1) Find all equilibrium solutions of the equation x = (1 − x)(x² − 4) and classify each one in terms of stability. Draw a phase space diagram and sketch by hand several typical solution curves. Describe the long term (t → ±∞) behavior of the solutions.

Q: Find the equation of the tangent plane to the surface z = 4x² + 7y² + 9xy at the point (1, -2, 14).…

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Q: Solve the initial value problem y' y² + 2xy x² 1 find the interval of the maximal sol =

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Q: Use the simplex method to maximize the following: Maximize f = 5x₁ + 4x2 + 8x3 subject to 2x1 + x₂ +…

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Q: Prove that, if K is an extension field of F, then [K:F] = n if andonly if K is isomorphic to Fn as…

A: It is given that, K is an extension field of F. We have to show that, K : F = n if and only if K is…

Q: Show that 2²) 2 (¡ f(x) dx + ½ (b² − a²) [[y yf(x) + xg(y)dy dx = ½¼½ (d² − c²) <²) (1 g(y)dy

A: We have to show that the given expression, ∫ab∫cdyfx+xgydydy dx=12d2-c2∫abfxdx+12b2-a2∫cdgydy.

Q: How many Sylow 3-subgroups of S5 are there? Exhibit five.

A: To find the Sylow 3-subgroup of S5.

Q: Using the concept of the Determination of Integrating Factors, find the general solution of the…

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Q: Define a set of (non-orthogonal) base vectors a = J + K, + K and c 1+J. q = i +4j and r = − (a)…

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Q: (g) 1302 3440 2 -2 3 2 1 -3 1 1 4 -1 3 0 (h) 1 -2 3 -12) -5 12 -14 19 -9 22 -20 31 -4 9 -14 15

A: We know that determinant of diagonal matrix, upper triangular matrix, lower triangular matrix is the…

Q: 6. If (I, T) is a T.S., prove that A is dense in I iff every open subset of I intersects A, if at &

A: It is given that, (X, T) is a topological space. We have to show that, A is dense in X if and only…

Q: 1. 13 9 12 + 2 9 12 -

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Q: Find a polynomial p(x) in Q[x] such that Q(V1 + V5) is ring- isomorphic to Q[x]/{p(x)).

A: We need to find a polynomial px in Qx such that Q1+5 is a ring isomorphic to Qx/px. We know that if…

Q: What is the integrating factor of the linear De of order one ydx + (2-xy) dy=0? A B с D 32 ey 1 32

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Q: He Wo Salve the following.. nhau cho xe Bở2ydya

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Q: For each divisor k . 1 of n, let Uk(n) = {x ∈ U(n) | x mod k = 1}. [For example, U3(21) = {1, 4, 10,…

A: For each divisor k &gt; 1 of n , Uk(n) =x∈U(n)| xmod k =1. To prove Uk(n) is subgroup of U(n).

Q: A person purchased a $185,299 home 10 years ago by paying 20% down and signing a 30-year mortgage at…

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Q: The linear combinations of v = (a,b) and w = (c,d) fill the planes unless _______. Find four vectors…

A: We know that two vectors in ℝ2 form a subspace containing planes if they are linearly independent…

Q: Sketch the region that corresponds to the given inequality. 3x + y ≤ 2 (image attached of question)

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Q: Determine positive integers A, B, C, D, E and F such that 122-13 A D Ex-F 6x²-13-5 Bx+C A = B = C =…

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Q: A computer chip manufacturer has determined the weekly demand of their product is given by the…

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Q: preimage, E(-2,-4), is reflected over the y-axis? a) (2,4) b) (4.-2) c) (4,2) d) (2,4)

A: Note: When we reflect any point about y-axis, the y-coordinate remains same, but the x-coordinate is…

Q: Prove that the empty set is a subset of every set Se

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Q: If a vector space has one basis that contains infinitely many elements,prove that every basis…

A: Basis: A set of vectors B is said to be a basis of the vector space V if the set B is linearly…

Q: e. ; f. TRA

A: Please find the answer in next step

Q: A clock is hung on a wall so that the center is 20 cm below the ceiling. The minute hand is 10 cm…

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Q: 1. Given A || do - do [0.5 0.5 0.5 0.5 -3 -2 1-3 1 -0.5 0.5 -0.5 0.5 1 4 If the Gram-Schmidt process…

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Q: If we want to use gradient descent approach to estimate the minimum of f (x) = x², and ï₁ = -2 while…

A: This is a problem of function of several variables.

