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Show that x^2 - x +2 is positive for all values of x

(x-1/2) 2 = (x-1/2)(x-1/2)=x 2 -x+1/4, add 7/4 to get x 2 -x+2 therefore x 2 -x+2 = (x-1/2) 2 + 7/4 squared numbers always positive so (x-1/2) 2 >= 0 therefore (x-1/2) 2 + 7/4 is always positive
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Answered by Pearse M. • Maths tutor
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Vectors a and b are defined by a = 2i + 3j and b = 4i - 2j, find 3a-b in terms of i and j

3a = 6i + 9j -b = -4i + 2j 3a-b = (6i-4i) + (9j+2j) = 2i + 11j
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Answered by Pearse M. • Maths tutor
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Find ∫(4x - 2/(x^3)) dx

Using the integer rule 1/ (x n ) = x -n question becomes ∫(4x - 2(x -3 )) dx Then using the formula ∫x n dx = (x n+1 )/n+1 and assuming there may be an integer value (+c) the answer is 2(x 2 ) + x -2 + c
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Answered by Pearse M. • Maths tutor
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How should I structure my essay?

As much as you may not want to hear this, there is no absolute, correct way to structure an essay. The essay structure that you use really depends on the question that you are being asked. However, there are...
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Answered by Stephanie M. • History tutor
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How to write an algebraic fraction in a given form e.g. (3+13x-6x^2)/(2x-3) as Ax + B + C/(2x-3) where A, B and C are natural numbers

I would break this down into simple steps: Step 1 - Equate the 2 expressions: (3 + 13x - 6x 2 ) / (2x - 3) = Ax + B + C / (2x - 3) Step 2 - Multiply both sides by the demoninator: 3 + 13x - 6x 2 = (2x - 3)*A...
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Answered by Alex T. • Maths tutor
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