kingjewel1

Does anyone have any idea of how to explain what's actually going on here, im completely lost. Id really love to understand it at last.

Vector spaces; metric: Consider R3 and the orthonormal frame (0; ei), i = 1,2, 3.

Let a, b and c be three vectors of that space, with contravariant components in

the basis (ei) given by

ai = (−1,−1, 0), bi = (0, 0,−2) and ci = (0, 1, 2).

(a) Calculate the contravariant components of the vectors a, b and c in the basis e′1 = e2 + e3

e'2 = e1 + e2 + e3

e′3 = −e2.

(b) Calculate the components of the metric tensor in the new basis, as well as

g^1/2 and (g′)^1/2

-------------------------------------------

Vector spaces; metric: Let a = e1 + e2 and b = e1 + 2e2 be two vectors of R2

where (e1, e2) is an orthonormal basis (i.e. g11 = g22 = 1, g12 = g21 = 0). In the

basis (e ′1 , e ′2 ), these vectors are given by a = e ′1 and b = e ′1 + e ′2 .

Calculate the covariant components g′ij of the metric in the basis (e'1 , e'2) in twodifferent ways

(i) without using the transformation matrix α relating the two bases

(ii) by using the transformation matrix α.

thank you in advance

Thank you swansont.

I dont really understand the first part, could you explain it a bit more please.

I really dont know where to go with this one.

A boat sails across a straight river of uniform width W, starting from a point O on one bank of the river. The velocity of the river at a distance y from the bank is u(y)=ay(W-y), where a is a positive constant. The boat travels at a constant speed v relative to the current and steers a course set at a constant angle p between 0 and pi. in the downstream direction.

a) show that the velocity of the boat is

(u+vcosP)e1+(vsinP)e2.

b)at what time does the boat reach the other bank?

c) show that when the boat has reached the other bank, the downstream distance it has travelled is equatl to

[math]\frac{aW^3}{6vsinP}+WcotP[/math]

please help me

thanks in advance

could you please help me with this question

I would be very much obliged. I cant hack it for my exam

A racing car of mass m travels along a straight road. While travelling the racing car is subject to a constant frictional resistance equal to ma (a is a positive constant) and aire resistance equal to k times thee square of its velocity v. The engine of the care can rpovide a constant propelling froce equal to mb (b is a positive constant) and can bring the car to a terminal velocity Vinfinity.

a) given that the racing car starts from rest, show that it reaches a speed of Vinfinity/2 in time

[math]\frac{v_{\infty}log3}{2(b-a)}[/math]

b) at this point the engine is switched off. Show that the racing car comes to rest in a further time

[math]\frac{v_{\infty}}{\sqrt(a(b-a))}[/math][math]arctan\sqrt\frac{b-a}{4a}[/math]

thank you very much in advance

I really dont know where to go with this one.

A boat sails across a straight river of uniform width W, starting from a point O on one bank of the river. The velocity of the river at a distance y from the bank is u(y)=ay(W-y), where a is a positive constant. The boat travels at a constant speed v relative to the current and steers a course set at a constant angle p between 0 and pi. in the downstream direction.

a) show that the velocity of the boat is

(u+vcosP)e1+(vsinP)e2.

b)at what time does the boat reach the other bank?

c) show that when the boat has reached the other bank, the downstream distance it has travelled is equatl to

[tex]\frac{aW^3}{6vsinP}+WcotP[/tex]

please help me

thanks in advance

The thing is, neither copper nor tin will react in your nitric acid. It's to do with the nitrate anion's complexing abilities. And so its size.

If however you manage it.

For the copper, you can add excess ammonia solution and you'll get a dark blue solution.

Where do you get the lead from? Test for lead nitrate, hmmm if i remember rightly (sorry long time now) gives a yellow ppte with excess ammonia which does not dissolve.

No test for tin that i can think of.

Cool! What can i do with these?

Hi! i had a query on the oxidation of ethylethanoate by H₂O₂

I made this rough n ready ester by reacting excess ethanol, with some ethanoic acid in an excess of Sulphuric acid.

