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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)=x²-x+1/4, add 7/4 to get x²-x+2 therefore x²-x+2 = (x-1/2)² + 7/4

squared numbers always positive so (x-1/2)²

Answered by Pearse M. • Maths tutor

10970 Views

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

Answered by Pearse M. • Maths tutor

7159 Views

Find ∫(4x - 2/(x^3)) dx

Using the integer rule 1/ (xⁿ) = x^-n question becomes ∫(4x - 2(x^-3)) dx

Then using the formula ∫xⁿ dx = (xⁿ⁺¹)/n+1 and assuming there may be a...

Answered by Pearse M. • Maths tutor

4131 Views

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 ...

Answered by Stephanie M. • History tutor

2403 Views

Explain how a bright line is formed by the diffraction grating at the first order diffraction angle

A diffraction grating is basically a series of very small, point-like light sources, where the adjacent ones are always a given distance away. To have a bright line, the light waves from all of the point-...

Answered by Abel B. • Physics tutor

19040 Views