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1. Communicating Vessels- how? (searched forum, didn't find it before)

Homework Statement I don't know much about physics, I'm using- F=m*a Homework Equations So say we got our 2 containers with a straight passage between them (they're cylinders for the sake of the question), and the right one has double the radius. So I'm assuming there are 2 forces...
2. Does an object make tons of micro movements while moving?

Homework Statement This isn't homework, just pursuing some physics on my own and curious. Homework Equations So I've got 2 questions which have been sorta bothering me. 1-When I throw something into the air, does it stop for a tiny time at each molecule it meets (Newtons third law)...
3. Newtons Square root method

Homework Statement Let e be the number close to sqrt(a) by Newtons Method (That is picking a number, diving a by it, and taking their average, divide a by average, get a number, find their average, so on). Using |e<sqrt(a)+e| prove that if |a/e-e|<1/10 then |sqrt(a)-e|<1/10 Note that e is...
4. X^2+x + lnx

Homework Statement So I have happily exploring function when I got to the equation 0 = 1/2(e^(2x))-(e+1)(e^x) +ex. Homework Equations Well, I guess the quadratic formula can help, although I can't seem to get to a situation where I can use it. The Attempt at a Solution I played...
5. Integration of composite derivative of function

Homework Statement While I was in school I thought to see what a function whose derivative is always perpendicular to another functions derivative would look like, so for example for X^2 we have -ln(x)/2. Homework Equations Well all those integration tables I guess The Attempt at a...