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a)    First we can rewrite y=arccos(x/2) as cosy = x/2 which allows us to use implicit differentiation to easily differentiate each side. Taking d/dx of each side gives u...

In general, the equation of a line is y-y0=m(x-x0), where m is the gradient and (x0,y0) is a point on the line. We need to find the gradient and a point on our tangent. Step 1: Find gradient. Since our ta...

There is a total of 7! possible ways in which the seven children can be seated on the bench. The number of favourable arrangements when four boys are seated on one side and three girls on the other side i...

1 ) Identify the information given in the question:Total number of cupcakes bought: 125Number bought by Emma is 50% more than Robin: mathematically we write that was Emma = 1.5 Robin as 50% = 0.5 in decim...

Apply FOIL (First, outside, inside, last): (x + 4)(x - 5) = x² - 5x + 4x -20 = x² - x -20 x(x + 4)(x - 5) = x( x² - x -20 ) = x³ - x²- 20x