verify that each given function is a solution of the differential equation

Q: 17. 2t²y" + 3ty' — y=0, t>0; y₁(t) = t¹/², y₂(t) = t-¹

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Q: Consider the linear transformation T: R³ → R³ that rotates vectors 90 degrees around the line (x, y,…

A: “Since you have asked multiple questions, we will solve the first 3 subquestions for you. If you…

Q: 16 -Σ(Σ») f(x, y, z) = Σ · (x + y + zn?) 2

A: Given: fx,y,z = ∑n=116∑k=1nk-x+yn+zn22

Q: 1. A = set containing elements of 2 where the 2nd and 3rd balls selected are blue

A: Please see the attachment

Q: y" - 2y' + y = 4e-t + 2et, where y(0) = -1, y'(0) = 2

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Q: Which of the following represents the area of the region bounded by y = 2, x = 0, y = 0, z = 0 and y…

A: Use the given information.

Q: In the use of RSA Cryptography, for the public key (11, 65), what is the decrypted original message…

A: Solution :-

Q: Thermic effect of food above RMR (kJ.h-¹) 80 60 20 h 5-- 5 x h kJ 0 0 1 2 3 5 6 Time (h) Figure 3.…

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Q: Question 4 (a) For complex numbers z₁ = 6 + 6j and Z₂ = 4 - 4j, (i) find z = 21. Present your result…

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Q: If n, k E Z. s. t. n is the square of an odd integer, then the perfect square of n must be of the…

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Q: Set up the triple integral that will give the following: (b) the volume of the solid B that lies…

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Q: (B) Use Tabular integration f(t³-4t² to evaluate the following: - + 5t+32) sin(t)dt

A: we have to evaluate given integral by tabluar method ∫(t3-4t2+5t+32)sin(t)dt

Q: 4. A firm can produce a quantity q(x, y) ((x + 1)³+y³)¹/3, in kg, of its good when it uses rkg of…

A: Solution:-

Q: Set up the triple integral that will give the following: (a) the volume of R using cylindrical…

A: —

Q: In a manufacturing process, the diameter of steel rods is distributed normally with a mean value of…

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Q: Find the Fourier coefficients of the periodic function f(x)=x-2x², (-<x<n); f(x+2) = f(x)

A: We have to solve by Fourier series.

Q: Find the formula for the number of ways for putting n identical balls into k distinct boxes so that…

A: Answer is given using concept of permutations and combinations.

Q: Jerry has a total of I dollars per year to spend on apples (x) and Polo-shirts (y). His preferences…

A: Given, Jerry has a total of I dollars per year to spend on apples (x) and polo shirts (y).

Q: For x = x(y + 3), y = y(x - 1), find the trace of the Jacobian at the fixed point x = 0, y* = 0.

A: Given system is x˙ =xy+3y˙ =yx-1 Fixed point :  x* =0, y*=0   Take   x˙ =fx, y,    y˙ =gx, y   then…

Q: 11. In each of the following, express the required series in summation notation (a) Obtain the…

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Q: Set up the triple integral that will give the following: (a) the volume of R using cylindrical…

A: Shaded region is the solid R

Q: ACME Thingamjigs ltd. produces two types of thingamajigs, Type 1 and Type 2. The demand for…

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Q: Fit the following data using Lagrange Interpolating Polynomial X 1.5 5 -4 10 f(x) -4 25 -10 7.5

A: Lagrange's interpolation formula for 4 points can be defined as :…

Q: Solve the following non-linear equations: 2 100x₁ - 10x₂² + 5x3³ = 70 3x₁² + 10x₂-X₁X3 = 5 X₁X₂ +…

A: Thank you for the question. According to our guidelines we can answer only  first question and…

Q: 3. (a) How many positive integers divide 10!. (b) How many partitions does the set [10] = {1, 2,…

A: Given, set={1,2,3,4,5,6,7,8,9,10} we have to calculate number of partitions required in which each…

Q: 5. The dimensions of a cylindrical object are increased by a scale factor of 3. The volume of the…

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Q: Determine y(t) Lly ✓ 3. y" 13y' + 40y = 0, where y(0) = 0, y'(0) = -2 -

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Q: to evaluate the following: - f(t³-4t² + 5t+ 32)sin(t)dt (B) Use Tabular integration

A: By using tabular integration , integrate the given problem...

Q: seconds after the start of the movement. (B) Use Tabular integration to evaluate the following: -…

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Q: y y = 1 (1, 1) A X=1 y=x² с X (0,0) Region A is bounded by the parabola x = y², the line y = 1, and…

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Q: What bound of error would you pose for each of the following cases? (consider rules of significant…

A: “Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: 9 The outward flux of the vector field F(x, y, z) = (+0 the boundary of the region E = {(x, y, z) =…

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Q: 18y"" + 27y" + 13y' + 2y = 0, where y(0) = y'(0) = 0, y" (0) = 1

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Q: 2. Let S be the set [9] = {1.2..9}. 1 (D) How many derangements of S have 9 in the 2nd position and…

A: We have the set 9=1,2,...,9 We need to find the number of derangements. There are 9 places to fill…

Q: y' - 2x²y = -x =−x

A: We have to solve given problems:

Q: 6.Given y'a = -2x³ + 12x² 20x + 8.5, y(0)=1, h=0.5 find y(2) using the 2nd-degree RK - a. 3.37500 b.…

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Q: Find the Fourier series for the periodic function giving below -1, -π < t < -π/2 x(t) 0, -π/2 < t <…

A: Fourier series of the given periodic function

Q: Consider the differential equation: dy dt y² +4y³-12y² a) What are the equilibra? b) On what…

A: Follow the steps.

Q: (B) let y 3sin5x - 2cos5x = show that y + 25y = 0

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Q: Evaluate x+y JF dx dy x² + y² + a² over the portion of the first quadrant lying inside the circle x²…

A: Answer is given using polar coordinates.

Q: Q2: (B) let y = 3sin5x2cos5x show that y + 25y = 0

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Q: Hand written plz Consider the full and reduced singular value decompositions (SVD) of a square…

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Q: If the following statement is valid, prove it if it does not state the reason why it does not apply.…

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Q: Q4) Find the root of f(x)= (x^2)-5, in interval [0,4] by using bisection method.

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Q: (3) Find the formula for the number of ways for putting n identical balls into k distinct boxes so…

A: Solution:-

Q: A) Consider the vector-field F(x, y) = 2xy³i+ 3y²x²j. 1. Show that F is conservative. 2. Find a…

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Q: If={1,2,3,4,5) and = (0,0, (1), (2,3), (4,5), (1,2,3), (1,4,5), (2,3,4,5)} then If Q=set of positive…

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Q: A symmetric encryption scheme has message space M given by M = {(m₁, M₂, M3, M4) | M₁, M2, M3, M4 €…

A: Follow the steps.

Q: Evaluate the double integral that will find the volume of a solid bounded by = = 1-2y²-3r² and the…

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