Maths Methods 3/4 Help Thread 2011

[thushan]

Hey guys doing methods 3/4 in 2011:

If any of you need help with Methods, this is another option; post on this thread and I'll help you all out with your questions.

I did Methods 3/4 in 2010.

[onur369]

Nice, try to bump this once in a while or try to get it stickied.

[taiga]

Thushan is #1 on the sticky posts

[thushan]

Haha thanks taiga

Yeah should try and get this stickied.

Moderators could you do so please?

[Andiio]

Hey thusan,

Could you help me with these 2 questions please?

A car travels half the distance of a journey at an average speed of 80 km/h and half at an average speed of x km/h. Define a function, S, which gives the average speed for the total journey as a function of x.

A cylinder is inscribed in a sphere with a radius of length 6 cm. For the cylinder: a   Define a function, V1, which gives the
volume of the cylinder as a function of the height (h). (State the rule and domain.)
***Shouldn't the V of the cylinder just be TTr^2h = 36TTh?***

Thanks in advance!

[thushan]

OK - my solution to your first question may be a little long-winded, if anyone has a nicer solution, just post!

Say car travels at 80 km/h for t₁ hours, and x km/h for t₂ hours.

Distance travelled over two legs = 80 t₁ and xt₂.

Now, 80 t₁ = xt₂





dom S = R⁺

Question 2:

Consider the cross section of the cylinder. The longest diagonal would have length twice the radius of the sphere (draw a diagram), i.e. 12 cm.

Let h = height, r = radius.







dom V1 = (0, 12)

Sorry for the delay, this was my first time using Latex

[pi]

Haha thanks taiga

Yeah should try and get this stickied.

Moderators could you do so please?

Ask TT by PM, worked for one of my threads (GMA resources)

[Andiio]

Thanks!
I just misinterpreted the 2nd question b/c one could interpret the radius of 6cm being the radius of the cylinder!

[thushan]

I'll just bump this; again, don't hesitate to ask qns in this thread if you have problems, I'm glad to help

[vea]

This guy definitely knows his stuff and he has a 50 to show it !

[shivesh]

Hey Thushan,

Thanks for the advice and I have one question so need help:

(12) let f(x) = (px+q)/(x+r)

(a) If f(x)= f(-x) for all x, show that f(x)=p for x is an element of R\(-r,r)

(b) If f(-x)= -f(x) for x does not = 0, find the rule for f(x) in terms of q

Thanks in advance 

[thushan]

Damn...you can't assume a condition when you are trying to prove it

f(x) = f(-x)

=> (px-q)/(x-r) (px+q)/(x+r)

Simplify and cancel, and you get:

=> x = 0 or q = pr. As x is an element of R except [-r, r] (i think you meant the square brackets, as x cannot be r or -r?), x cannot be 0.

=> q = pr

=> f(x) = (px + pr)/(x+r) = p.

Now, for the second bit:

f(x) = -f(-x)

=> (px +q)/(-x-r) = (px - q)/(x-r)

Simplify and you get

px^2 = qr.

f(x) = (px + q)/(x+r) = (px^2 + qx)/(x^2 + rx) = (qr + qx)/(x^2 + rx) = q(r+x)/(x(r+x) = q/x, where x =/= 0. Technically x cannot be r or -r either as the original condition dictated so.

[dude]

I think it should have been curly brackets, as 0 is between -r and r

[thushan]

Nah, should be square, otherwise x can be 0, and f(0) = q/r which is not necessarily equal to p.

Proofs are really tricky, there's a lot of technicalities and lines of logic that can trip us up

[hakke]

A hiker walks from point A on a bearing of 010◦ for 5 km and then on a bearing of 075◦ for 7 km to reach point B.
a   Find the length of AB.
b   Find the bearing of B from the start point A.
A second hiker travels from point A on a bearing of 080◦ for 4 km to a point P, and then travels in a straight line to B.
c Find:
i   the total distance travelled by the second hiker
ii   the bearing on which the hiker must travel in order to reach B from P.

Plz help with part ii of c!
Thank yu!!!!!