Mathematics Question Thread

[RuiAce]

But how do u just 'know' that x = e^2? 
Sorry....i should know

From the definition of the logarithm.

\( y = \log_a x \) is defined to be equivalent to \( x = a^y\). This is something that we've essentially declared to be the case as mathematicians.

In your case, also recall that \( \ln 2\) is a shorthand for \(\log_e 2\)

[LaraC]

Yep dur!! Sorry. Thanks so much

[Mate2425]

Hey, i don't understand why in HSC 2013 Answers they drew all those lines and were somehow able to deduce the answer from that, any help would be appreciated.

Thanks. 

[RuiAce]

Hey, i don't understand why in HSC 2013 Answers they drew all those lines and were somehow able to deduce the answer from that, any help would be appreciated.

Thanks. 

Already addressed in the compilation. Check out the GeoGebra simulation for more details

[Mate2425]

Already addressed in the compilation. Check out the GeoGebra simulation for more details

Hey Rui, i understand it down to the last part. Is the reason why m = -2/3 is because or perpendicular gradient or something?

[RuiAce]

Hey Rui, i understand it down to the last part. Is the reason why m = -2/3 is because or perpendicular gradient or something?

Fair, I'll add some detail to it. Basically, I just computed the gradient of the line that passes through the points \( (0,1) \) and \( \left(\frac32, 0\right) \) using the usual gradient formula \( m = \frac{y_2-y_1}{x_2-x_1} \)

[chayek]

Hi, I am having difficulties with this question if I could please get some help.
Thanks

A worker's salary was $10500 at the beginning of 1977 and it increased by 5% at the beginning of each year thereafter. Find the worker's salary at the beginning of 1994.

[RuiAce]

Hi, I am having difficulties with this question if I could please get some help.
Thanks

A worker's salary was $10500 at the beginning of 1977 and it increased by 5% at the beginning of each year thereafter. Find the worker's salary at the beginning of 1994.

Or one could've done all that working out in one line by quoting the compound interest formula.

[askaerdf]

Hey sorry to be a bother but from 2013 q 11(f) i got to a point where 1/3 (ln 2 - ln1) and it supposedly equals  1/3 ln 2 and i dont really understand it

[RuiAce]

Hey sorry to be a bother but from 2013 q 11(f) i got to a point where 1/3 (ln 2 - ln1) and it supposedly equals  1/3 ln 2 and i dont really understand it

You can plug \( \ln 1 \) into your calculator and check that it equals to 0.

[askaerdf]

Well i feel dumb now, thanks though

[kauac]

Hi, could someone please explain HSC 2016 MC Q10?
(Sorry I couldn't type it out).

[Em1313]

Sorry if i post this in the wrong place this is my first time on the site. Can someone please help me with this question. 
f(x) = x^3 - 3x^2 - 9x -2
f'(x) = 3x^2 - 6x - 9
= 3(x-3)(x+1)

By sketching y = f'(x) show that f(x) is increasing when x > 3 or x < -1

[ee1233]

Hi, could someone please explain HSC 2016 MC Q10?
(Sorry I couldn't type it out).

Hey kauac,

What I did was write 4 as logbase216.

So the expression would look like logbase216 + logbase2x. Using log laws (loga + logb = logab), the expression would then look like logbase216x (D).

Hope that helps/makes sense!

[imogen.b]

Hey guys!
I'm having a bit of trouble with part 2 of this question, I can find the time in terms of t = d/s, but not sure how to then find theta.

Thanks!