1. Consider the curve F(x, y) = 0. Show that if F has continuous second derivatives, then a formula for the second derivative of y is FF22FFF + FF2 d²y dx² F3 Y

Q: If a is a non-real complex nth root of unity, find the values of:

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Q: Q1: Solve ýex+y 2 = cosh x + √√cosh² x − 1 + 7e*

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Q: 4 Find the eigenvalues of A, given that A = -6 0 ,02= -2 and 3 = and its eigenvectors are v1 = The…

A: Given matrix  A is ,                                                         A =     4    0    0-6…

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Q: aplace transform for L'" (ett (e4r + cosh 2t)dt

A: Laplace transform of the function

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Q: Given z = cos (2) + i sin (2241), where n is a po

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Q: Find a basis for the column space of Basis = 4 2 4 0 0 -2 -3 -4 4 -2

A: The solution is given as

Q: In Exercises 9 to 12, determine whether the two graphs are equivalent. 10. B с A E D с E D B

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Q: A is an n x n matrix. Check the true statements below: A. A matrix A is not invertible if and only…

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

Q: ermine the constant a so that the vector V = (x+3y)i + (y-2z)j + (x+az)k is solenoidal

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Q: Let K be extension of the field of rational numbers Q show that any automorphism of K must leave…

A: Given a (usually finite normal) extension K ⊇ F, we have considered group G(K/F). On the otherhand,…

Q: (31) Use Newton's Method to make the second approximation x2 to the solution of 2e* = ex. Take ₁ =…

A: Solution :-

Q: After gym class you are tasked with putting the 28 identical dodgeballs away into 6 bins. a. How…

A: To find the given questions when there is restriction and there is no restriction :-

Q: 6. Suppose A = (3, -2, 4), B = (-5, 7, 2) and C = (4, 6, -1), find A × B.A+B-C.

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Q: The personnel department of a particular company has observed that 20% of the people the company…

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Q: 3. A probability mass function for a particular random variable y having nonnegative integer values…

A: We obtained the pmf and moment generating function. The detailed solution is attached below.

Q: Which are true?

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Q: 4) Find the largest eigen value for the matrix 1 ^-['s 2] wi A= with x (0)=(7/17_1) 54

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Q: Q5: find the Fourier series of the following equation -x -1 < x < 0 f(x) = x 0 < x < 1 1<x<3 1

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Q: Find what value of c does f&dx = 1? с Answer:

A: Solution

Q: (32) Find the derivative: d cos(x) a (16) √ 1 - 13dt). t²dt dx

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Q: Describe the surface with cylindrical equation r=6. Hint The 8 and 2 components of points on the…

A: We have to find the surface whose cylindrical equation is given by: r = 6.

Q: Supppose A is an invertible x n matrix and is an eigenvector of A with associated eigenvalue-2.…

A: Here we use the properties of eigenvalues of matrix to answer the appropriate question as below.

Q: Find the value of dz and dz/ dy at the point A when x changes by (0.01) and y changes by (-0.01) xe…

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Q: Which of the following is the normal form of the equation 5x + 12y + 39 = O? 12 5 12 5 13 √x + ₂ y y…

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Q: Q2: Find Partial derivative of the function with the respect with each variable f(x, y) = (x² - 1)(y…

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Q: Suppose f: A→ B and g: B→ C are functions, show that a) If both f and g are one-to-one, then go f is…

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Q: Consider the four statements (a) 3r ER Vy ER (b) Vr ER By R (c) VER Vy ER (d) 3r ER Vy ER 1. Are the…

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Q: How many 8-bit strings of weight 5 start with 101 or end with 10 or both?

A: If the 8-bits strings has a weight of 5 , then From the 8 places to have digits , there are 5 places…

Q: Let W be the set of all vectors of the form with r, s and treal. Find a matrix A such that W =…

A: Solution:-

Q: Let f(x, y, z) = g (x² + y² + z²) where 2 9 is some nonnegative function of one variable such that…

A: If S is a surface given by parametric form r→ u,v =x u,vi^+y u,vj^+zu,vk^…

Q: Prove that the sum of the three variables of the sum exponent f(x) = Σe is strictly convex. For this…

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Q: so that the vector V = (x+3y)i + (y-2z)j + (x+az)k is solenoidal.

A: Solution :-

Q: e-3t sin (4t) y (0) ==

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Q: The amount, in milligrams, of a medicinal drug in the body t hours after it was injected is given by…

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Q: y" + y = sec x tan x

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Q: Use Laplace transform to solve the partial differential equation: d²u du ди(x,0) , t> 0, 0<x<1,…

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Q: If A, B, C are sets, show that a) A x B= 0 ⇒ A=0 or B = 0. b) (AUB) x C = (AXC) U (BxX C). c) (An B)…

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Q: Q2: State and prove the first isomorphism theorem.

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Q: What is the value of k such that the lines 3x + 6ky-7 and 9kx + 8y=15 will have the same positive…

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Q: Q4:- if you know that data ( 12, 10,12,10, 10,6) find the :- Mode, median, mean, variance and…

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Q: Sheep's Wool Length: For sheep maintained at high environmental temperatures, respiratory rate,…

A: Introduction: A linear feature is described as a feature with one or variables and no exponents in…

Q: problem: Using the Laplace transform, solve the following initial value y" + 4y + 3y = e, y(0) = 1,…

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Q: Hi the equation for the cone is z^2= x^2 + y^2, and not z=x^2 + y^2, could you please do this…

A: Here we will use Cylindrical co ordinate system  x= r cosθ , y = r sinθ , z=zx2+y2=r cosθ2 + r…

Q: Use separation of variables method to solve: ди ổn ôn + =u where u(0, y) = 0 and ду Əx² du(x,0) ду =…

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Q: Giving the joint pdf of a bivariate R.V. (X, Y) as shown below. (A) Determine the constant k. (B)…

A: Solution : Probability  P=∬P(x,y)dx dy A)  Total probability =1 ∫01∫y1kdx dy=1⇒∫01k(1-y)dy=1⇒k=2 B)…