Without expanding along any row or column, use the properties of determinants to find the determinant of the following matrix. 1 0 0 0 1 0 00 3 -200 2 04 0 1 0 0 00 4 0 0 0

Q: 1. Prove by induction that for every n ≥ 1 we have 1 2n (2n + 2) 1 + 2.4 4.6 + + = n 4(n + 1)

A: 12·4+14·6+....+12n2n+2=n4n+1 Let Pn=12·4+14·6+...+12n·2n+2=n4n+1

Q: -1 The graph of y= -1 1 -2 -5+ 5 4 3 f(x) is shown below. 5 6 8 9

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Q: (b) Check all of the following that are true for the In(2n)+3n n² series Σ n=1 A. This series…

A: Series and sequence

Q: a) What is the largest area of the two rectangular of a common side, see below, that a farmer can…

A: Let the length and width of the rectangular block be x and y respectively. The perimeter of the…

Q: 5. Find the equation for the ellipse with foci (±√11,0) and semimajor axis a = 6. (a) (c) 36 + + y²…

A: The given problem is to find the equation of ellipse with given foci (+√11,0) and semi major axis…

Q: au cp. pot = 2(0² 21 -- au a'u a²u कुर Qy² oz² tial equation :-

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Q: of f(x) to dollars. Both functions have domain 1 ≤ x ≤ 25. (A) Sketch a graph of the revenue…

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Q: 12. Draw a frequency curve for the following data. Monthly Wages (in Rs.) 0-1000 1000-2000 2000-3000…

A: We have to draw the frequency curve for the given data.

Q: n is an even negative integer. Quantity A A Quantity B (-3)"

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Q: 4. Masunurin borrows a loan of 20,500 and promises to pay it back monthly for a period of three…

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Q: all Give an example to show that a convergent Sequence under on metric may be divergent under…

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Q: When solving an inequality, in which situation is it necessary to reverse the direction of the…

A: When solving an inequality necessary  condition to reverse the direction of the inequality is…

Q: DIFFERENTIAL EQUATION 1. dy+2x²y=2xe* dx 2. az -x²cosy-w ay 3. ax² d'x d'x\/d³x dt dtª dt³ +X=t 4.…

A: Ordinary differential equation:  An differential equation is said to be ordinary, if dependent…

Q: (1) a) Match each of the following differential equations with one of the direction fields. (6) (ii)…

A: “Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Q: 1. Solve the following differential equations using variation of parameters. If no solution is given…

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Q: Expenditure items Food Clothing Education Housing Rent Miscellaneous Monthly expenditure (in Rs.)…

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Q: If the percent increase is 10%, what is the common ratio?

A: The common ratio is the amount between each number in a geometric sequence. It is called the common…

Q: Determine whether f(x) approaches ∞ or -∞ as x approaches 2 from the left and from the right.

A: We are given  f(x) = tan(πx/4)  We need to find the limit on left hand and right hand side of 2

Q: Find the Inverse Laplace Transform of the following: 4. F(s) = 5. F(s) = 1 √2s+3 e4-3s (s+4)5/2

A: The given problem is to find the inverse Laplace transforms of the given functions F(s).

Q: The bending moment of a beam, M, at a distance, x, along its length, L, is given by M = wLz_wa² 4 4…

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Q: (#12) Show 0 € int(S) implies Sº is bounded.

A: int(S) = interior of the set S S° = polar of S

Q: Given the following sets: U = Kazoo, French Horn, Guitar, Ocarina, Bamboo Flute, Viola, Saxophone,…

A: U = {Kazoo, French Horn, Guitar, Ocarina, Bamboo Flute, Viola, Saxophone, Harmonica, Whistle,…

Q: Find  C(n, x)pxqn − x for the given values of n, x, and p. (Round your answer to four decimal…

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Q: Consider the following. X lim X-0 Create a table of values for the function. (Round your answers to…

A: Consider limx→∞sin2xxTo estimate the limit and complete the given table.

Q: Consider F and C below. F(x, y, z) = yz i + xz j + (xy + 8z) k C is the line segment from (2, 0, -1)…

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Q: Find the indicated trapezoid approximations to the following integral. 10 √2x²0 2x² dx using n = 2,…

A: Solution :-

Q: A forest fire is found at midnight. It covers 1200 acres then. It is spreading at a rate of f(t) =…

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Q: Show that aj +2 aj ↑ 217 Since h> 2, therefore, the series is convergent.

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Q: Find the volume of the region that is bounded by the parabolic cylinder x = y^2 and the planes z= 0…

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Q: A signal can be sent from one location to another by running different colored flags up a flagpole,…

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Q: 2. Let G be a group, and let A be a non-empty subset of G. Define Ca(A) = {g G | gag¹ = a for all a…

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Q: Two-Finger Morra is a game in which two players each hold up one or two fingers. The payoff, in…

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Q: G(s) = ,+x2g

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Q: List all numbers x such that 0≤x<100 and x ≡ [3,1] mod [4,5]

A: Given,           0≤x&lt;100, and  x ≡ [3,1] mod [4,5].

Q: Let y(t) satisfy the following 2nd order ordinary differential equation: 4y" - 5y' - 2y = -6, with…

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Q: Suppose A has eigenvalue X = - 1 with corresponding eigenvector u = [1]. 4 with corresponding…

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Q: Consider ϕ: ℤ × ℤ → ℤ defined by ϕ(a,b) = a-b. Given that ϕ is a homomorphism, determine ϕ (ℤ × ℤ).

A: Consider ϕ:ℤ×ℤ→ℤ defined by ϕa, b=a-b.   Given that ϕ is a homomorphism.   To determine: ϕℤ×ℤ

Q: The partial differential equation (PDE) by eliminating the arbitrary function f from: z = xy +…

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Q: (1) Let ƒ(x) = x³₁· (i) Show that f(x): = −3.₁¹, and then use the geometric sum formula to expand…

A: Expansion of the function using Taylor series

Q: a. Find a Trapezoid Rule approximation to 1 dx0 0 (Round to six decimal places as needed.) Sex 0 dx…

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Q: 3) Suppose X = Uier Ui, with each U₁ an open subset of X. If for each i E I, the subset U₁ is a…

A: Kindly refer Step 2 for the solution.

Q: 5. Use projections to find the distance from the point (0, -1, 3) to the plane 2x-3y+z=4. Show your…

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Q: find Zet for: 2(x, y, t) = (as(2+46) < Sin(23) x Sin{(64)

A: Kindly refer to Step 2 for the solution.

Q: Exercise 2 Let X be a topological space. 1) If A CX is dense in A, show that, for every open subset…

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Q: Suppose we wanted to use mathematical induction to prove that for each natural number n Σ(3n-2)…

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Q: 4. As a business student and a computer scientist, a research has been conducted and the problem has…

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Q: Let f(x) = 0 5 It may be b -3 if 0 < x < 3 0 if x ≥ 3 and g(x) = f(t)dt if x < -3 if -3 < x < 0 x -3…

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Q: What is the largest rectangular prism (in terms of its volume) that just fits in the ellipsoid 2²…

A: Given equation of the ellipsoid is x22+y2+2z2=1 Let 2x be the length 2y the width and 2z the…

Q: Given that f(x, y) = 8x(y + 2)² +8y(x − 2)² is a potential function for F = (8(y + 2)² + y (16x —…

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Q: QUESTION 10 The following is a unit vector: n-hat= [0.281, 0.186, 0.942] Let alpha be 20 degrees. We…

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