is there a shorter way to do this where you don't get decimals in your answer?

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Q: 1. Consider a new addition for real numbers, denoted by , and defined as a b = 3a + 3b, where is the…

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A: We have to find out the inverse Laplace transformation.

Q: 2. Considering a 2D rotation matrix R € SO(2), two 2D points x, y with coordinates (-√2, 2)¹, (1,…

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Q: A small company produces three types of goods. The profit function is given by P(x, y, z) = 5 ln(x +…

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Q: = [#1, #2, #3]T 2. Let T = 2x2 - 6x32 2 221 +2 ≤8 271 +372 +13 < 5 #1 -

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Q: 4. In each case, rewrite the given statement in the conditional form: then "If (a) When I stay up…

A: Part a) If I stay up late then it is necessary  that I sleep until noon Part b) If you eat an apple…

Q: Let S be the upper half of the ellipsoid S 1/ 5 = {(x, y, z) | + ² + ² + 100 = 1.22 20} with…

A: GivenLet and   S be upper of the ellipsoid So,

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Q: 12. Prove that if d divides a and d divides b, then d divides ax + by for all integers a and y.

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Q: Let f H²H² have the form f(x, y) = (x, g(x, y)). Determine the conditions on g(x, y) which imply…

A: Let such that .To find:The conditions on  which imply that f preserves the hyperbolic area.Give a…

Q: Consider the following data points. P₁(1, 8), P₂(2, 6), P3(5, 6), P4(6, 5), Pg(10, 1) (a) Find the…

A: The equation of the straight line, obtained using least squares method, is y=8.4882−0.685x.

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Q: Show directly from definition that if limx→2- f(x) = 1 and limx→2- g(x) = 4, then lim-2-f(x) · g(x)…

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Q: Let the Universal Set, S, have 193 elements. A and B are subsets of S. Set A contains 59 elements…

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Q: 6. Find the eigenvalues and corresponding eigenspaces for 1 3 2 -1 2 1 4 -1 -1 A = -

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Q: Determine the inverse transforms of the following. 2s 6 (a) (c) (S-2) (S-4) (b) 5s-8 s(s - 4) $²25…

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Q: 2 Divide, using the Egyptian method of division. (If you need to refer to the n a. 37 ÷ 15 b. 757…

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Q: Consider all binary operations on the set with two elements S={a,b} 1) how many binary operations…

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Q: From the text, the derivative of the function f(x) is f'(x) = lim h→0 following. lim h→0 f(x + h)…

A: The derivative of a function f is given by f(x)=limh→0f(x+h)−f(x)h.

Q: (b) V = R₂[X], W = R¹, By defined by = (1, X, X², X³), Bw T(a+bX+cX²) = (c) V = W = M2×2(R), Bv = Bw…

A: c) Given that vector spaces with bases are the following:       and Now defined linear map is Now

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Q: Based on the pattern, how many dots would be in the 35th figure? 1 dot 4 dots :00 12 dots 8 dots 16…

A: According to the given data, find the 35th figure dots.