need Maths P3 help

[deathvalley]

I've got confusion in some question, can anyone explain to me
question 6(i) and question 9(i)
here is the link
http://www.xtremepapers.me/CIE/International A And AS Level/9709 - Mathematics/9709_s10_qp_31.pdf
many thanks

 

[WellWIshER]

i dont get it either!!!

 

[deathvalley]

anyone knows ?????

 

[ahmed t]

here
q6i)
make two equations one for the shaded region and one for the semicirlce
for shaded region
the angle is pi-x
so
0.5*r^2*((pi-x)-sin(pi-x))
for ur info sin(pi-x) is the same as sin(x)
so it will be 0.5*r^2*((pi-x)-sin(x))

for the semicircle it is just 0.5 pi r^2
so 4*the shaded region is equal to the semicircle

so that will be 2*r^2((pi-x)-sinx)=0.5 pi r^2
elimenating the r^2 leaves us with
pi-x-sinx=1/4pi

bring x to the RHS and everything else to the LFS u will get the desired equation

 

[ahmed t]

as for 9i)
all u do is differenciate using the quotient rule and then the chain rule
take this differential and inverse it an change its sign cause u want the normal gradient
this part is trikky u have to pllay around with ur results until u get the correct anser took alot of time to figure it out

 

[destined007]

Open the attachments. I have attached the solution.
First part. second part in the reply below.

 

[destined007]

2nd part

 

[destined007]

i hope it helps.

 

[deathvalley]

thanks, it does help me alot