2. Express every solution to the following equation as the sum of a specific solution plus a solution to the associated homogeneous system. 2 3 -1 1 -1 1 1 -1 2 -1 0 <-2 1 2 X =

Q: 1. Find the optium path for f=xy³ from (2,1,2)

A:

Q: 1)   If A =         2  -1     and   B =         1          -2                           7   0…

A: We are given A=[2-17  0],  B=[1-23-3]

Q: find the directional derivative of the function in the direction of the vector u = cos i + sin j

A: Consider the given function, fx,y=sin2x+y Here we need to find the directional derivative of the…

Q: 2. A right circular cylindrical container with volume 167 cm³ is to be made. Use the method of…

A: Note:-  Volume of right circular cylinder is V =πr2 h Given information Let the radius of right…

Q: Encontre a expressão da transformação linear T: P3(R) → P₂(R) definida por T(1 + 2t + ²) = 4+ 5t²,…

A: We will use the property of linear transformation to find the expression of the given linear…

Q: 5. So S2. by reversing the order of integration. Evaluate 8y dardy (x³ + 1)² 5

A: We want to find the integral ∫01∫2y28yx3+12dxdy

Q: Solve until the 6th derivative and provide the summation notation of the taylor series. f(x) =…

A: To solve until the 6th derivative and provide the summation notation of the Taylor series.…

Q: Let S be the surface defined by the vector function R(u, v) = (v +4, 4u - v, uv²). Set up an…

A: Given, The surface S defined by the vector function R→(u, v) = v+4,4u-v,uv2 We have to set up an…

Q: man recieves ghc36 as his salary.he is expected to contribute 12 and half of his to a social…

A: Total salary =ghc36 Contribution paid to social security fund = 1212%

Q: Set up an iterated double integral equal to the volume of the solid in the first octant bounded only…

A: To set up a double integral equal to the volume of the solid in the first octant bounded only by the…

Q: Expand f(2)= (2-1)(2-2) in a Laurent series valid for the indicated annular domain. (Give all terms…

A: Given function is f(z)=1(z-1)(z-2)          (1) annular domain is 0&lt;z-2&lt;1 Partial fraction of…

Q: 2. Use successive substitution to determine the roots of 2x² + 5xy = 25 x + xy = 30 Initiate the…

A: Solution :-

Q: solve y''-y'=xex  using undetermined coefficient. The characteristic equation will be r2-r=0

A:

Q: π Σn=13 + (-1)"+1n! Зе 3"

A: Ratio test: Suppose we have the series ∑n=0∞an Define, L=limn→∞an+1an. Then, (a) if L&lt;1 the…

Q: 1. Solve for y3 using the method of successive approximation. dy dx = x+y; y(1) = 1

A: Consider the given differential equation, dydx=x+y where y1=1 The method of successive approximation…

Q: Use the nth-term test for divergence to show that the series is divergent, or state that the test is…

A:

Q: Solve until the 6th derivative and provide the summation of the taylor series. f(x) = ln 4x ; c = ¼

A:

Q: Use the method of undetermined coefficients to find the general solution to the given differential…

A:

Q: Use the scratch method to add the numbers below. If the number needs a scratch, put a scratch (/)…

A:

Q: Use the shell method to find the volume of the solid generated by revolving the region bounded by…

A:

Q: 6. If: u = z * sin y/x where: x = 3r ^ 2 + 3s y = 4r - 2s ^ 2 z = 2r ^ 2 - 3s ^ 2 partial u…

A: A scalar function f(x,y,z) is a rule that is used to associate a number, or quantity with a…

Q: An object is traveling along the line y = 2x + 1 heading up and to the right. If the temperature at…

A:

Q: a) An engineering problem is modelled by the formulae below. If the distance travelled by some…

A: Given integration is I=∫0πsin(x)dx Here f(x)=sinx Number of subinterval is n=10 Then step size is…

Q: Let S1 = {(x,y)/ x2y-3), S2 = {(x,y)/ 0≤ x ≤3, 1≤ y ≤5) and S3 = {(x,y)/ 0<x<3, 1sy≤5}. Then: * O $1…

A: Result: A set in ℝn is compact if and only if it is closed and bounded. Hence, to find which of the…

