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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...

If possible, you should try to factorise a quadratic. To do this, look a the factors of the constant, in this case -35. 35 is clearly divisible by 5, and 35 / 5 = 7, so 5 and 7 are one pair of factors. Th...