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Q: 7. Evaluate ſxy dA as the limit of a sum, where R is the rectangle with vertices (0, 0), and (xi,…

A: We have to evaluate ∫∫RxydA as the limit sum , where R is rectangle with vertices (0,0),(0,1), (1,0)…

Q: Let CE Rxn be a matrix such that xCx>0 for all nonzero vectors x ER". Prove that C is nonsingular.

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Q: Use Variation of Parameters e2x 1+ e²x (D² - 3D + 2)y=

A: (1). Given,                  D2-3D+2y=e2x1+e2x.

Q: Find E₁ = 0 1 Consider the following Gauss-Jordan reduction: 2 -5 -2 0 0 1 E₂ = 0 2 ⠀⠀⠀⠀⠀ 1 -2 0 → 1…

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Q: Let T: R³ → Rº be a linear transformation whose standard matrix is 3 3 1 A Enter the vector in the…

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Q: Question 1. Consider the points P such that the distance from P to A(2, −5, 0) is twice the distance…

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Q: Consider the 6-elements set A = {a, b, c, d, e, f}. How many subsets of the set A have 3…

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Q: 7.2. A consumer has a utility function u(x₁, x₂) = max{₁, 2}. What is the consumer's demand function…

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Q: If β is a zero of x2 +x + 2 over Z5, find the other zero.

A: Given: The expresion x2+x+2 over  Z5 have β as zero. To find: The zero of the given expression.

Q: Substitute y=ex into the given DE to determine all values of the constant r for which y=erx is er…

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Q: 12. Shove that 53 103 39|53 1⁰ +103

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Q: The coefficient of x6y12 in the expansion of (x + y)18 is ___________.

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Q: Find an equation of the plane with the given characteristics. The plane contains the lines given by…

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Q: ) Given the first-order system i(t) = u(t), x(1) = 3. The performance measure J = 2² (5) + [² / ²…

A: Given: In this problem, the given details are The given first-order system is x˙(t)=u(t)  ,  x(1)=3…

Q: Exercise 4 Let (fn) be a sequence of functions defined by In(2)=√(n.2n}(2). 1. Prove that (fa) is…

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Q: Applying the integrating factor method to the DE + y (² + ¹) = ²/1, t > 0, y'+y transforms the DE…

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Q: Find the change of basis matrix from B₁ to B₂. B₁ = OLD 0 -8 eBook 4 B₂ = 2 -3 -1 3 7 4 (HH) -2 2 -8

A: The given bases  B1 and  B2  are ,   B1 =  542 ,    8   0-8  , -3   3   2    and             B2 =…

Q: Find the kernel and range of each of the followinglinear operators on P3: L (p(x)) = p(0)x + p(1)

A: We know that Pn is the vector space of all the polynomials of degree less than or equal to n. This…

Q: 1. Let 3 be the permutation α, β € Σ3 such that Here a² = aa. group of {1,2,3}. Find two…

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Q: 9. As a sled is pulled over the top of snow, the frictional force on the sled varies due to the…

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Q: Given: dP = 0.3(1200)-1)P, where P(t) is population at time t. dt

A: An initial value problem is an ordinary differential equation together with an initial condition…

Q: Approximating the shaded area with the (a) Trapezoidal rule and a step size of h=1 yields square…

A: (a) Given h = 1 and from figure, lower and upper limits are 1 and 3.  The required formula is ∫abydx…

Q: 1. Let n be a positive integer and a, 6 € Z. Show that ab € Z. In other words, show that ZX is…

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Q: Tracksaws, Inc. makes tractors and lawn mowers. The firm makes a profit of $30 on each tractor and…

A: Solution: Formulate a linear programming model for this problem. Use the graphical method to solve…

Q: In Exercises. use an iterated integral to find the area of the region bounded by the graphs of the…

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Q: If the Accumulated Value of an investment at time t is AV₁ = 1.2+.1t², what is & when t=2? A. .05 B.…

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Q: Let n > 1. We have > φ(n) = Σμ(α) din