I then let it cool, and in the same solution added an equal part of hydrogen peroxide: placed it on ice to observe properly, and now notice inmiscible swirls in the solution. At room temperature, the characteristic smell of the ester has gone and a fine white ppte is left in suspension.

Any ideas?

Yeah! that sounds good. I hadn't thought about the size of the cation which you mentioned in the complexing part.

So that's also why sulphuric acid is prefered as a catalyst over HCl, apart from the fact that H2SO4 is a dehydrating agent!

Thanks very much!

Ok

What are you doing with NaNO3, making bombs?

You don't have to be cynical about everybyody who asks a question. I just read the sticky about pointing out hazards (which i agree with), but NaNO₃, and it's bro KNO3 are used in meat preservatives aswell are they not?

Hi there!

I'm just wondering why my nice lil equation isn't working in reality:

2Al+3H₂SO₄=>Al₂(SO₄)₃+3H₂ excess sulphuric is always used.

The Sulphuric acid is battery grade, so I'm guessing it must be contaminated, but isn't it usually just some Pb?

Even when I concentrated the acid, still nothing appeared to happen a d no effervence was noted.

I know the Al has an oxide coating, but it should still go to completion.even if

i do get a drop of water, shouldn't it still continue on with evolving H2.

Al2O3+3H2SO4=>2Al2(SO4)3+3H20

What am i doing wrong here? It seems pretty simple, but hmmm (I haven't done formal chem for some months now so maybe i'm just a bit rusty)

so

Sorry.

I've got to admit I don't know what it's supposed to look like exactly, but as far as i can see, we're creating a cirleshape with a segment missing, ie between the two z points.

But i cant find an example method to use(not in my book or net) to find the proper segment and so i can draw it. Any ideas of where i could look? Cheers that's great!

yep fine. BE Careful with changing your letters.

(in math examiner mode ) they need to see what you're integrating with respect to.

ie in this case is it dx or du?

only coving your back!

Cheers guys!

I have to admit, I don't follow all your workings, as I'm not familiar with transformations.... (looking them up in a min).

But as you both say: the locus is two segments of a circle, which seems right to me.

The first line from (0,0) with arg pi/4, okay, but its inverse would not meet the original line apart from at (0,0) So how do i know where these two converge on the edge of the circle?

What would this locus look like?

l

no. you're right, my mistake radius should be 2, should it not?

because sqrt(1^2+1^2-(-2)=2

fixed it! mistake in the algebra

[math]1=\frac{-2y}{x^2-2x+y^2} [/math]

centre (1,-1) radius 4

correct?

Hi guys!

I'm told arg( z/z-2)=pi/4

How do i find the locus of this?

so far i did. but i don't know if this is correct.

from argz - argz-2=pi/4

[math]\frac {\frac{y}{x}-\frac {y}{(x-2)}}{1+\frac{y}{x}\frac{y}{x-2}}[/math]=[math]1[/math]

then

[math]=> (xy-2y-yx)(x-2)=(2x-2)x(x-2)[/math]

therefore [math]-2y=2x-2[/math]

so y=1-x

Thanks in advance

Cheers i've just seen the light!

Thanks very much.

A (5j+5k), B(3i+2j-k)

[math]r=5j+5k+t(3i-3j-6k)[/math]

C is perp to r

so [math]C is (5i+5j)[/math]

O,A,B,D form the vertices of a parallelogram OBAD

Find position vector D. How do i do this one?

Cheers. As you can see, i've got my exam tuesday morning.

I'd appreciate it if you could give me a hand.

Thank you.

Ahhh! yes that would sound reasonable.!

Cheers Matt

Hi there

[math]\int\frac{2}{\sqrt{x}(x-4)}[/math]

I need to integrate this, but i'm not getting the right answer. Apparently the answer involves logs but i don't see why. Substitution is [math]u=\sqrt{x}[/math]

Can anyone give me some help with this guy

Thank you in advance.

Ok thanks

I admit to my ignorance Matt. But if it "is integratable in every sense of the word" why can you not prove it? What is the definition of this function, as this seems to be the crux of the matter?

Thank you.