution: d³y d²y +2 = dx3 dx² 0 when x = 0, y = -3, y' = 0, y = 12

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Q: A = 2 0 1 2 0 0 0 2 For each matrix below find the SVD:

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Q: The height, h, in metres, above the ground of a car as a Ferris wheel rotates can be where t is the…

A: Given  h(t)=16COS(πt120)+18 where h(t)= height in meter t= time in second we want to find the…

Q: eries solution y(x) corresponding to the larger root

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Q: Given the equation A(t) = 12e -0.027t, where t is the time in months, calculate the corresponding…

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Q: The function f(t) is defined by 3t+2 0<t≤ 4 -3 4 < t ≤ 5 f(t) = with f(t+5) = f(t). Evaluate…

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Q: where computed by ----- pupward velocity, u velocity at which fuel is expelled relative to the…

A: Given: The upward velocity of a rocket is given as v=ulnm0m0-qt-gt, where t denotes time. u=1800m/s,…

Q: I think there is a typo. It's supposed to say A has no finite subcover since any finite subset of A…

A: R is not compact with standard topology.

Q: a- Find the power and energy of the following: x(t)=e-³¹; 0≤i<∞ x(t) = A sin(@t); 0≤t <∞

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Q: Jo sin(z + 3) (z + 3)² 2 dz

A: ∫Csinz+3z+32dz C be the circle z-1&lt;2.

Q: Let E={(r.0.2) : Os es z, 05 zs 1, 9√/25 rs 9). Compute dv.

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Q: 6. Write the following expression in product (II) notation. 32.43.54.4342 7. Compute the value of…

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Q: You are given the following system of differential equations:  dx/dt = -2x - 6y, dy/dt = -6x + 7y…

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Q: x=t(e²t+4)

A: This question is about ordinary differential equation in which solution is given and we find…

Q: E. Show that both R and R² may be covered by countably many open balls.

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Q: 6. Use the following form graph of yos-2 is the below 162 que lo miog snil letnosion of 20 (anato…

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Q: at what time after 7:00 will the second hand bisect the hour and minute hand for the first time?…

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Q: 2- Fill in the multiplication table and the addition table z₂ = {0,1}

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Q: Find the Fourier series of the function f(x)=cos2x.

A: Given: fx=cos2x To find the Fourier series of the given function.

Q: Suppose a bond has a price today of $800, a coupon rate of 4%, and six years remaining to maturity.…

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Q: use the noise terms phenomenon to solve the following Fredholm integral equations |- 14) α (X) = √x…

A: Given Fredholm integral is ux = πx +cos-1x - ∫-11 x ut dt. Find the solution using noise term…

Q: pl ef 器 (P-1)(q - 1) = (−1) 4

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Q: What's wrong? Consider the rotation field F (-y, x) x² + y? * a. Verify that the two-dimensional…

A: The given vector field is, F=-y,xx2+y2. (a) To Show: Two-dimensional curl of F is 0 and double…

Q: the common difference of the AP.

A: A

Q: Find the differential equation such that y(x) = (x − 1) [c sin(ln(x+1))+c cos (In(x+1))] Od²y +2 dx²…

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Q: X |_ [² é

A: Given differential equation x'=x+2y-6e-ty'=4x+y-8e-t From the homogeneous solution given it is clear…

Q: Let B: I + e₁2e3 + е3 e₁ where I is the identity tensor in R³ with basis vectors (e₁,e2, e3). What…

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Q: 3. (a) Use the Method of Undetermined Coefficients to find the general solution y(t) of the…

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Q: Find the future value of an ordinary annuity if payments are made in the amount R and interest is…

A: Givan that, R = 100 6.2% interest compounded semi annually for 12 years.  The future value of the…

Q: By showing that any sequence in A ∪ L has the same limit as some sequence in A, prove that A ⊆ A ∪…

A: Given Data : L is the set of accumulation points of sequences in A. To Prove : A⊆A∪L

Q: Let H be the set of all points (x, y) in ℝ2 such that x2 + xy + 3y2 = 3. Show that H is a closed…

A: Given that H=x∈ℝ2:x2 + xy + 3y2 = 3 here we have to show that H is closed subset of ℝ2

Q: Verify that y(x) = xJ 1(x) is a solution to the differential equation xy′′−y′+xy=0, x &gt; 0.

A: Given the differential equation xy''-y'+xy=0 with x&gt;0. To verify whether the yx=xJ1x is a…

Q: [223] -2 - Show that the eigenvalues of the given system are complex. - Find the general solution of…

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Q: Question 1. If the Fourier transform of (3 0<t<2 to elsewhere is F(w). express the Fourier transform…

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Q: t series representation and the region of c f(z) = z+2 6-52 +2²

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Q: Show that a set A in ℝ2 is open in the Euclidean metric ⇔ it is open in the max metric. Hint: As…

A: Answer given below.

Q: A and B are N×N matrices with eigenvalues αα and β, respectively. Under what condition/s will the…

A: Given Data: Let us consider the given A and B are N×N matrices with eigenvalues αα and β,…

Q: Apply the inverse power method to approximate, for the matrix A , the ei­genvalue that is smallest…

A: Given matrix is: A=406-131604 The initial vector is: x0=11-1 The number of iterations are: k=5 Use…

Q: v=x²e=x + 4e²

A: Given solutiony=x2e-x+4ex

Q: find the sum of 1X ¹x (2-6) X (2-60²) + 2X (3 - w) x ( 2² w²) + -+ (-1x (m-w) x (m-1²);

A: A

Q: Problem: If v is an eigenvector of A with eigenvalue 3, show that v is an eigenvector for B = A²…

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Q: Let A be a nonsingular 2 × 2 matrix with singularvalue decomposition A = USVT and singular valuess1…

A: Given That :  A be a nonsingular 2×2 matrix with singular value decomposition A=USVT and singular…

Q: find the mass and the indicated coordinate of the center of mass of the solid region Q of density ρ…

A: Given: ρx, y, z=k x+y+z=10, x=0, y=0, z=0. To find: (a) Mass of the solid. (b) Centre of mass x of…

Q: Suppose that a fire truck is parked in front of a building as shown in the figure. The beacon light…

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Q: Using simplex method and graphical method solve the dual problems, Objective function: Min w=14x,…

A: Given dual problem:- Objective function: Min   w= 14x1 +20x2 +24x3 Constraints: x1 +x2 +2x3 ≥7x1…