Q: there are 18 people from the mathematics department and 325 people from the computer science…

A: see my solution below

Q: Determine the zeros and their orders for the given function. (Order the zeros from smallest to…

A: This a simple question of complex analysis to find the zeroes of a function. The answer is given…

Q: Consider the weighted voting system [7: 7, 4, 2]. Find the Shapely-Shubik Power distribution.…

A:

Q: Find the solution of the initial value problem 1 3y" - 4y + y = 0, y(0) = 3, y'(0); 3 Then determine…

A: Find the solution to the initial value problem 3y'' – 4y' +y=0, y(0)=3, y'(0)=13 Then determine the…

Q: 10. The profit, P, of a video company (in thousands of dollars), is given by P(x) = -5x² +550x-5000,…

A: Sol Part D :- Graph the Function &amp; Domain:- The domain of a function is the set of input or…

Q: let -heoram a, ber about a) Find such that acb. Use the axioms and that : prove R to b) Find CEIN:…

A:

Q: a. Solve the system for a = 0.5. What are the eigenvalues of the coefficient matrix? Classify the…

A:

Q: c) Create a system of linear equation that is convergent and would have a unique solution. Discuss…

A: Now create a system of linear equations with  2 variables as x+2y=1x+3y=2 or 1213xy=12 Now the…

Q: Use the method of variation of parameters to determine the general solution of the given…

A: Here given the differential equation as y4+2y''+y=3sin t or D4+2D2+1y=3 sin t

Q: Given the function y₁ = x² is a solution to the differential equation x²y" - 3xy' + 4y = 0, find a…

A:

Q: 7. Set up an iterated double integral equal to the mass of the lamina in the shape of the region…

A:

Q: 100 8. The nth partial sum of the series = 1 an is given by Sn Find the 5th term using the sum.…

A:

Q: 4(t) = It cos (6ㅠt +풍)

A:

Q: Check convergence of cos s-¯¹ ( ²2/1). -n=1 COS (41)

A:

Q: Determine discrete numeric function corresponding to the following generating function: A(Z)=1/1-Z³

A: Given generating function is A(z)=11-z3 We can write it as A(z)=1-z3-1⇒A(z)=1+z3+z6+z9+....

Q: Find the general solution to the differential equation. y" - 16y' + 64y = 0

A:

Q: Expand the given function in a Laurent series valid for the indicated annular domain. (Give all…

A: Laurent Series : It is a power series expansion for a function. If the function f(z) is analytic…

Q: The figure below shows the graph of a linear function, f(x), whose limit at an unspecified…

A:

Q: 13. Using that 1 1-x k=0 a, find the power series representation of f(x) = the power series…

A:

Q: Find all the strictly monotonic functions f: R→R such that f(x + f(y)) = f(x) + y, for all z, y € R.…

A: a. Consider the given condition, fx+fy=fx+y, for all x,y∈ℝ. Here we need to find the strictly…

Q: where Consider the initial value problem y" + y = fk (t), c. Observe that U₁_k(t) — U4+k(t) 2k a.…

A: Given below clear Explanation. As many sub questions mentioned only answered first question as per…

Q: Use the Mean Value Theorem to prove that, for all x, y € IR, cos x - cos y ≤|x-y.

A:

Q: Each of the ODEs shown below is second order in y, with y₁ as a solution. Reduce the ODE from being…

A: We are given second order differential equation using the method of reduction of order we need to…

Q: The side lengths of a triangle are 17,15,9. Is the triangle a right triangle? Yes, the triangle is a…

A: A triangle is said to be right angle triangle if it satisfy the Pythagoras theorem formula

Q: In the weighted voting system [8: 6, 4, 3, 2], which player is pivotal in the sequential coalition…

A: Given the weighted voting system [ 8 : 6, 4, 3, 2 ] Quota = 8 Weight of P1 = 6 Weight of P2 = 4…

Q: a = 268 b = 752 e. Prove that if g = gcd(a, b) then gcd (2) = = 1

A: Given that a = 268 = 2 × 2 × 67 b = 752 = 2 × 2 × 2 × 2 × 47   Now let g = gcd (a, b) = gcd ( 268,…