Hi there Critical_Fallacy!

There's nothing much for me to say at this point, but, I just wanted to inform you that I'll be off to my national service (PLKN), which is in 3 months time starting from tomorrow. So, it means that I mostly won't be online for the next 3 months. Anyway, I would like to thank you, for giving me ample of insights and lots of lucrative notes and tutorials concerning Math at pre-u level. At the same time, not only I was able to further deepen my insights regarding several topics/subtopics in Math T(STPM), I too was able to superficially learned a few tricks and bits of subtopics that're even out of the Form 6 Math T syllabus.

I would also like to take this opportunity to thank v1n0d and crazywing26 for mostly supporting me and came to my aid when I was in a muddle for several occasions.

I do hope that after I'm back from PLKN in March, I'll be able to resume my Math/Physic training with fellow members in this thread. Oh, and, do expect lots of questions from me too after I'm done with my PLKN training

This post has been edited by RED-HAIR-SHANKS: Jan 3 2014, 12:45 PM

I too would like to know a bit more about this.

From what I recall in my physics classes (this was 10 years back OMG! ), both the acorn and the arrow will accelerate vertically at the same rate, which is due to gravity. Critical_Fallacy am I right in assuming that since the acorn has no horizontal force component, whether or not the arrow hits the acorn is completely dependent on the arrow's initial velocity?

Also, have fun at PLKN RED-HAIR-SHANKS, it's an amazing experience!

This post has been edited by v1n0d: Jan 3 2014, 01:17 PM

Can anyone do and explain the part c?

This post has been edited by delsoo: Jan 3 2014, 04:47 PM


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Aren't both x and y functions of s?

x=x(s), y=y(s)?

How could you differentiate sxy and only treat one as a function of s?

Good point. Looks like I've made a mistake. I've edited my previous post to reflect the corrected version.

This post has been edited by v1n0d: Jan 3 2014, 08:00 PM

Luckily v1n0d and studyboy are here!

Sorry, I'm bad at discrete math. Can you check this working?

studyboy is right! In other words, both x(s) and y(s) are parametric equations and we have to deal with the system of implicit parametric equations with Implicit Differentiation. Sweet!

Holy cow it's been ages since I've seen cycle notation!

I have to be honest, all but forgotten how to multiply cycles. Will need to read up and refresh before I can answer your question.

You're right, and there is a condition imposed by the initial velocity as mentioned by v1n0d.

If there were no gravity, the arrow would fly straight to Scrat and the acorn. Since gravity gives the dropped acorn and the released arrow the same constant acceleration downward, they each fall the same vertical distance below the positions they would have had with no gravity. Thus, the arrow ends up hitting the acorn no matter what the initial velocity** of the arrow. The higher the velocity of the arrow, the sooner they meet and the shorter the vertical distance that the acorn falls before being hit.



** Assuming the arrow is fired from ground level, the initial velocity of the arrow must be higher than the minimum velocity given by:



where hmax is the height of the acorn from ground before it is dropped, xmin is the horizontal distance of the archer away from Scrat / acorn, and tmax is the time of the acorn strikes the ground after it is released by Scrat.

Thanks!

Regarding your previous question, is what does the operation o in SoD represent? I automatically assumed you were working on permutation cycles, but I can't get the same results as you.

The question is from kingkingyyk. Perhaps we should let him clarify here. It is the notation for composite function.

Can you put up your answers for Part (a) & Part (b), and check the formulas for electrostatic potential & gravitational potential (look at your textbook) here? It should obey the superposition principle of potentials.

Okay, I think I understand now. Instead of functions, we're working with sets in terms of their elements (x,f(x)).

I obtained SoD={(2,4),(3,3),(3,4),(4,2),(4,3),(4,4)}.

Critical_Fallacy I think your results are for DoS since SoD=S(D(x)).

P.S. Composition of Functions in Set Form

This post has been edited by v1n0d: Jan 3 2014, 08:10 PM

The ans is super concise. Here is it


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According to the syllabus, this is under relation.
Meanwhile, there is another chapter called as function.

I wonder are they the same for the mapping?
Function is what we learnt is form 4, but the way to map relation is different (according to the lecturer answer).

This post has been edited by kingkingyyk: Jan 3 2014, 08:02 PM

Ah, okay. Then the solution given in this post should be the correct one. You can refer to the link I attached for more details.

This post has been edited by v1n0d: Jan 3 2014, 08:05 PM

You have missed out (3,4)?
(2,4)o(3,2) => (3,4)

By the way, does it mean that the working is same with the mapping of functions?
The lecturer made the things really blur, the ways she did in lecture note and tutorial answer are different

This post has been edited by kingkingyyk: Jan 3 2014, 08:09 PM

Ah! Thank you. I've edited my post to reflect this.
Yes, it's the same as the composition of functions. The wiki page for this explains how the sets look like.

Owh, that clarifies everything.

Here's another question, according to the lecturer :
Question 1 :
How many ways to arrange all alphabets in M A T H E M A T I C S such that the vowels are together.
Consonents : M T H M T C S => 7
Vowels : A E A I => 1
Answer = (7+1)! = 8!

Question 2 :
How many different ways to arrange all alphabets in M A T H E M A T I C S such that the vowels are together.
Consonents : M T H M T C S => 7
Vowels : A E A I => 4
Answer = (8!/2!2!) x (4!/2!)

Do you know what is the difference? I think they are the same (Question 1 answer should be same with Question 2 answer).

In the first question, repetition is allowed. AAEI can be shuffled to yield AAEI again (by swapping the first and second letters). Similarly, there are 2 Ms and 2 Ts in the list of consonants, which can also be affected similarly.

In the second question, repeated results aren't counted, so we eliminate them by dividing by their individual factorials (hence the 8!/2!2! and 4!/2!).

If you're still having difficulty with this topic, I suggest reading these lecture notes. The instructor has made them quite easy to understand.