If it were going to be the algebriacally equal to the average, it would have worked out regardless of what values the pi took. But if you wanted, you could think of it as a limit of positive values that are tending to zero and you'll still get the same basic result.

It's probably not that useful, but your expression can be rewritten as the following:

p = 1 / (1 + prod( (1 - p_i)/p_i ) = 1 / (1 + ( [prod (1 - p_i)] / [prod (p_i) ] )

I don't see an immediate interpretation of it but someone else might see something there.

Well, the equation comes from this site: https://en.wikipedia.org/wiki/Naive_...spam_filtering

I tried many hours to use the advice given on this wiki page to no avail. I ended up just using Bayes theorem (https://en.wikipedia.org/wiki/Bayes'_theorem) to find the smamliness for each word (based on my training data) and then, instead of using the p equation mentioned above (which gave me huge problems for unseen words b/c words that were unseen in my training data gave a value of zero) i just used average instead. If the average spamiliness of each word in the input eamil was > 0.7, i called that email a spam email. It worked wonderfully. I wish I had never seen this equation and even more that I never read this wiki page on the subject. The wiki page on Bayes Theorem is all I needed >.<

Maybe you shouldn't give unseen words a value of zero then...?

It seems like you did the wrong thing.

https://en.wikipedia.org/wiki/Naive_...spam_filtering

I'm getting different answers for (a) and (b). I've looked it over a few times but I can't find my mistake. If anyone has a minute it would be appreciated.

If the pulley was massless and frictionless/didn't rotate, what would the acceleration of the masses be? Once you determine that, do any of your answers no longer make sense?

Then the acceleration woukd just be g. The massive pulley is going to slow down the acceleration, and both of my answers are less than g so I don't think I'm grasping your hint.

I'm not agreeing with you, but just so I'm understanding you, based on that, you're saying that the 2m mass is accelerating upward at a=g, and the 3m mass is accelerating downward at a=g?

What if the masses were equal?

Solution to my modified version of the problem:

Ok I made a mistake, the a would be g/5. And now i see where my error was. On my f=ma i set the right sides equal to ma instead 3ma and 2ma. I feel silly. Thanks!

Fyi I posted my last response before i read your most recent reply. Thanks again.

hey..need help with this problem..actually I've almost solved it but it seems I've got something wrong..can you have a look at it, please??actually tried asking some experts from https://www.chegg.com/homework-help and http://yourhomeworkhelp.org/do-my-math-homework/ but that's not free and I'm not willing to pay for the problem I've almost solved..thanks

The partial fractions look correct.

The only thing I see wrong is that your integral of (x/(x^2+1)) dx is wrong. It looks like you tried trigging that out unnecessarily, it is a much more simple integral than that.

I should have clarified, your integral of (x/(x^2+1)) dx isn't wrong per se, your steps (albeit unnecessarily complicated) are correct, it's just not completed.

If you have a triangle where arctan(x) = theta, then you have a right triangle with a leg opposite theta = x, a leg adjacent to theta = 1, and a hypotenuse of (x^2 + 1^2)^(1/2). From there you should be able to simplify your trig statements with substitutions using these values and come up with the simplified solution.

Your answer is kind of like answering the question "What is the square root of 4" with an answer of "ln |e^(2*cos(0))|"

Can anyone recommend a decent reference manager?

I'm having some trouble figuring out an angle or constructing a triangle from the pivot point (to the left of the 'w' block, all the way up to the 60 degree hook on the top right). Trying to determine the distance in terms of L and angle for torque.

I'm reading your question as looking for generating a triangle using the length L, the rightmost L/2, and drawing a line from the point where the leftmost L/2 and L meet, up to where the rightmost L/2 meets the wall. That being the case:

We can calculate the upper angle between length L and the rightmost L/2 as follows:

We know this angle is 360° - (the lower angle between L and right L/2). The lower angle is This is because we can generate two right triangles and a right angle by drawing a line straight down and straight right from the right pivot point. Therefore the upper angle is

Given that, the remaining side can be found using the law of cosines, and the remaining angles can be found using the law of sines.

Naive mechanics question. I drop an object and it hits the ground. While it is falling, its acceleration is g. In the instant it hits the ground, its acceleration changes to some other value k. Does it change discontinuously, or does it pass through all the values between g and k?

Naive statistics question. Why is height normally distributed? Does everything which is normally distributed have some physical property in common that accounts for this?

https://en.wikipedia.org/wiki/Central_limit_theorem

It isn't discontinuous. There will always be a time (delta t) when a goes from g to k, and during that time a is continuous from g to k.

all though in most classroom mechanics it is assumed to be instantaneous.

That would mean infinite de-acceleration. And infinite doesn't exist in the realities we live in.

So, no, if not out-of-reality classroom. And if, then ignore.

I'm not so sure whether infinities exist or not, I don't thin it can be proven that they don't.

Of course I do believe that the acceleration doesn't change instantaneously

Your words warm my heart.