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Q: 35-40 Find the functions (a) fo g, (b) gof, (c) fof, and (d) go g and their domains. 35. 37. f(x) =…

A: We are given f(x)=1x, g(x)=x+1 to find the compositions of the function (fog(x), gof(x), fof(x),…

Q: Customers buy 11 units of regular beer and 17 units of light beer monthly. The brewery decides to…

A: Given :- Customer buy 11 units of regular beer and 17units of light beer monthly,

Q: Use Green's Theorem to evaluate the line integral of F = = (x², 7x) around the boundary of the…

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Q: Find the values of a, b, and c that make the following matrix symmetric. 3 a 2-b 4 0 a+b 2 7 C…

A: Given matrix is 3a2-b40a+b2c7

Q: Why can’t the nearest-neighbor method with a (4, 2) binary linearcode correct all single errors?

A: Let C be a binary linear code such that it can correct any single error with the nearest neighbor…

Q: (EQUATION OF VALUES) What single payment at the end of 6 years would replace the following debts? A.…

A: Given that the amount is compounded semi-annually with 8.5% interest.  Also given that, Debt1:…

Q: Let CE Rxn be a matrix such that xCx > 0 for all nonzero vectors & Prove that for k= 1,...,n, the…

A: Given : xTCx > 0 , C∈ℝn×n , Ck  is nonsingular . To Prove : yTCky > 0 , y∈ℝk

Q: 1. Let K be a subgroup of R*. Let H = {g E GL(n, R): det (g) E K}. Prove that H is a subgroup of…

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Q: The distance between the centers of the following two spheres: is x²-58x+y2+36y+z²=-1164,…

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Q: For each series, determine whether it converges absolutely, converges conditionally, or diverges.…

A: (a) ∑n=0∞-1ncosn3n-2 it is known that a series ∑nan is absolutely convergent if ∑nan is convergent…

Q: The bartender is totally amazing (must have studied physics). She slides your beer with an initial…

A: Initial velocity = 11.188ft/s d = 120.079 inches 1 Feet =12 inches 1 Inch = 2.54cm Notations Used :-…

Q: For f(x, y), find all values of x and y such that f(x, y) = 0 and f(x, y) = 0 simultaneously. f(x,…

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Q: Find all values of k for which the given augmented matrix corresponds to a consistent linear system.…

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Q: 2 2 1+ 5+² µ² = (1 + 2/² ) E" - M+² = 2

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Q: Du те Әи +(-u) =y-x. ду

A: Given P.D.E u-y∂u∂x+x-u∂u∂y=y-x ∴dxu-y=dyx-u=duy-x Then  dx+dy+duu-y+x-u+y-x=dx+dy+du0 Also…

Q: proof that it An ↑ then Linn An= An 608 Lim An = An n nzl it and then Lim An

A: Given: An is sequence of sets . To show : limn→∞An=∪n=1∞An if A1⊂A2⊂A3⊂......  and limn→∞An=∩n=1∞An…

Q: For two real numbers x and y, if 2x + 3y > 7. Prove by contradiction: 18, then either x ≥ 3 or y ≥…

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Q: Consider the DE: tant (y")6 + 7e²t (y")10 - 2ty' = 87t² +6t³+1 + a) Its order is b) Its degree is (y…

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Q: Find the inverse of the matrix B = B-1 - absin (a) 131 188 43 151 57 151 79 151 f di 8 40 151 151 21…

A: Solution:  To find inverse of the given matrix B And use the desmos matrix calculator with all…

Q: 2. Suppose a space curve ř₁(t) = (f(t), g(t), h(t)) has curvature (t) and torsion 7(t). (a) What is…

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Q: Prove: For all prime number a,, b, and c, a² + b² ‡ c². [Hint: a² = c² − b² = (c − b)(c + b)]

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Q: Kelly has 1,400 ft. of irrigation piping he wants to use to irrigate his back lawn. He wants to lay…

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Q: A certain invasive species of fish was introduced in a small lake and their  population growth can…

A: Given: A certain invasive species of fish was introduced in a small lake and their population growth…