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I thought this thread was lost! seeing it back again has made my day

I've got my first year 12 specialist mathematics exam today... wish me luck!
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Hey, I remember this thread. Keep them questions coming.
Quote by denizenz
I'll logic you right in the thyroid.

Art & Lutherie
Howdy again DarkStar

Regarding Line integrals,
If they don't give you what the limits are e.g. integrate from between 1 and 0

Then how do you find them out?

Q. Line Integral, (x+yz)dx + 2xdy + xyz(dz) from line segments (1, 0, 1) to (2, 3, 1)

Now I got the parametrisations,
x = 1 + t
y = 3t
z = 1

What are the limits?
Quote by denizenz
I'll logic you right in the thyroid.

Art & Lutherie
Cheers! You are a math genius, have you finished or are you in your last year?
I would need some pdf files of vectors in space! Stuff like how to calculate the distance between a point and a plain (plane-engrish not my expertise), rules for calculating vectors....
I have an exam in two weeks so there is still time. I curently have Linear Algebra and Linear Algebra Done right 2nd edition
Paul's Online Calculus notes are awesome. Just google it

He has one for calc I, II and III and probably more but i haven't looked.
So, long time lurker, first time poster.

Stuck with my waves and optics tutorial work.

Q "By shifting my weight on a floating boardwalk I have produced waves on a previously calm lake surface. I observed that the boardwalk performed 12 oscillations in 20 seconds, each oscillation producing a wave crest 5cm above the undisturbed surface of the lake. A given crest reached a moored buoy 20m away in 10 seconds. Find a suitable equation to describe this wave."

I recon that I want to get this information into something resemling the form ;

x(t)=Acos(wt)

x(t)- displacement at any given time.
A- ampitude (max. and min. displacement values of the wave)
cos- cosine, keep up
w- omega, angular frquency (radians/s)
t- time (seconds)

What I can get from the question is:

frequency= 12/20 (12 oscillations in 20 seconds)= 0.6Hz
From that I can then get w, w=2pi*f= 3.77

I'm not sure where to go from here though. I'm still missing t, would it just be 10s?

But if thats the case, then the equation will only work at that particular time?

I'm not too great at SHM so I might be wrong with that last statement, which I think is whats throwing me.

Any help would be much appreciated!
You're looking at an equation that's in the form of x(t) = Acos(kx - wt) and k = 2pi/wavelength. Find k and you've got yourself all the information you need. You know the amplitude is 5m, and you found w.
Quote by denizenz
I'll logic you right in the thyroid.

Art & Lutherie
Great now I can get some help on the C2 sequences and series....
Theres just one thing about geometric sequences I can't get my head around...

-A geometric sequence has 3rd term 36 and 5th term 81. Find the first term, a, and the common ratio, r.

Now, I know that
kth term=ar^(k-1)

and I know how to work out the sum to nth terms and to infinity, I just don't understand how to work it out!
This is AS-level maths, module Core 2.
Quote by Renka
OddOneOut is an Essex S&M mistress and not a pirate or a computer program.

Quote by darkstar2466
You're looking at an equation that's in the form of x(t) = Acos(kx - wt) and k = 2pi/wavelength. Find k and you've got yourself all the information you need. You know the amplitude is 5m, and you found w.

Funkin' lifesaver!

I owe you (and this thread) one!
Quote by chubbychunks
Ah, geometric progressions. We've only just started them, so I can't help you, sorry.

Too much information going into my head at once. Am on last chapter of C1, and I'm still trying to remember D1...glad I'm not doing single maths though...
Quote by Renka
OddOneOut is an Essex S&M mistress and not a pirate or a computer program.

Quote by OddOneOut
Great now I can get some help on the C2 sequences and series....
Theres just one thing about geometric sequences I can't get my head around...

-A geometric sequence has 3rd term 36 and 5th term 81. Find the first term, a, and the common ratio, r.

Now, I know that
kth term=ar^(k-1)

and I know how to work out the sum to nth terms and to infinity, I just don't understand how to work it out!
This is AS-level maths, module Core 2.

Un = ar^n-1

36 = a r^2. Call this equation 1.

81 = a r^4. Call this equation 2.

Equation 2/Equation 1.

2.25 = r^2

r = 1.5

36 = a 1.5^2

36 = 2.25a

a = 16.

Yeah, this one wasn't too bad, we know how to do these.
Well, I'm only doing single maths, so you should have no excuse!
Quote by OddOneOut

-A geometric sequence has 3rd term 36 and 5th term 81. Find the first term, a, and the common ratio, r.

1st) read the book, it has everything you need to know

2nd) because geometric series go a + ar + ar^2 etc you get:

1)36 = ar^2
2)81 = ar^4

you can eliminate a by dividing 2 by 1.

r^2 = 81/36 = 2.25 => r=1.5

then you can work back to get a? i'm not doing it all
"And after all of this, I am amazed...

...that I am cursed far more than I am praised."
Last edited by Sol9989 at Nov 18, 2007,
Quote by darthteet
Funkin' lifesaver!

I owe you (and this thread) one!

Wrong notation. It's y(x,t) not x(t). It's dependent two variables. You got the gist thought.
Quote by denizenz
I'll logic you right in the thyroid.

Art & Lutherie
Quote by chubbychunks
Well, I'm only doing single maths, so you should have no excuse!

