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Calculate the value of 2^(–3) as a fraction in its simplest form.

To calculate the value of 2 -3 first we know that a negative exponent is equivalent to the inverse of the same number with a positive exponent. Therefore 2 -3 = 1/2 3 , the next step is to calculate 2 3 , 2 ...
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Answered by Joseff S. • Maths tutor
249437 Views

Calculate the largest share when £400 is shared in the ratio 1 : 2 : 5.

To calculate the largest share, first we need to find out how much each part that makes up a share is worth. To find out how much the smallest part is (i.e 1 part), we divide the value £400 by the sum of the...
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Answered by Joseff S. • Maths tutor
26311 Views

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
13707 Views

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
9839 Views

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
10858 Views