For which real numbers k is the matrix [3] k -31 A: k> 3 B: k=3 C: k <3 3 positive definite matrix? D: Non of these

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Q: 1. Use the characteristics of the given function to graph the function and it's reciprocal on the…

A: Given: f(x)=-x2+7x-6 To sketch: The graph of given function and its reciprocal function.

Q: Use the Laplace transform to solve the initial value problem Note: Use u for the step function. y''…

A: We have to solve the given problem.

Q: -49 fy y(u)du = sen (7t) * g(t) for some function g(t). 11. By solving the equation y(t) = = sen…

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Q: Ва ut = Zuxx – ucot )=32 т и (ч, t ) = 52 та heat equation Ic = 4 (xio)= 5x+2 осхи

A: What is the meaning of equal sign before Ut. Ignoring this sign solve by separation of variables…

Q: 6. Check the convergence of the following series: 8 n (a) (1+-!-)" 2

A: As per the company guidelines we are allow to solve one question at a time so i am solving first one…

Q: 41. y' + (1/t)y= 3 cos 2t, t> 0

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Q: Find the differential equation such that y(x)=c₁(x-4) 8+c₂ln(x-4) (x-4) 8 O 64x2 d²y d²y dx² +60x dy…

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Q: 3. Consider the vectors 1 W1 E W2 = and the subspace W = span{w₁, W2, W3} CR¹. (a) Find an…

A: Given, as a matrix: 10-1121011000    ~       10-1022000000   Rank = number of pivot elements =2w1,…

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Q: ar = Consider the linear system = AY with A = dt 26 20 and Y₂ (t) = (22(1)) - (+1(0)) Find the…

A: Introduction: In linear algebra, eigenvalues are related to eigenvectors. In the analysis of linear…

Q: 3 (=-2)* 2. Show that - = 00,

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Q: downtown parking lot charges $5 per hour for the first 2 hours, then $2.50 per hour after that.…

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Q: 3 lim Z→2 (Z-2)4 ∞

A: We have to find the limit.

Q: The solution

A: I have added the missing part

Q: Let 21 = 8(cos(190°) + i sin (190°)) and Z2 = 17(cos(14°) + i sin(14°)). Compute each of the…

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Q: Q5. Check whether the given points A (1, 2, 3), B (3, -1, 4) and C (-2, 3, -4) are collinear.

A: If there points A,B,C are co linear then we can have  |AB|+|AC|=|BC| . (A,B,C may have interchanged…

Q: ] From the following frequency table

A: Given the frequency table  C 0-4 4-8 8-12 12-16 16-20 F 2 3 5 4 6

Q: Solve the equation (x+2) Siny dx + X cosydy=1 собуду=0

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Q: Let f [0, 1] → [0, 1] be continuous. Show that there exists an element x = [0, 1] such that f(x) =…

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Q: e al HIIL equ U VILII the discrete topology T, then (X,T) is compact. * O True O False

A: Given that X be an infinite set equipped with the discrete topology T.

Q: o q Lor -00 10 The function determining the shapes above is f(x) = a√z. The area shown on the first…

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Q: let W be vector that space and suppose USV SW are subspaces of W. Show that W N/u W ~ V/₁ defined…

A: Let W be a vector space over F   and suppose that U⊆V⊆W are subspaces of W. To show: WUVU≈ WV

Q: given data. Ro

A: Let the equation of regression line by least-squares method is y = a + bx Where y is dependent…

Q: 5. Solve log 3x² - 5x=1 Solution [3T]

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Q: An earthquake in Peru was measured at 5.3 on the Richter Scale. The following day a second…

A: For the solution of the problem follow the next step.

Q: Identify the vertex, axis of symmetry, and x-intercept(s). vertex     (x, g(x)) =…

A: Given, equation of parabola is g(x)=(x+5)2 Now compare with g(x)=a(x-h)2+k a=1, h=-5, k=0 So vertex…

Q: f: X → Y be a surjective function. Define a relation on X by setting ay iff f(x) = f(y). Show that…

A: Please check the solution in next step

Q: Problem 13. Let q be an integer. Suppose that q> 2, and that for any integers a and b, if Attach…

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Q: The number of domestic feral rabbits in Nose Hill park can be modelled by the logarithmic function…

A: Given that the number of domestic feral rabbits in Nose Hill park can be modelled by the logarithmic…

Q: Question 2. Let E be the solid region inside the surface x² + y² + z² = 25 and above the surface z =…

A: Note : (i) Cross section of two surfaces is a common curve lying on the both surfaces           (ii)…

Q: A function f:R →→R, where R is the set of real- ax² + 5x - 8 numbers, is defined by f(x) = Find a +…

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Q: Maximize P = 20x + 75y Subject to x+8y ≤ 16 x, y ≥ 0 …... What is the maximum value of P? Select the…

A: Maximize P=20x+75y subject to x+8y≤16x, y≥0

Q: 17. y' 2yet, y(0) = 2

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Q: 9. Find inverse Laplace: | es S

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Q: y' + x(y² + y) = 0, y(2) = 1

A: Given differential equation here is first order differential equation which is variable separable.…

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A: The given problem is to write the given trigonometric term in terms of single term as u =…

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Q: when I typed into my online assigemnt

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Q: The value of a piece of a vehicle after t years is given by V = 47,500 (0.7). Round all your answers…

A: Find the value of vehicle after 2 and 5 years :-

Q: Sketch a graph of a function f that satisfies all of the given conditions. lim_ f(x) = -00, X→ 2 lim…

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Q: Describe the set {TER²: doo (r,(0,0)) = 1}.

A: Given: Set x∈R2:d∞(x,(0,0))=1 We have to describe the set.

Q: determine the volume of the solid lying above the xy plane bounded by surface z = x² + 4y² and…

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Q: The area bounded by the curve y = f(x) and the lines x = 0, y = 0 and x = t lies in the interval (a)…

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Q: Solve using Power Series Centred Around Zero. xy" + 2y' — xy = sech²(y)

A: Given: xy''+2y'-xy=sech2(y) To find: Solution

Q: Question 2. Let E be the solid region inside the surface x² + y² + z² = 25 and above the surface z =…

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

Q: If u and v are the two solutions of d'y dy dx² + P + Qy = 0 dx uv₂u₂v + P (uv₁ - u₁v) = 0 (uv₁u₁v) =…

A: The given differential equation is d2ydx2+Pdydx+Qy=0.....(1) To prove: (a) uv2-u2v+Puv1-u1v=0…

Q: Ва ut = Zuxx – ucot )=32 т и (ч, t ) = 52 та heat equation Ic = 4 (xio)= 5x+2 осхи

A: Using separation of variables method

Q: y=-3log10 (x-1) +2 Parent Function y = log10x (x, y) VA Domain Range State the transformations…

A: Use the following rules, to obtain the transformation of the parent function y=fx. Replace x by…

Q: 9. Find inverse Laplace: 1 es S ܀

A: Given: F(s)=e-1ss To find: Inverse Laplace of given function.