Mathematics Question Thread

[RuiAce]

Could i get help with this question. I asked it a while back but didn't get a response

Although I should look at it more closely later

[jakesilove]

Although I should look at it more closely later

For the record, I started doing a tree diagram, and after about twenty minutes decided I had never wasted time as unbelievably as I was then.

So, I stopped.


As for the real method... not really sure here. That tree diagram has me wanting to quit maths altogether.

[RuiAce]

For the record, I started doing a tree diagram, and after about twenty minutes decided I had never wasted time as unbelievably as I was then.

So, I stopped.
(Image removed from quote.)

As for the real method... not really sure here. That tree diagram has me wanting to quit maths altogether.

Well seeing as though you used technology and not pen and paper to draw it.. welp..

[jamonwindeyer]

Could i get help with this question. I asked it a while back but didn't get a response

Hey! So as Rui said, I think this is a more natural question for combinatorics, but here's a long shot.

We can pick 9 numbers, which means we need to pick the 6 correct ones, and then just 3 others. We always pick 9, so really, it's just the probability of picking the 6 correct ones out of the 44. Which would mean:



This seems appropriate for a lotto - This is what I'd propose at least

Edit: Perhaps some sort of adjustment for the fact that, if we miss, we get three extra chances to nab them all. Not sure how I'd do without combinatorics

For the record, I started doing a tree diagram, and after about twenty minutes decided I had never wasted time as unbelievably as I was then.

So, I stopped.

As for the real method... not really sure here. That tree diagram has me wanting to quit maths altogether.

Save this to display with your vulgar study notes at next lectures

[katnisschung]

pls help last min study for my exam tmr

so i have a couple of questions...which i will split into separate posts
1. find the area enclosed between the hyperbola y=3/x and the line y=-2x+5
ok so i know how to do this but i had a lot of trouble trying to determine which curve lied on top
becos i integrate to find the area by top curve-bottom curve. I mean I found it by putting the curves into geogebra
but im not gonna have that in the test rip. pls help

2. don't no how to do this...(so far i've only been exposed to sth like with no 'x's in the numerator or ones i could easily cancel out)

thanks! u guys are absolute legends

[RuiAce]

pls help last min study for my exam tmr

so i have a couple of questions...which i will split into separate posts
1. find the area enclosed between the hyperbola y=3/x and the line y=-2x+5
ok so i know how to do this but i had a lot of trouble trying to determine which curve lied on top
becos i integrate to find the area by top curve-bottom curve. I mean I found it by putting the curves into geogebra
but im not gonna have that in the test rip. pls help

2. don't no how to do this...(so far i've only been exposed to sth like with no 'x's in the numerator or ones i could easily cancel out)

thanks! u guys are absolute legends

[jamonwindeyer]

pls help last min study for my exam tmr

so i have a couple of questions...which i will split into separate posts
1. find the area enclosed between the hyperbola y=3/x and the line y=-2x+5

If you did it the wrong way around, you will get a negative answer - That's one easy way to tell! More generally, you can sketch the curves - This is the best approach. \(y=\frac{3}{x}\) is just a hyperbola and \(y=5-2x\) just a straight line, so by the HSC (even if not right now) those should be easily sketched for you. As a last minute fix, you can check the  \(y\)-value for given \(x\) coordinates within the region of integration, see which one is bigger - Just watch out for intersections (which you can find with simulteneous)!

2. don't no how to do this...(so far i've only been exposed to sth like with no 'x's in the numerator or ones i could easily cancel out)

Just a little trick of addition and subtraction at the top there to make it a little nicer - It's a good one to remember!

Edit: Beaten by Rui, except for the sign - Should be a positive logarithm

[katnisschung]

could someone pls explain this to me? thanks

(sorry it won't let me attach the image)

find all the values of theta for -pi is less than or equal to theta which is less than or equal to pi
for which sin theta= cos theta

[jamonwindeyer]

could someone pls explain this to me? thanks

(sorry it won't let me attach the image)

find all the values of theta for -pi is less than or equal to theta which is less than or equal to pi
for which sin theta= cos theta

Sure!



Now the tricky bit is adjusting to suit our domain - We know \(\frac{\pi}{4}\) is in there, so that is one answer. The other answer would normally be \(\frac{5\pi}{4}\), but  that isn't in the given domain. To get it there, we just subtract \(2\pi\), remember that doesn't change the 'value' of our angle!



Does this last bit make sense?

[katnisschung]

got it 100% thanks. u explain it way better than my textbook

[jamonwindeyer]

got it 100% thanks. u explain it way better than my textbook

You are too kind! I'll be sure to put that on my CV/Resume aha awesome! Feel free to shoot any other questions our way

[JuliaPascale123]

[RuiAce]

(Image removed from quote.)

[JuliaPascale123]

[Fahim486]

Hey, I'm having trouble doing these questions because I suck at trigonometry.
Thanks!