n (x - 1)" The sixth term of the expansion of x is 1287 8 X 3125 . Determine n.

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A: Given as dN1dt=0.15N11-N150-N250dN2dt=0.05N21-N275-N175

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Q: For the following Lp values, find k Lp = 8.41 k =  d =  Lp = 2.4 k =  d =  Lp = 3.77 k =  d =

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Q: Evaluate log, m² a. n 2 b. n² C. d. mn 2n

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Q: 3. Solve the DE: y45y" +4y=0

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Q: 1. Find and classify the critical points of the function f(x, y) = 4x²y - 2x - y².

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Q: Good

A: We use QR theorem.

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A: We need to determine the particular solution of the differential equation: y'''+2y''-y=ex+cosx.

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Q: 1. Define a mathematical function f(x) such that f(0) = 1 and f(1) = = 0 using only , +, -, Xx,,…

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Q: Use Stokes' Theorem to find [F. · [F. F. dr where F = 4yi + 6zj + 4zk around the boundary of the…

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Q: Q3: Evaluate z + 1 $c (z6 + 5z5 + 4z¹) (z + 4) dz where C is the circle |z1| = 5

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Q: b. If y 114 1625 e* cos(3x) is a particular solution of y" +25y' = 4e* cos(3x), write the general…

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Q: y" + 4y = 1² + 8e', y(0) = 0, y'(0) = 7

A: we are given second order non homogeneous linear differential equation with constant coefficients to…

Q: To prove the statement: Any two consecutive integers have opposite parity. Which method do we use?…

A: Correct Answer is Division into Cases:

Q: Problem 3 Solve using method of Laplace: y" — 2y' – 3y = 0, y(0) = 1, y′(0) — 15

A: Given equation is y''-2y'-3y=0 Also given y0=1,  y'0=15   To Solve: using method of Laplace.

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Q: This is an example of an Undamped Forced Oscillation where the phenomenon of Pure Resonance Occurs.…

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Q: The solution of the exact differential equation (²+y' cos x)de+ (2xy+3y sinx)dy=0 is:

A: The given equation is y2+y3cos xdx+2xy+3y2sin xdy=0 The given equation is of the form Mdx+Ndy=0…

Q: Evaluate the following expression. Type answers exactly. If the answer does not exist, then type…

A: We have to evaluate arccoscos17π12.

Q: For any sets A and B, which statement is false? OA NA = {} OAUB CANB OAN BC B OA CAUB

A: Remark:  We know that The union of two sets A and B is the set of all those elements which are…

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Q: Va, beZatb = a + b +2 and aob = a tabtb is a Ring!

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Q: A cylindrical can with one end is to be made with 24π cm2 of metal. Find the dimensions of the can…

A: Given that a cylinder with one end is to be made of a material whose area is 24π cm2. To find the…

Q: What is the Laplace transform of 2?

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Q: II) Let f be the piecewise function f(x) = 2³ +6x² + 8x x+2 21-2, 1- x - 2, x≤-1, x -2 -1 1 1)…

A: The given function is: f(x)=x3+6x2+8xx+2x≤-1,x≠-221-x-1<x≤11-|x-2|x>1 1) To Sketch: the graph…

Q: The function y = sin X has been transformed. It now has amplitude of 3.4, a period of 36, a phase…

A: This is a question of linear transformation.

Q: Express the given quantity in the form a + ib. cos(6-7i) cos (6) cos(7h) + i sin (6)sin (h7) eBook X

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Q: (b) Find the fundamental matrix Þ(t) for the system x' = Ax which satisfies (0) = I. (c) Use Þ(t) to…

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Q: A mass m = 4 kg is attached to both a spring with spring constant k = 485 N/m and a dash-pot with…

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Q: Find the mass and center of mass of the lamina bounded by the graphs of the equations for the given…

A: Introduction: If an object is in a uniform gravitational field, the center of mass is also referred…

Q: Consider the real-valued function of one variable f: R → R defined by - {₁+2²+ (a) Show that f'(0)…

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Q: Find the Laplace Transform of sin2t + cos2t. a. (s-2)/(s2-4) b. (s2+4)/(s+2) c. (s2-4)/(s-2) d.…

A: We know Laplace  transform of sin(at) is as2+a2 We know Laplace  transform of cos(at) is ss2+a2

Q: sin has been transformed. It now has amplitude of 10.1, a period of 26, a phase shift of 0.5 units…

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Q: y" +2y+3y= sint + 8(t-3л); y(0) = 0, y'(0) = 0

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Q: 1%AY ₁.1 Using the method of undetermined coefficients, The general form of a particular solution of…

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Q: Find and classify the critical points of the function f(x, y) = 4x²y - 2x - y².

A: We need to determine and classify the critical points of the function: f(x, y)=4x2y-2x-y2.

Q: Use the Integral Test to determine the convergence or divergence of the following series, or state…

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Q: Find a formula involving integrals for a particular solution of the differential equation y" - 30y"…

A: We solve by Variation of Parameter.

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Q: Let n be an integer such that n mod 7 = 5. What is n² mod 7? 04

A: Given 5≡nmod 7 using the result a≡bmod n then n/b-a Therefore 7/n-5 now  using if a/b then ac=b…

Q: A mass suspended from a spring is pulled and released at a minimum height of .5m. After 7 sec. it…

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Q: Evaluate: 3/20° × 15/45°

A: the given expression is 3∠20°15∠45° Multiply the polar magnitudes and add the angles of the complex…

Q: 6. Show that the vector field 1 1 x²y' xy²¹ is conservative by finding all its potential functions.…

A: The given vector field is F→(x,y,z)=-1x2y, 2z3sinh(2y-1)-1xy2, 3z2cosh(2y-1)-5zln5. To Prove:…

Q: Find the transform in Z of the following exercise: z² (z-1)²(z²z+1)

A: Introduction: We are familiar with continuous or analogue signals in the temporal domain. However,…

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Q: Comment on using the Newton method to compute the root of the function f(x) = x¹/3, i.e., if your…

A: The given function is f(x)=x1/3. We have to explain whether Newton's method works in finding the…