Let P(n) be the statement 1² + 2² + ... + n² = for the positive integer n. What is the inductive step? O n(n+1) (2n+1) k(k+ 1) (2k + 1) 6 6

Q: The indicated function y(x) is a solution of the associated homogeneous equation. Use the method of…

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Q: 382. x = u cos(e"), y = u sin(e")

A: 382 Given that x=ucosev and y=usinev. We have to find the Jacobian J. The Jacobian J is given by…

Q: 1. Calculate by the Power Series Method the value of y as general solution (term-by-term from n = 0…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Show that xp-yq=z and x^2p+q=xz are compatible and solve them

A: Given   :   xp-yq =z and  x2p+q =xz To find : Solution of Differential equation

Q: 16) The fastest 25% of women participants ran the marathon how quickly? A) More than 155 minutes. B)…

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Q: 1) Let V, W be F vector spaces. Recall that a skew-symmetric map is a function f: V × V → W such…

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Q: How many minutes and seconds after 2 o'clock will the hands of the clock be perpendicular for the…

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Q: Use taylor formula for f(x, y) =ln(2x+y+1) at the origin to find quadratic and cubic approximations…

A: Introduction: Like single variable function, Taylor series expansion can also be performed for a…

Q: P 0.00942 + P(0-2) 0.00105 Find the P... ? <87.61

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Q: Determine whether linear or nonlinear:  y(t) = -jt*x (t) y(t) = j+x (t)

A: A linear equation is the one in which the highest degree is 1. A non-linear equation is an equation…

Q: (c) Hence determine the type and stability of the equilibrium point Xe = 0. (d) Solve the initial…

A: Given :                 dxdt =1447x    ,   x0 =21 To find  : type and stability              : solve…

Q: Question: (additive) onder Let abilian grup mm, Libre (min). G - {8EG₂₁ cocher (8) Im] and G₁ = [ht…

A: It is given that G be a finite(additive) Abelian group of order mn with  (m, n) = 1 And,  Gm = g∈G :…

Q: ● By power series method, Solve the following ODES & C₂ x² e² + 2X =-2 X-2X Ans: Y = C₂ X e + 2 X…

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Q: 2 Solve the following ODES by Inverse Operator method 2X (D-1) y = 2 sinhx + sinx -X Ansoy chế…

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Q: 3) How many arrangements are there of the letters in the word Neutrogena?

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Q: 4X у - 16 y = 19.2 е + 600 бос Х , усо) =ўс - о -ЧХ 4X 4X Ans. Y= 22e +he +2,4хе - X Че

A: Given,            y''-16y=19.2e4x+60ex; y(0)=y'(0)=0

Q: Write the sentence with variables p, q, r and connectors, A, V for the following two truth tables. T…

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Q: Let {₁,..., wk, Wk+1,...,n} be a basis of R" and c₁,...,CER be nonzero scalars. (a) Prove that S =…

A: Note that we used one fact in this prove which state that if B is basis of V and C is any linearly…

Q: Find the area between the curves. x = -5, x=2, y = 3x, y = x² - 4

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Q: 2. Define a function f(X) = c. X = C₁x₁ + C₂x₂ + C = (C1, C2, ..., Cn) E R is constant.…

A: Given,  f:ℝn→ℝ  such thatf(X)=c.X where X=(x1,x2,...,xn)∈ℝnand c=(c1,c2,...,cn)∈ℝn is constant tuple…

Q: 1. Let A = a b c def ghi B ba bb b c gh i de f If de+ (A) = -1/24 then what is det (B-¹)? and AUT

A: Square matrix: If a matrix A has the number of rows equal to the number of columns. Then, the matrix…

Q: Solve the following BVP using finite difference approximations with the step-size 1/3: d²u 3 dx²=u²,…

A: Given IVP is d2udx2=32u2,      u(0)=4,  u(1)=1           (1) step size h=14 By finite difference…

