# Search results

1. ### Double integral, cylindrical coordinates

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 )...
2. ### Circuit breaker problem

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...
3. ### Mathematica Prompt user to enter mathematical function

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
4. ### Photoelectric effect with free electrons.

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...
5. ### Integration Question

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...
6. ### Special Relativity Question

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...
7. ### Flux through each face on a cube

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...
8. ### Laplace operator help

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'...
9. ### Mechanics question

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...
10. ### Coordinate geometry of the circle question

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...
11. ### Trig identity question

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...
12. ### What is the largest poker bet that cannot be made?

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...
13. ### Integer expression

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...
14. ### Integral homework help

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.
15. ### Congruence problem.

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...
16. ### Differential equation problem

1. Homework Statement Solve y \frac{d^2y}{dt^2} + (\frac{dy}{dt})^2 = 1 2. Homework Equations 3. The Attempt at a Solution \frac{dy}{dt} = v \frac{d^2y}{dt^2} = v \frac{dv}{dy} yv \frac{dv}{dy} + v^2 =1 \frac{dv}{dy} + \frac{v}{y} = \frac{1}{vy} I(y) =...
17. ### Linear congruence

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...
18. ### Differential equations

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}...
19. ### Euler's Method

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...
20. ### Integration by parts

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...
21. ### Medical Possible for the body to fight cancer on its own

Hi, Is it possible for the body to fight cancer on its own with out the help of any medicine?
22. ### Proof by induction help.

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}...
23. ### Continue the sequence

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!
24. ### Which modules?

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...
25. ### Study theoretical physics in UCD

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...
26. ### Chemistry What biomolecule is this?

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.
27. ### Electronic music

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.
28. ### Medical Lose weight.

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.
29. ### Difference between a neutrino and an antineutrino

Hi all. What is the difference between a neutrino and an antineutrino if they both have no charge and aren't made up of quarks? Thanks.
30. ### .99 = 1?

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.