#welcome #general-chat (7 Viewers)

[laterz laterz]

Currently on average it's been a good 6-8 hours a day with breaks and it's been quite chill

bruh relax, enjoy your holidays a bit too, chill out with friends and fam

 

[Etho_x]

bruh relax, enjoy your holidays a bit too, chill out with friends and fam

Ofc I'm relaxing with the fam, have friends but would rather say I don't as they're the types of people who will tell you to have a break and go outside, but won't invite you to things and give you a good reason to go outside

 

[laterz laterz]

Ofc I'm relaxing with the fam, have friends but would rather say I don't as they're the types of people who will tell you to have a break and go outside, but won't invite you to things and give you a good reason to go outside

how do you manage 6-8 hours tho

 

[idkkdi]

Wasn't the exact same question View attachment 29803
Only difference really was part iii but I'm sure what had to be done there could have also been applied to iii in my exam
Here's the link

finding exact value is unnecessary. but u could do it.
4x^2+2x-1 = 0 is equivalent to proving
x^2 + 1/2x - 1/4 = (x- cos2pi/5)(x-cos4pi/5), for x = cos2pi/5, x = cos 4pi/5.

2(cos2pi/5 + cos4pi/5) + 1 = 0 (original eq), cos2pi/5 + cos4pi/5 = -1/2
(cos2pi/5 cos4pi/5 )^2 x 1 = 1.
cos2pi/5 cos4pi/5 = -1 or 1.
cos2pi/5 1st quadrant 4pi/5 2nd quadrant.
therefore -1.

hence lhs = rhs.

(messed up somewhere oops.)

 

[laterz laterz]

Ofc I'm relaxing with the fam, have friends but would rather say I don't as they're the types of people who will tell you to have a break and go outside, but won't invite you to things and give you a good reason to go outside

I think studying 4-5 everyday is more than enough

 

[Etho_x]

how do you manage 6-8 hours tho

Because I haven't been asked by a single person this holidays if I want to go out somewhere LOL

 

[Etho_x]

finding exact value is unnecessary. but u could do it.
4x^2+2x-1 = 0 is equivalent to proving
x^2 + 1/2x - 1/4 = (x- cos2pi/5)(x-cos4pi/5), for x = cos2pi/5, x- cos 4pi/5.

2(cos2pi/5 + cos4pi/5) + 1 = 0 (original eq), cos2pi/5 + cos4pi/5 = -1/2
(cos2pi/5 cos4pi/5 )^2 x 1 = 1.
cos2pi/5 cos4pi/5 = -1 or 1.
cos2pi/5 1st quadrant 4pi/5 2nd quadrant.
therefore -1.

hence lhs = rhs.

(messed up somewhere oops.)

Ye I know I could have done it like that but I just can't stay in zen mode during exams lol I look at the time and I start freaking out and shit when I see a question I don't know how to do or I do but it looks insane at first glance

 

[laterz laterz]

Because I haven't been asked by a single person this holidays if I want to go out somewhere LOL

I can kinda relate haha, maybe just watch Netflix or something lol

just have fun bcoz 2021 is gonna be crazy stressful for all of us

 

[Etho_x]

I can kinda relate haha, maybe just watch Netflix or something lol

just have fun bcoz 2021 is gonna be crazy stressful for all of us

Believe it or not but study is part of my daily routine now so it's gotten to the point where, dare I say, I find studying rather fun. I got sick with the flu 2nd last day of school for Term 4, went home mid-day and immediately got stuck into some maths

 

[laterz laterz]

Believe it or not but study is part of my daily routine now so it's gotten to the point where, dare I say, I find studying rather fun. I got sick with the flu 2nd last day of school for Term 4, went home mid-day and immediately got stuck into some maths

bruh, you're a beast

I kinda find studying fun too, but not to that extent lol

 

[idkkdi]

Believe it or not but study is part of my daily routine now so it's gotten to the point where, dare I say, I find studying rather fun. I got sick with the flu 2nd last day of school for Term 4, went home mid-day and immediately got stuck into some maths

working out was basically completely wrong lol. forgot that roots are cis form xd.

 

[Etho_x]

bruh, you're insane lmao

There's like times where I won't even want to study but it's like I'm subconsciously moving my body to sit at my damn table and do work but generally at those points in time I'll look at a question and wonder why I even got up from my bed or the couch

 

[Etho_x]

working out was basically completely wrong lol. forgot that roots are cis form xd.

This was my teacher's working

 

[idkkdi]

View attachment 29804
View attachment 29805
This was my teacher's working

ye that works. ur teacher probably should have shown sin's cancelling out tho.

 

[idkkdi]

ye that works. ur teacher probably should have shown sin's cancelling out tho.

View attachment 29804
View attachment 29805
This was my teacher's working

exact value way is faster tho tbh.
solve for cos2pi/5 using double angle or some other way in that cos2pi/5 + cos4pi/5 equation.
solve the x in the 4x^2 + 2x -1 equation.
equate.

 

[idkkdi]

exact value way is faster tho tbh.
solve for cos2pi/5 using double angle or some other way in that cos2pi/5 + cos4pi/5 equation.
solve the x in the 4x^2 + 2x -1 equation.
equate.

nvm it might be longer actually.

 

[Etho_x]

nvm it might be longer actually.

I reckon this question would have been doable if I knew the content a lot better but oh well what can I do besides revise those types of questions for HSC

 

[hibaxx]

Believe it or not but study is part of my daily routine now so it's gotten to the point where, dare I say, I find studying rather fun. I got sick with the flu 2nd last day of school for Term 4, went home mid-day and immediately got stuck into some maths

ooffff what time do you sleep and wake up I feel like I'm the only one with a horrid sleeping schedule

 

[Drdusk]

View attachment 29801
Saw a video after on a similar question to this and I regret it so much for not watching it as my understanding of roots of unity was crap at the time I was taking this exam ~ teacher didn't explain it too well.

Ye I was given the step to differentiate, but I for some reason forgot at the time about double roots and stuff so I wasted time trying to find sum and product of roots and didn't even end up getting the full question

For part C expand out the RHS and you will get an equation which has sums and products of the two roots of the quadratic in it. You can make an argument based on that and prove that the roots satisfy the product and sum of roots formulae.

 

[laterz laterz]

ooffff what time do you sleep and wake up I feel like I'm the only one with a horrid sleeping schedule

everyone sleeps at 3 in the holidays haha, not just you