June 06 q 5iii

v1990

solve for 0<B<90
5sin2BsecB=3
i know that secB is 1/cosB, but how would you get the rest of the line as the answer has to be in terms of sin

Reply 1

generalebriety

Expand sin 2B in terms of sin B and cos B.

Reply 2

v1990

thanks i got up to
5sinBcosB=3cosB
then i tried using s+c=1 and rearragned it all but that didnt work
how woul you finish off the question?

Reply 3

v1990

yeah factorising did work, i had no idea why i wrote s+c=1 :s-smilie:

ive got another question, its the last one in the paper
curve has equ y=2ln(x-1)
Point P has coords(0,p)
Region R is shaded by x=0, y=0 and y=p
region R is completely rotated around the y-axis to form a solid, units on axis are in cm.
i)show that the volume is V=pie(e^p + 4e^0.5p +p -5)
ii) given that point P is moving in positive direction along y-axis at a constant rate of 2cm min^-1. find the rate at which the solid is increasing at the instant when p=4.

Reply 4

Daniel Freedman

Can you show us your working so far? Where are you stuck?

Reply 5

v1990

well volume is pie of the integral x^2, the limits are P and 0.
but im stuck with rearranging y=2ln(x-1) and then squaring it to give the x^2.
as for the second part of the question i have no idea how to do rates of volume