3U Maths Question Thread

[RuiAce]

I would like to know how you simplify:
1. (sin3x-cos3x)^2
2. 1-2sin^2(10(Theta))

Thanks

[legorgo18]

2 quick questions:

1) For equation x^3 + px -1=0 how do i find a^4 + b^4 + c^4 if they are roots... (i tried (a + b + c)^4 and got myself into...
2)  Long question: A tank initially contains 1000L of pure water. Salt water begins pouring into the tank from a pipe and a stirring blade ensures it is completely mixed with the pure water. A second pipe draws the water and salt water mixture off at the same rate so that there is always a total of 1000 L in the tank
i) If the salt water entering the tank contains 2 grams of salt per litre and is flowing at the constant rate of w L/min, how much salt is entering the tank per minute? Im not sure if im right (since 2g/L so 2w (g) / w L so 2w (g)/ min??)
ii) If Q grams is the amount of salt in the tank at time t, how much salt is in 1 L at time t? (wait wtf? little bit of explanation and i think i should be right)
iii) Hence write down the amount of salt leaving the tank per minute

Thank you very much

[RuiAce]

2 quick questions:

1) For equation x^3 + px -1=0 how do i find a^4 + b^4 + c^4 if they are roots... (i tried (a + b + c)^4 and got myself into...

[f_tan]

How do I do 11b?

I thought about it and from the velocity equation in the question, the velocity can never equal zero because the denominator can't equal zero? Doesn't this mean that the particle never stops moving?

Thanks!

[RuiAce]

How do I do 11b?
(Image removed from quote.)
I thought about it and from the velocity equation in the question, the velocity can never equal zero because the denominator can't equal zero? Doesn't this mean that the particle never stops moving?

Thanks!

Hint: In part a) you found t in terms of x. Rearrange to get x in terms of t and use what you know about inverse trig functions.

If you need further guidance, please give the equation you found in part a)

[beau77bro]

2 quick questions:

2)  Long question: A tank initially contains 1000L of pure water. Salt water begins pouring into the tank from a pipe and a stirring blade ensures it is completely mixed with the pure water. A second pipe draws the water and salt water mixture off at the same rate so that there is always a total of 1000 L in the tank
i) If the salt water entering the tank contains 2 grams of salt per litre and is flowing at the constant rate of w L/min, how much salt is entering the tank per minute? Im not sure if im right (since 2g/L so 2w (g) / w L so 2w (g)/ min??)
ii) If Q grams is the amount of salt in the tank at time t, how much salt is in 1 L at time t? (wait wtf? little bit of explanation and i think i should be right)
iii) Hence write down the amount of salt leaving the tank per minute

Thank you very much

Ok so I did this at the dinner table - quite messy so I apologise. Message me or post if you would like a clearer version.



I'm sorry for very little explanation - it's quite hard but essentially rate of change of a substance in a volume where some is leaving as it goes in, meaning some of the salt is taken out at the same time. So we have to account for both, by doing rate of change of salt, Q. That means rate = inflow - outflow of mass. That's where the equation comes from.

[f_tan]

If you need further guidance, please give the equation you found in part a)

I still can't figure out where to go from here - t = 2sin2x

[RuiAce]

I still can't figure out where to go from here - t = 2sin2x

[legorgo18]

Beau tyvm, i got the entire q done i realised what was going on after.... guess im not that bad at math after all hehe xd

anyway quick q so for a=-4x and v^2 = 72- 4x^2 how do i find greatest acceleration? Do you make v=0 then sub to a?

[RuiAce]

Beau tyvm, i got the entire q done i realised what was going on after.... guess im not that bad at math after all hehe xd

anyway quick q so for a=-4x and v^2 = 72- 4x^2 how do i find greatest acceleration? Do you make v=0 then sub to a?

Yes, this is acceptable as the motion described is clearly SHM.

[bluecookie]

For the proof of a=-n^2(x-x0) is equal to: v^2=n^2(A^2-(x-x0)^2) why do we have to sub in v=0, x=x0+A to solve the integral?

[RuiAce]

For the proof of a=-n^2(x-x0) is equal to: v^2=n^2(A^2-(x-x0)^2) why do we have to sub in v=0, x=x0+A to solve the integral?

Think about the properties of SHM.

For SHM, the particle is at rest when it is at the extreme points of motion.

If the equilibrium point is \(x_0\), then the endpoint is \(x_0+a\) where a is the amplitude.

[jingyi.ren1999]

Anyone have tips for parametrics? im struggling a little bit. if anyone can, im working on fitzpatricks 3u book page 78 from 7 onwards. if theres any answers please provide me with some.
Thank

any tips for trials guys?? thanks

Mod edit: Merged double post. Unnecessary.

[RuiAce]

Anyone have tips for parametrics? im struggling a little bit. if anyone can, im working on fitzpatricks 3u book page 78 from 7 onwards. if theres any answers please provide me with some.
Thank

any tips for trials guys?? thanks

Mod edit: Merged double post. Unnecessary.

There are worked solutions to every second question for the Fitzpatrick textbook, so if you are using that one to study you should consider buying that textbook.
Assuming you're using the new one. The old one is honestly quite poor and not worth it. If you're using the old one, just switch over to past papers that come with solutions. You should be aware of sources such as THSC that provide ample past papers..

All the other questions are very generic. Please provide more details on what you would like clarified, including exactly what's difficult and appropriate questions if you wish.

[f_tan]

Can anyone help me with this question please?



Thanks!