1. Give one example of coherent logical argument, its premises and conclusion.

Q: 1. Newton's Law of Cooling: At 9:00PM., a thermometer reading 70°F is taken outdoors where the…

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Q: y" + 2y' + y = −e* [(− x² + 4x+3)cos x + (− x² + 4x + 3)sin x]

A: As per the question we are given a second order linear non-homogeneous differential equation. And we…

Q: Evaluate. [ 10.xªtan (2x³ + 3) dx

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Q: Solid S is bounded by the given surfaces. (1) Sketch S and label it with its boundaries. (2) Give…

A: We will sketch the region bounded and find boundary curve to use polar co ordinate for volume .

Q: 7.Find a²z of z = 2x³-5xy² xy

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Q: Numerical Differentiation: ƒ(x) = eª 1. COS X - 2 . Find f(1.5) and step size of h=0.75 and 0.1

A: As per the question we are given a function : f(x) = ex - cos(x) - 2 And we have have to find its…

Q: Q-3: Let W= a) b) :c=3a-2b, a, b ER be a subset of R³. Show that Wis a subspace of R³. Find a set S…

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Q: 22. Find the moment of inertia form the given figure. 3

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Q: 1. Let G be any group. Show that the function f: GG defined by f(x) = x² is group homomorphism if…

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Q: The Fourier coefficients of a system with period T are bm all am 0. What is the frequency of the…

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Q: 1. The Maximum point of y = (x²+2x+10) (x-3)

A: For relative maximum or minimum To maximize or minimize  a function f(x) 1st we need to find its…

Q: A metal sphere cools from 80°C to 70°C in 5 minutes. How much more time (in minutes) will it take to…

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Q: Name three logs that would probably reveal the presence of shales. Explain your answers.

A: Following three logs: 1)Resistivity logs  2)Gamma ray logs 3)Induction logs

Q: 4-Let (Z12, +12) be a group and let S={4,6}, find subgroup H generated by S. if exist

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Q: whether it is transitive. a) {(2, 2), (2, 3), (2, 4), (3, 2), (3, 3), (3, 4)} b) {(1, 1), (1, 2),…

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Q: 3. Which is NOT the correct statement of a degree of a vertex? B F A) d(E)=6 B) (B) = 4 OC) d (C)-3…

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Q: 1. How many corner points are there in this LP problem A. 1 B. 2 C. 3 D. 4   2. Which of the…

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Q: For the function f(x, y) = 4x³ + x² − 7, find the solution of the differential equation from x = 0…

A: To solve: The initial value problem dydx=4x3+53x2-7, y(0)=3, Analytically.

Q: For the function f(x, y) = -xy2, find the solution from x = 0 to x = 1 with an increment of 0.2 by…

A: Given function: f(x, y) = -xy2 and the initial condition is x = 0 at y = 1. To find the solution…

Q: Find the dimension of the splitting field of each of polynomials x+1 and x² - 2.

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Q: 5. Let (a) Find the compact SVD of A. +B A

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Q: a. Find the Fourier transform of the given function. 2A f(t) == t + A, 75150 2A f(t) = osts/ f(t) =…

A: This is a problem of Fourier expansion.

Q: Let X = {1,2,3,4,5} and let T = = {x, Ø, {2,3,4,5}, {1,2,5}, {2,5}, {1}}. O (X,T) is Hausdorff but…

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Q: Evaluate. 2x lim (e²x + 2) 8118

A: The solution is given as

Q: 10. Particular solution of y"-4y' + 8y = x³, when x = 0, y = 2, y' = 4

A: We have to find the particular solution of y''-4y'+8y=x3,  when x=0, y=2, y'=4.

Q: Table 8.2 Condition for s y = 1/s xy 1.00 x 10 4.00 x 10-² S₁ 3.13 x 10-² 9.77 x 10-¹ S₂ $3 45 2.22…

A: Given the data, to use linear regression to find the y intercept. Then to find the focal length…

Q: I. EVALUATE THE FOLLOWING LIMITS. SIMPLIFY AND ENCLOSE FINAL RESU 4. Lim (2 4 Arctanx.

