To add onto the marathon, here's a new question:
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It can be done using only high school algebra as 1729 did, but admittedly it probably wouldn't come up in a HSC paper (not without any guidance anway).
You can find out more about weighted averages at the Wikipedia article for it: https://en.wikipedia.org/wiki/Weighted_arithmetic_mean .
Last edited by InteGrand; 28 Jan 2017 at 7:41 PM.
I came across a question in the Cambridge textbook today and I haven't looked at the answer yet.
I'm assuming its a constant of 1 next to the dx when we integrate it? Somebody could confirm
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Congruency test
I came across this question tonight and wanted to clear a couple of things up. At times could we use either RHS test or SAS test to explain parts (b) and (f)? They are exactly the same shape as one can see and the Cambridge textbook gives 2 solutions:
The answer for part (b) was RHS in the textbook
The answer for part (f) was SAS in the text book
Last edited by davidgoes4wce; 8 Feb 2017 at 12:59 AM.
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I would say no (may be wrong).
In (b), the angle is not included within the two sides marked and therefore can only be RHS (SAS is side, included angle, side)
On the other hand, in (f) it is SAS as they are giving you two sides and an included angle but the hypotenuse is not one of the sides. Therefore it is directly SAS and I would say, indirectly RHS.
^^ I can see it now . It's something that I never really looked into specifically.
SO I take it, if they give the hypotenuse length and a right angle, we can conclude its a RHS . (also one of the adjacent or opposite lengths)
If we are given a right angle, adjacent and an opposite length, then its a SAS.
| B Eng (Hons) | IB Mathematics SL | IB Mathematics HL | Australian Cricket | Casual University Statistics Tutor
I was also looking to compare (b) v (f)....................earlier I mentioned (b) v (d)
| B Eng (Hons) | IB Mathematics SL | IB Mathematics HL | Australian Cricket | Casual University Statistics Tutor
I learnt something new I guess, I always had the assumption that with congruency tests, that if there was a right angle in there, it was always RHS.
Not sure if the majority of HSC and prelim students knew that in the back of their mind. (And I'm not afraid to say this was from a Year 9 Maths textbook )
| B Eng (Hons) | IB Mathematics SL | IB Mathematics HL | Australian Cricket | Casual University Statistics Tutor
Show that x^3 - 8 has only one linear factor over the real number field,
What is the real number field?
To solve it in a different way, we can look at the roots, since is a cubic polynomial then there are three roots, .Obviously one of the roots is 2,so let
then sum and product of the roots imply
then
which implies
and no real number satisfies above equality, hence there is only one linear factor
Last edited by Mahan1; 17 Feb 2017 at 11:26 PM.
Mahan Ghobadi
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Hey guys,
I've got little to no idea about how to solve the logarithmic equation questions I've come across in the past hsc papers.
Can someone help me solve: 2lnx=ln(5+4x) AND 2log(base5)^3=log(base5)^x-log(base5)^6
Herooo, Pls help with this
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HSC 2017- 90.85
Goal: get 90s in all subjects... rip
English Adv: 85
Math Adv: 89
Biology: 86
Chemistry: 81
Economics: 86
Business Stud: 91
edit: My bad, didn't see there was an answer already
Oh you can do that? My teachers a bit weird and would want us to actually write the whole solution out. How could you prove Tn = Sn - Sn-1?? ^^D
HSC 2017- 90.85
Goal: get 90s in all subjects... rip
English Adv: 85
Math Adv: 89
Biology: 86
Chemistry: 81
Economics: 86
Business Stud: 91
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