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An implicity function is one that is not expressed in the form y = f(x) such as the equation in the question. Instead of rearranging the equation to make y the subject, the equation can be differentiated ...

A scalar quantity is one that only has magnitude while a vector has magnitude and an associated direction. For example, temperature is a scalar quantity because temperature only has magnitude/ size, there...

The method we shall use is substitution. We shall replace y each term by 'x + 1' so we are able to obtain an equation in one variable. x^2 + (x+1)^2 + 18x + 20(x+1) + 81 = 0. We now expand the brackets. x...

The Le Chatelier principle was estates that if there is a change in the conditions in a dynamic equilibrium system, the equilibrium of the system will move in order to counteract the change. The condition...

Multiply through by both denominators, giving us the equation (2x + 3)(2x + 1) - (2x - 8)(x - 4) = (x-4)(2x +1). If we expand the brackets, we arrive at 4x^2 + 8x + 3 - (2x^2 -16x + 32) = 2x^2 -7x -4. If ...