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This is a classic "picture frame" resolving forces question. By resolving horizontally we can use the "assuming the particle remains stationary" meaning the forces must cancel...

Firstly, we need to make the unknown variable(p) the subject of the formula. As this is the denominator of a fraction we can multiply both sides of the equation to get rid of the denominator on the right ...

First, we're going to split this 1 fraction into 2 fractions. Let (x+2)/((x+5)(x-7)) = A/(x+5) + B/(x-7) then multiplying by (x+5)(x-7) gives A(x - 7) + B(x + 5) = x + 2 multiplying this out we achieve Ax...

a prime number is a number which is only divisible by itself and one e.g 2, 3 , 5, 7when writing a number (in this example 36) as a "product of its prime factors" you need to find the prime numb...

Given that the equation is quadratic and has two distinct roots , this implies that the discriminant (b² - 4ac) in the quadratic formula is equal to zero. Comparing terms a = (k+1), b = (5k -3)...