Heya's
how would one go about spanning a vector say 'u' onto a plane spanned by vectors v1 and v2.
I have a formula for projecting a vector onto say a subspace w:
projw(u) = <u,v1>v1 + <u,v2>v2 + .... <u,vn>vn
But I'm unsure how to use this for when I need to project the vector onto a...
Heya's
Having some problems with the following question:
Trimethylacetic acid C_4 H_{11} COOHis a weak monoprotic acid. When 0.0010 mol of Trimethylacetic acid was dissolved in 100mL of water, the concentration of trimethylacetic ion was found to be 3.0 \times 10^{ - 4} mol.L^{ - 1}
a)...
Hey, I need some help with the following question:
A sample of 0.1964g of Quinone (C6 H4 02, Relative Molar Mass = 108.1) was burned in a bomb calorimeter that heas a heat capacity of 1.56 kJ/M. The temperature in the caolorimeter rose from 19.3 to 22.5 degrees celcius.
(a) write a...
The exhaust gas from a car is tested and found to contain 8% by volume of carbon monoxide. If the molar volume of CO at SLC = 24.4 L/mol, what is the mass of carbon monoxide in 1L of exhaust gas?
I'm very new to these calculations and am unsure how to approach it.
Heya's
Im a bit confused reguarding gravitational potential energy.
I've seen 2 different calculations
U(h) = mgh
where h is the height above the ground.
and
U = -GMm/r (off the top of my head, havnt got my notes here with me right now)
Could anyone help clear this up for me? Why...
Here is the problem:
{\mathop{\rm Im}\nolimits} \int {e^{x(2 + 3i)} } dx
One sec, I'm having another go at it.
= {\mathop{\rm Im}\nolimits} \int {e^2 } e^{3ix} dx
= {\mathop{\rm Im}\nolimits} \int {e^2 } [\cos (3x) + i\sin (3x)]dx
\begin{array}{l}
= \frac{{ - e^2 \cos...
Think I've worked it out for myself.
Method was sorta wrong.
Once I have Grad F, all I need to do is sub in the values of the point and It will give me the normal vector and from that I can work out the equation.
I think thats right.
I'm having trouble working out the tangent plane of an equation at a specified point (4,1,-2)
The equation being 9x^2 - 4y^2 - 25z^2 = 40
now
\nabla f = (18x, -8y, -50z) yeh?
Just reading off this should give us the normal vector shouldn't it? (18,-8,-50)
and from that we can work out...
Here's some pretty funny stuff regarding maths and physics in Futurama:
http://www.mathsci.appstate.edu/~sjg/simpsonsmath/futuramamath/
Futurama πk - Mathematics in the Year 3000, pdf is pretty interesting.
actually upon inspection of above above URL...
c = \left[ {\begin{array}{*{20}c}
{2 - x} & 5 & 1 \\
{ - 3} & 0 & x \\
{ - 2} & 1 & 2 \\
\end{array}} \right]
a) Calculate det(C).
My answer was x^2 - 12x + 27.
b) Calculate det(2C).
Umm, would this just be 2*det(C)?
Couldn't find anything more helpful in my notes...
How would one use the complex exponential to find something like this:
\frac{{d^{10} }}{{dx^{10} }}e^x \cos (x\sqrt 3 )
I'm guessing we'd have to convert the cos into terms of e^{i\theta } but the only thing I can think of doing then is going through each of the derivatives. Im guessing...
Heya's
I need to find the direction in the xy plane in which one should travel, starting from point (1,1), to obtain the most rapid rate of decrease of
f(x,y,z) = (x + y - 2)^2 + (3x - y - 6)^2
now, \nabla f = (2(x+y-2), 2(3x-y-6))
so I'm thinking now I have to find the the unti vector...
Thanks for that, think I'm getting the hang of it....
Yeh, the first limit problem was a typo, it was meant to be:
\mathop {\lim }\limits_{n \to \infty } (n + 4)^-2 =0
I don't suppose you could show me that, I 'think' I may have done it but I REALLY can't be sure :(
Hey, I was watching Good Will Hunting today to motivate me for my oncoming exams. In movies like these there are usually some scenes of chalkboards filled with math or what have you and I've always wandered if they made sence or if the maths was legit.
Check out this screep cap...
I'm sorry, I don't really understand the 'method' or the reasoning behind that. I need to learn it, but can't for the life of me understand it at the moment.
Where did the epsilon in the 3rd last line come from?