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f(x) = g(x), 2x+5=8x-7, 12=6x, 6x=12 therefore, x=2.

The key here is to recognise that this is in the form f'(x)/f(x). We can use the idea that integration is the inverse of differentiation, and the knowledge that the derivative of ln(f(x)) is equal to f'(...

Kepler's 3rd law states that the cube of the radius, r from a planet is directly proportional to the square of the orbital period around it, T: r³ ∝ T² (this is the result we want!)<...

A leaky heart valve is called valve regurgitation and is caused by the valves not completely closing. Any valve in the heart can have a regurgitation whether that is the aortic, mitral, pulmonary or the t...

Generally, the null hypothesis is the one we want to reject, and the alternative is the one we want to prove is true. For example, if we were testing whether growing in the Sun made a plant grow healthie...