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Integrate dy/dx = 2x/(x^2-4)

Integrate dy/dx = 2x/(x 2 -4). We can answer this question using integration by substitution, where we set u = something in terms of x. In this case we are going to set u = x 2 -4 (the denominator). When we ...
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Answered by William R. • Maths tutor
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Find the first three terms in the binomial expansion of (8-9x)^(2/3) in ascending powers of x

Rewrite (8-9x)^(2/3) as (8(1-(9/8)x)^(2/3)=4(1-(9/8)x)^(2/3). Now apply the C4 binomial formula in the formula booklet, so: 4(1 - ((9/8)x)^(2/3)= 4[ 1 + (2/3)*((-9/8)x) + (2/3)((-9/8)x)^2 .....]= 4[ 1 - (3/4...
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Answered by Anthony R. • Maths tutor
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The curve has the equation y= (x^3)/(2x-1). Find dy/dx.

To differentiate a function with respect to (wrt) x you multiply the function by the power and then lower the power by one. For example, if f(x)=x^3, then to differentiate you multiply the function by 3 (the...
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Answered by Poppy C. • Maths tutor
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A school has 1200 pupils. 575 of these pupils are girls. 2/5 of the girls like sports. 3/5 of the boys like sport. Work out the total number of pupils in the school who like sport.

As we are told the number of girls that are in the school, our first step should be to calculate the number of boys in the school through a simple subtraction (1200-575 = 625). After this we are told that 2/...
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Answered by Gianluca B. • Maths tutor
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A radio sells for £63, after a 40% increase in the cost price. Find the cost price.

X+2/5X = 63 or 63 = 140% First we need to understand that the original price (X) has been increased by 40%. Hence, by 2/5 (40/100 = 40%) of its original value, in other words, 2/5X. To find the answer we the...
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Answered by Gianluca B. • Maths tutor
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