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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...

First solve the equation with only one unknown to find y:y-6=15Add 6 to both sides to get the value of y:y=15+6y=21Now there is only one unknown we can solve for x:x+21=11x=11-21x=-10Check the values are ...

While this can appear intimidating at first, the key to simplifying this expression is through factorising and identifying common factors. Let's start off by factorising the denominator as this is simpler...