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1. ### Calculus Revisiting Single-Variable Calculus after Multi-

Hello all! I was thinking about strengthening my knowledge of Calculus after I finish the course I am taking in Multivariable Calculus. I am in a particularly unique situation, as I am only going to enter high school next year. I took the AP Calculus BC Exam last year and got a 5. The course I...

3. ### Potential Energy of three charged particles

No, you could also put it on the outside. If you put it to the right, the equations would then be $$\frac{1}{0.05}-\frac{1}{x}-\frac{1}{x-0.05}=0,$$Which gives you an answer of 13 cm, is this correct? Thank you for your insight. Edit, I meant .05, I accidentally wrote 5.05.
4. ### Potential Energy of three charged particles

I set up an equation for the sum of all the potential energies and when cancelling out ##k## and ##q^2##, I got ##\frac{1}{0.05}-\frac{1}{x}-\frac{1}{0.05-x}=0##. However, this has no solutions, so I must've gone wrong somewhere. Could someone just give me a hint, not a solution, that would put...
5. ### Submarines that don't use compressed air to sink and rise?

Wow, thank you so much. That really cleared up my understanding. Thank you!
6. ### Submarines that don't use compressed air to sink and rise?

Hmm, thank you for the reply. That makes sense. Conventional submarines seem to be able to move like helicopters (Hovering and controlling their buoyancy), whereas subs like the one you showed are more analogous to planes, their thrust and lift (if I can call it that) come in pairs. When a...
7. ### Submarines that don't use compressed air to sink and rise?

I have been wondering about submarines for a while, and especially their ability to sink and rise on command. I understand that they do this through ballast tanks and replacing water with compressed air, which increases the buoyancy force and helps them rise. (I understand that my knowledge is...