If z be a differentiable function of x and y and if x = c c cosh u cos v, y = csinh u sin v, then 1 prove that du? = 5c°(cosh 2u – cosh: - cosh 2v) + %3D

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A: "Since you have posted a question with multisubparts, we will solve the first three subparts for…

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Q: Solve the initial value problems: (a) ý = 6 + 5y + y°; y(0) = 0 (b) y/ + 2ry + xy = 0; y(0) = 1

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

Q: Question 1: 259 11 12 (hours) L (t) 15 40 24 68 18 (cars per hour) The rate at which cars enter a…

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Q: 3 Evaluate F. dr along the curve C if F(x, y) = (x² + y²) ²(xi+yj), and C : r(t) = e' sin ti+ e' cos…

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Q: U sing induction ,prove that : can+1)! for n>o (1) (3)(5)... (an+1) = a" n!

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Q: v An Euler's equation can be solved using ordinary power series method. v In the equation 3xy" + y'…

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Q: Find the area of the region enclosed by the inner loop of the limaçon r = 3+6 cos 0. [Hint: r < 0…

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Q: Chain rule and implicit differentiation Suppose that F(x,y,z) = 0 defines z as a function of x and y…

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Q: 2. Write the given (total) area as an integral. a. The area above the x – axis and below y = 4 – x2…

A: The double integral is given as  I=∫ab∫f(x)g(x)dydx or I=∫ab∫f(y)g(y)dxdy   Double integral is used…

Q: A and B are two cities. N x B a) Measure the bearing of B from A. Ах b) Measure the bearing of A…

A: Solution:-

Q: 6. Show that if f : X Y and g : Y → Z are both onto then fg : Z -→ Z is onto. (Note this is function…

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Q: 2.) Let Tv = Av represent the linear transformation T: R2 → R3 where - 1 21 A = -2 4 L-2 2. Find a…

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Q: Orthogonally diagonalize the matrix, giving an orthogonal matrix P and a diagonal matrix D. To save…

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A: Note: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question…

Q: Let W = Lin and U= Lin 2 (a) Show that R' = W U. Explain.

A: Note:- As per our guidelines, we can answer the first part of this problem as all the parts are…

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Q: I. Solve for x. All final answers must be in Znwhere nis the modulus.  (a) x≡3(15) + 45 mod 18 (b)…

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Q: 9. Show that the function f:x V-1 is a ring homomorphism f: Z[x] C. 10. What is the kernel of f?…

A: Given: The function, f:x↦-1, which is a ring homomorphism f:ℤx→ℂ.   To determine: The kernel of f…

Q: (b) Determine the following Laplace transforms: (i) L{cos² 3t}. (ii) L {cos t sin t}. (iii) L{e'…

A: As per our guidelines we are supposed to solve only one problem. For the solution of the first…

Q: A)Determine the value of (-9+j 6) , expressing the result in polar, exponential and rectangular…

A: A) Consider the given complex number, -9+j65 Here we need to find the value of the complex number.…

Q: Solve the initial value problems: (a) / = 6+ 5y + y?; y(0) = 0 (b) / + 2.ry + ryt = 0; y(0) = 1

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Q: u = t+1.3 -sin(u+t +5.09) with u(1) = 0.29 Let . Approximate the maximum value of ult) to 5…

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Q: [1 0 (i) Decode the cipher text "19, 45, 26, 13, 36, 41" using A->0, B>1, .z->25 and A = 2 1 0 [1 1…

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Q: Calculate ri(t) r2(t)] and ri(t) x r2(t)] first by differentiating dt the product directly and then…

A: Given that ddtr1(t)×r2(t)=r1(t)×dr2dt+dr1dt×r2(t) Where                r1(t)=cos(t)i+sin(t)j+2tk,…

Q: Find sine half range for f(x) = \cos x for -t< a <n %3D cosx for f(x) for 0<x <n. cosx

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Q: In Exercises 1- 4, apply the Jacobi method to the given system of linear equations, using the…

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Q: d Given  = and B = x², and for dx arbitrary f(x) II. Calculate for the following: (1) ÂBƒ(x) (ii)…

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Q: 2 0 2 -2 -5 1 -1 0 -3 3 3 Find a basis for R(A), C(A) and N(A) of the following matrix: A = -8 4 1.…

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

Q: If money is invested at an interest rate of 7.8 percent per year, find the annual percent yield…

A: Since you have posted a multi subparts question according to guildlines I will solve first three…

Q: (a) Show that {e¬*,xe¯} is a fundamental set of solutions of y" + 2y' + y = 0 on (0, 00).

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Q: 16-30 INTEGRATION Integrate by a suitable method: 16. 4z3 + 2z from -i to 2 + i along any path

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Q: If T4O isa bounded Linear ope rator. show that Forany XEDCT) such that llx ||<1 we have the strict…

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Q: Evaluate the line integral -ydx + xdy along the curve C : y? = 24x from (24, 24) to (0, 0). %3D…

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Q: 3. (a) Find a prime factorization 2 for n = 3333. (b) Compute p(3333) where p is Euler's phi…

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Q: Consider the following position function in the plane: ř (t) = (t3 – 3t)i + 3t?j. %3D For this…

A: Position vector of any parametric curve r(t) can be given by a vector joining origin with that point…

Q: d³y d²y +6 dx3 dx² dy -+ + 11 ax+6y = ex + cosx dx

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Q: 5. Given that X, - px, 2 = 4 where p and q are constants. a) Find the general solution of x in terms…

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