A: Solution:-

Q: Numerical Differentiation: f(x) = e² 1. COS X -2 Find f(1.5) and step size of h=0.75 and 0.1

A: We will use Forward Differentiation formula f'(x) = {f(x+h) - f(x)}/h  to find the value of f'(1.5)…

Q: Evaluate the iterated integral by converting to polar coordinates. "√4x² [² [V² - x²-x² - y² dy dx

A: A more than one critical is a specific critical of a characteristic of numerous actual variables in…

Q: 5. (D²2D+1)y=e* arctan x

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Q: Let f(x + y) = f(x) f(y) for all x and y. Suppose that f(3) = 3 and f'(0) = 11, then f'(3) is given…

A: Solution

Q: K(G) < K'(G) < 8(G).

A: Let κ(G), κ'(G) and δ(G) denote the vertex connectivity, edge connectivity and minimum degree of the…

Q: 2. Evaluate: √₁² √2 - x + x da −

A: We know that the modulus function fx=x is defined as x=-x,x&lt;0xx≥0. If we take x=-2, then f-2=2…

Q: Consider the function f(x, y) = x²(y + 1)² + k(x + 1)²y². (a) For what value(s) of k is the point…

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Q: X L479 1 4 11 f(x) 12 -23 -15 33 -13

A: Lagrange's interpolation polynomial for n points can be defined as:…

Q: Simpson's Three-Eighths (Use n = 12) 9. So¹ (3x²+3) dx 10. (2 sin x + 3cos 2x) dx

A: First we find general solutions: 9.  ∫13x2+3dx=∫13(x2+1)dx=13∫1(x2+1)dx=13tan-1x +c    then…

Q: II. Find the determinants or prove the equations in the following. Properties of determinants or…

A: We need to find , determinant of a2 + 2a2a + 112a + 1a + 21331 We will use cofactor method ,  For…

Q: 5. Given z arctan (;-), Find az/ay

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Q: Find the solution. y'= 1 + 3ytanx (A) 3y tan³x=c+ 3sinx-cos³x B 3y cos³x=c+3sinx - sin ³x D 3y…

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Q: 10. At what rate is the vertex angle of a right circular cone changing when the radius is 3 ft and…

A: This is a question of the application of calculus.

Q: 1. Let G be an abelian group with the identity element e. If H = {x²|x € G} and K = {x € G|x² = e},…

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Q: Use multiple equation Newton-Raphson method to determine one of the roots of the following…

A: Given x2+3y2=10x-22+y-12=3

Q: SOLVE THE FOLLOWING NON-HOMOGENOUS LINEAR DIFFERENTIAL EQUATIONS.

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Q: Using the Euler-Lagrange equation of the Calculus of Variations Optimize (-16y² + 144y + 11yy' -…

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Q: Determine the parametric equations of the curve of intersection of the ellipsoid 4x2 + y2 + 4z2 = 4,…

A: The given ellipsoid is 4x2+y2+4z2=4. The given equation of half-cone is y2=x2+2z2. In this question…

Q: Determine inverse z-transform of the following equations: 2² b. (2-1)(z-0.5)

A: Solution

Q: ƒ(x) = 3x4 +√4x; ƒ"(1.2) 6

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Q: I. EVALUATE THE FOLLOWING LIMITS. SIMPLIFY AND ENCLOSE FINAL RESULTS. In(x+1)³ 3. Lim 3 X→∞0 6x

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Q: f(t) = 1, 0≤t≤ 0, <1<T f(t+T)= f(t), t≥ 0. T72 - T 3T/2 - 2T

A: This is a problem of Laplace Transform.

Q: (D² - 4D + 4)y = 0; when x = 0, y = 1, Dy = - 1.

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