Recent content by AimlessWander

Homework Statement You have a light bulb where the filament (in vacuum space) starts to glow. This light hits the glass of the bulb at 90 degrees from distance R and is transmitted through the glass of thickness s into the air, of index of refraction nair. So light travels like this: vacuum...

So basically imagine you are observing an object in space with a telescope and it is moving away from the sun. More specifically, the question states that: you are observing a source that is on the y-z plane, the sun is on the origin and the Earth is moving around the sun. The source is moving...

Homework Statement Let's say you want to find the minimum and maximum observed frequencies of light observed on Earth from the sun, when considering the Earth's motion around the sun. How would you go about doing this if you assume Earth takes time X to complete a revolution around radius R...

Hey, thanks for helping out! Please note the small change in the second constraint equation: it's x -y + 2z = 2. I did exactly that, but it didn't really seem to help solve for the unknowns. By plugging in the expressions obtained into the constraint equations, I got 11λ + 7μ = 12 and 7λ+ 17μ =...

Homework Statement Using Lagrange multipliers, find the max and the min values of f: f(x,y,z) = x^2 +2y^2+3x^2 Constraints: x + y + z =1 x - y + 2z = 2Homework Equations ∇f(x) = λ∇g(x) + μ∇h(x)The Attempt at a Solution Using Lagrange multipliers, I obtained the equations: 2x = λ + μ 4y =...

Awesome, yeah that's a lot cleaner and less redundant than mine. Thanks so much! Really appreciate it. :)

Preferably delta-epsilon. I know how to prove it with squeeze theorem, but I got stuck at δ-ε proof. I think I have an idea of how to prove it with δ-ε, but I'm not sure. EDIT: Oh, and by restrictions, I mean what is taken as δ so we can focus on one function of x, since it's not multiplied by a...

Homework Statement Prove: Limit of x3sin(1/x)=0 as x→0 The Attempt at a Solution Intuitively, I understand that since sin(1/x) always lies between 1 and -1, and since x approaches zero, x3sin(1/x) must also approach zero. When formally expressing proof, however, which do we...

Thank you :) Sorry, I just realized I posted in the wrong place.

Homework Statement A river flows with a velocity of 3 m/s east. The river is 300 m wide. A boat is moving 10 m/s due north. If the river flow is not corrected for, how far will the boat have moved downstream by the time is reaches the far shore? Homework Equations Trigonometry and...

A river flows with a velocity of 3 m/s east. The river is 300 m wide. A boat is moving 10 m/s due north. If the river flow is not corrected for, how far will the boat have moved downstream by the time is reaches the far shore?

Okay, I see. So it seems that there is no mathematical direct proportionality between intensity and power then. Right?

I mean a direct relationship between power and intensity. Two teachers were arguing on the relationship between sound intensity and power. In the end, they said something about a direct relationship between power and intensity. I was thinking that I misunderstood something. Right now it seems...

Hello :) Is there a mathematical relationship between sound intensity and sound power?

I understand the inverse square relationship between sound intensity (I) and distance (r). There was a misunderstanding in physics class today about the mathematical and theoretical relationship between sound intensity and power according to the equation: I = P/4∏r2 Sound intensity is...