D1 stole my brain.
as did accounting with its depreciation. Cos they make you work out 10 years depreciation the long way (work out the amount, subtract, repeat) ><

not to mention in C1 i still can't figure out when to use => and <=.
Don't have an easy way to figure those out do you?
Quote by Renka
OddOneOut is an Essex S&M mistress and not a pirate or a computer program.

Lol no sorry, no idea what you're on about. :p
Quote by chubbychunks
Lol no sorry, no idea what you're on about. :p

..damn you.
Tis in the last chapter of C1-the language of mathematics. Should in theory be really easy, if it wasn't so those stupid 'is sufficient condition that' and 'is a necessary condition' symbols *waffles on*
Quote by Renka
OddOneOut is an Essex S&M mistress and not a pirate or a computer program.

Quote by OddOneOut
..damn you.
Tis in the last chapter of C1-the language of mathematics. Should in theory be really easy, if it wasn't so those stupid 'is sufficient condition that' and 'is a necessary condition' symbols *waffles on*

Well in truth it is rather easy, p=>q means 'p implies q'. All of the 'necessary conditions' etc are just other ways of saying that.
actually, the necessary condition is <=, sufficient condition is =>. but I can't tell them apart very well.
I just get so confused with them
Quote by Renka
OddOneOut is an Essex S&M mistress and not a pirate or a computer program.

MASSIVE BUMP!!!

Edit: I laughed at this joke... maybe i need to get out more
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Haha that is rather funny.
Sat in a lab, curing diseases. They actually LET me play with chemicals!
Ah maths jokes. I heard a good physics one: Work is not talk.

Work = Force * displacement
Torque = Rotational force * displacement from pivot

But both = Fs

But talk/torque is not work! I think I explained that in too much detail.
A circle x^2 + y^2 = r^2 and an ellipse x^2 + 16(y-r)^2 = r^2 are both drawn on a graph. Frind, in terms of r, the area between the ellipse and the circle. [Hint: you may use the substitution x=rsinu to find the integral S(sqrt(r^2 - x^2)dx) ]

Any help?
Quote by bassplayer33333
Sinisa Rules all.

Quote by zbest
That is part of the reason that the mafia does so much drug trafficing, its so they wont die of hunger because they dont have anything.
11. The points A(0,2) B(7,9) and C(6,10) lie on the circumference of a circle.
i) Find the length of AC.
Prove that triangle ABC is right-angled at B.

___

From Section B of a C1 past paper.
I can find the length of AC but after that I'm a bit stuck. I have no clue about the diameter.

Help anyone?
Quote by Renka
OddOneOut is an Essex S&M mistress and not a pirate or a computer program.

start by drawing the triangle ABC. You should have already worked out that AC = 10. Use the same method to find AB and BC. Use pythagoras' theorem to then prove its right angled.
I tried that and ended up with AB=sqrt98 and BC=sqrt2

OH!
Silly me just realised.... of course AB^2+BC^2=AC^2
No wonder I couldn't make any sense of my answers..
I totally forgot about squaring them...Thats alright then, all I have to do is write out a couple of sentences and I'm all done.

___

Also, in order to prove that the sum of 3 consecutive numbers is divisible by 3 where n is the smallest number

n, n+1, n+2

n+n+1+n+2
3n+3
3(n+1)

Would that be correct?
Quote by Renka
OddOneOut is an Essex S&M mistress and not a pirate or a computer program.

^That looks right. The only thing I would do is divide by three to show that the result is an integer, but that's getting picky.
Quote by shigidab0p
Ah maths jokes. I heard a good physics one: Work is not talk.

Work = Force * displacement
Torque = Rotational force * displacement from pivot

But both = Fs

But talk/torque is not work! I think I explained that in too much detail.

I kinda got it, but I have a good one to.

A thermometer is talking to a graduated cylinder when the thermometer says, "You may have graduated, but I have all my degrees."
Calling all Mathematicians... Please heed my call in my hour of need!

How can i solve this differential equation:

dy/dx + y = e^x

It is probably something very basic that I'm missing but i can't seem to get it and it's driving me crazy
It's a first order ordinary differential equation. Find a tutorial on how to solve one. I can explain it to you if you want.
Quote by denizenz
I'll logic you right in the thyroid.

Art & Lutherie
Quote by darkstar2466
I can explain it to you if you want.

I'd very much appreciate that
Quote by denizenz
I'll logic you right in the thyroid.

Art & Lutherie
Thanks man! that took you way more effort than i thought it would.. i appreciate it
Couple of quick questions...

Should there be a 'C' in the mu(x) term in front of the integral?

and can the 1/2 can be included in the 'C'? it would just make it a different constant, but the answer would be neater.
Quote by soulflyV
Just the thread I need...

I'm doing my chem revision and I came across this:

What mass of solute is contained in 750mL of 0.500M CaCl2?

How would I start this off? I have no idea :s.

Moles = Concentration x Volume / 1000

Moles = 750 x .5 / 1000

Moles = 0.375 moles.

Moles = Mass / RMM

Mass = Moles x RMM

Mass = 0.375 x 111

Mass = 41.625g

Edit:

For these types of questions you only need 2 equations:

Moles = CxV / 1000 and Moles = Mass / RMM
Sat in a lab, curing diseases. They actually LET me play with chemicals!
Guitardude19 you just beat me to it, I got 41.619
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