Topology let X be a let discrete Space ACX. Find (i) int (A) (ii) ext (A) (iii) boundry of A and b(A)
Q: a) Find the Laplace transform of h(t)= cos 5t-3u (t-5) cost (1) Jutransfo 2133 Ordinc Lapl
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Q: 10. x 유 3 4 X, x, x(0) = (2 ; see Problem 2.
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Q: Suppose that Y = Z - X is independent of Z and of X. Show that Y is a constant.
A: Given that Y=Z-X. To show: Y is a constant function.
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Q: Suppose we know that for a function f we have Vf(x, y) = (6x, 6). Find the directional derivative of…
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Q: What pattern can be seen in our surroundings?
A: There are many mathematical patterns in the surroundings.
Q: A: Find the solution to the following linear programming problem using the simplex method Max…
A: find the solution to the following linear programming problem using the simplex method max…
Q: 16. Determine whether the statement is true or false. If it is true, explain why. If it is false,…
A: Introduction: The differentiability is an advanced property shown by a continuous function. From the…
Q: Find the elementary matrix E₁ such that E₁A = B where A = 8 9 1 7 -17 −1 18 1 10 and B = 18 7 8 1…
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Q: Problem 2.2. Consider the ODE u(t)= u(t), 0 < t < 1; u(0) = 1. Compute its Galerkin approximation in…
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A: Given that: X=Inner product space. The objective is to show that the projection theorem holds if and…
Q: Let a > 3 be a fixed number. Evaluate the following improper integral -3)² dx
A: Given improper integral ∫a∞1x-32dx
Q: 2. U = {1, 2, 3, 4, 5, 6, 7}, A = {1, 2, 3}, B = {2, 4, 6} and C = {1, 4, 7} i. Find the value of A'…
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Q: Q.2: Find the trigonometric Fourier series of the periodic function f(t), and show if it is odd or…
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Q: solve the following linear programming problem using graphical method Min (z) = 300x₁+200x2 S.T.…
A: Min(z)=300x1+200x2S.T.20x1+20x2≥16030x1+10x2≥120x1≥0, x2≥0 We have to solve using graphical method
Q: B/ solve the following linear programming problem using graphical method Min (z) = 300x₁+200x2 S.T.…
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Q: B/ Put the following program in matrix standard form Min (z) = 10x₁+11x2 S.T. X1+2x₂ ≤ 150 3x₁+4x₁ ≤…
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Q: Consider the given function k (x) = x² + 12x+35 (a) Write the function in vertex form. (b) Identify…
A: Note: Hi! Thank you for the question, as per the honor code, we are allowed to answer three…
Q: 5.12 Given A = I 0 0 1 0 0 0 2 3 4 S/ find a permutation matrix P, a unit lower triangular matrix L,…
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Q: Q1 a) Find the distance between the points A(-5, -6, 2) and the plane that includes the y-axis and…
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Q: 2. Maximize profit = 2X + 4Y Subject to; i. ii. X + Y ≤ 40 2X + Y ≤ 60 X X X,Y ≤ 50 ≥ 5 ≥ 0 Fine the…
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Q: Use a software program or a graphing utility with matrix capabilities to write vas a linear…
A: Consider the given vectors, v=5, 2, -9, 11, 8u1=1, 2, -3, 4, -1u2=1, 2, 0, 2, 1u3=0,1, 1, 1, -4u4=2,…
Q: a) 2-3u(t-5) cost = -t Find the 33 Ordine Lap of
A: The given function is ht=-t cos5t-3ut-5cost To find: the Laplace transform of the given function.
