Devise a formula for the sum of the first n consecutive numbers, i.e. 1202, KUDA LA and prove its correctness. 1+2+...+n,

Q: Let > 0 and 6 > 0 be real numbers that satisfy e' (1+a+²) = eª (1+b+ 2 ) eb Prove or disprove that a…

A: Its given that a>0 and b>0. We have to prove or disprove that eb1+a+a22=ea1+b+b22 is satisfied…

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A: ∫∇·Vdt=∫5cosθ-8sinϕr2sinθdrdθdϕ

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Q: ) Let f: R2 R be a function which has continuous partial derivatives. Consider four points A=(2, 1),…

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Q: 2 4 1 l [64] n=1 4 3. n=A 5 2 3 n=2 ? 1 20 3 X n=5 d 402 19 1 T n=3 233 a to duniy INhat is formula…

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Q: ithout dividing the numerator by the denominator, how do you know if 5/45 is a term a…

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A: Using double integral, volume of a solid can be written as V=∫∫D1 z2-z1dA=∫∫D2 y2-y1dA=∫∫D3 x2-x1dA…

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A: We recall the subring test for this problem.

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Q: 14. Use Dual simplex to solve the following LPP. Max. Z = X₁ + 2X₂ + 3X3 Subject to X₁-X₂ + X3 ≥ 4…

A: Max z=x1+2x2+3x3 subjected to x1-x2+x3≥4x1+x2+2x3≤8x1+0x3-3x3≥2x1,x2, x3≥0 Note: We are allowed to…

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Q: Suppose the density of the rectangular surface in the image o=x 2y. 7 2 1 5 Determine the mass of…

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Q: Q1 xxxxxx Given the data: -3 0 2 f(x) 320 32 0 Construct Lagrange interpolating polynomial, then…

A: Since you have posted multiple questions, we will provide the solution only to the first question as…

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Q: Question 7. Consider a one-parameter group G of transformations defined by y 1-ay 1- ay (i) Find the…

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Q: Find the average rate of change of the function f(x) = 2x² + 6x - 5, on the interval z € [-1,3].…

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Q: [6K] Given f(x) = intercept and zeros. x+x-12 (x - 1)(x+4) determine the equations of all…

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Q: Ordinary annuity, $175 monthly payment, 618% inter- est, eleven years.

A: P=Payment per period=$175r=Interest rate per period=618%=6.18n=Number of periods=11 years

Q: (e) Let A = {1,2, (3,4,5)), B=(2, 3, 4, 5, 6, 7). Find i. An B. A x B. P(AB), where P(X) is the…

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Q: The function f is graphed below. State the values that fulfill the following requirements. If there…

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Q: Store A: 5 video games for $8.95 Store B: 7 video games for $10.50   Find the price per video game…

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Q: 1) Calculate the inventories if the current ratio of a company is 2.37 and quick ratio is 1.23 and…

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Q: 1. Find the supremum, infimum, maximum, and minimum of each subset of R, if it exists. a. A = U[-¹,…

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Q: af Use the Chain Rule to evaluate the partial derivatives and ди f(x, y, z) = x³ + yz², x=u² + v,…

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Q: Suppose a 2nd order constant coeficient ODE has a characteristic equation with complex roots equal…

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Q: Let f(x, y) = 7exy and c(t) = (4t², 15). Calculate (f. c)' (t). Use the first special case of the…

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Q: Q1: If y" + y = x², then yp = (A) x² Q2: If y" + 3y' +2.25y = -10e-1.5x, then yp = (A) Ax²e-¹5x (B)…

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Q: Use the Chain Rule to evaluate the partial derivative esu sin(v). y = (Use symbolic notation and…

A: Here we have to evaluate the partial differentiation at (u, v) = (0 , 2).

Q: Find the rank of the matrix A.

A: A matrix is the rectangular array of the numbers or the functions arranged in rows and columns is…

Q: Find the radius of convergence and the interval of convergence of the (-3)* (k+2016) 8k+1 (x-1)2k 8…

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Q: It is often easier, quicker and more accurate to enter exact values for trigonometric fu For…

A: We have                 tanπ6=13 We have to find the exact values of  sin56π  and cos56π , and we…

Q: Q9: Use L{1}={coswt} = s²+w²1 1-cos2t -¹ {53 +45-} = (A) ² (B) 2 (1-cost) (C): s³+4s 4 9 to find…

A: L-11s3+4s

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A: Since this problem is a multiple sub-part problem, as per the QSolPro guidelines we will solve only…

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Q: Zain flies planes to drop supplies to people who need it. He's flying at 167 km/h at a bearing of S…

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Q: (2) 2 let f(x) be a function of period 2π such that f(x) = x², over the interval -TT<x<T and has…

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Q: Let f(x) be a function which is twice differentiable with f"(x) > 0 on the interval [a - 1, a + 1]…

A: Given that f(x) is a function which is twice differentiable with f"(x)&gt;0 on the interval…

Q: 1. Find the interior and the boundary for each of the following sets. Classify it as open, closed,…

A: Given: A=∩n∈ℕ-2-1n,1+2n B=-1n+2n:n∈ℕ C=x∈ℚ+:x2≤2 To find: Interior Boundary Closed/Open/neither…

Q: (a) Let [a, b], a <b, be any closed interval. Prove that |[a, b]| = |[0, 1].

A: Let a , b , a&lt;b be any closed interval. Prove that: a , b=0,1 "As per the policy we are allowed…

Q: Question # 27- The function is continuous at which x-values? a) x = 1 b) x = 1 and x = 4 c) x = 3 e)…

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Q: Use the alternating series remainder estimate to find what value of n required to estimate the…

A: First we shall state the ALTERNATING SERIES REMAINDER ESTIMATION result. If the alternating series…

Q: 16. Use the distributive property of multiplication to find the product of

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Q: (i) If m / ±1 is a square-free integer prove Xn-m is irreducible in Q[X]. (ii) Prove that for every…

A: m≠±1 is a square-free integer.Polynomial : Xp-1+Xp-2+...+X+1Polynomial : X4-X-4

Q: Consider the following lines in S² a with pole = (1, −1, 1)/√3 B with pole n = (1, 0, 1)/√2 y with…

A: Given that the following lines in S2 α with pole ξ = (1, -1 , 1)/√3 β with pole η = (1, 0, 1)/√2 γ…