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Matthew gets £100 for his 16th birthday and chooses to invest the money into a bank with a 2% annual interest rate. By which birthday will Matthew have more than £150 in his account?

This a geometric sequence with first term 'a' as 100 and common ratio 'r' of 1.02. 100 x 1.02ⁿ > 150 1.02ⁿ > 150/100 =1.02ⁿ > 1.5 log₁₀(1.02ⁿ

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A car is travelling with a velocity of "0.5t^2+t+2" m/s at t=0 (where t is in seconds), find the acceleration of the car at a) t=0 b)t=2

Acceleration can be described as the 'rate of change of velocity' as it is simply how quickly the car is increasing/decreasing in velocity. Therefore as the velocity is described...

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Find d/dx (ln(2x^3+x+8))

Use the chain rule: dy/dx = dy/du * du/dx
Let y = ln(2x^3+x+8)Let u = 2x^3+x+8
dy/dx = d/dx (ln(2x^3+x+8)) = dy/du * du/dx
dy/du = 1/udu/dx = 6x^2 + 1
dy/dx = 1/u * (6x^2 + 1) = (1/(2x...

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Use integration by parts to find ∫x e^(x)

So to integrate this function we would need to use a method called Integration by parts that you may have come across in your studies.
This is where we separate the function into two parts to make it...

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Find (dy/dx) of x^3 - x + y^3 = 6 + 2y^2 in terms of x and y

In order to differentiate this expression, we need to use implicit differentiation. An expression in the form y = f(x), where f(x) means "a function of x", is called an explicit equation and nee...

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