12): x € R. Is W a subspace of V? Expalin your 3x- Q1. Let V = R³ and W = answer? Q2. Show that M2x2 , the set of all 2× 2 matrices is a vector space. Explain your answer?

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A: This is problem of optimization and application of differential calculus.

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A: R(x), F(x), I(x), and D(x) represents the output amount in dollars if an input  of x dollars  is dec...

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Q: Combine the methods of row reduction and cofactor expansion to compute the determinant. - 1 - 5 - 4 ...

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Q: 3.1.4. (-) For each of a, a', ß, B', characterize the simple graphs for which the value of the param...

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Q: The conjugate harmonic function v(x, y) of u(x, y) = In (x2 + y2) is *(;) + -1 1. 2tan () + -1 2tan ...

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Q: 5-14 1 Solve the differential equation. 5. у' + у — 1 6. у' — у — е* 7. у' — х — у %3D 9. xy' + y = ...

A: According to our guidelines we can answer only three sub-parts and rest can be reposted. 

Q: Q2. You are planning to control pollution from four manufacturing facilities those are discharging p...

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Q: b. Let {a,} be a sequence of real numbers. We say that {a,}, decreases without bound, written lim an...

A: this is a problem of sequence.

Q: 1. In the following weighted voting system example, identify the quota and the weights. [115: 25, 35...

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any ...

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Q: What is the expanded formula for a family with 8 children? O a + 56a'b + 70 b² + 256a b + 320atb + 2...

A: Pascal's triangle

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Q: How much money would have to be deposited now at 4.5% interest compounded monthly to  accumulate to ...

A: Let us consider the principal P then the amount obtained after 4 years at the rate of r%  A=P1+r100x...

Q: Pisalve The fallowing systemusingGauss EliminatiohMéthodt メ メs216 12X i- 8Xz 6x3 oy 6 3x -13Xa+9X3+3...

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Q: Prove or disprove the following statement: Let A, B, X be sets. If X ⊆ A ∪ B, then X ⊆ A or X ⊆ B.

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Q: Problem 2: instructions for series on the coversheet of this exam. Explain whether the series below ...

A: Series and sequences

Q: Consider the points A(3, –3, 5), B(5, –5, 2), C(-1, –4, 2), and D(4, 1, –8). (a) Find the volume of ...

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Q: 4. Consider the weighted voting system [14: 14, 10, 2, 1]. a. What is the quota? b. How many players...

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Q: Use metaphor/layman's term to discuss Ridder's method for solving nonlinear equations

A: To discuss: The Ridder's method for solving nonlinear equations.  

Q: Examples: 1.) A curve wedge is cut from a cylinder of radius 3 by two planes. One plane is perpendic...

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Q: dy dx take 2. Solve xy +1 with ycu) = 1 for finding yo.075) %3D h=0-025

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Q: Find SL (xy) dl Lis Jquare 1x|+ lyl= 1 where.

A: The integrals in the form ∫Lf(x,y)dl involve the integration over the specific path L. In this case,...

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Q: Let A(r) f(t)dt where f is the function given by the graph below. /3 4+ 2 -2 -3 -4+ i. A(4) =

A: Introduction: The two point formula of straight line is widely used. When a straight line passes thr...

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Q: Show that - a is not the inverse of a e N for the addition operation + on 1 N and - is not the inver...

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Q: C. Given: ATAN ~ATKJ. 1. If TJ = 8cm, AN = 10cm and TA = 12cm. Find TN and KJ %3! K 2. TN = 5x -7cm,...

A: It is given that two  triangles ∆TAN ~ ∆TKJ  

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Q: Use the fact that the volume of a tetrahedron with adjacent edges given by the vectors u, v and w is...

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Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to y or x. ...

A: Let us consider the curve y=f(x) and y=g(x) the area under the curve y=f(x) and y=g(x) between the i...

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Q: a) g(x) = In( 1 – 2 x ) %3D b) f(x)= 7/(5+x^2) %3D

A: This is a problem of series. Taylor expansion, power series.

Q: 3.1.8. (!) Prove or disprove: Every tree has at most one perfect matching.

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Q: The tangents to the rectangular hyperbola xy = c² and the parabola y = 4ax at their point of interse...

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Q: Q2 /| Find a cubic polynomial of x (5, 147). given points (0, 2), (1, 3), (2, 12),

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A: We have to apply the pigeon hole principle to solve this problem.

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A: The probability of selecting two items whos individual probability are p and q is given by; P(x)=p·q

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Q: 2. Let the rref of a matrix A be, (1 0 0 1 2 0 -2 -5 0 -3 0 0 1 6. Determine A if the first, second ...

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Q: State the quadratic form of a general multivariate function in two variables and give the matrix rep...

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Q: Let R be the relation defined in the set A = {1, 2, 3, 4, 5, 6, 7} by R = {(a, b) : both a and b are...

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Q: Submit test d's = 60 yt - 27 , subject to the conditions that Vi A particle moves on a coordinate li...

A: Solution:-

Q: Compute * sin x dx. x4 + 1 p.v.

A: