case. What is the relationship between the three numbers below? Explain why it is the xyzb xyz0b xy.zb Here x, y, and z are all valid single-digit values in the number system in base b and b is an integer larger than 1.

Q: Prove that 45 is irrational.

A: To prove: We have to prove that 453 is irrational.

Q: For all n E N and x € Z, x² = 1 mod n Which of "if", "only if", "iff" in Which of "if", "only if",…

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Q: Match each unit price to the correct graph. $1.00 1 lb $4.00 1 lb ? ? Price (dollars) Price…

A: price/weight Graph Explanation $1.001 lb When the weight is 1 lb the price is 1 $ $4.001 lb…

Q: Please do and explain d, e, f

A: (d) We are given that (x, y) ∈ R if and only if            x ≡ y (mod 7)       Now, it is obvious…

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A: As per the question we are given a operator L̂ on the Hilbert space over ℂ [a, b] and we have to :…

Q: Solve the following differential equation of separable variables. xy + 3x-y-3 xy - 2x + 4y - 8 dy dx…

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Q: Let (Q be the set of negative rational numbers and () is the arithmetic multiplication. Then (Q,) is…

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Q: Consider the term In(N!). Compare this exact value with the more accurate Stirling approximation,…

A: The given term is lnN!. We have to compare this exact value with the more accurate Stirling…

Q: Write the number 3.093535353535... as an infinite sum; then use the appro- priate formula to write…

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Q: Let p, q ∈ Z. Suppose that for all s ∈ Z with s > p, we have q < s. Prove that q ≤ p. Is the same…

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Q: For an invertible matrix A, prove that A and A-1 have the same eigenvectors. How are the eigenvalues…

A: x is the eigen vector of Agives Ax=λx, where λis the eigen value of  A Ax=λx⇒A-1Ax=A-1λx⇒Ix=λA-1x…

Q: 3.-. 3) The general solution of y" - 5y' +6y=0 is. A. y = ce² +₂e³ B. y ce2 + c₂e-3 C. y cie-2z+c₂e³…

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Q: Find, correct to the nearest degree, the angle of the triangle with the given vertices. A(1, 0, -1),…

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Q: In (Z103, +mod 103, -mod 103 ), the multiplicative inverse of 102 is 102. Select one: O True O False

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Q: Prove that f(x) = x ⋅ |x| is continuous at all points c in ℝ.

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Q: 1. Given the following table of values, approximate the indicated partial derivatives. ƒ (3, 4) = 6…

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Q: The general solution of r2y" + 3ry' + y = 0 is. +₂2² B. y = cx + c₂ln(x) C. y=+(2) D. y=2+2

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Q: Q2: Why (z-zo)" dz = 0, at n # -1, where y is given by lz - zol = r.

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Q: 11m b) Use a compound angle formula to determine an exact value of sin 17.

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Q: a) Now consider another function g(x) expanded in the above basis as (inluded in image). Prove that…

A: As per the question we are given a function g(x) expanded in the basis φn(x) and we have to prove…

Q: Verify that λ; is an eigenvalue of A and that x; is a corresponding eigenvector. A₁ = 5, x₁ = (1, 2,…

A: Answer follows by matrix multiplication

Q: ) Let f be a real function, defined everywhere on R. Prove that if = L, then also lim f(-x) = L.…

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Q: The profits of a small company for each of the first five years of its operation are given in the…

A: Given that The profits of a small company for each of the first fiveyears of its operation are given…

Q: y" - 4y' + 4y = cos t ; y(0) = 1; y'(0) = −1

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Q: 2. Which of these graphs is NOT a function? Output 9 8 7 6 5 4 32 andino 1 10 0 0 1 2 3 4 5 6 7 8 9…

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Q: 1. LD = 2. LE= 3. LF = Find the measures of the three angles, in radians, of the triangle with the…

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Q: 3. 3x -X For the equation given, determine the differential equation by eliminating the arbitrary…

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Q: Consider the function ƒ: R \ {-3} → R : x → x x + 3 (a) Determine the general expression for…

A: Since there are many parts, so find the solutions of the first two parts.

Q: 27. dy dt dy -y², y(0) = 1/2 28. =t²y³, y(0) = -1 dy dt dy

A: We have to solve given differential equations.

Q: Consider the matrix A defined as [1/2 1/2 A = 1/2 1/2 0 0 0 1 a) Using the standard relations of the…

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Q: 2. Determine the equation of: a. The cubic function with zeroes 1, -2, -5 and y-intercept 10. b. The…

A: (a) Let fx=ax3+bx2+cx+d The function  has zero at 1,-2,-5 and y- intercept at 10 that f0=10…

Q: (i) Let E₁ denote the 4 x 4 elementary matrix which corresponds to the elementary row operation R₂…

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Q: Ifv+w= and v = [1]. C W= , compute and draw the vectors v and w.

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Q: Solve the following edo of ricatti dy dx = y² + xy + 2x - 4, 3/₁ = -2

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Q: Volumes of solids Use a triple integral to find the volume of thefollowing solid. The wedge bounded…

A: Given: A wedge bounded by the parabolic cylinder y=x2 , z=3-y z=0. To Find: Volume by using a triple…

Q: 4. Find the maxima of the following functions (assume (a) f(x) = − x² – x4. ≥ 0).

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Q: C = C₁ ( √ ( 1² + 54²2)) + C₂ (√(K-150)² +54²)) 6

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Q: Define the linear transformation T: R^ → Rm by T(v) = Av. Find the dimensions of Rn and Rm. A = 0 0…

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Q: Determine the points of intersection of  y=x^2   and   y=x+1

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Q: RP(n + 1) 2N R=0.36, P = $6593, n = 56, and N = 28 Evaluate RP(n + 1) 2N for each of the following…

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Q: can you write it?

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Q: 1. Solve the following linear programming model using simplex method. Maximize Subject to: z = 3x₁ +…

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Q: 6. Given a Z transform 2-1 X (z) (1-z-¹) (11.4z¹+0.482-2)' determine the initial and final values of…

A: Given: Xz=z-11-z-11-1.4z-1+0.48z-2To find: a) xkk=0 and xkk=∞              b) Inverse Z-transform,…

Q: 5. Solve the equation xydx + (x + 1)dy = 0. ex = cy(x + 1) yex = c(x + 1) c. y = cex(x + 1) d. ye*(x…

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Q: Find an equation of the circle that has center (-5, -1) and passes through the origin.

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Q: Solve the system of equations 2x - y = 3 (3x + 2y = 1

A: The equation given are 2x - y = 3 --- (1) 3x+2y = 1 --- (2) multiplying equation (1) by 3 and…

Q: dy 2. Consider the Differential Equation (DE) =-1-2y. dt a. Sketch (ie, draw by hand) a direction…

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Q: Choose O if the statement is ALWAYS true. Otherwise, choose X. No need for justifications. ◆ (a.)…

A: Disclaimer: Since you have posted a question with multiple sub-parts, we will solve first three sub…

Q: a. Find the Riemann sum for f(x) = 1/x, 1 < x < 2, with four terms, taking the sample points to be…

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Q: Solve the following differential reducible to exact (y² + xy³)dx + (5y2 - xy + y³siny)dy = 0

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