Classify the following quadratic forms: (a) 2x² + y² +22² - 2xy - 2yz (b) 3x² + 7y² +22² - 4xy - 4xz (c) 16x² + 36y² + 172² + 32xy + 32xz +16yz (d) -21x² + 30xy-12xz - 11y² + 8yz - 22²2 x²-3y²-52² + 2xy + 2xz + 2yz (e)

Q: Find the Inverse Laplace Transform of the following functions 1) F(s)=- Ans. f(t)=1-e¹ S+S 2) F(S) =…

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Q: (a) Sally wants to join one of the following saving plans in 2 banks: (i) In ABC Bank, Sally…

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Q: FIND Y(S) OF THE GIVEN EQUATION. 2y" + 3y' – 2y = te-2, y(0)=0 y (0) = -2 y" - 10y' +9y = 5t, y(0) =…

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Q: Determine whether the statement is true or false.   b) The set of all ordered triples (x, y, z) of…

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Q: Find the area of the region bounded by the curves 1 y = (x+6)² y = 4 and the x-axis using vertical…

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Q: The von Bertalanffy growth model states that the rate of increase in the length L(t) of a shark of…

A: according to question, rate of increase in length of a shark of age t in years is proportional to…

Q: Consider the function f(x) = cos x − 3x + 1. Since ƒ (0)ƒ (²) < 0, ƒ (x) has a root in [0]. If we…

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Q: 1. The diagram below shows the left hand side of the main window (one period) of a periodic…

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Q: Gordon is making a chocolate dome by coating a plastic dome with a layer of chocolate 2 mm thick. If…

A: Answer: 40π cm³ or 125.66 cm³

Q: Problem 3. Let VCR³ be the region bounded by the planes z = 0, x= 1, and the surface defined by 2² =…

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Q: Determine the values of r for which the given differential equation has solutions of the form y = t'…

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Q: Find the volume of the solid generated by revolving the region bounded by 2y = e-x², the x-axis and…

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Q: Consider the function f(x) = cos x − 3x + 1. Since f (0)ƒ () <0. f(x) has a root in [0, 1]. To solve…

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Q: Evaluate: ³4²₁²[z³(x + y)³] dz dy dx

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Q: A hemispherical tank of radius 6 feet is positioned as in the figure below. How much work is…

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Q: Consider the function f(x) = cos x - 3x + 1. Since f (0)ƒ () <0. f(x) has a root [] If we use secant…

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Q: Find the area of the region bounded by x = and the y-axis using the horizontal strip. 2y²+1

A: Given curves are x=42y2+1 and y-axis.

Q: -3 -4 Evaluate: ₂₁ (4x²y - z³) dz dy dx

A: ∫03∫-24∫10(4x2y-z3) dz dy dx

Q: X ди Әх || ди u + Y əy

A: The given differential equation is             x∂u∂x=u+y∂u∂y

Q: Find the area of the region bounded by 2x and the y-axis using the horizontal strip. 3 y²+1

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Q: Find the volume of the solid generated by revolving 1 the region bounded by y = e-x², the x-axis and…

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Q: Consider the function f(x) = cos x − 3x + 1. Since ƒ (0)ƒ (²) < 0, ƒ (x) has a root in [0]. To solve…

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Q: Consider the function f(x) = cos x - 3x + 1. Since f (0)f() <0, f(x) has a root in [0,1]. If we use…

A: The given function is               f(x)=cos x-3x+1 It is known that f(x) has a root in 0, π2. Using…

Q: Using Laplace Transform What will be the time in which Tank 1 will have % of the salt content of…

A: please comment if you need any clarification. If you find my answer useful please put thumbs up.

Q: f₁ = x² - 6x f₂ = x² + 6x f3=x²-3

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Q: N J 9. Consider the permutations f and g = = 5 2 1 3 4 set {1, 2, 3, 4, 5). Then go f = 1 2 3 4 5 1…

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Q: The fixed-points of f(x) = (x² + 2); are and

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Q: Consider the function f(x) = cos x − 3x + 1. Since ƒ (0)ƒ () < 0. f(x) has a root in - [0,1]. If we…

A: We are given f(x)=cos(x)-3x+1 and x0=0.5 Newton-Raphson method xn+1=xn-f(xn)f'(xn) now…

Q: Find the 1 y = (x+8)²² ОТ egion by y = 4 and the x-axis using vertical strip.

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Q: 32u at2 J2u a2 дх2

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Q: Find the Inverse Laplace Transforms of the following. 4) 48-60√/s s4 4

A: F(s) = L-148-60ss4 F(s) = L-148s4-60ss4 F(s) = L-148s4 - L-160ss4

Q: y' (t) = 1 Sin(t) -t y (u) cu -> (1)

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Q: Consider the function f(x) = cos x − 3x + 1. Since f(0)f < 0, f(x) has a root in [0]. If we use…

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Q: Consider the function f(x) = cos x − 3x + 1. Since ƒ (0)ƒ (1) < 0. f(x) has a root in - [o,]. If we…

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Q: Consider the function f(x) = cos x − 3x + 1. Since ƒ (0)ƒ (²) < 0, ƒ(x) has a root in [0₁]. To solve…

A: We have g(x)=(13)(1+cos(x)), x0=0 iteration formula: xn=g(xn-1)

Q: I.* Determine all the isolated singularities of each of the following functions and compute the…

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Q: Prove that the function f: R - {2} R {5} defined by f(x) = 5x + 1 * - 2 is bijective.

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Q: -4 3 (x²-y²)²] x+y Evaluate: ₁ du dt

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Q: Consider the function f(x) = cos x − 3x + 1. Since ƒ (0)ƒ (²) < 0, ƒ (x) has a root in - [0]. If we…

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Q: Consider the function f(x) = cos x − 3x + 1. Since ƒ (0)ƒ () <0. f(x) has a root in [0]. To solve…

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Q: Analyzing the functions below, compare and contrast the two functions in each problem situation. Be…

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Q: II. Problem Solving/Proving. Show all complete solutions. 1. Show that V = M22, the set of all 2 x 2…

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Q: 6. Determine the values of C₁ = 922 @ +923 and C₂ = 924 @ +925 if y(t) = e2¹ (C₁cos(1) + C₂sin(t))+…

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Q: Evaluate: ₁²-du So -3 (x² y²)²7 x+y du dt

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Q: J2u 0t2 J2u a² дх2

A: please comment if you need any clarification. If you find my answer useful please put thumbs up.…

Q: Evaluate the integral: 2е π/3 10₁52²² ƒºƒ²² ƒ/³ t ln u tans ds du dt 0

A: To Evaluate: ∫-10∫e2e∫0π3t lnu tans ds du dt

Q: Let R be the region in the first quadrant bounded by x = = 1, (x − 2)² + y² = 1, and x² + y² = 4.…

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Q: Find the area of the region bounded by the curves 1 y y = 4 and the x-axis using vertical strip.…

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Q: Determine the total solution of the differential equation (D²+8D+16)y = 64cos4x.

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Q: A feedback control system modelled by the differential equation * + ax + kx = 0 is known to be…

A: Problem is solved using concept of Lyapunov Function.