You are given the following system of differential equations:  dx/dt = -2x - 6y, dy/dt = -6x + 7y  It has the general solution (as pictured). What is the particular solution of this system that satisfies x = 3 and y = 4 when t = 0  The answers to choose from can be seen in image 2.

Q: Let n be = (0,1) and 1 2) fn does not strongly converge to 0 in Lº(). 3) {f} is bounded uniformly…

A: Solution:

Q: Let S be the cylinder x² + y² = a², 0≤zsh, together with its top, x² + y² sa², z=h. Let F= -9yi +…

A: Given S be the cylinder x2+y2=a2, 0≤z≤h, together with its top x2+y2≤a2, z=h. And  F→=-9yi+9xj+9x2k.

Q: Given a metric space M with metric d , verify that any ε -ball is an open set.

A: Let B(x,ε) be any ε -ball centered at x, for some x∈M. Let y∈B(x,ε). Then d(x,y)<ε. So…

Q: P... 144 £(+).m... 7 t -3 for 3 to... far as £ 3. 4 (+) $ -t t 2P=6 ……………….………………. *****

A: The given function is: ft=-tfor -3<t<0tfor 0<t<3 We have to find the Fourier series of…

Q: State and prove Euclid’s Lemma.(you may assume without proof that for integers x and y there exist…

A: If x and y are integer not both zero then there exist integer k and l such that kx+ly=gcdx,y

Q: 7. Assume that the carrying capacity for a certain region is 800 million. The population was 282…

A: Since you have posted a multi subparts question according to guildlines I will solve first three…

Q: Consider the linear system X' = [223] -2 X. 1. Show that the eigenvalues of the given system are…

A:

Q: Show that the p-series ∞∑n=1/1np converges for p>1.

A: We have to show that the p-series ∑n=1∞1np converges for p>1.

Q: 1 Problem 1 Are the following statements true or false? If true, prove the statement. If false, give…

A: Given Data: Let us consider the given A∈Rn×n and aij denote the element in ith and jth column. Then…

Q: You are given the matrix:  [5 4 -7] [4 5 -2] [-7 -2 17]  And told that it has the following…

A: The given problem is to find the corresponding eigenvalue for the given eigenvector of the given…

Q: Which of the following is the edge set of the graph (G) below? () E C () Referring to the graph (G)…

A:

Q: 5 Let A (1,2,3, 4, 5, 6, 10, 12, 15, 20, 30, 60). These are the factors of 60. Draw the Hasse…

A:

Q: 2. Let T: R³ → R³ such that T (e₁) = (1, 0, 1),T(e₂) = (0, 1, 1), T(e3) = (1, 1,0). What is the…

A: Given: T : R3→R3 such that Te1=1,0,1, Te2=0, 1, 1, Te3=1, 1, 0. To find: The standard matrix for T.…

Q: Use the simplex method to solve the linear programming problem: Maximize z = x1 + 2x2 + x3 + 5x4 ,…

A: The given linear programming problem is given as follows. Max Z=x1+2x2+x3+5x4Subject…

Q: Find an SVD of the indicated matrix.

A: The given matrix A=34. We have to find the SVD.

Q: Problem 3: Invert these matrices A by the Gauss-Jordan method starting with [A I]: A = 100 213 001…

A:

Q: The graph of f' (not f) is given below. At which of the marked values of x is A. f(x) greatest? x =…

A: From the given graph, we have to marked values of x.

Q: Use the surface integral in Stokes' Theorem to calculate the flux of the curl of the field F across…

A: Given the field F is                 F=4yi+(5-2x)j+(z2-2)k, and      S:r(ϕ,…

Q: aut ha аллах papunoa 9 pies out to ашиал 24+ риу sphere x² + y² + z ² ·+·y ² = 16 and bellow by the…

A: Given:  Sphere: x2+y2+z2=16 Cone: z2=x2+y2 To find: Volume of the solid.

Q: Find the volume of the solid inside the hemisphere Z= x² + y² - 4x = 0. 16-x² - y² and the cylinder

A: Given:A hemisphere: z=16-x2-y2 and a cylinder x2+y2-4x=0. We have to find the volume of the solid…

Q: 1. Consider the initial value problem dy dt y-1 t+3' for points close to the initial point (to, yo)…

A:

Q: You are given the following system of differential equations:  dx/dy = 6x + 2y, dy/dt = 2x + 9y…

A: We can write the system of differential equations in the matrix form as below: dxdtdydt=6229xy Here,…

Q: Complete each statement by filling in each blank with the correct word or phrase to give it a…

A:

Q: (a) Sketch a graph of a function f such that: o f' 0 and f" > 0, for x > 3. (b) Does the graph of…

A: Inflation Point (definition): an inflection point, point of inflection, flex, or inflection is a…

Q: Question 9 Compute (V × F) · în dS for the vector field ♬ given by F F = xî + (y + z + 4)ĵ + (2xyz8…

A: 9. Given the vector field F→ is                 F→=xi^+(y+z+4)j^+(2xyz8+6xz)k^.     where B is the…

Q: Q2: Find the solution of 143x³ + 22x¹ + 5x² + 3x + 1 = 0 (mod 11), if any.

