a. = (x² − 1)(x² − 3) dx dt dx b. da = (x − 1)(x − 2)³ dt

Q: x²y" + 2xy' - 2y Y₁ (x) = X

A: Given differential equation We have to find the complete  solution.Let the complete solution be

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Q: Solve 3y"+y"-8y' + 4y = 7+35x. (No calculator: try 1 as a root)

A: The given differential equation is .We have to find the solution to the differential equation.

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A: The square root function  is always continuous , when

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A: Given that  and , where  are distinct prime numbers and  for all .We need to prove that:, where  for…

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A: We get eigen functions only when there is non trivial solution. So, we find non trivial solution…

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Q: (ye²xy + x) dx + (kxe²xy) dy = 0

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A: The given LP isThe aim is to solve the maximization problem.

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A: The  given equation  is                                      Then, auxiliary equation  is…

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Q: Calculate the third term of the power series of ln (1 + x) if x = 0.5.

A: Calculate the third term of the power series of  if .

Q: (b) Find an integer solution (x, y, z) to the equation 18x-27y +39z = 6. (c) Find all the integer…

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Q: i. L-1 k. L-1 [2s3 + s² +3] S4-1 3s +1 2 S3-s²+s-1

A: We have to find the Note: According to the guidelines we are allowed to solve one question at a…

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Q: Find B and t for the space curve r(t) = (8 sin t) i + (8 cos t) J T T = 4 4 (cost) + (-sin 1) 1+ (3)…

A: A binomial vector refers to a mathematical object that consists of two components or elements. It is…

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A: Given thatThe radioactivity of certain element decreases 10 percent every year.We have to determine…

Q: Let X = Z₂. Define a subset of X to be a block if it has 4 elements that add up to O in Z. Find the…

A: Given:  . To Define: A subset of to be a block if it has elements that add up to  in . Find the…

Q: can you do this question one more time just to double check. I got a different answer

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Q: 2. n, meZ+, A₁ = {p: asal; p/n}. Aşağı layınız: n i) gcd(n, m) = 1 ⇒ AmA = 0 ii) d = n.m⇒ Ad = AmUAn…

A: 2) Let define  i)   .         divides m  and divides n.     divides

Q: Find the standard matrix of the given linear transformation from R2 to R2 Projection onto the line y…

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Q: Determine whether the alternating series Σ (−1⁰+1 converges or diverges n=2 1 3(In n) Choose the…

A: The given series is .We have to check the convergence of the series.

Q: Determine whether the linear transformation T is one-to-one and whether it maps R³ onto R…

A: 1. Determine whether the linear transformation  is one-to-one and whether it maps  onto .A.  is not…

Q: Could you also do part (a) (b), so I can see how the entire thing flows. Greatly Appreciated!!

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Q: Suppose f(): R" → R is a function. Consider the optimization problem min f(x) over XER". P) 3)…

A: Given: A function . Consider the optimization problem  min  over Aim: If , What is the second-order…

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A: We have to find the n(L)  means the number of elements in L

Q: Prove that the following sets are equivalent (a) Intervals (0, 1) and (1,6) What is the cardinality…

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Q: 1 { 2(n-2,5)(n-3.5) } monotonic, bounded below, bounded above and/or bounded. 1. Determine if { n=1…

A: Let's analyze the sequence   Monotonicity (Increasing or Decreasing): We can examine the behavior of…

Q: E 4 5 into 5 1 аг

A: Given system of equations is 6x1-x2=89x1+7x2=3 and 4x1-x2=1Then the system can be written as…

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Q: solve the congruence 2²-7x+6=0(mod3³.7³)

A: Given congruence: Objective: Solve the congruence equation and find the solutions for  modulo .

Q: Question 5. Apply the definition and prove that the set A = { } } } } denumerable. } is

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Q: 4 12 ↑y 4. 2- [0] -2

A: Given graphWe have to find the inverse of it.

Q: Question 5 ▼ hemisphere z= decimal places. Mass = π Find the mass of the solid bounded below by the…

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Q: Find the eigenvalues ?nand eigenfunctions yn(x) for the given boundary-value problem. (Give your…

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Q: Find the eigenvalues and eigenfunctions y(x) for the given boundary-value problem. (Give your…

A: The given problem is to find eigenvalues and eigen functions for the given boundary value problem…

Q: 3. Let p be an odd prime. Define sets A and B by A = {a € Z: 1 ≤ a ≤ (p-1)/2} and B = {b Z: (p+1)/2…

A: Given that  be an odd prime. Now the defined sets are: and .Now we need to identify the cardinality…

Q: Problem #6: Let Problem #6: f(1) = S8 3 -8 0 <1 < * < 1< 2π and assume that when f(t) is extended to…

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Q: Explain why the function is differentiable at the given point. f(x, y) = 7+ x In(xy-7), (4,2) The…

A: .To Do:Explain why the given function is differentiable.Also, find the linearization.

Q: 17. Find the curvature of an elliptical helix that is described by r(t) = a cos ti + b sin tj + ctk,…

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Q: 8. If 4x³ + 18x² + 8x - 4 is divided by 2x + 3, find the remainder using the remainder theorem. a. 7…

A: and We have to find the remainder.Note: According to the Bartleby guideline we are suppose to answer…

Q: Find the general solution using eigenvectors: x₁ = −2x₁ +4x₂ x₂ = 6x₁ - 4x₂

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Q: 1 P and Q are points on the sphere x² + y² + x² = 4. P₁ and Q₁ are the foots of two perpendiculars…

A: To find the maximum of the expression 2|PQ|² - |P₁Q₁|² - |P₂Q₂|², we need to analyze the geometric…

Q: Find the 5th term in the expansion of (x³ - 2²). x2 a. 290x6y6 b. 470x6y6 c. 560xy8 340x³y d.

A: To find the fifth term in the expansion of , we can use the binomial theorem. The general term in…

Q: Solve the following a. y' - 5y = e5x; b. y’ + y = xe-* ; c. y' + 4y = 2 cost; y(0) = 4 differential…

A: a. We have to solve the given differential equation.

Q: 2. y" +9y = 2x+1, y(0) = 0, y'(0) = 1

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Q: Problem 4: Solve the initial value problem y" + y = g(t) and with y(0) = 0 and y'(0) = 0. where g(t)…

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