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If f(x) = 2x+5, g(x) = 8x-7 and f(x)=g(x). Find the value of x. Show your working.

f(x) = g(x), 2x+5=8x-7, 12=6x, 6x=12 therefore, x=2.
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Answered by Natalie R. • Maths tutor
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How do you integrate (2x)/(1+x^2) with respect to x?

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'(x)/f...
Answered by • Maths tutor
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How do I derive Kepler's 3rd law using Newton's Law of gravitation, in the case of a circular orbit?

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: r 3 ∝ T 2 (this is the result we want!) We know Newton's Law of...
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Answered by Greta C. • Physics tutor
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Explain how a leaky heart valve can cause health issues

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 tric...
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Answered by Vishnu S. • Biology tutor
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How do I know which is the null hypothesis, and which is the alternative hypothesis?

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 healthier, w...
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Answered by Tegan C. • Maths tutor
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