Recent content by bob012345

Someone brought really nice big cookies which might have skewed the experiment and also people are unpredictable as they don’t always obey the probabilities. But the cheesecake was good and I used the occasion to talk a little bit about math.

It turned out that only 7 of the 9 people came and I bought only one cheesecake platter, which had twelve slices, two of each kind. That computed to a 54% chance at least someone would be unhappy. There were at least 5 slices left over so maybe that’s why? Here is a good site with a birthday...

I guess they all do! No, never mind. There are conditions. One can’t even make a quadrilateral with just any four sides and some combinations will not be real in the formula.

I did not see this problem until last night but I solved it at least numerically by using the chord formula and knowing the sum of the half angles is ##\pi##. I got $$\pi =sin^{-1}(\frac{2}{2r})+sin^{-1}(\frac{3}{2r})+sin^{-1}(\frac{4}{2r})+sin^{-1}(\frac{5}{2r})$$ Regarding Parameshvara’s...

Here is what I got.

Not necessarily. This is referring to the quote “I think it’s reasonable to assume each variety is equally desired by people”. That statement does not mean each of the nine likes each variety the same. It means among the population as a whole each variety is equally popular.

I could buy just one platter and call each person offering them a choice among the available varieties. The first person can choose among the six…assorted possibilities happen…for the ninth person there are four slices left so they still have a choice. The last person has a choice which could be...

I believe one can think of this problem like the birthday problem (in a group of ##n## people, what are the odds that at least ##m## share the same birthday where ##m<n##). In this case the ‘birthday’ is the preferred variety of cheesecake and there are only 6 of them.

This is a real life problem. The party is tomorrow. In my OP I stated that there are 12 slices of 6 varieties on each platter. That is two slices of each kind per platter. There are two platters because each platter only holds 12 slices and I wanted more for the party. That’s just how they are...

There are nine people at a party. Dessert is a variety of cheesecake slices on two platters. Each platter contains 12 slices of 6 varieties. The two platters are identical. What is the probability that someone will not get what they want?

Just because I can do it in my head does not make it good practice for a student in my opinion. If it were in my class I would expect the student to draw something to make it clear they understand the problem setup. If it were a problem on a quiz or test and they just write “0.5” how do I know...

When forces are involved. Yes. At least in my head.

We routinely tell student to use free body diagrams so I don’t think it wise to argue not to on PF.

It could be argued that the video is solving a slightly different problem which was not implied by the OP. I consider varying the gear ratios to be a separate problem.

Are you saying a free body diagram would not help for this problem?