Q: If A = -2 -8 7 32 then det (A) 02-745 0024 -4 000-5 -1 Lo 0000 -3 = 1

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Q: 1 In(k + 2) 4.) Answer the following for the series *((-1²- A.) Determine how many terms should be…

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Q: Find the Wronskian of the given pair of functions: X O x² et O xet i, xet

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Q: Define the binary operator by: ab=a² + b² Find each of the following: a. 203- = b. 404- c. 32 d. hod…

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Q: Determine any planes that are parallel or identical. (Select all that apply.) OP: 30x + 120y + 30z =…

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Q: 3x + 4y = 8, 4y - 3x = 8, 4y - x² = 1. Sketch of the region D and describe its symmetry. Find the…

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Q: y dV, where E is the solid bounded by the parabolic cylinder z = x² 14 - 2y. Find and the planes y…

A: Introduction: The goal is to assess the triple integral that is presented. And ∫∫∫EydV is the…

Q: n=1 -7 about the point zo = -3i. Specify the region of validity. 1 6. Calculate the Taylor series of…

A: The Taylor's series of the function fz about the point z=a has the representation ∑n=0∞ anz-an,…

Q: Step 1 We are given the following homogenous differential equation and pair of solutions on the…

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Q: Solve the y" + 5y' + 4y = x²e²x following CDES by variation of parameters method

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Q: is because the integral gives the wrong answer in poorly chosen coordinates. For example r0=2π r=R 1…

A: Given is a statement as: The reason we need different coordinates systems when calculating area…

Q: 20. A Honda Insight has fuel economy of 3.2 litres consumed per 100 kilometres driven. It has a fuel…

A: It is given that Honda Insight has fuel economy of 3.2 litres consumed per 100 kilometers and it has…

Q: Let C be the projection of A onto B and D be the projection of B onto A. If the dot product of ac…

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Q: Find the area of the plane z = 4x + y for all (x, y) = R where Ris the region in the first quadrant…

A: Consider the equation of the plane, z=4x+y for all x,y∈R,where R is the region in first quadrant…

Q: Suppose that y^-1= 7x ^-2/6z^-1 Which equivalent to y? A. 6x^2/7z B. 7x^2/6z C. 7z/6x^2 D. 6z/7x^2

A: I have given the answer in the next step. Hope you understand that

Q: -6 w Find an equation for the graph above. N 3+ g(u) 2- 1 -1 N -3- ·~ m +48 q

A: We need to determine the equation of the given graph.

Q: 3 Solve the following ODES by Inverse Operator method 2 • (B²+1) y = cos x Ans : y = C₁ C3 x + C₂…

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Q: Find the solution of the following initial value problem. 4y" y=0 y(-2) = 1, y'(−2) = −1 y(t) =

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Q: Given that z = cos + isin and u-iv-(1+z)(1-22). Show that 30 v = utan 2 r = 4² cos² (2). where r is…

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Q: 3. Prove by contradiction, that if x and y are odd integers, then there is no integers z such that…

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Q: Find the remainder in the Taylor series centered at the point a for the following function. Then…

A: Given function is f(x) = e-x

Q: 5. Vn EN, Prove the following by mathematical induction. Σ(2n-1)² = n(2n − 1)(2n +1) 3 i=1

A: Let p(n) be the statement,   ∑i=0n(2i-1)2=n(2n-1)(2n+1)3

Q: Find the general solution of the following differential equation. y" + 4y - 12y = 0 NOTE: Use c₁ and…

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Q: For the finite state automaton given by the transition diagram in figure 1, find the states, the…

A: Given Transition diagram: The DFA state transition diagram shown above shows that it has both…

Q: 8. Consider the solutions Y(t) of Y'(t) + ay(t) = de-bt with a, b, d constants and a, b > 0.…

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Q: An object moves with velocity as given in the graph below (in ft/sec). How far did the object travel…

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Q: Find the general solution to the equation y(4) — 4y"" + 4y" = NOTE: Use C₁, C2, C3, and c4 as…

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