2 4) The graphs of y=x and y=x make it obvious that x >x for all real number x > 1. Use induction (not graphs) to prove that 3 3 2 n >n for all integers n > 1.

Q: Define linear dependence and independence of vectors. Examine for linear dependence [1, 0, 2, 1],…

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Q: Consider the topology T = {X,0, {a}, {b, c}} on X = {a, b, c} and the topology Tz = {Y,Ø, {u}} on X…

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Q: 12. Find the positive root of x2 +2 Inx – 4 = 0.

A: Q12 asked and answered.

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Q: 2. (a). 3.

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Q: Examples of how linear programming can help managers make better decisions Give detailed examples…

A: examples of how linear programming can help managers make better decisions ans- it is known that…

Q: 1. Let V = span{(1,1,0,1, 1), (1,2,0,2, 1), (1,3,3,3, 1)} be a subspace of R°. (a) Using the…

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Q: Consider the differential equation y' (t) + 8y(t) = 6cos(lt)u(t), with initial condition y(0) = 6,…

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Q: Using mathematical induction, prove that for all nonnegative integers n 2n+1 + (-1)" 3. 2" %3D j=0

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

Q: Use Teller's method to Solve the differential equation y-X JJ when h=0-2 s y(1)=2 Use The fifth rank…

A: We can solve this using Taylor method

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Q: 7. Fill in the blanks An object starts from rest from its starting position and moves along a…

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Q: If a < b, then [a,b] CR does not have con- tent 0. In fact, if U1,. . .,Un) is a finite cover of…

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Q: Find the laplace transform of f(t)=2t^2 e^-t - sin^2 t

A: We have to find the Laplace transform of f(t)=2t2e-t-sin2t .

Q: dy Sketch the vs. vs. y graph. dt

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Q: Three invoices for the amounts of $34,200, $25,000, and $41,450 were received on November 27, 2014,…

A: 3/7 means a 3% discount if paid within seven days after the date of invoice.  2/30 means a 2%…

Q: x2 - y² =2xy

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Q: Question 7 Let T be a linear transformation given by 2 1 0 1 T Is T one to one? Is T onto?

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Q: Determine whether S is a basis fa S = {9 – t, t³, 6t², 2t +

A: S is the basis of P3 if the vectors are linearly independent. Therefore for the vectors to be…

Q: 4. All the sets in this problem are subsets of N. For any A C N, let us use the notation AN - A Now…

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Q: Find the Laplace transform of 6e5 cos2t - e7: 6(s-5) A (s- 5)2+4 s-7 (s- 5) (B) (s - 5)2+4 s+ 7 6s…

A: We have to find the Laplace transform of f(t) = 6e5tcos2t - e7t

Q: (4, w/8) 1. (y cos xy dx + x cos xy dy) (0,0) (0,5) 2. e2* dx + ye2 dy) (5,0) (1,1) 3. 2(x dx +y dy)…

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Q: 10x2+125-5 Q2) Find lim x-0 3x2

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Q: Ex. 1. Obtain the formal expansion of the function f(x) = TX – x, 0SXST, in the series of…

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Q: Use Simpson's rule with n = 18 to calculate the circle's area, which is specified overhead by f(x) =…

A: Given: The circle, which is specified overhead by fx=3-x2 and beneath by gx=-3-x2.   To calculate:…

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A: To solve this problem you need to know the followings :   1 year = 52 weeks  1 year = 12 month

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Q: Which of the following is the solution of the linear system -x+2y-2z= -6 , -2x-2y-4z=9 None of them…

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Q: 1. Consider the initial value problem, 2y 3y2 1<t<2, (la) y(1) = 1. (1b) The exact solution to (1)…

A: The complete solution is in given below.

Q: Find the solution. dy - +y= dx 1 1+e* A y = ce*+e*In (1+e*) B y = ce¯ - e -*In(1-e*) (© y =…

A: By Bartleby policy I have to solve only first one as these are all unrelated problems.These are all…

Q: -4지 (2) %3D y(e) %3D

A: The given differential equation is y'=-4xy,y(2)=3 dydx=-4xyydy=-4xdx integrating both sides

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Q: If 1 4 1 A = 2 3 -2 1 -1 1 1 determine the following entries: a14 a32 a23

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Q: How many members of the Mathematics for All Club submitted their ballots?

A: (AJB),(JAB),(BAJ), (BJA) are disjoint sets  then there are 6 permutations. so the others two…

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Q: 6. evaluate iz/iu and az/ov at the given point (u, v). 2 = tan (x/y), x = u cos v, y = u sin v; (u,…

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Q: sina cos α sin (α + δ)| . Without expanding, evaluate the determinant sin ß cos B sin(B + 8) sin(y…

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Q: Let V be a tree with internal vertices of degree 2, 7, 5, 4., and 6. How many leaves does V have?…

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Q: Consider a square with a side of length 1. Construct another square, inside the first one by…

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Q: Find the value of zo so that dz = -2ri Izl=13 (z – z0) (z – 14i)

A: Given integral is ∫|z|=13z(z-z0)(z-14i)dz = -2πi   ---(1)

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Q: 2. (a). 3.

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Q: Example 14. Given the function S x + a?, f (x) = if x 0, find the real constants a and B s.t. the…

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Q: Who was the Winner by the HARE METHOD? (AJB) = 5, (BJA) = 4, (JAB) = 4, (BAJ) = 2 A-Amber B B- Bill…

A: Given: AJB=5, BJA=4, JAB=4 and BAJ=2   To determine: The winner by Hare Method.

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Q: One of the optimal condition for the non-linear programing problem z = x² + 3y + 5z Subject to x + y…

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Q: Show that the set is linearly dependent by finding a nontrivial linear combination of vectors in the…

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