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Circle theorem: angle in a semi-circle is a right angle.Therefore angle BAE = 90 + 31 = 121 degrees ABDE is a cyclic quadrilateral and:Circle theorem: Opposite angles in a cyclic quadrilateral sum to 180 ...

dx/dt = 3(t-1)²dy/dt = 3 + 16t^-3dy/dx=(dy/dt)(dt/dx) dy/dx = 3 + 16t^-3 / 3(t-1)²
At t=2 dy/dx= (3 + 16/8) / 3 = 5/3 Gradient of the normal = -3/5with t=2 y...

A function, y = f(x), with y on the vertical axis and x on the horizontal axis, can be transformed by 3 different ways: It can be stretched (or shrunk)If y = f(ax), the function is stretc...

Because we're told that x = 6, we can just rewrite the original equation but replace the x with a 6. So:
y = 15 + 5(6 + 2)
6 + 2 = 8, so we can rewrite this again as:
y = 15 + 5(8)
5(8...

With simultaneous equations like these, you first want to get to a point where you have one equation with only one variable. To do this, you must eliminate one of the variables. In this case, if you multi...