Let C be the positively oriented circle x² + y² = 1. Use Green's Theorem to evaluate the line integral 3y dx + 10x dy.

Q: a) Let u(x, t) = X(x)T(t) and show that and X" + XX=0, X (0) = 0, X' (L) + yX (L) = 0, T' + Aa²T =…

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Q: 1. Consider the curve C = C₁ UC₂, where C₁ is the line segment from (0, 1, 1) to (1, 1.0) and C₂ is…

A: As you have asked more than one different question, we shall solve first question only.

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Q: Fill in the blank. The symbols C₁, C₂, and k represent constants. - (C₂ sin kx + C₂ cos kx) = −k²…

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Q: 1. Let A = a. V 4-0 -8 and b = 1 3 -5 -3 -7 V V Solve Ax = b by hand and write your solution in…

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Q: Answer true or false. F(s) = s²/(s² + 4) is not the Laplace transform of a function that is…

A: We have, F(s) =s2s2+4 =s2+4-4s2+4 =1-4s2+4

Q: Find the volume of the region cut from the solid cylinder x² + y² ≤ 49 by the sphere x² + y² +2²=64.…

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Q: 25. Consider the problem a²uzz ut, 00 u(0,t) =0, uz(L,t)+yu(L,t) =0, t>0 u(x,0) =f(x), 0≤x≤L. (a)…

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Q: 2.17. A load cell is calibrated in an environment at a temperature of 21°C and has the following…

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Q: Show ▼(E) - G&F - FVG G² G=0

A: Given : G≠0 To Show  : ∇FG =G∇F-F∇GG2

Q: dy Write down a differential equation of the form dt 11 12 solutions all approach y = y' = as t→∞. =…

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Q: Find the eigenvalues of the matrix and determine whether there is a sufficient number to guarantee…

A: Sol:- Let A be a square matrix,  η a vector and λ a scalar that satisfy Aη=λη, then λ is called the…

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A: given function ∫1221+x2dx using trapezoidal rule with n=4 let fx=21+x2 h=b-an substitute the values…

Q: DETAILS ZILLDIFFEQMODAP11 1.2.013. MY NOTES ASK YOUR TEAC his problem, y c₁ex + c₂ex is a…

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Q: 43. If f is differentiable and is periodic with period T, show that f' is also periodic with period…

A: First we prove that f'(x) is periodic by definition of derivative. Then we give an example to prove…

Q: Determine the determinant and inverse of the matrix. A = 3 8 8 -7 -1 –4 -1 -4 5

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Q: 2. Another equation that has been used to model population growth is the Gompertz equation dy/dt =…

A: Given Data: dy/dt =ry lnKy where r and k are positive constant (a) Find the critical points (b) To…

Q: Q2: Find The Fourier cosine and transform of the following functions: SSint, ostse (1) f(t) = 10₂…

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

Q: Use the function to find the image of v and the preimage of w. T(V₁ V₂ V3) = (4V₂ - V₁₁ 4v₁ + 5V₂),…

A: Let us consider a transformation T:R3→R2 defined as T(v)=w Here T(v) is the image of v v is the…

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Q: Which of the following correctly states how the velocity of liquid changes with temperature? A)…

A: Viscosity decrease with increase in temperature.  As temperature rises the force of attraction…

Q: Find the largest interval where the following IVP is guaranteed to have a unique solution: (t²-4) y"…

A: To Find: The largest interval where the following IVP is guaranteed to have a unique solution:…

Q: 4. Let S be the triangular region in R3 with vertices at (2,0,0), (0,6,0), and (0, 0, 3) with upward…

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Q: The equation 0.5(e* + e*)-5=0 has at least one solution in the interval [1.5,2.5]. True False

A: Let   ex = y The equation will become 0.5(y + 1/y) - 5 = 0 0.5(y2 + 1) - 5 y = 0 y2 + 1 - 10y =  y2…

Q: b B 36° b≈ a Note: Triangle may not be drawn to scale. Given the triangle above, find the following:…

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Q: Compare the monthly payment and total payment for the following pair of $180,000 loan options.…

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Q: Consider the initial value problem (x + 2) y" + with initial condition x 1 5Y' + e²y=x³ y (0) = 7 y'…

A: Given the Initial Value Problem x+2y"+1x-5y'+exy=x3 with given initial conditions. y0=7,y'0=2

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Q: 0)2= (?????) 16 (??? ???)2=(?????) 16 (?? ??) 10 (?????)₂ = (???

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Q: Find the magnitude of the vector and the angls 0, 0 degrees less than or equal to 0 < 360 that the…

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Q: Suppose P, Q and R are statements. Complete the truth table for the statement (P⇒Q) or (P and (not…

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Q: Choose the answer of the correct answer. Let f: D-R and c be a cluster point of D. If f=p(x)/q(x),…

A: Given f:D→ℝ f(x) =p(x)q(x) , D =ℝ\x|q(x) =0 and deg p &gt; deg q

Q: x²y" - xy + xy = 0, y(1) = 0, y (L) = 0, L > 1

A: As per the question we are given a second order linear differential equation as : x2y'' - xy' + λy…

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Q: (b) A x (BNC) = (A x B) n(A XC).

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Q: The figure to the right shows the letter L in a rectangular coordinate system. The figure can be…

A: We need to addition operation of matrix to move L .

Q: Analyze and sketch a graph of the function. Find any intercepts, relative extrema, points of…

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Q: 5. Determine whether or not matrix A shown below is orthogonal and justify your answer. 1 0 A = 0 1…

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Q: The profit function of a certain firm is f(x) = −2x² + 396x - 400, where x denotes units of product…

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Q: Let F be a vector-valued function such that 1 1+ t²⁹ F' (t) = = tet. 3t² and F(0) = (-1, 0, -2) 1.…

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Q: Consider the following. Find the intervals of convergence of f(x), f'(x), f'(x), and f(x) dx. (Enter…

A: The given power series is f(x)=∑n=1∞(-1)n+1(x-7)nn. To Find: Interval of convergence of f(x), f'(x),…

Q: 50 At Q₁/ Find Aso, ett for A = 0 O -20 16 G

A: Given, A=010001-2016-1 So, A2=010001-2016-1010001-2016-1=001-2016-120-3617…