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How do I solve the simultaneous equations 5x - 3y = -1 and 3x + y = 5?

One method of solving these is by elimination . We can try to subtract a multiple of one equation from the other to cancel the x's (or y's). 5x - 3y = -1 (A) 3x + y = 5 (B) In this case, we can add 3*(equati...
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Answered by Alex K. • Maths tutor
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What is the difference between personification, anthropomorphism and pathetic fallacy?

These three literary devices are often misidentified and confused with one another. However, there are some easy ways to work out which one you are observing in use in a given text. Personification refers to...
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If y = 5x^3 - 2x^2 + 2, what is dy/dx?

Differentiation can be done term-by-term, so we can treat the 5x 3 , -2x 2 and 2 separately. We can also 'take out' the coefficients: to differentiate 5x 3 , for example, differentiate x 3 first and then mul...
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Answered by Alex K. • Maths tutor
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Explain the different types of wave.

There are two different types of wave: longitudinal and transverse . When you hear the word "wave" you are probably thinking of a transverse wave. Imagine you are floating in the sea. The waves of ...
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Answered by Harry C. • Physics tutor
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Rationalise the complex fraction: (8 + 6i)/(6 - 2i)

The problem with this fraction is the "i" on the denominator, it is not rational. To rationalise this fraction we use the complex conjugate . This sounds more complicated than it is. If a + ib is a...
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Answered by Harry C. • Maths tutor
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