7. The pair of equations dx dt dy dt -5x + 2xy -4y + 3xy models two coexisting species with populations x(t) and y(t). It has an equilibrium solution x(t) = 0, y(t) = 0, representing both species being extinct. Find an equilibrium solution for this model where both species have positive population.

Q: 6. Consider the sequence defined recursively by 1 2 an+1 = an + N an If ao = 1, does the sequence…

A:

Q: Let a bilinear transformation be a bilinear form ß: R² x R² R by B(x, y) = X1₁ V₁, and x = (x1, x2)…

A: Bilinear form is defined as, β:ℝ2×ℝ2→ℝ2 , β(x,y)=x1y1 , x=x1,x1, y=y1,y2. To Find: An example of a…

Q: Definition: Let V be a vector space and U₁, U₂, U be subspaces of V. Then V is said to be a direct…

A:

Q: Solve the followig non linear gebraic equation to fined one non Zevo root. P(x) = Sin [√ Secx + x…

A: Newton-Raphson method uses the formula: xn+1=xn-f(xn)f'(xn) to perform the iterations and to…

Q: 2. Solve the general cubic equation x³ + ba + bx + c = 0 with the trick of Cardan's Ars Magna.

A: The general cubic equation x3+ba+bx+c=0. We have to solve this equation using Cardan's Ars Magna.

Q: Determine whether the given function is a solution of the differential equation. y = √√√x; xy' - y =…

A: Given a differential equation xy'-y=0. To determine whether function y=x is a solution of the…

Q: Let ux,t=XxYy Given…

A: Note: As per your requirement I answered here on papar.   The required answer is in below step.

Q: (b) Let T: R³-R¹, T(v)=(v, w) w; +(v,w₂)w, where w; = (1,-1,0) and w₂ = (0,-2,1). (i) Find the…

A: It is given that,  T : ℝ3→ℝ3 be the linear transformation defined by ; Tv = v, w1w1 + v, w2w2…

Q: Let G be a bipartite graph of order p. Then i(G) ≤ 2.

A: please find the attached image

Q: Prove that every minimal dominating set in a graph G 26. is a maximal irredundant set of G.

A: Given that, Every minimal dominating set in a graph G is a maximal irredundant set of G. We have to…

Q: Let A = P = [-17 2 2 2 -14 4 2 4 -14 D = Find an orthogonal matrix P with rational entries and a…

A:

Q: Find the Fourier series of f(x) = |sin x| on the interval [−π, π]. Draw a sketch of f(x).

A:

Q: 11. Definition: An n x n matrix N is said be nilpotent whenever Nk smallest such k is called the…

A:

Q: Problem 4. Let (X, dx) and (Y, dy) be metric spaces. Show that the sup norm metric do we defined on…

A:

Q: 6. 7. 5. 8. In the figure above, the circle is inscribed in a square that has area 16. Quantity A…

A:

Q: Min 5x11 + 6x12 + 8x13 + 8x21 + 7x22 + 10x23 s.t. x11+x12+x13=6000 x12+x22>=8000 x13+x23>=5000 x11,…

A: Given the primal, min z=5x11+6x12+8x13+8x21+7x22+10x23 such that…

Q: 3. Ruel is the brother of Bella. Dina is the sister of Ruel. Matthew is the brother of Tanya. Tanya…

A:

Q: Pentagon H'I'J'K'L' is the image of pentagon HIJKL under a rotation about the origin followed by a…

A:

Q: How much should Kelsey have in a savings account that is earning 3.75% compounded monthly, if she…

A:

Q: Consider the recursive definition of the function f(n) f(0) = 0 f(n) = 1+ f(n-1) Find ƒ(1), ƒ(2),…

A: Recursive relation: It is an equation which represent a sequence based on some formula. From the…

Q: Evaluate the value (a) sin(2) (b) tan (5) (c) sin-¹(√3/2) (d) sin-¹(sin(¹1))

A:

Q: (2) Evaluate ³ dAwhere D is the region bounded by 2y=√xand y = 5-x, yz 0 gử

A: Double integral is denoted as ∫ab∫g(x)f(x)F(x,y)dydx or, ∫ab∫g(y)f(y)F(x,y)dxdy

Q: y+1 Z Find the acute angle between the lines 1 m n and 1, m, n are the roots of the cubic equation…

A:

Q: solve the following to find one real non zero root: non-linear algebraic equation. f(x) = sin…

A: The given function is, f(x)=sinsecx+x3 e5xtanx-e-x. To Find: One non-zero real root of the above…

