We are making 5-letter words from the set of letters a, b, c, d, e, f..., in such a way that we have exactly the first 5 letters available so that we use all letters. a. How many 5-letter words can we make from the letters without repeats that do not contain the sub- word "bad" in consecutive letters? a. How many words don't contain the subword "bad" in not-necessarily-consecutive letters (but in order)?

Q: Find the derivative: cos(z) de (1060) √ 1 - 13dt). dx

A: We have solved using the standard formulas of integral then proceed further as in next step.

Q: Write 843 in scientific notation

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Q: State and prove the first isomorphism theorem.

A: As per the guidelines we are supposed to solve the first questions only.kindly post another…

Q: 3) Determine the rule writing it below and then complete the tablic 3

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Q: ABC is a triangle having the angle C a right angle. Equilateral triangles ADB, AEC are described…

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Q: Use Laplace transform to solve the partial differential equation: d²u du ди(x,0) t> 0, 0<x<1, u(x,0)…

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Q: Let G be a group and H be a normal subgroup of G. If H and G/H are solvable then so is G.

A: Given that Let G be a group and H be a normal subgroup of G. If H and G/H are solvable then so is G.

Q: Q1: Solve ýex+y 2 = cosh x + √√cosh² x − 1 + 7e*

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Q: Use Laplace transform to solve the partial differential equation: o'y dy ox² at +xl where y(x,0) =…

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Q: Let f(x, y, z) = g (x² + y² + z²) where 2 9 is some nonnegative function of one variable such that…

A: If S is a surface given by parametric form r→ u,v =x u,vi^+y u,vj^+zu,vk^…

Q: Problem 9. Consider a triangle and its inscribed circle. Join each vertex with the point of tangency…

A: Given: AB=c, AC=b,BC=a

Q: If u1= then A(01+02) = and A(-201) = and 2 = Gl are eigenvectors of a matrix A corresponding to the…

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Q: Verify that the given functions are linearly independent by evaluating the Wronskian at x = = 0.…

A: Solution :     e2x ,  xe2x , cosx , sinx Let ,          y1 = e2x ,          y2 = xe2x ,         y3 =…

Q: 1. Find a basis for the subspace of R4 spanned by the vectors (1,1,-4,-3), (2,0,2,-2), (2, -2,3,2)

A: Solution:-

Q: Consider the ordered bases B = ((5,-9), (-1,2)) and C = ((3, 1), (-4, 3)) for the vector space R².…

A: Note: According to our guidelines we can answer only first three subparts

Q: Directly from the definition compute the Laplace transform 2t if 0≤t≤ 1, { 0 if t > 1. Problem 11…

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Q: y"+y' = sec² x

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Q: Use Taylor's formula for f(x,y) at the origin to find quadratic and cubic approxim

A: Given,         f(x, y)=11-2x-y

Q: Use Laplace transform to solve the partial differential equation: d'y dy +xt where y(x,0) = 0,…

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Q: 3. Find the area of the region bounded by y = x², y = 8 - x² and y = 4x + 12.

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Q: Hiwo- solve the hyperblic partial differential equation numericaly where d²u d²u dx² = with initial…

A: Given  ∂2u∂x2=∂2u∂t2 The wave equation is ∂2u∂t2=c2∂2u∂x2 So c2=1 The difference for the given…

Q: 2. Find the first five nonzero terms of the power series solution of the initial value problem: y +…

A: Given initial value problem is ,                            y''+4xy'-4y =0    ,    x0=2…

Q: Be sure to show all work and all problem solving strategies. Give complete explanations for each…

A: Solution : a) X1 matrix is product of A and X where, X1(i,1)=Ai1X0(11)+Ai2X0(21)+Ai3X0(31) where,…

Q: (b) Consider the second-order differential equation: x" + 3x² + 4x = t² +3e¹ Using the method of…

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Q: Supppose A is an invertible x n matrix and is an eigenvector of A with associated eigenvalue-2.…

A: Here we use the properties of eigenvalues of matrix to answer the appropriate question as below.

Q: Let Gbe an open set in R". Two points x, y = G are said to be equivalent if they can be joined by a…

A: Solution:-

Q: If ƒ (x, y) = log (x² + y²), then f +f, is equal to XX yy 1 (a) x² + y² (b) 0 2 1,² - x² (c) (d) (x²…

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Q: Establish the following set theoretic relations: a) AUB=BUA, AnB = BnA (Commutativity) b) AU (BUC) =…

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Q: Let A be a Hermitian matrix with eigenvalues A1 A2 > An and orthonormal eigenvectors U₁,...,Un. For…

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Q: Problem 14 problem: Using the Laplace transform, solve the following initial value y" + 4y + 3y = e,…

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Q: Exercises: Find the Taylor series for the function at point T a = f(x)= cosx , ● f(x)=√x a = 4 f() =…

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Q: ₁ = [₁] and √₂ = [1] ₁ A is a 2 x 2 matrix with eigenvectors V₁ Find A⁹x. 131075 256 A³x = 131069…

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Q: Find all possible values of a e and Iz+2a-(a + 1)i> 3 simult

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Q: (20) Evaluate the integral: ²1+√√/x dx.

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Q: Using divergence test, which of the following diverges A. 1/√n from n=0 to n=∞ O B. B. (6 +8n+9n²) /…

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Q: 1.a) Apply the Trapezoid and Corrected Trapezoid Rule, with h=, to approximate the integral ₁³e-2x²…

A: 1. a) Consider the given integral, I=∫13e-2x2dx, with h=18. The trapezoid rule states that,…

Q: Q2/ Solve the following differential equation for (0 ≤ x ≤ 1.5) by using Euler method, use {h= 0.50,…

A: Given differential equation is y''1+y'2 =x2 -y2 with initial conditions  y0=1,  y'0=0 Step size:- h…

Q: If A = 3ai +4j-k and B = 4i+j-3k, find the value of a if A normal to B.

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Q: Let A be an n x n matrix. Assume that the inverse matrix of A exists. The inverse matrix can be…

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Q: T/3 (29) Evaluate the integral: 73 - csc? rdr. π/4 (30) Find the derivative of the integral…

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Q: Use Taylor's formula for f(x,y) at the origin to find quadratic and cubic approximations of f near…

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Q: The knapsack problem (KP) can be solved with dynamic programming (DP) in O(nS), where n is the…

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Q: ý t + 45 зух P(x) = = 2x Q(x) = 2х 2

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Q: Use Laplace transform to solve the partial differential equation: d'y dy +xt where y(x,0) = 0,…

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Q: Use Laplace transform to solve the partial differential equation: 8² y dy = +xt where y(x,0) = 0,…

A: Solution

Q: Consider the four statements (a) 3r ER Vy ER (b) Vr € R y R (c) Vr ER Vy ER 3r ER Vy ER (d) 1. Are…

A: First we will tell the meaning of the symbols used in the given statements. The symbol ∃ is used for…

Q: Q2: (A) State only: Krull-Zorn theorem, Lagrange theorem. (B) Prove that: 1. Every Boolean ring is…

A: We can solve this using given information

Q: problem: Using the Laplace transform, solve the following initial value y" + 4y + 3y = e, y(0) = 1,…

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Q: Prove that every Boolean ring is commutative. Is the converse true? Explain your answer.

A: We can solve this using definition of boolean ring

Q: Volume of Solid Revolution(Circular Disk and Washer Method) Find the volume of the solid generated…

A: given curve x2+y2=4 find the volume of the solid generated by revolving the area bounded by the…