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A: There are total 364 students in the first year including girls and boys. We have to find the number…
Q: B/ Put the following program in matrix standard form Min (z) = 10x₁+11x2 S.T. X₁+2x₂ ≤ 150 3x₁+4x₁ ≤…
A: Given Min z=10x1+11x2S.T.x1+2x2≤1503x1+4x2≤20036x1+x2≤175x1, x2≥0 which can be written as Min…
Q: Question 2 a) { ] Show that the equation 4x8y + 12z + 2x² + 2y² + 2z² = -20 represents a sphere, and…
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Q: s{3 – 9t* + 8sin(2t) + tel} 2. 7 2-¹ { / +(6+²1²5 - 11/12 + 3-2 3s s²+49 :}
A: 1. L3-9t2+8sin2t+t5e3t 2. L-19s4+7s+15-11s-2+3ss2+49
Q: het H be a Hilbert space. Consider A, B & BL(H) Prove that || A* || = || A|| and | A²A|| = ||A||²2 =…
A: Let H be a Hilbert space. Consider A,B∈BLH To prove : A*=A and A*A=A2=AA*
Q: a) 27 " dᎾ 5 + 4 sin 0
A: To solve the given integral ∫02πdθ5+4sinθ
Q: 5. Which of the following formulas are in CNF? a. (q^r) ⇒ (p ^ (q Vr)) b. p^((q^r)) ⇒ (q^r) c. d. ¬q…
A: To find: which of the following are in CNF.
Q: N -10+ -30+ (x)+(x)=x too-
A: Graph of h(x)=f(x)+g(x) is given where f(x) is cosine function. To determine: The function g(x).
Q: 3. Solve the following boundary value problem =-3₁ +5₂] V₁=₁+₂ 31(0)2, ₂(0)=1
A: The given problem is to solve the given boundary value problem with given boundary conditions by…
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A: Introduction: One of the fundamental shapes in geometry is the triangle. The smallest polygon is a…
Q: Solve the equation. (3x²)dx + (y - 3x³y-1)dy=0 What is an integrating factor for the equation? H(y)…
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Q: 2. Does Picard's Theorem imply the following initial value problem has a unique solution? Explain y'…
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Q: Sketch and identify the curve defined by the parametric equations x = sin²t, y = 2 cost
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Q: ction f(x, y) = [x² + y² if x # (0,0) if x = (0,0) over the x-axis, the y-axis and the two bisector…
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Q: у 10 y 10
A: Given rt=t7i+t-1j We know that rt=xi+yj Therefore comparing we get xt=t7t=7xyt=t-1 substitute the…
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Q: The demand function of a product is q = 75-p².2≤p≤7. where q is the quantity of the product that can…
A: given demand function of the product is q=75-p2 2≤p≤7 where q if the quantity of the…
Q: C. Solve the problem by working backwards applying Polya's 4-step in problem solving. In consecutive…
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Q: Determine the radius and interval of convergence for the following power series. 8 n=1 (-1)"n 4" -…
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- Which part Given or Prove of the proof depends upon the a hypothesis of theorem? b conclusion of theorem?Which lines or line segments or rays must be drawn or constructed in a triangle to locate its a orthocenter? b centroid?Let (R,d) be diserete metric space then R is not compact . True or false.??
- Pseudometric spacesProve that topological space E is not homeomorphic to the spaceY = {(x, y) ∈ E^2 : y = ± x} (E represents R equipped with Euclidean distance, E^2 represents R^2 equipped with euclidean distance)19. A research facility is located at the centroid of the triangle made by highways connecting three towns as displayed.
- Let (X,m, µ) be a major space and (Y,?) be a topological space. Let f:X→Y be a function. Assume Ω={E⊆Y:f^-1 (E) ∈m} prove that Ω is a σ- algebra. please do not provide solution in image format thank you!Derive the De Moivre's Theorem?Let H be the set of all points (x, y) in ℝ2 such that x2 + xy + 3y2 = 3. Show that H is a closed subset of ℝ2 (considered with the Euclidean metric). Is H bounded? Bear in mind I can't use facts about continous functions. So this is what I learned in this chapter: Balls/neighborhood centered at a point a consists of all points strictly within some radius r of the point. A set is open if every point in the set has a small ball around it that is contained in the set. A set is closed if its complement is open, and sequentially closed if every sequence in the set has all accumulation points in the set. We proved these are equivalent. A set is sequentially compact if every sequence in the set has accumulation points in the set. A set is compact if every cover by open sets has a finite subcover. Compact sets are sequentially compact. In the reals, compact, sequentially compact, and closed + bounded are equivalent.