Q: If B is the inverse of A 2, show that AB is the inverse of A.

A: A square matrix A is said to be invertible if there exists a square matrix B such that AB=I, where I…

Q: Use Fubini's Theorem to evaluate the double integral ff f(x,y) dA, where f(x, y) =-3x²-x²y - 3y² and…

A: Given, f(x,y)=-3x2-x2y-3y2 and R=2,4×0,4 To evalute: ∫R∫f(x,y)dA by using Fubini's Theorem

Q: A lamina occupies the part of the rectangle 0 ≤ x ≤ 8, 0 ≤ y ≤ 6 and the density at each point is…

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Q: Determine the real root of -12- 21x + 18x² - 2.75x³ graphically (choose your limits). In addition,…

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Q: 4.1.7. Let G = Dg act on N = D8 by conjugation. Make an 8 × 8 table, where the rows are indexed by…

A: It is given that G=D8 act on Ω=D8 by conjugate. So it follows that, D8=e, r, r2, r3, s,sr, sr2,…

Q: Find all values of a, if any, for which the given matrix is invertible. Enter acceptable values of a…

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Q: If random variable X has the density function f(x)= e, -∞ <* < 0. 1 Show that M(t) = - 2 -1 < t < 1.

A: Definition of Moment is given below and conditions for that integral to exist(give a finite value)…

Q: A cat climbs up the side of a tree, tilted at a 10 degree angle relative to the vertical (the cat is…

A: Let Fp is the force required to push into the tree in order to climb up at constant speed. Given…

Q: Indicate the values of x and y such that the following equation holds for every sequence {an}n>0 60…

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Q: Locate all of the KKT points for the following problem. Con show that these points are local you…

A: Let us consider that, A=a1,a2,a3……,amn, where A∈Rm×n then there exist a constant b=b1,b2,……,bn, such…

Q: (b) y" + 2y = 3 + 4 sin 2t 2 21

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Q: Jenelle bought a home for $300,000, paying 22% as a down payment, and financing the rest at 5.4%…

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Q: Hey how did you get 25 and 60 to multiply with?

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Q: Prove the following statement using mathematical induction. Do not derive it from Theorem 5.2.1 or…

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Q: 1. 39 (7).. 10 A. (10.0101) ₂ equals to B. (100.101) 2- C. (101.111) 2- D. (1001.11) ₂- 2 39 2. Up…

A: Solution:

Q: Solve dy = tan y cot x - sec y cos x, simple dx substitution [Hint: Express the functions first in…

A: dydx=tanycotx-secycosx We have to solve it . Remember : A differential equation Mdx+Ndy=0 is called…

Q: What is the integrating factor of the linear De of order one y'= 1+ 3ytanx ? A B с D sec ³x cos³x *…

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Q: Compute the standard deviation for set ​{8​,8​,9​,9​,9​,10​,10​}.

A: Data set = ​{8​,8​,9​,9​,9​,10​,10​} Here, n=7 Mean of the data is (8​+8+9​+9​+9​+10​+10​)/7 = 63/7…

Q: 2π 7 SS π 4 π/2 4 cos 0 a) Sketch the region and calculate the area. rdrde b) Sketch the region and…

A: We will use relation between cartesian and polar co ordinate system x=r cosθ , y=r sinθ , Here r is…

Q: 2. (LI-2) Consider the equation r2y" - xy + y = 0. It is given that y₁ = z is one solution to this…

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Q: Find x so that the dot product of the vectors u and v below is 23.

A: dot product will be 3*5+2*(-2)+2x so this must be  23

Q: mich. daß. B. I. . . . . x 2 y.).dy. ....

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Q: Suppose f: A→ B is a non-zero group homomorphism. Which of the following are true? (i): If A = Z36,…

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