-4 If A = [4 3 5 1. Find the Eigen values and the Eigen vectors of A. 2. Compute A¹ = P[^² 0 221 P-1,where P is the Eigen vectors of A.

Q: a) x³y" - x²y" + 2xy' - 2y = 0, x > 0, y(1) = -1, y'(1) = -3, y" (1) = 1

A: (a) To Solve: x3y'''-x2y''+2xy'-2y=0, x>0, y1=-1, y'1=-3, y''1=1   (b) To Solve:…

Q: 2. Set up the formulation to find the surface generated when the curve y=x is revolved about the…

A: Let f(x) be a nonnegative smooth function over the integral [a,b]. Then the surface area of the…

Q: 150m

A: A natural draft cooling tower is in the shape of a hyperbola with an equation x2302-y2442=1. Given:…

Q: Given r(t)=(t+cost)i+(t-cost)j+(sqrt(2)sint)k, find the frenet frame, curvature and torsion.

A: Given  rt=t+costi+t-costj+2sintk

Q: Solve 8-¹ = 4*3 algebraically by using a common base.

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Q: Find the remainder in the Taylor series centered at the point a for the following function. Then…

A: Given function is f(x) = e-x

Q: e) x³y" - 6xy' +12y = 20x¹, x > 0, y(1) = , y'(1) = 5, y"(1) = 14

A: e Given differential equation is x3y'''−6xy'+12y=20x4.......1, y1=83,y'1=503 and y''1=14. We have to…

Q: a) Find the values A and B that allow the vector field given below to be conserved. F(x,y,z)=2xlnz…

A: (a) Given vector field is Fx,y,z=2xlnz i+3Bz j+x2zA+y3k Now, F1=2xlnzF2=3Bz F3=x2zA+y3

Q: For the division problem, do your prep work by using the doubling method (double as far as…

A: Given 629÷44

Q: Use the method of undete A= =7 51 42 f(t)= - 12

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Q: 2. The company Shirts Galore has figured its total cost of producing and selling x units of T-shirts…

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Q: e) x³y" - 6xy +12y = 20x¹, x > 0, y(1) = , y'(1) = 5, y" (1) = 14

A:

Q: Use the method of undetermined coefficients to determine only the form of a particular solution for…

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Q: Use Lagrange multipliers to find the indicated extrema, assuming that x and y are positive. Maximize…

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Q: 3. Set up the formulation to find the surface generated when the curve y = x² is revolved about the…

A: 1st we need to convert the curve in x=f(y) form and corresponding limits for y , Then use given…

Q: 1. Let A = a b c def ghi B ba bb b c gh i de f If de+ (A) = -1/24 then what is det (B-¹)? and AUT

A: Square matrix: If a matrix A has the number of rows equal to the number of columns. Then, the matrix…

Q: -t 9-y" + 2y +y = 3e¯t

A:

Q: You are to randomly pick one disk from a bag that contains the disks shown below. Find…

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Q: Solve the given initial value problem. x'(t) = x(t) = □ 20 -9 3 8 |x(t),x(0) = 귀

A: Solution of initial value theorem

Q: Consider the following ODE, 4x²y" — 4xy' + 3y = 0 (a) Find the general solution y(x) = Ay₁(x)…

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Q: Simplify tan ¹(− ª) to a single trig function using the sum or difference of angles identity. 2

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Q: The set B = {x² – 2, 4x² − (8+3x), 15x² − (28 + 9x)} is a basis for P₂. Find the coordinates of p(x)…

A: Result: Let B be the basis of P2 and let p(x)∈P2. Then the coordinates of p(x) relative to the basis…

Q: 3. Prove by contradiction, that if x and y are odd integers, then there is no integers z such that…

A: solution : let x and y are odd integers . Therefore , we can write x=2m+1 and y=2n+1 for some…

Q: Let B be the standard basis of P₁, and consider the basis B' [T]B¹,B. = {(1)· (9)}< of V. Find

A:

Q: 2.An object whose temperature is 100°C is placed in a medium whose temperature is A°C. The…

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Q: Solve the following ODES by Undetermined Coeff V X T 22X "Y + 5y + 4y = x² ² ² "y xe -4X -X 2X Ans:…

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Q: Let x(k) = ku(k) h(k) = {0, ( 1, 0≤ k ≤ 4 elsewhere Let N = 11. (a) Plot x(k) for 0 ≤ k ≤ N-1. (b)…

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Q: Find the Wronskian of the given pair of functions: X O x² et O xet i, xet

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Q: 2. Define a function f(X) = c. X = C₁x₁ + C₂x₂ + C = (C1, C2, ..., Cn) E R is constant.…

A: Given,  f:ℝn→ℝ  such thatf(X)=c.X where X=(x1,x2,...,xn)∈ℝnand c=(c1,c2,...,cn)∈ℝn is constant tuple…

Q: Let A(x) represent the area bounded by the graph, the = 0 and t = x horizontal axis, and the…

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Q: SOLVE STEP BY STEP IN DIGITAL FORMAT Determine the volume of the function f(r,0,z) in a complete…

A: Volume can't negative so neglect negative sign.

Q: 1. This question is to find the best straight line y=mx+c that fits the data given below: X y -1 1 3…

A: note : As per our company guidelines we are supposed to answer ?️only first 3 sub-parts. Kindly…

Q: Initially, when the car passes the point P, it is moving with a constant speed of 16 ms¹. T seconds…

A: Area under v-t graph is displacement(=distance if does not change direction).

Q: In each of Problems 1 through 16, find the general solution of the given differential equation: 1.…

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Q: Show that x + 5[x²] is 0(x²).

A: This is a problem of complexity.

Q: Find the power serious in the power of x.(2x^2-3x+1)y''+2xy'-2y=0

A: Given differential equation is 2x2-3x+1y''+2xy'-2y=0         (1) Let the solution be y=∑k=0∞akxm+k…

Q: 55 Z 230 Y 380 X

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Q: Find the Wronskian of two solutions of the differential equation t²y" - t(t-4)y' + (t - 2)y=0…

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Q: 7 The monthly sales each salesperson has made for four car brands is shown in the matrix S below.…

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Q: 92 8 x'(t) = 10-02 [9] |x(t),x(0) = 29 2

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Q: In the semigroup with identity (R,) we define Va E R+, fa: (R, +) → (R, +) by Vx E R, fa (x) = ax.…

A: Given : fa : ℝ, + → (ℝ, +)  defined as  fa(a) = ax  and  τ = fa : ℝ→ℝ , a∈ℝ+. To find : We have to…

Q: The value of a brand new car is $27,000 and the value depreciates 19% every year. Write a function…

A: It is provided that the initial value of the car is $27000 and the depreciation rate is 19%. We need…

Q: dy dx 2x = (3y + x).

A:

Q: Use the method of undetermined coefficients to find a general solution to the system x' (t) = Ax(t)…

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Q: 3² dx dy + 2xy = sin y,x(n) = 1

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Q: Given differential equation y"" - sy" -4y' + 8y = ²³x +8x²

A:

Q: dy dx =y²-2xy + 2

A: We need to solve the differential equation:dydx=y2-2xy+2.

Q: the function... f(x)..=. X CX < = TT-X <x<TT

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Q: Write an equation for the function graphed below -7 -6 -5 -4 -3 -2 4

A: We will use vertical asymptotes concept to find function of given graph .

Q: A. Match the following differential equations and their type. The differential equations may be…

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