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1. Ma = mg - Lmv        2) dv/dt = g-Lv 3)-1/L *(ln(g -Lv)/(g - Lu)) = t             4) g - Lv/ g - Lu = e^-Lt 5) Rearrange to.... v = 1/L *(g-(g - Lu) e^-Lt) Missed some steps as i...

The cosine rule,

a²=b²+c²-2bccosA,

where a, b, & c are the sides of a triangle and A is the angle opposite side a, is the general version of Pythagoras' ...

The derivative can be found by using the chain rule. i.e. let g(x) = |sin(x)|, so f(x)=ln(g(x)), hence df/dx = df/dg * dg/dx

df/dg = 1/g, dg/dx = |cos(x)| so df/dx = |cos(x)|/|sin(x)|

For th...

Implicit differentiation involves differentiating expressions for which it is difficult to rearrange into y in terms of x. It is important to note which variable is being differentiated by the other as, f...

For part i) we use the basic method of differentiation by considering each term individually. The first term, x³ goes to 3x² by multiplying the original term by the original power, b...