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dx/dt=-5x/2 Int(x, dx)=Int(-5/2, dt) ln(x)=-5t/2+c x=60 when t=0 ln(60)=c ln(x)=ln(60)-5t/2 x=e^ln(60)-5t/2 x=60/e^5t/2

sin(x)² + cos(x)² = 1

Dividing by cos(x)² gives:

tan(x)² + 1 = sec(x)² 

Which rearranges as:

sec(x)² - tan(x)<...

Economies of scale are when firms experience a fall in long run average costs due to the growth of the size of the company. Firstly an example is financial economies of scale. This is when a company can b...

Rearrange to get cos(x+25) = 0.6

Use inverse cosine to get (x+25) = -53.13... 53.13... 306.86... 413.13...

Isolate x to get x = -78.13... 28.13... 281.86... 388.13...

Apply the limits...

fg(x) = 7(4/x-2) -1 = x

28/(x-2) - 1 = x

28/(x-2) = x +1

28 = (x+1)(x-2)

28 = x² - x - 2

0 = x² - x - 30

0 = (x-6)(x+5)   x=6 x=-5