Prove that k(K) a) combinatorial b) algebraic proof (1) for integers n and k with 1 ≤ k ≤ n, using a: k proof; = n

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Q: 1. Solve by Gauss Elimination 6x + 3y+6z=30 2x+3y+32= 17 x+2y+2x=11 w+y+2=19

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Q: Exercise 1) Consider the group (S3, 0) and H= {e, fs). Prove that HS3. 2) Consider the group (Z.)…

A: Note: Hi! Thank you for the question as per the honor code, we’ll answer the first question since…

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Q: Exer. 43-50: Simplify f(x), and sketch the graph of f. 2x²+x-6 43 f(x) x² + 3x + 2

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Q: QUESTION 10 If Ax=b is an inconsistent linear system, then ATAx=A¹b is also inconsistent. O True O…

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Q: a. Write the equation of the line that represents the linear approximation to the following function…

A: Given function is fx=2x+1 and a=0; 21.3. a We have to write the equation of the line that represents…

Q: Plot the following and their normal vectors. |2x -2y + 2z = 15 3x - 3y + 3z = -13 Describe the…

A: Normal to the plane ax + by + cz =d is n→=a,b,c As angle between planes as angle between there…

Q: 4. If f ) و show that fg & LC₂.

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Q: Use the method of variation of parameters to solve the initial value problem x' = Ax + f(t), x(a) =…

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Q: . Use the result obtained in (i), and the method of Laplace transform to solve the following initial…

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Q: The instantaneous rate of change of a ball (in ft/s) is given by f'(x) = √x Select one: 1 4 O a. sec…

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Q: Question: The shaded regions R₁, R₂, and R3 (see figure) are formed by the graphs of the following.…

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Q: 2. Determine the positive real root of In(x²) = 0.7 (a) graphically, (b) using three iterations of…

A: We'll answer the first question since the exact one wasn't specified. Please submit a new question…

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Q: You must show all work! (You may check your answers using your graphing calculator.) = -[. 52 1 4 -2…

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Q: Find the indicated limit. Note that l'Hôpital's rule does not apply to every problem, and some…

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Q: Plot the following and their normal vectors. 2x-2y + 2z = 15 3x - 3y + 3z = -13 Describe the…

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

Q: A) Compute F.dà using the Divergence Theorem. SHOW WORK. S B) Compute the flux of F out S, which is…

A: Given that S is the outward oriented closed cylinder  x2+y2=9, 0≤z≤2 and  F→=xi^+yj^+2zk^ Solution…

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Q: dn Find a general formula for den by identifying a pattern in parts (a) through (c). To begin,…

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Q: If || fn-fl|p. os no prove that lim 11 fn V = || f 11 p. له در

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Q: Problem 3) Given a football in the figure: 1 d L=12 in The diameter is measured at some points and…

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Q: H = 1 -3 2 -4 Determine the dimension of the subspace H, where 7 9 -6 12 2 -1 4 2 5 - -3 7

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Q: 1. Determine the convergence of the following sequences. 1 b. n²n! l(n+2)! S

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Q: Find all points of intersection of the given curves. (Assume 0- enter POLE in the first answer…

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Q: L {y" + 2y²-3y=0} where; y(o)=0 y'(o) = 2

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Q: Determine the inverse Laplace transform of the function below. 2s + 38 s² + 10s + 41 Click here to…

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Q: 1.) 201 4sin (x) cos (x) dx dy 0 y² + 1 [¹ylnª (y² + 1)

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Q: Suppose m is a positive f& La(μ), 11 £1100 2o and 2n = Ln Prove that = √ 1+1" 1₂" (n=1₁2,...)…

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Q: Find the general solution using the method of variation of parameters. y" + 4y + 4y = 6e-2x

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Q: Determine the inverse Laplace transform of the function below. 6 s² + 49

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Q: MODELING WITH MATHEMATICS You and your friend are standing on the baseline of a basketball court.…

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Q: 5. Let W₁ = equal to (a) 0 and W2 = (b) 1 0 be subspaces of R³. Then dim(W₁ W₂) is (c) 2 (d) 3 V

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Q: xp z/1 (1 − 1-x7)x^ S 4.

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Q: Use the Laplace transform table and the linearity of the Laplace transform to determine the…

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Q: What interest rate was applied if a loan of ₱65,468 will amount to ₱125,000 borrowed for 2.5 years…

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Q: Find the matrix A of the quadratic form associated with the equation. 9x2 - 6xy +9y2 + 24z² - 29 = 0

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Q: B: Find Laplace Transform of f(t)= cos3t By DEF.

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