Let a be a complex zero of x2 + x + 1 over Q. Prove thatQ(√ a)= Q(a).

Q: The rate of change of the variable y in terms of another variable t is equal to the expression 5t4 -…

A: Firstly we find first order linear differential equation from given data then solve for y(t). Then…

Q: 3. Generate differential equation by elimination of arbitrary constants. 2. y=x+c₁e* + С₂е¯X

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Q: let p be a prime and f(x) = (x-1(x-2)-₁ (2- (P-1)) - (2₁²-11) them all the co-efficient of this…

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Q: Suppose Set B contains 67 elements and the total number elements in either Set A or Set B is 145. If…

A: as given nB=67nA∪B=145nA∩B=12 claim- to find nA

Q: There are 550 students in your graduating class. Are there at least 3 people that share the same…

A: There are 550 students in your graduating class. We need to determine wheather there are at least 3…

Q: A simplified economy involves just three commodity categories agriculture, manufacturing, and…

A: Given: Economy involves just three commodity categories - agriculture, manufacturing and…

Q: What are the possibilities for the number of elements of order 5 in agroup of order 100?

A: In this question, we have to determine the number elements of order 5 in a group of order 100.

Q: 5. Bernoulli's Equations a. 6y²dx - x(2x³ + y)dy = 0

A: Given diffrential equation is 6y2 dx-x(2x3+y)dy=0.The equation of the form  dydx+P(x)y=Q(x)yn  or…

Q: Prove that if p is a prime and a² = 6² (mod p), then either a = b (mod p) or a = −b (mod p).

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Q: Problem 5. Given implicit function by formula: x²+3y-sin(x+y²) = 0 Find ƏY əx ƏY ax = - Fy/Fx

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Q: the space curve (t) = (2t, t², 2t)

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Q: Solve for the value of C in the equation: (3xy² + 2y)dx + (2x²y + x)dy = 0 when y(1) = 2 OA. 4 O B.…

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Q: QUESTION 1 (1.1) Let f: R→ R be defined by f(x) = r². (1.1.1) Is f one-to-one? Explain. (1.1.2) Is f…

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Q: 2. Given the following transformation: a) b) T: RR² by T Show that it is linear. Find its matrix. =…

A: We use definition of Linear Transformation to show given map T is linear. And we find required…

Q: 1. Show that there is no maximum principle for the wave equation.

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Q: dy Which of the following is TRUE about the differential equation x +y=1/2² dx O A. The equation is…

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Q: Graph each system of Inequalities below. Name the coordinates of the vertices of the polygon formed.…

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Q: Which of the following equations is NOT an exact equation?| OA. (2x sin y + y)dx + (x² cos y + x)dy…

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Q: Problem 10.7_2 Find the Taylor expansion of f(z)=(z-1)e about the point z=1.

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Q: What is the standard form of this linear equation in one variable: (y + 1)dx + (4x − y)dy = 0? None…

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Q: Let

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Q: Σlogp 318 X = x logx + O(x).

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Q: QUESTION 2 Define a relation on Nx N as follows: (a, b) R (c,d) a+d=b+c (2.1) Is (3,6) R (3,5)?…

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Q: . If (OM M_ON) 1 OA. OB. D. O E. es e-5 ys > -5 -- then what is the integrating factor? None of the…

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Q: +∞ (-1)" n=1 3+1 Determine if the series Σ+ Use Alternating Series Test. is convergent or divergent.

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Q: O A. Which of the following is NOT true about the linearity of differential equations? O B. The…

A: A linear equation or polynomial, with one or more terms, consisting of the derivatives of the…

Q: dy Solve for the value of C in the equation: + ycotx = 5ecosx when y dx O A. -5 O B. 5 O C.-4 O D.4…

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Q: PLEASEE ANSWER ASAP Let p, q and r be the propositions: p: Wild foxes have been seen in the…

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Q: {,-5,-4,-3,-2,-1} U [0, +∞0) in E₁

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Q: The integrating factor (IF) of the equation: (2x³y² + 4x²y + 2xy² + xy² + 2y)dx + (2y³ + 2x²y +…

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Q: Suppose c is an unknown number (but not a variable). Consider the following function: ¹a²+3, c+ 9,…

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Q: The characteristic polynomial of the matrix A = is p(A) = (A - 3)²1² The matrix has two real…

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Q: cermine if logical notation is tautology, contradiction, or contingency a. (pVq)A (pr)^(q→r) → r b.…

A: Tautology: If all truth values are T of last column of Truth table. Contradiction: If all truth…

Q: Let U={1,2,3,...,10}, A={1,3,5,7}, B={1,2,3,4}, and C={3,4,6,7,9}. Select (A∩B)^c from the choices…

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Q: I 2. After watching a major musical production at the theater, the patrons can purchase souvenirs.…

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Q: ୯ . 2 3 4

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Q: Which of the following equations is NOT a variable separable differential equation? O A. 2xydx + (x²…

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Q: Solve for the IF of the equation y(x + y + 1)dx + x(x + 3y + 2)dy = 0 O O A. B. ev elny D.y E. None…

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Q: Rearrange the f(x) =  2x^4-x^3-9x^2+4x+1 so that x is on the left-hand side of the equation.

A: The function: f(x) can be rearranged using basic algebraic operations.

Q: . If (OM) ay OA. e5 O B. -5 e O C. y5 D. E. -5 ƏN 1 ax) M 5 दाज = -- y " then what is the…

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Q: State the corresponding corner point for the given simplex tableau.      x       y         s1   s2…

A: The given simplex table  x y s1 s2 s3 p constant 8 0.25 1 0 0 0 72 6 3 0 1 0 0 17 4 0.75 0…

Q: x² - y² lim (x,y) →(a,a) x² - y² Here a is a constant. (Find the limit assuming x + y) Find the…

A: Given,            limx, y→a, ax4-y4x2-y2=

Q: 2. cos xdy = -(sin x) ydx + dx

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Q: • Let W = {ax²+bx+c+d €R[x] |a + 2b = 0, c = 2d}. Find a spanning set for W. • Let A RJ and define…

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Q: What is the unit's digit in the decimal representation of 3100?

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Q: Q1) Find the equation of the plane passing through the point (4,-1,-5) and perpendicular to the…

A: We have to find the equation of the plane passing through the point (4,-1,-5) and perpendicular to…

Q: quation for the level curve

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Q: 周 紀 =xlogæ+O(x).

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Q: Let a be a group element of even order. Prove that a2 is not in cl(a).

A: Let G be a group and a is an element of even order in the group. Prove that a2 is not in Cla.…

Q: Which of the following classification of the differential equation, +5 d²y dx² O A. dependent…

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