The integral (ydx - xdy) is evaluated along the circle x² + y² - traversed in counter clockwise direction. The integral is equal to

Q: 3. a. Determine the vector, parametric, and symmetric equations of the line passing through points…

A: The vector, parametric, and symmetric equations of the required lines are determined as shown below.…

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A: given graph f(x)=3x2-12x+1

Q: 22. Find the area enclosed by the curve r²-4coss. c. 16 B. 8 D. 2

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Q: The gradient of the function 2x1 + x2 - 3 evaluated in x = (0 0 0) is: OA. Vf=(1 2 3)T OB. Vf=(0 0…

A: Solution:

Q: (d) Let F be a subfield of a field E. Define what it means by an evaluation homomorphism. (e) Let F…

A: (d.) Given: F is a subfield of a field E. To define: An evaluation homomorphism.   (e.) Given: F=ℤ7…

Q: Find the standard matrices A and A' for T = T₂ ° T₁ and T' = T₁ ° T₂. T₁: R² - R², T₁(x, y) = (x -…

A: Given T1:ℝ2→ℝ2 by T1(x, y)=(x-2y, 2x+3y), T2:ℝ2→ℝ2, T2(x, y)=(0, x)   To Find: The standard matrices…

Q: Solve the following boundary value problem: 1 0 u Hu 1ди + ar2 r ar + r20Ф2 =0, 0<r < 3, -n < ф<n,…

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Q: Q2: Expand f(x) in a sine-cosine Fourier series TT 20, f(x) = { -<x< '4' π ¹4, 1<x<T. 4

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Q: For sketching the function y = 3-e² 2e² determine the following

A: Note: As you asked only for subparts 4, 5, 6, and 7 so, I answered here only that.

Q: 0. The curve has an equation of x² + y² = 25. Find the length of arc from x=3 to x = 4. A. 1.88 C.…

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Q: Solve the given initial value problem. y'' +64y=0; y(0)=2, y'(0) = 1 y(t) =

A: Given IVP is  y"+64y=0 .....(1) y(0)=2,y'(0)=1 ......(2)

Q: ind the solution of y'+; =y given y(1) = 1.

A: We have to solve given problems:

Q: By using Gauss-Jordan method, the solution of set following above equations will be 2x1 – 4x2 + 6x3…

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Q: 5. The area bounded by the graphs of y= 2x + 3 and y = x² revolves about the x-axis. Determine the…

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Q: You deposit $1,000 in an account at the Lifelong Trust Savings and Loan that pays 8% interest…

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Q: Solve the given initial value problem. w"-6w' +6w=0; w(0) = 0, w'(0) = 1 w(t) =

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Q: Please use the formula Speed = distance ÷ time as instructed

A: use the formula Speed = distance ÷ time as instructed .

Q: Mrs Devi gave some money to her three children, Muthu, r Gul. Krishna's share was 3 of Muthu's…

A: # As per the guidelines we are entitled to solve one question at a time, please resubmit the other…

Q: sits $13,000 at the beginning of each year for 16 years in an account paying 8% compounded annually.…

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Q: solve 4 only

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Q: For 16 years, Janet saved $250 at the beginning of every month in a fund th 5.75% compounded…

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Q: 1. Use Euler's method to obtain a numer- ical solution of the differential equation dy =3 = 3-2,…

A: The Euler's method is one of the basic methods in solving a first order ordinary differential…

Q: Let X be a Banach space and T = B(X) an operator with ||T|| € (T). Show that || id +T|| = = 1 +…

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Q: dz/dx&dz/dx at the point (1,1,1) Find the value of if the equationxy + z³x - 2yz = 0.

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Q: A) Write the formal (integral) solution to the following SDE dVt =dWt dXt =Vtdt B) Calculate the…

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Q: Find an explicit solution of the given initial-value problem. dy 12-11-14 y(3) = 3 dx y = =

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Q: 8. Express the given function using unit step functions and compute its Laplace transform y=sint A 1…

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Q: A function is of the form y = sin(kx), where x is in units of radians. If the value of k is 3.70,…

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Q: The four-digit number has a digit sum of 20. The sum of its last two digits is equal to its second…

A: Since you have posted a multiple question according to guildlines I will solve first question for…

Q: The gradient of the function 2x1 + x2 - 3 evaluated in x = (0 0 0)¹ is: OA. Vf= (1 2 3)T OB. Vf=(0 0…

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Q: Example: Solve: 10 -1 2 0 -1 11 -1 3 2 -1 10 -1 03 -1 8 X1 x2 X3 X4 6 25 - 11 15

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Q: - Using Lagrange interpolation formula, find the value of sin points 6 X: 0 π/4 π/2 sinx: 0 0.707107…

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Q: OL XL 2, 4 Utt = Uxx u (o₁ t) = u(2₁ t) = 0 u(x₁0) = I sIMITX COSTTX ut (x,0) = 0 Solve the heat…

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Q: 2. Use the graphical method to find ₁ and 2 so as to minimize z = f(x₁, x₂) = a₁ +422 subject to ₁…

A: We have to find the solutions x1 and x2 using the graphical method.

Q: How Solve the eqution to find the complex roots Z½ -1 + = find the qubic roots of (-27i) {Z=√√5=-=i}…

A: Since you have asked multiple question we will solve first question for you. If you want any…

Q: If M = {x: Lx = 0}, where L is a continuous linear functional on H, prove that M¹ is a vector space…

A: Given the M={x,Lx=0}  where L is a contineous linear function on Hilbest space H. We have to Prove…

Q: əz Find ( (). If (x, y, z)variables, and (2) a function in (x, y), and achieve the equation: 1 x-2 +…

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Q: Find the singular values of the matrix. 02 Select one: O A. -8,2 O B. 64, 4 O C. 8,2 O D. -64, 4

A: Let A be m×n matrix. Singular values of A are the square roots of the positive eigenvalues of ATA or…

Q: Find the area bounded by the given curves, or as described. I.) Sketch the graph II.) Find the…

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Q: Evaluate: √ye dx By using Gamma function. is

A: I have given the answer in the next step. Hope you understand that

Q: Use one of the two comparison tests to determine whether the series converges or diverges. n²-1 7n5…

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Q: Solve the given differential equation by finding, as in Example 4 of Section 2.4, an appropriate…

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Q: To index Qn [6, 20] using N as the index set.

A: We need to find ℚ∩6, 20 and we have the index set is ℕ Now, ℚ∩6, 20=6, 20

Q: 3. 2 A cylindrical water heater in your garage is 4 feet tall and 30 inches in diame To save money…

A: INTRODUCTION: The formula of the surface area of a cylinder with radius r and height h is given by,…

Q: The divergence of a vector D for rectangular coordinate is equal to [1/p / dp (pDp)] + [1/p Dø/dø]+…

A: We have to find divergence in rectangular coordinate

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A: TRUE

Q: Assume that is a continuous real function on (a, b) such that φ √(x+³) <; p(x) + 3 p(y) for all x…

A: If the line segment connecting any two points on the graph of a real-valued function does not lie…

Q: Q3. Let G be a connected graph. What is the relationship between bond of G and minimum edge cut of…

A: A bond with one edge

Q: If A = [0, 2π] and A is measurable, prove that lim cos nx dx = lim sin nx dx = 0. n∞ JA

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Q: 5. Find the total length of the curve r-4 (1-sin e) from 0-90° to 0-270° and also the total…

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