Use Lagrange multipliers to find three positive numbers whose sum is 30 and the sum of whose squares is as small as possible. (Enter your answers as a comma-separated list.)

Q: a) If y = 3x – 2, x = 3t + 2, and t = 3k – 2, find b) Express y as a function of k ify = 2x + 5, x…

A: Introduction: A function is an expression, rule, or law in mathematics that defines a relationship…

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Q: whathis the chifHfeme betueen Cautinity gnal Vaitamıy Continity?

A: Use definitions to write the difference.

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Q: 2. (x- 3y + 3)dx + (3x + y + 9)dy = 0

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Q: 5- write the following expression in terms of logs of x,y and z. Y= log 4vx³ y/z*

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Q: Theorem 10 Let (a, b] c R and f: [a, b] → R be a function of bounded variation on [a, b]. Then f is…

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Q: f(x, y) = 7x2 + 7y2; xy = 1 Step 1 We need to optimize f(x,y) = 7x2 + 7y2 subject to the constraint…

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Q: Solve the differential equation with the appropriate method. Finalize answer equated to y.…

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Q: Q2. (a) If b – 4ac = 0 and y1 = emz solves ay" + by' + cy = 0, use reduction of order to get a…

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Q: Q1. Solve the following first order equations: (a) (r²y² + 1)dx + 2x²dy = 0, use the substitution ry…

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Q: Find all integer x satisfying the condition x = gcd(5x + 2 3r) lustify vOur ancu

A: The complete solution is in given below

Q: Using Reunge-kutta method of fourh oxden Solve dy (0)%3D1at 2. with | 2. 2=0.2,0.4.

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Q: Let S(n) be a statement parameterized by a positive integer n. Consider a proof that uses strong…

A: Given, S(n) be a statement parameterized by a positive integer n. We have to consider a proof that…

Q: Using Reunge-kutta method of fourh oxden Solve dy (0)%3D1at 2. with | 2. 2=0.2,0.4.

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Q: 11. Find the second partial derivatives of the following function and show that the mixed…

A: 11

Q: UAing Runge - kutta mothod of fourth oxden Selve dy - - ithy (0)=1 at 2. Fx² 2. 2= 0.2,0.4.

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Q: QUESTION 9 Find the measure of the missing side of the right triangle below using the Pythagorean…

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Q: A. Compute the bound B of the error when approximating f(x)=sin(x) with a polynomial of degree 1 in…

A: The given function is fx=sin x. Find the error bound for f approximating with a polynomial of degree…

Q: Let A and B be nonempty sets. Prove the following statements. (a) For any function f : A → A, if f o…

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Q: 2. The function Y1 x? is one solution of the differential equation x²y" – 2xy' + 2y = 0. Use…

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Q: Q2) Find the least -5quaras line y=fca) = Ax +B for the following data 2 2. -1 2. 3.

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Q: Given that ニえらin(inz) Solve 211 xg"-zy'+ay =o de termine the gpeneral golution? yend

A: Given that, the differential equation is x2y''-xy'+2y=0 and one solution is y1x=xsinlnx. Rewrite the…

Q: 10. Curtis bought a condominium for $319 000 and made a down pa for a five-year fixed rate mortgage…

A: Introduction: The formula of the monthly payment is given by, Monthly Payment=A×RN1+RNNT-1 where A…

Q: Find the Lebesgue integral fio.11 f, where f(x) = x. Note: although this can be done by various…

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Q: Using Runge-kutta mdhod of fouth oxden Solve dy with ylo)%=1at 2 +x2 2=0.2,0.4 .

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Q: Determine an equation of the form Ax t By t (z t D=0 for the plane that coutains the line (x, Y,z) =…

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Q: f (x, y) = 3x? + y + 4xy + 8 %3D af(z,y) when x = 2 and y = 1? dy What is the value of

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Q: H.W:- Used Cramer's Rule to find the value of the variables in the following equations: 5x + 4y = 11…

A: Creamers rule is used

Q: Consider the following function. (x) - Complete the following table. (Round your answers to two…

A: Introduction: Suppose, x=a is a point where the function fx is undefined. The independent variable x…

Q: occur in 10! 2. Show that 12!+1 is divisible by 13, by grouping together pairs of inverses modulo 13…

A: To show that 12!+1 is divisible by 13, by grouping together pairs of inverse modulo 13 that occur in…

Q: 3) Donnie has a pool and recently discovered a leak. He continues to patch the leak until someone…

A: Let us take the capacity of the pool as x liters.

Q: Calculate the real values of x and y such that (x + jy)³ is real and |x + jy| is 8. 3

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Q: Find the general solution of the given second-order differential equation. y" – 6y' + 10y = 0 %3D…

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Q: Determine the monthly payment for the installment loan. Annual Amount Financed (P) Rate (r) Number…

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Q: r3 Consider the function f(x) whose graph is a parabola with a hole in it. Give the equation of this…

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Q: 3. Graph the following piecewise functions. -x - 3, if x <1 x², if x21 (2) = {*7,if x 2 1 f(x :

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Q: 1. a) Define a fractal. b) Use the definition and defining nature of a fractal to create your own…

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Q: Match the formula of the exponential function to its graph. Graphs of Exponential Functions Formulas…

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Q: 5s + 31 Let W be the set of all vectors of the form 2s+t Find vectors i and i in R such that W =…

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Q: A can of soda is a cylinder that is about 4.75 inches tall with a radius of 0.875 inches. What is…

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Q: 1. Norah's bank offers personal loans for one to five years at 7.5% per year, compounded monthly.…

A: The formula we need to use here is n = lnDiDi-Pln1+i

Q: 1-Cosx The value of limx→0 by using series is 1+x-e*

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Q: Let x E Z. List all possible remainders of 10x² when divided by 3. Justify your answer. (b) […

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Q: For each of the exercises in this chapter, give a parametric description of the curve, and then…

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Q: Let A = {1, 2, 3, 4}. Let F be the set of all functions from A to A. Define a relation R on F as…

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Q: Use Lagrange multipliers to prove that the rectangle with maximum area that has a given perimeter p…

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