Let ℓ be a line and let H be one of the half-planes bounded by ℓ. Prove that H ∪ ℓ is a convex set.

Q: Let V be the vector space of all functions from R  into R; let V\index{e} be the subset of even…

A: Let V be the vector space of all functions from R into R. and                Ve  = { f(x)  :  f(-x)…

Q: =(x,y) = 2x²+√6xy + y²

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Q: 3. Sketch the graphs of y = x² + 4, x = 3, x = 0 and y = x. Shade the region bounded by the curves.…

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Q: (d) If W is a subspace of R", then (W¹)¹ = W. (e) If W is a subspace of R", then WW¹ = {0}. (f) For…

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Q: Finite Math - Graphing Linear Inequalities Purchasing   Enormous State University's Business School…

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Q: A= -6-2j B = 12 2137° the (cos 5° + jsin 5°) C = D = 21e 520 i 52° - 1. A + B - C

A: A=-6-2jB=12∠137°C=16(cos 5°+jsin 5°)D=21e-52°i

Q: Suppose the series, converges to a number S. Let R, S-S n=1 Determine the truth of the following…

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Q: Another Field 13 We'll let Q(√2) represent the set of numbers that can be written in the form a+b√2,…

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A: Solution:  We  have  to  first  recall the  formula  of  directional  derivatives of  a  function…

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Q: Suppose dy/dx= 3/√1-(3x)^2 and y(0)=4. what is y(pi/12)?

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Q: Consider the ordered bases B = ((1, 2), (-1,-1)) and C = ((-3, 1), (3, 1)) fo a. Find the transition…

A: B=1,2,-1,-1C=-3,1,3,1E=1,0,0,1 As per the guidelines I am answering first three parts only. Kindly…

Q: Problem 1. Given the curve Find the following at point P(1, 0, 0). 1. the unit tangent. 2. the unit…

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Q: Find the gradient field F = Vip for the potential function p= 2x +2y for x ≤4 and y ≤ 4. Sketch a…

A: The answer provided below has been developed in a clear step by step manner

Q: 14. Gender Selection The Genetics and IVF Institute conducted a clinical trial of the YSORT method…

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Q: Write the elements of the following in terms of powers of X: 1. Z₂ / 2.Z₂/ 3.Z3/

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Q: FIND: Minimal annihilator, L, of y = (x² − 2x + 1)e-²x

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Q: ar Transformations y (7) + rank (T) = dim (V) in this case, namely,

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Q: Problem #4: Let Problem #4: A 0 0 -65 35 0 1 0 0 0 1 35 -12 0 -65 0 -12 Find the eigenvalue…

A: Definition :-  Let  'A' be a square matrix of order  'n'  over the field 'F' . Then a non - zero…

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Q: The equation of a parabola is y=x²-4x-5. a) Express this equation in factored form and state the…

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Q: Consider the quadric surface given by Enter the matrix A in the box below (a) Express this equation…

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Q: Problem 8. Let CCR be a closed convex set, and suppose that X₁,..., XK are on the boundary of C.…

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Q: Suppose that A is the set {a, ß, y, d, ε}. A.) Construct a relation r on A that is a partial…

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Q: = Find the inverse Laplace transform f(t) = £¹{F(s)} of the function F(s) = f(t) = = L 6s+2 s² + 100…

A: The function: Fs=6s+2s2+100. We have to find the inverse Laplace transform of the given function.

Q: The matrix has two distinct, real eigenvalues. a) 5) The smaller eigenvalue is = The larger…

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Q: Solve the LP problem. If no optimal solution exists, indicate whether the feasible region is empty…

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Q: Problem #6: Consider the linear transformations S: P3 → P3 and T: P3 → P3 defined as S(p) = p(0)x²…

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Q: equivalent to symmetry MV applied to the original figure (Figure 5), so we can express the final…

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Q: Suppose that a, converges, but not absolutely. Then (a) both series (an] ±an) = ∞o, and (b) liman =…

A: Suppose that ∑an converges, but not absolutely. Then a) both series ∑an±an=∞, and b) limn→∞an=0. We…

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Q: x7 = x8 = x9 = (ii) To see how well the term x N you found in the previous part approximates √946,…

A: note : Since you have posted multiple questions, we will provide the solution only to the first…

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Q: 7y" +46y" 175y' - 1150y = 4e t y(0) = 0 y (0) 0 y" (0) = 1 into an algebraic equation by taking the…

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Q: When factoring it's important to factor out the GCF because_____________.

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Q: -2 2 0 C 0 1 5 -235 (ii) (iii) For any bin R, the equation Cx=b has a solution. (If false, give an…

A: According to guidelines we can do only first three sub parts thank you.   A matrix is in row…

Q: In problems 9-13 below, let DR be the 2x2 square centered at (1,0), DS be the 2x2 square centered at…

A: (9) To Evaluate: intRf where f(x,y)=x+y, and the surface R is given by 2X2 square centered at (1,0).…

Q: Suppose that for x = 3, the predicted value is  = 5. The data pair (3, 5) is part of the sample…

A: A residual is defined as the difference between an actual value (observed value) and a predicted…

Q: Find Vw. w = 6 ln √10x² + y² +82² NOTE: Give your answer in unit vector notation; that is, in terms…

A: w=6ln10 x2+y2+8 z2Find ∇w

Q: ) Use power series to solve the initial-value problem. Answer: y = 8 n=0 2n + 8W n=0 y" + 4zy'…

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