Recent content by Cutter Ketch

Sad !?!? Why are you busting my chops? Go look at my posts. I never said don’t use the negative binomial expansion. I never said you can’t use the negative binomial expansion. I only said I got there a different way. I haven’t said one thing wrong and yet you keep needling me like I’m doing...

In mathematics you can test for equality. I show a solution where each coefficient can be constructed from the previous coefficient. The polynomial exists. Proof by induction.

I saw that. I also saw your first post (the very first reply on the thread) strongly suggesting using that. I also saw that in that post it is described as a different expansion. I saw I could get there without it.

You don’t have to justify it. Assume it can be written as a polynomial and then see if you can derive coefficients that make it true.

As I mentioned, I liked the OP’s first step of pulling out one power of the numerator and making that squared term $$ \left( \frac{1+3x}{1+2x} \right) ^2 $$ Because it seems much simpler to me to expand $$ \frac{1+3x}{1+2x} $$ Writing $$ \frac{1+3x}{1+2x} = \sum_{k=0}^\infty C_k x^k $$ Becomes...

Because the negative binomial series is not the binomial theorem.

Hmmm. I couldn’t do this using the binomial theorem alone. Maybe I did it the hard way, but I, personally, liked what you did in your first step separating out that squared term. Somehow you have to get x out of the denominator. I’m thinking if you can’t do it with that simple thing in the...

Well, sort of. A) What is that force to the left? Where does it come from. B) it’s not F=ma as you indicated for relevant equations, it’s ##\sum F## = ma so what should you do with that free body diagram?

Draw the free body diagram for B. The method for solving the problem should then be apparent.

You didn’t do the derivative correctly. Write the formula more carefully and then take the derivative more carefully. Hint: D is not ##\Delta D## (but also careful with the constants)

Yes, that integral is going to be very useful. Now, can you put the two ideas together?

No movement or redistribution necessary. Assume such a fixed charge distribution exists but you don’t know the functional form. What can you write down about the electric field as a function of radius?

If B were not there, would there be any force on that side of A? If B was super small, would it take much force to keep it accelerating along with A? What if it was very large? So, you see, B’s inertia is the reason there is any force between B and A and B’s mass is what you need to figure...

I agree with @DaveC426913 that what you were thinking about is not what the problem intended. However, what you were thinking about is also very interesting. Call it “volume of metal”. You note that the change in volume of metal is not the same for the two spheres. However, the original...

I believe the idea they are trying to convey is that the coaster is moving so fast and the curvature of the top of the hill is so tight that it takes more than just the force of gravity to keep the train on the tracks. The required v^2/r is greater than g, so there must be another downward...