A:

Q: uestion 3. efine an odd periodic extension of =2+3t, 0<t≤4 d hence find its half-range sine series…

A:

Q: pls solve the laplace transform of this function. you can use the table of laplace transformations…

A:

Q: Using the Fourier integral representation of the function a, x |k| we find = S TT JO where a=9,…

A: Answer given below.

Q: Question 4. The Fourier transform of f(t) is F(w) = 5e-3jw wj 8 4+ Using the Convolution Theorem,…

A:

Q: 7. The goal of this exercise is to find the maximum and minimum values of Z = 4x + 3y Subjected to…

A: The given function is, z=4x+3y. The given constraints are, x+2y≤20, 4x+y≤20, x≥0, y≥0. We have to:…

Q: Question 3. If F(w) is the Fourier transform of f(t), then the Fourier transform of g(t) = 4e5jt…

A:

Q: Solve the linear equation y u_x +x u_y = u with the Cauchy data u(x, 0) = x^3       and u(0, y) =…

A: As per the question we are given the following linear partial differential equation : y ux + x uy =…

Q: To 1 decimal point, what angle has a tan ratio of 0.2589? degrees

A: tan ratio is 0.2589

Q: A cone will be inscribed in a sphere of radius 10 in. Part A: Find the exact dimensions of the cone…

A: We will find volume of the cone in single variable and then maximize it by using 2nd derivative test…

Q: The appropriate Fourier transform to solve ²²u_du дх2 д' = u(x,0)=e-1x1, 0 0. is: -,0Q, k#0 O None…

A: Given one dimensional heat flow equation is     k2 ∂2u∂x2=∂u∂t   ,   0 &lt; x &lt; ∞ ,  k ≠ 0 The…

Q: determine two linearly independent power series solutions to the given differential equation…

A:

Q: Use the Laplace transform to solve the given initial-value problem. v = s(t − ½ n) + s(t – 2/2),…

A: The given problem is to find the solution for the given initial value problem with given initial…

Q: 2. (a) Use the method of Laplace transforms to find the solution y(t) of the initial value problem…

A:

Q: Find the equilibrium points of the following nonlinear system. Find its linearization about each CP.…

A:

Q: Use Definition 7.1.1. DEFINITION 7.1.1 Laplace Transform Let f be a function defined for t≥ 0. Then…

A:

Q: Miscellaneous volumes Use a triple integral to compute the volume of the following region. The…

A: Given: Vertices of parallelepiped0, 0 ,0, 2, 0, 0, 0, 2, 0,2, 2, 0, 0, 1,1, 2, 1, 1 0, 3, 1 and (2,…

Q: Prove the statement. Let f : A → B . If X ⊆ A, Y ⊆ B , and f-1[Y] = {x ∈ A|f(x) ∈ Y}, then f[X] ∩ Y…

A:

Q: . Let H be the set of all points (x, y) in R² such that x² + xy 3y² = 3. Show that H is a closed…

A: Given That : Let H be the set  of all points x , y in R2 such that x2+xy+3y2=3 or x2+xy-3y2=3. Show…

Q: sequence a1, A2, A3, 2 2 - 2 + ... an 2 ... 2 is an A.P., th n 102 =

A:

Q: Given: 1 2 Ï(x) with Ï(1) = (1, 2,−1) and Ï'(x) = { }, - (= -2) X a. If Ả(x) = (−2, −3x,x²) × Ì'(x),…

A:

Q: Examples. Find the Fourier half range Sine expansion for the fallowing function. far ast F(t) et ...…

A: Fourier Theorem states that any periodic waveform can be expressed as a sum of sine and cosine…

Q: Given the data for the transportation problem in Table 12.21: (a) Use the northwest corner method to…

A: The solution of the problem is calculated using North West Corner method as shown in the next step.…

Q: Consider the equation y" - y - 6y = 0, y(0) = 2, y(0) = 1. Bl 1. Using the substitution X write the…

A:

Q: the differential equation = 2

A: