#161

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!

I've got my first year 12 specialist mathematics exam today... wish me luck!

#162

Hey, I remember this thread. Keep them questions coming.

#163

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?

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?

#164

#165

Cheers! You are a math genius, have you finished or are you in your last year?

#166

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

I have an exam in two weeks so there is still time. I curently have Linear Algebra and Linear Algebra Done right 2nd edition

#167

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.

He has one for calc I, II and III and probably more but i haven't looked.

#168

thanks man!

#169

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!

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!

#170

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.

#171

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.

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.

#172

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!

#173

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...

#174

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.

#175

Well, I'm only doing single maths, so you should have no excuse!

#176

-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

*Last edited by Sol9989 at Nov 18, 2007,*

#177

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.

#178

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?

#179

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

#180

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*

#181

..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.

#182

actually, the necessary condition is <=, sufficient condition is =>. but I can't tell them apart very well.

I just get so confused with them

I just get so confused with them

#183

MASSIVE BUMP!!!

Edit: I laughed at this joke... maybe i need to get out more

#184

Haha that is rather funny.

#185

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.

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.

#186

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?

Any help?

#187

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?

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?

#188

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.

#189

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?

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?

#190

^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.

#191

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."

#192

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

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

#193

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.

#194

I can explain it to you if you want.

I'd very much appreciate that

#195

#196

Thanks man! that took you way more effort than i thought it would.. i appreciate it

#197

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.

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.

#198

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.

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.

#199

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

#200

Guitardude19 you just beat me to it, I got 41.619

Will Lane

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