hey guys, stuck on q. 8(ii)(iii) and 9(ii) on this paper
for 8(ii), I simplified my partial fractions expression into:
(1+x)^-1 - (2+x)^-1 + 2(2+x)^-2
= (1+x)^-1 - 2(1+0.5x)^-1 + 4(1+0.5x)^-2
= 1-x+x^2 - 2[(1-0.5x+0.25x^2)] + 4[(1-x+0.75x^2)]
= 1-x+x^2 - (2-x+0.5x^2) + (4-4x+3x^2)
= 3.5x^2 - 4x + 3.
However the mark scheme says the answer is 1 - 1.25x + 1.25x^2, where have U gone wrong? also, how do I approach part (iii) on this q?
and for 9(ii), i've re-arranged and integrated and have:
-kt + c = ln (theta - 20)
When t = 0, theta is 100 so sub them in and get c = ln80
Sub in other data they tell u:
-5k + ln80 = ln48
k = -1/5 ln(3/5) therefore -(1/5 ln 3/5)t + ln80 = ln (theta - 20)
However the mark scheme says k = -1/5 ln(5/3), any ideas where I have gone wrong? and also how would you convert this equation into the way they want it, i.e. in terms of e?
cheers!