Use variation of parameters to solve the differential equation x²y" + y = x. [Leave u₁ and u₂ in integral form.]

Q: What is the x-coordinate of the centroid of the plane region bounded by y = 2x + 1, x + y = 7, and x…

A: We have to find the x-coordinate of the centroid.

Q: What is the volume in cubic units of the solid formed when the region is revolved about x = -1?…

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Q: M(x,y) dx + (x,y) dy=0 to be exact

A: Solution :

Q: With the use of: local linear approximation Estimate: In (V0.99)

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Q: (b) Find the largest eigen value and the eigen vector for the matrix A = x¹ (0) = (1 1) 1² il where

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Q: Evaluate the double integral: 2 So® S³ #7² +1 x7 y¹/3 (Hint: Change the order of integration to dy…

A: Double integration by changing the order of integration

Q: Evaluate J by means of trapezoidal rule using n = 10 and n = 20: 1 1 = [ exp(-x²)dx Note that this…

A: When n=10

Q: Use trapezoidal rule to approximate the integral f√3+2x³dx; n = 6 O 11.50676706 O 11.20676706 O…

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Q: 17. Given the following degree of the vertices of an undirected graph H = (4,1,5,3,4,3), we can…

A: For the given degree of the vertex of an undirected graph which of the following is correct :-

Q: What is the center of gravity of the solid formed when the plane region bounded by 2x + y -2= 0, y =…

A: Solution: Given plane is bounded by equations, 2x+y-2=0 Its equation of straight line with x, y…

Q: .Given the following degree of the vertices of an undirected graph H = {4,1,5,3,4,3}, we can…

A: Sum of the degrees is 4+1+5+3+4+3=20, which is even. So H is a graph. Therefore, option C is not…

Q: 2. SET-UP the definite integral that will give the area of the region specified using (a) x as the…

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Q: Use forward, backward and central difference to estimate the first derivative of f(x) = In(x) at x =…

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Q: Q4) Find the largest eigen value for the matrix 2 T A with x (0)=(7/17 1) 54

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Q: Follow the instructions below: a. Use Laplace transforms to solve the following Differential…

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Q: 3. In calculating the Laplace transform L{(t+2) H(t-5)} using the formula L{f(t-a)H(t-a)} =…

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Q: Suppose f(x, y) = (x − y)(9 — xy). Answer the following. Each answer should be a list of points (a,…

A: Given function is fx,y=x−y9−xy. We have to find the local maxima or minima of the given function.…

Q: (ii) Show that the differential equation is not exact. (2y² + 3x) dx + 2xydy = 0

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Q: 14. A constant force of 10 newtons is being applied at a constant angle of 45° on an object at the…

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Q: Let A be a nonempty subset of a bounded set B. Why does inf A and sup A exist? Show that (a) inf B ≤…

A: Use the following definitions, to prove the result. A set S is said to be bounded above if for…

Q: For any n N, define the function Xn RR by : if x ≥n Xn(2)= 0, if a <n. Show that the sequence of…

A: We will use definition of limit of sequence of function.

Q: Find the orthogonal projection of onto the subspace W of R4 spanned by projw() = -197 1 -13 10 5 8-6…

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Q: 2 =1'1₁ 2] Q4) Find the maximum eigen value for the system 4 = x¹ (0) = (1 1) with initial vector

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Q: H K M 10 C Graph1 For items 46-48. Please refer to Graph 1 46.Using Brute Force Algorithm, how many…

A: Given, the graph

Q: 4. Find the center and the radius of convergence of the following power series. 00 2100n n! zn

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Q: The region in the first quadrant is bounded by the curve y = e^x and the lines x = 0 and the x = 1.…

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Q: What is the center of gravity of the solid formed when the plane region bounded by y = x, y = 2x,…

A: Let us start solving the problem step by step

Q: Determine the causal signal x(n) if its z-transform is given by 1+22-2 1+z-2

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Q: What is the volume in cubic units of the solid formed when the region bounded by y = x^3, y-axis,…

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Q: Show that the function f(x) = -x²(x + 1)² on (-001 +00) Show that it has an absolute maximum and…

A: f(x) = - x2 (x+1)2       = - x2(x2 + 2x +1)  f(x)= - x4 - 2x3-x2 f'(x)= - 4x3-6x2-2x

Q: If F(x) = [~√4t a. F'(1) b. F(2), by interpreting F(2) as an area √4t-t2 dt, evaluate the following:

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Q: Let f be a bounded function on [a, b]. Show that f is integrable on [a, b] if and only if there is a…

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Q: of the following is a subgroup of (R+, *) where a*b = (ab)/2? A. (Q, *) B. (Z.*) C. (Q+, *) D. (Q-,…

A: Given group G = ( R+ , *)  where ,                       a*b = ab2 (.)  Group :  Let G be a non -…

Q: Set up the double integral that will find the volume of a solid bounded by z = 1- y²x² and the xy-…

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Q: Show that the function f(x) = x²(x + 1)² on (-∞0; +∞0) has an absolute maximum, and (ii) find that…

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Q: Find the 6 roots of -i

A: We have given that ,  z = -i We need to find sixth roots of z = -i. First we will find polar form of…

Q: . A binary operation A. B. C. D. a*b = (a+b)/3 defined on Real Numbers is just a groupoid a…

A: Solution :  Options (i) is correct

Q: -2x² Find the absolute extremum values of f(x) = xez 3 (Note: e 2≈ 0.22) on the interval [0, 1].

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Q: Optimize z=f(x,y)=20×x×y-(x2+y2), subject to x+y=4 Do in 45 minutes to upvote

A: Optimization problem

Q: 4. A binary operation a*b = 1/(ab) defined on positive Rational Numbers (Q+) is just a groupoid a…

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Q: 5 -2 a.) [² 1 0 1 b.) [5 2²2 31 -5 5 8 040 c.) [0 204] 4020 -2 0 -4 1 0 -4 1 11 2 20

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Q: 6. A binary operation A. B. C. D. a*b = |a - b| defined on Real Numbers (R) is just a groupoid a…

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Q: Find the solution of x = X₂ JED -6 where u(t) = 2 and x(0) = [1 -1]. 11 0 JUCE + u(t) (10)

A: The problem is solved using the concept of eigen value and eigen vector.

Q: 8. The specific solution of a state space equation is given below. Express the solution Q terms of…

A: Given: The specific solution of a state space equation, Qi=0.3jejt1j-0.3je-jt1-j   To express: The…

Q: 3. Which of the following operations is BOTH associative and commutative on positive integers C. a*b…

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Q: Classify the point (-37, 0) for f(x, y) = sin² x + y² by using Second derivative test if POSSIBLE.…

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Q: (4) Let A be a nonempty subset of a bounded set B. Why does inf A and sup A exist? Show that (a) inf…

A: let A be a nonempty subset of a bounded set B. why does infA and supA exists? show that  (a)…

Q: Question 7 - Using a suitable linearization to approximate √101 show that the approximate value is…

A: Given, 101 we have to approximate it by using linearization.

Q: Evaluate J by means fo trapezoidal rule using n = 10 and n = 20.  a. If n = 10, solve the length of…

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Q: Calculate the area boundes by the curve r = 2(9)cos^2 theta. Final answer should be rounded off to…

A: Given curve is r=29cos2θ. We have to find the area bounded by the given curve. The region bounded by…