Use Fourier-Motzkin elimination to give a linear combination of the following in- equalities that proves that there is no (r, y, z) satisfying all four inequalities. (a) (b) (c) (d) -x - y – 2z < -1 I-y -z -2 -r+y - z <-1 y + 3z <0

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Q: IT X) IS defined as foilows, ina (a) i( – 2), (D) (U), and (C) I(2). x? if x 0 (Simplify your…

A: Since the given function is a piecewise function therefore we need to take care of the branch of the…

Q: (1) The domain of the function f(x, y) is the set: y+1 (a){(x, y)– 2sxs2,y # -1} (d){(x, y)| –…

A: Explanation of the answer is as follows

Q: a. f(x + y) = (7x+7y,2x+2y,-7x-7y-2) f(x) + f(y) = (7x,2x,-7x-2) + (7y,2y,-7y-2) Does f(x + y) =…

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Q: Find the critical numbers of the functions. a) f(x) — х2 + 4х b) f(x) — х3 —7x? — 5х с) f(x) 3 2x3 -…

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Q: x+ y +z = 4 2x - 3y + z = 2 -x +2y - z =-1

A: Given, system if equations is-                       x+y+z=4                      2x-3y+z=2…

Q: 8r -1 is 2r + 4 4. The range of the function f(r):

A: follow next step

Q: b. Маx z %3DX1 + X2 s.t. 2x1 + x2 < 20 X1 +3x2 < 15 X2 < 4 X1, X2 2 0

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Q: For trajectory generation of an industrial robot, evaluate the coefficients of the fifth-order…

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Q: Find the order of the one-step method Un+1 = Un +5f(un +5f(Un))+ (f (Un) + f(un + hf(uUn))) 2 2 4…

A: We are given an one-step method and we have to find its order. To do that we will use limits and…

Q: Shade the area of the region bounded by the parabola, x² +p² – 2(p + 7)x – 5y + 59 + 14p = 0 and the…

A: We rewrite the equations  of parabolas and straight lines with p=9 as…

Q: (b) The revenue R(x, y) that Scoot Airline collects from selling its normal seats and premium seats…

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Q: 3 • xy²-2y = x ²cos4x (x-2) • FY+ 2(x-2) ³

A: As per our guideline if multiple questions are posted we are supposed to answer only the first one.…

Q: Let f(x) = x5 + x³ + 2x? – 1 € Z3[x]. Then x = 1 is a root for f(x) of multiplicity: 2 4 None 3

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Q: (c) Express the quadratic form Q(x1,x2, x3) = 6x + 3x3 + 3x3 – 4x1x2 - 2x2x3+4x3x1 %3D to the sum of…

A: A detailed solution is given below.

Q: Find the order of the one-step method h h Un+1 = Un +f(Un + 5f(un)) + (f(un) + f(Un + hf(un))) 2 2…

A: As per the question we have to check the order of the one-step method. And find the number of…

Q: Let f(x) = x5 + x3 + 2x² – 1 € Z3lx]. Then x = 1 is a root for f(x) of multiplicity: 4 None

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Q: The domain of f(x) =/4 – x +V x – 4 is (- 4,4] R – {4} (-00,4] [4,00) None of the above

A: Solution:Given   f(x)=4-x+x-4To find the domain of f(x)

Q: Find the order of the one-step method h h h Un+1 = Un + „f(un +5f(un)) + (f(Un) + f(un + hf(un))) 2…

A: Here we have to show that the given one-step process is atleast of order two. Then we have to check…

Q: Let f(x) = x* + 2x + 3x + 4 € Z,[x). Then x = -1 is a root for f(x) of multiplicity: 2 None 4

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Q: y +2z x+3y x Let det (A) z+ 2x y +3z y Then which of the following is the det (B) that satisfies the…

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Q: 2 and g(x) = x + 2x + 11 Let A = Find the sum of the entries of g(A).

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Q: 7. Show that the equation p(x) = q(x)m(x) + R(x) is equiva- lent to the equation p(x) = m(x) + R(x)…

A: Given equation is  px=qxmx+Rx

Q: 1. Find the order of the one-step method Un+1 = Un + „f(un +5f(un)) + (f(Un) + f(un + hf (Un))) 4…

A: As per the question we have to find the order of the one-step process and the number of…

Q: 2. Prove or give a counterexample to • If X ≤Y then Var (X) 0 . Var (X) ≤ Var(X)

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Q: Let f(x) = x + 2x - ax + bx (i) Find the values of a and b so that the multiplicity of the root -1…

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Q: Find all second-order three-step methods in the form Yn+1 = aoyn+q₂yn-l + a₂yn-2 +h[b_f (tn+1• Yn+1)…

A: Second-order three-step methods in the form you provided are used to solve initial value problems…

Q: ! (10) If f(x) =. then f(x) is irreducible in Z7[x]. 3 (i) x² + 2x² + 2x + 1 Option 1 (ii) x² + 3…

A: An irreducible polynomial is, roughly speaking, a polynomial that cannot be factored into the…

Q: 3) 4) Find g(3) for g(x) = √-x5. Find p(-x) for p(x) = x³-√1-x .

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Q: P1=(x1,y1,z1) and P2=(x2,y2,z2)  prove that distance of P1 and P2 ; |P1P2|=((x2-x1)2 +(y2-y1)2…

A: Solution: The objective is to prove that the distance of P1 and P2   |P1P2|=((x2-x1)2 +(y2-y1)2…