Exercises 3.1 A. Let W = {(s, 3s, -s): sreal}. Show that W is a subspace of R³. 2. Let U = {(s, -2s, s + 1): s real}. Show that U is not a subspace of R³.

Q: 2. Solve utt = c²uxx, u(x, 0) = log(1 + x²), u₁(x, 0) = 4+x.

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A: See next step for answer

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A: here we need to model this question as a mathematical maxizing problem.

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Q: كو 135 ی۔ ما ? 120 و

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A: Given,        z216-x281-y29=1, in the XZ-plane.

Q: b. The price of a car is $25,000. You have saved 25% of the price as a down payment. After the down…

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Q: Let v= Answer: Find a basis of the subspace of Rª consisting of all vectors perpendicular to v.…

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Q: What is the degree of exactness m of the quadrature rule Q[ƒ; 0, 1] = ½ ƒ(;²(1 − 3)) + ½ƒ({(1 + ))?…

A: we check  by hard and trial method.  the desired equation to check up is ∫01f(x)dx= 12f(12(1-13))+…

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Q: A: Find the solution to the following linear programming problem using the simplex method Max…

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Q: b- 2 (1+hi + 2 (1+x) = (h²x15

A: For a function: z=f(x, y), the set of real values of x, y for which f(x, y) is defined is called the…

Q: III. WITHOUT SOLVING the given problem, DEFINE the variables and unknown quantities, and SET-UP ONLY…

A: Solution:   Cost of one book case is 400 pesos.   Then, total cost for 300 - 2x book cases is…

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Q: 1. Using all the letters of the word GIFT how many distinct words can be formed? A. 22 words words…

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Q: 6. Use Newton's method to find solutions accurate to within 10-5 for the following problems. et + 2x…

A: We are to answer a. , b. and c. here.

Q: 5.2.2. a) Suppose that a < b and n € N is even. If f is continuous on [a, b] and f f(x)x"dx = 0,…

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Q: What is the solution of the differential equation (D³ +2D² +D+2) y=0? Oy=C₁e²+ C₂ cos x + C3 sin x…

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Q: X 1 + ; in the form of inequality 3 2 3 2. x(x + 1) ≥ 2x + 6; in the form of interval(s) 3. x(x² −…

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A: Sol:- The value of table for T and v T 700 720 740 760 780 v 0.0977 0.12184 0.1406 0.15509…

Q: B: Iraq Glass Industries Company produces two types of products, A and B, each one goes through two…

A: We will form a linear programming problem (LPP)  to maximize company profit .

Q: Let f: X→Y. Let y E Y and BCY. Describe the difference between f-¹(y) and f-¹(B)

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Q: (The hammer blow) Let p(x) = 0 and √(x) = 1 for [x] 3a/2. Continue in this manner for each case.]

A: Given Data: Let us consider the given equation is ux,t=12c∫x-ctx+ctψsds =12clength ofx-ct,x+ct∩-a,a…

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Q: 11. In how many ways can a group of 5 men and 2 women be made out of a total of 7 men and 3 women?…

A: See next step for answer

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Q: ) Let S be the non-empty set containing all a for which f(x): = monotonic for all xe R. Find S. 4a-7…

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Q: TEST FOR HOMOGENEITY: 4. e √x x-2xy x - y

A: A function f(x, y) is said to be homogeneous if f(Kx, Ky) = Knf(x, y)  where n is any real number…

Q: JJJ Evaluate the triple integral E tetrahedon with vertices (0, 0, 0), (6, 0, 0), (0, 4, 0), (0, 0,…

A: Given information Vertices of tetrahedron are 0, 0, 0, 6, 0, 0,  0, 4, 0,  0, 0, 9. Triple…

Q: 2.30 Let r denote a position vector r = x= xiêį (r² = x₁x₁) and A be an arbitrary constant vector.…

A: Given: The position vector r=x=xie^ir2=xixi and A be a constant vector  To Show : a) ∇2rn=nn+1rn-2…

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Q: (a) If f, is integrable on DCR, n € N, and if Ef uniformly converges to f, then f is integrable on D…

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Q: What is the degree of exactness m of the quadrature rule Q[f; 0, 1] = = {}ƒ(/(¹ − ») + {{ƒ(²/(1¹ +…

A: Given : quadrature rule       Qf; 0, 1=12f121-13+12f121-13 To find : degree of exactness m of the…

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A: Given :  f(x) = 3cox4x + 10cos3x + 6cos2x - 3,  0 ≤ x ≤ π To find :  The intervals in which the…

Q: 4. Find the Fourier transform of f(r) given by (b) - {* f(x)= e if-asasa otherwise

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Q: Prove the following identity for any positive n≥1 1 =12 = n(n+1)

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Q: Συντηρη n=1

A: We will use the fact that a series ∑an  will be convergence if an+1an&lt;1

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Q: 4. Find the Fourier transform of f(x) given by (b) (show the full calculation). f(x) = = fe if-assa…

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Q: 7. How many 3-digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9, which are divisible…

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