1. Homework Statement
The problem states: Use cylindrical coordinates to evaluate
\iiint_V \sqrt{x^2 +y^2 +z^2} \,dx\,dy\,dz
where V is the region bounded by the plane z = 3 and the cone z = \sqrt{x^2 + y^2}
2. Homework Equations
x = r cos( \theta )
y = r sin( \theta )...
Hi all!
I have an issue with the circuit breaker in my house and was wondering would anyone be able to shed some light on whats going on.
So last night, I plugged in the hoover and all the electrical devices in my house switched off. I wasn't surprised as I had many devices on at the time so I...
Hi all,
I am trying to prompt the user to enter a mathematical function in matlab.
Any suggestions on how to do this?
I have looked at the inline functions but I am not sure how to code it.
Any help is greatly appreciated.
Ed
1. Homework Statement
Is it possible for a gamma ray to interact with a free electron by mean of the photoelectric effect?
2. Homework Equations
3. The Attempt at a Solution
I'm not really sure. I think the answer is no simply because of the mechanics of the photoelectric...
1. Homework Statement
\int \frac{sin(\sqrt{x})}{\sqrt{x}} dx
2. Homework Equations
3. The Attempt at a Solution
I'm not too sure how to approach this. The only thing that rings a bell at this moment is
\lim_{x\to\0} \frac{sinx}{x} = 1
and I don't feel that it is of any...
1. Homework Statement
Show that if motion could occur at arbitrary speed, then time travel would be possible.
2. Homework Equations
3. The Attempt at a Solution
I'm not sure where to start of. I'm guessing that it has something to do with the light-cone and space-like vectors...
1. Homework Statement
A point charge q is placed at one corner of a cube of edge a. What is the flux through each of the cube faces?
2. Homework Equations
3. The Attempt at a Solution
I drew a diagram of the situation. I'm pretty sure that I should use Gauss' Law and some...
1. Homework Statement
Let x = (x,y,z) .
Recall that the vector x is determined by its direction and length
r = |x| = \sqrt{x^2 + y^2 + z^2}
and assume we are given a function f which depends only on the length of x
f = f(r)
Show that
\Delta f = f'' + \frac{2}{r} f'...
1. Homework Statement
Let r = \sqrt{x^2 +y^2 +z^2} = \lVert x \rVert _\mathbb{R} _^3
be the Euclidean distance of the point x = (x,y,z) \in \mathbb{R} ^3 from the origin.
And e_r := \nabla r
Let F be a central force , i.e.,
\underline{F} = - \nabla U(r)
for some...
1. Homework Statement
Fairly straight forward question but I just can't see whats wrong.
A circle passes through the point (2,-4) and touches both the x-axis and the y-axis. Find the equations of the two circles which satisfy these conditions.
2. Homework Equations
x^2 + y^2 + 2gx...
1. Homework Statement
Basically I am finishing of a projectile question and I get stuck here:
Trying to find \theta
\frac{1}{2} (sin2 \theta) tan^2 \theta -tan \theta + \frac{1}{2} sin2 \theta = 0
2. Homework Equations
3. The Attempt at a Solution
I tryed spliting tan \theta into...
1. Homework Statement
The local poker club plays with blue chips worth €5 and red chips worth €8.
What is the largest bet that cannot be made? (Hint: Use induction)
2. Homework Equations
3. The Attempt at a Solution
I honestly have no idea how to start this question...
1. Homework Statement
Prove that the expression \frac{a(a^2 + a)}{3} is an integer for all integers \geq 1
2. Homework Equations
3. The Attempt at a Solution
a(a^2 + a ) = 3q + r
r can be:
r = 0,1,2
for r = 0
\frac{a(a^2 + a)}{3} = q
q is an integer by the division...
1. Homework Statement
I'm trying to solve \int \frac{dy}{\sqrt{y^2 + C}}
2. Homework Equations
3. The Attempt at a Solution
Is it ln |y + \sqrt{y^2 + C^2} |
Or is it sinh^-^1 something.
Thanks.
1. Homework Statement
Let p be a prime and let a be an integer not divisible by p satisfying a \not \equiv 1 mod p
Show that
1 + a + a^2 + a^3 + ...... + a^p^-^2 \equiv 0 mod p
2. Homework Equations
3. The Attempt at a Solution
a^\phi^(^p^) = a^p^-^1 \equiv 1...
Hi all.
Can someone please tell me what is going wrong here.
Solve
12x \equiv 1(mod5)
gcd(12,5) = 1
By Euclid's Algorithm =>
1 = 5.5 - 2.12
So r is 5 in this case.
x = r ( \frac{b}{d} )
Where b is 1 and d = gcd(12,5) = 1
x = 5 ( \frac{1}{1} )
x = 5...
1. Homework Statement
Solve \frac{d^2 y}{dt^2} = y
2. Homework Equations
3. The Attempt at a Solution
\frac{dy}{dt} = v
\frac{d^2 y}{dt^2} = v \frac{dv}{dy}
v \frac{dv}{dy} = y
v dv = y dy
\int v dv = \int y dy
v^2 = y^2 + C
( \frac{dy}{dt}...
Hi all.
Could someone give me a hand with this:
Using Euler's method find an approximate solution to the IVP using step size h = 0.1
\frac{dy}{dx} = 4xy + 3 , y(0)=0
I know how to use Euler's method for something simple like \frac{dy}{dx} = x + y
But I'm just not to sure what...
1. Homework Statement
Show using integration by parts that:
\int x^3 e^x^2 dx = e^x^2 ( \frac{ x^2 -1}{ 2 })
2. Homework Equations
3. The Attempt at a Solution
Integration by parts obviously.
\int u dv = uv - \int v du
Let u = x^3 and dv = e^x^2 dx
\int...
1. Homework Statement
Prove by induction on k that for all integers
\frac{d}{dx} \prod_{i=1}^k f_i (x) = (\sum_{i=1}^k \frac{ \frac{d}{dx} f_i (x)}{f_i (x)} ) \prod_{i=1}^k f_i (x)
2. Homework Equations
Product rule
\frac{d}{dx} (uv) = u \frac{dv}{dx} + v \frac{du}{dx}...
Hi I was wondering could some one give me some guidance with this:
F4E,S9,...
You have to write down the next term in the sequence.
Its probably very easy but its late and I can't see it.
Thanks for the help!
Hi all.
Starting an undrgraduate programme in Theoretical Physics in two weeks and I have to choose two modules to take for the year. These modules can be of absolutely any topic that is availible in my college, they are called elective modules. I have come to a conclusion that it probably...
Hi all,
I just got accepted to study theoretical physics in UCD in Ireland for the next four years. At the end of it I will come out with a BSc, hopefully.
My ambition is to later get an MSc in Cambridge. I have heard so many stories about the level of difficulty associated with getting into...
C_x (H_2 O)_y
What biomolecule is this?
At first I thought carbohydrate but the ratio of hydrogen to carbon is not necessarily 2:1.
And then I said lipid, but then the hydrogen and oxygen are in a ratio of 2:1.
Thanks.
Hi all.
Recently I have started to make electronic music, mainly using Reason.
Just wondering does anyone else have any recommendations on software I should check out.
Thanks.
Hi all.
For a person trying to lose weight should they decrease their calorie intake or their fat intake or both.
Sorry if its a stupid question, I know very little about this stuff.
Thanks for any help.
Hi all.
I can't remember where I saw this but it really confuses me.
If
x = .999999999.....
10x = 9.9999999......
10x - x = 9x
x = 1?
So does that mean if that .9 recurring is 1 exactly?
Thanks for any help.