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First we must multiply out the brackets, using FOIL (first, outer, inner, last). This gives f(x) = -x^3 + 5x^2 - 3x + 15. Alternatively you could leave the brackets as they are, and use the product rule t...

Quarks are the building blocks of protons and neutrons, as found in the nucleus of atoms. They are as far as we know, fundamental particles, but this could change in the future. There are 6 types, named u...

Differentiation is a very important tool for mathematicians. Although finding the gradient of a line can seem to lack a point, it does have some very important applications. For example, in mechanics the ...

1. y = cos2θ . 2) cos2θ = 1 - 2sin²θ. 3) x = 2sinθ. 4) x² = 4sin²θ. 5) (1/2)x² = 2sin²θ. 6) y = 1 - (1/2)x².

An advantage of open questions is that respondents are given the freedom to elaborate on their answers providing in-depth accounts compared to closed questions. A disadvantage is that responses may lack r...