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This question requires differentiating the equation to find where its gradient is equal to zero. Differentation is done via a simple equation -->  if y = xⁿ then dy/dx = nx^n-1

In order to answer this question, we must transform this equation for a circle into the general form of an equation of a circle; namely something like (x-a)²+(y-b)²=r². On...

To solve the equation in the form (ax + b)(x + c):

Method 1

1. Rewrite the x term as the sum of 2 different x terms. Start by multiplying the x^2 term and the final number term...

a) at most 960 ml

Let X be the volume of liquid in a particular bottle, then we want to find P(X <= 960). We first need to transform from X to Z (to the standard normal distrib...

The product rule states that y=uv and dy/dx=(u)dv/dx + (v)du/dx. As the equation is in this form we can let u=2x and v=sinx. Therefore du/dx=2 and dv/dx=cosx. Substituting for u and v we get dy/dx=(2x)(co...