Use spherical coordinates to find the volume of the solid. 2 Solid inside x² + y² y² + z² = 9, outside z = √√x² + y², and above the xy-plane

Q: The indicated function y₁(x) is a solution of the given differential equation. Use reduction of…

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Q: Show that (ℤ,∗)?ℎ??? r ∗s = (r +s)−(r ∙ s)??? ??? r,s ∈ ℤ is group using variable r, s and t.

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Q: Problem 1 Find the Laplace transform by definition of the following function: 1 0 4.

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Q: Match the functions below with their level surfaces at height 3 in the table at the right. B с A E B…

A: We need to identify the sketches of level curves at the height of 3 of the given functions: 1.…

Q: Evaluate using Wallis' Formula. Show your complete solution. No any other method will be accepted.…

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Q: Question 27 Use algebraic techniques to determine whether the following function is even, odd, or…

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Q: Solve the given differential equation by undetermined coefficients. y" - 2y' 3y = 8ex - 3 y(x) =

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Q: Evaluate the following real integrals by residue theorem 3 03 S <-1 X Sin mx X4 +1 OSH dx πT -m/√z…

A: As per the question we are given an improper integral from -∞ to +∞ and we have to evaluate it by…

Q: Find the area of the triangle with vertices (0,0), (2, 0) and (2,2) by computing a double integral…

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Q: Question 2. Find all functions A and B such that the following equations are Exact. Do Not solve the…

A: A equation is exact if it satisfies differential, df=0 Explanation follows

Q: State what method should be used in solving the followings (either the substitution rule or the…

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Q: 2. For each graph, identify a) the coordinates of the vertex b) the equation of the axis of symmetry…

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Q: Suppose that the domain of the propositional functions p(x) and g(x) consist of the integers 1, 2,…

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Q: calculation for P.I ур cos²x b²+1 2 cos²x D² + 1 + {² 22{ -} 1+ cos2x D² + 1 HOW DID HE GET THE…

A: The particular integral is solved as  yp=1D2+1(cos2x)

Q: differential equation by variation of parameters. 1 4 + ex y" + 3y + 2y = the question, you will not…

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Q: Estimate the following definite integrals using the Trapezoidal rule and Simpson's rule. Estimate…

A: Given : ∫121s2ds           n =4 To find : Trapezoidal rule                Simpson's rule

Q: Find the general solution of the given higher-order differential equation. y"" - 6y" - 7y' = 0 y(x)

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Q: we have found the following Wronskians. W = -3x; We want to find functions u₁(x) and u₂(x) such that…

A: W=-e-3x; W1=-e-2x2+ex-1; W2=-e-x2+ex-1; u1'=W1W; u2'=W2W;

Q: the initial-value problem. y = y = C₁ + C₂ cos(x) + C3 sin(x), (-00, 0); y""+y' = 0, y(n) = 0, y(t)…

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Q: Q.5 Solve the wave equation: U₁=Uxx-ex-6x, U(0,1)=8, Ux(1,1)=3, U(x,0)=4sin ³x+ex+x³-ex+7 **********

A: Using separation of variables

Q: A manufacturing plant makes two types of inflatable boats—a two-person boat and a four-person boat.…

A: A manufacturing plant makes two types of inflatable boats—a two-person boat and a four-person boat.…

Q: • I= 8 ∞ dx (x²+1)(x² +9)

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Q: Given: Q = f(L.K) = KL2-L³, where Q is output and L and K are the labor and capital inputs,…

A: Consider the given equation, Q=KL2-L3 Since, we have given that K=15, so we get, Q=15L2-L3 The…

Q: form a piecewise function by using exponential, quadratic and linear unction. Domain for the…

A: We need to find a piecewise continuous function using exponential, quadratic, and linear functions…

Q: calculation for P.I ур cos² D²+1 cos²x 2 { 2005x } D² + 1 y = 1+ cos2x D² + 1 HOW DID HE GET THE…

A: We are just multiplying and dividing by 2 on the right hand side.

Q: In the following exercises, find the Jacobian J of the transformation.

A: Introduction: A partial derivative matrix is a jacobian matrix. Jacobian is the determinant of the…

Q: Local minima are none Saddle points are none

A: Given the function: fx,y=x4+y4+81xy To find the local minima and saddle points of the given…

Q: The given family of functions is the general solution of the differential equation on the indicated…

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Q: • Y _₂y = 4y + 8y = 2³x + 8x² - 3x -23 2X <-2X Ans: y = ₁2x + c₂xe + Cze 4 1 25 -3X 2 2³ + x² + x +…

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Q: True or False. Justify if answer is False. Give a counter example or a proof or well-written…

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Q: Find the area between y = 2 and y = (x − 1)² integration and answer to 2 decimal places. 10 9 8 6…

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Q: 5. Vn EN, Prove the following by mathematical induction. Σ(2n − 1)² = n(2n − 1)(2n+1) - 3 i=1

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Q: → (D²-1) y = 2 sinhx + sinx X

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Q: 2. During the class, we derived in detail the first order Richardson extrapolated derivative, by…

A: Given Data: Dh1 ≡f'(x0)-h4/480 f(5)(x0) + O(h6) let during class, we derive in detail the first…

Q: The indicated function y(x) is a solution of the given differential equation. Use reduction of order…

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Q: Given differential equation yay" -4y' + 8y = e (D³-30²-4D +8)y=e +8x Auxilary equation m³ - 2m² 4m +…

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Q: Question 5. Solve (e² - 1/1²) de and find the solution passing through (0,0). dx + (exy) dy = 0

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Q: Sketch the following g(x) and then find the total area between the curve g(x) and axis. Explain if…

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Q: 2 Solve the following ODES by Inverse Operator method 2 (B²+1) y = cos x Ans & Y = C₁ C3 x + C₂ sinx…

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Q: Solve the given differential equation by undetermined coefficients. y" - 2y' - 3y = 4e* - 9 y(x) =

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Q: Write an equation for a rational function with: Vertical asymptotes at x = -6 and x = -5…

A: Use the given information.

Q: Use multiple equation Newton-Raphson method to determine one of the roots of the following…

A: Given x2+3y2=10 (x-2)2+(y-1)2=31 Let f=x2+3y2-10 g=(x-2)2+(y-1)2-31

Q: The given differential equation is already in standard form, as the coefficient of the highest order…

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Q: Define the binary operator* by: a+b = a +8b and V by: aVb=6 Find the following. When simplifying,…

A: Given operators: a * b = a + 8b   .......(1)  a ∇ b = 6    .......(2)

Q: 5 [In this question i and jare horizontal unit vectors due east and due north respectively] A…

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Q: An artist has decided to finish their piece of artwork by balancing it on a fulcrum and putting it…

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Q: Examples. Find the general solution of the differential equ -X 2 y² + 2√² +2y = 2 e² faix

A: Using the method of variation of parameters

Q: Solve the following ODES by Undetermined Coef y - 16 y = 19.2 e + 60%, y() = 0 e ₂ y(0) = Y(u) = HO…

A: We are given non homogeneous linear differential equation with constant coefficient to solve this…

Q: Pls help ASAP

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Q: (a) Suppose that Ax = b is a consistent linear system, and that p is a solution of it. Prove that…

A: We have to show that solution of given system can be written as x=p+z.