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Problems like this need to be broken down into steps: i) Factorise, ii) solve and iii) check. The aim of this question is to find values of ...
We know from trigonmetric identities that cos(2x) = 2cos^2(x) -1, therefore cos^2(x) = 0.5(1+cos(2x)).
Subbing this in gives the following integrand: 0.5(1+cos(2x))sin(2x).
We can now split ...
Questions like this ask you to solve an equation; this means to find a value of x that when put into the equation allows each side of the equation to be equal.
There are th...
Numerator and denominator of a fraction 6/16 can be divided by 2 to get 3/8.
Numerator and denominator of a fraction 9/24 can be divided by 3 to get 3/8.
Numerator and ...
By the chain rule ds/dt = ds/dr * dr/dv * dv/t. At a height of r, the water fills a hemisphere. So ds/dr = 6pir. dr/dv = 1/(dv/dr), so we need to find dv/dr. Students should have the formula for the v...
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