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y= ln(4x-7)+18 y= a(x^2 +b)^1/2
At x=2 dy/dx = dy/dx and y =y
At x =2 y = ln(8-7) +18 y = ln 1 +18 y =18
At x = 2 18=a(4 +b)^1/2 18/(4+b)^1/2= a
y=ln(4x-7)+18dy/dx= 4/(4x...

a) Integrate the given expression using integration laws we have learnt to give [(x^4)/4 + (3(x^2))/2 + 2x ] and you do not need a +c constant as we have limits.b) Substitute the limits into the equation ...

To work out the total volume of the composite solid, we need the volumes of both the cone and the hemisphere. GCSE Maths students are expected to know these respective formulae; volume of a sphere = ⁴/₃πr...

Firstly rearrange the quadratic such that the coefficient of x² is positive (already done in this example) and the quadratic is in the form of ax² +bx + c, then solve for ...

For N to be not divisible by 3, N can either be of the form 3k + 1 (1,4...) or 3k + 2 (2,5...), where k is an integer.
The proof can then be done by checking both 3k + 1 and 3k + 2 when N is squared...