Q: Consider the matrix A = 10332 -3 3 1 3 1 10 06-1 4 -2 1 0-4-2 Its rank is 634215 → and its nullity…

A:

Q: Use the Definition to find an expression for the area under the graph off as a f(x) = x² + √√1 + 2x,…

A:

Q: Knowing that S+x x² e ²² dx. +∞ +∞ Se-¹² dx = √√2π, find x2 е

A: Given:  ∫-∞∞e-x22dx=2πTo find: ∫-∞∞x2e-x22dx

Q: The table shows the result of a restaurant survey. Meals Service good Service poor Total Lunch 68…

A:

Q: rotate the vector v = The rotation matrix R = H IT by an angle of in the CLOCKWISE direction. The…

A:

Q: This extreme value problem has a solution with both a maximum value and a minimum value. Use…

A: Given function is fx,y=x2+y2+z2 and contraint x4+y4+z4=7. To Find : Extreme value of the function…

Q: 11.[2] Show that vectors A = 4ax - a₂, B = ax + 3ay + 4az, and C = -5ax 3a, 3az form the sides of a…

A: We know that if the vector form sides of triangle then A→+B→+C→=0 Given,…

Q: In the Fourier Series an and bn (for any n) are found by multiplying the signal by the nth harmonic…

A: Given: Fill in the blank statement about the Fourier series.We need to fill in the given statement…

Q: Suppose b is changed to b' . How large relative change can this change produce in the solution to Ax…

A: The given matrix is, A=1112501-12,  and b=123. To Find: The maximum change in the solution of the…

Q: f(x)=xlnx−1

A:

Q: Suppose that U₁,...,Uk are subspaces of V. Prove that V = U₁ ☺ · · · ÐUk if and only if the…

A: Please find the attached solution

Q: (1) Let E= R, fn = X[0,1], and f = X[1,2]. Check which converse implications do not hold in Question…

A: Please find the attached image.

Q: Find the coordinates of the wedge product a ^ b^c for a = = (−3,−1, 5, -7), b = (-5, 7, 6, 3), =…

A: Here, We have to find the wedge product  The details calculation is given below

Q: a) Let 3-4 5 B-2 4-1 00 S be a nonsingular matrix. Then find the values of s using row operations.…

A:

Q: 2. Complete each of the following. a) Let [x] € Z/nZ. What is the additive inverse of [x]? b) Show…

A:

Q: Problem No. 1. Three products are made by the Wright Company. The contribution of each of these is…

A: Max Z=2x1+4x2+3x3 subjected to 3x1+4x2+2x3≤602x1+x2+2x3≤40x1+3x2+2x3≤80 The problem is converted to…

Q: if sis a group of order p", then its center 24, peing a primes

A:

Q: If w1, w2, w3 are independent vectors, show that the sums v1 = w2 + w3 and V2 = W1 + W3 and V3 = W1…

A: Given:  v1=w2+w3, v2=w1+w3  and v3=w1+w2 Where w1,w2,w3 are independent To show : v1,v2,v3 are…

Q: Let F = {(x, y, z, w) ≤ R¹ : z = x + y, w = -2y-x} = . Which of the following statements is false? O…

A: Given that z= x+ y and w = -2y - x Therefore (x,y,z,w)= (x, y, x +y , -2y -x)…

Q: A company has $7,490 available per month for advertising. Newspaper ads cost $170 each and can't run…

A:

Q: (b) Let T: R³ →R³, T(v) = (v₂w;)w; +(v, w,₂)w, where w, = (1,-1,0) and w₂ = (0,2,1). (1) Find the…

A:

Q: Given the function g of the two real variables t and u by g(t,u)=t^2 + tu-u^2+(6+2)u c) Determine…

A: Linearization of a function g(t,u) about (a,b) is  L(t,u)=g(a,b)+(t-a)gt(a,b)+(u-b)gu(a,b)

Q: See how th e Rayleigh quotient method ap­proximates the dominant eigenvalue more rapidly than the…

A: Given : A=310131013 , x0=111 , k=6 To find : Dominant eigen value.

Q: Evaluate p(x) = 2x4+x²-3x²-x-5 at x = 2 33.a O 183.b O 21.CO 145.d O

A:

Q: 4) The marketing committee at a company decides to vote on a new company logo using Approval Voting.…

A: Answer :-

Q: a) Prove that every integer can be written a sum of powers of 2. b) Write 14, 17, 27 as a sum of…

A: We have to prove the every integer can be written a sum of power of 2 and write 14, 17, 27 as a sum…