I have a solid steel sphere, 600mm in diameter and a machine that can convert the sphere into a single length of wire, with no wastage of material.

The produced wire has the same density as the original sphere.

I have set the machine to produce a wire of 1mm in diameter - exactly how long is the 1mm diameter...

How long is the piece of wire?]]>

I was trying to find roots of some equations using the calculator TI-92 Plus (Voyage 200 and TI-89 are similar in functionality to 92 Plus). The calculator only gives me distinct roots and I can't know which roots are repeated. For an example, please have a look on the attachment. Thanks for the help.

Regards

PG]]>

The king has spent many months to find a suitor for his only daughter from amongst all the eligible bachelors within his kingdom. The king’s primary criteria is that the man who will marry his daughter will be a man of intelligence.

Following a series of intelligence tests, you have made it to last three, from whom the future son-in-law of the king will be chosen.

The king has devised a final intelligence test, the first of the three remaining suitors...

Royal Wedding Fever]]>

To those who have never encountered the problem, it is a worthy problem that has stumped many – including myself. Even when informed of the answer, many still refuse to accept it.

In essence the problem is this – you are the winner on a TV game show, but to win the star prize you...

The Monty Hall Problem]]>

When I first encountered the problem, I was not convinced that there is sufficient information to give a definitive answer.

I have seen a number of worked solutions to the problem – but the simplest solution involves very little maths. In giving an answer, please show your working.

Q: How wide is the river?

Two ferry-boats start moving at exactly...

How wide is the river?]]>

I have attached a file(right down below) that gives an example and the solution.

for the first problem they use mu, but the second one they use trou, why is that?]]>

This is NOT homework! My homework was to do the opposite.

I’m wondering if it’s possible to derive a function if you are given a plot drawn on a graph?

This is totally arbitrary. A function didn’t create it. I made it up.

It’s to accelerate quickly from zero toward 32 or 33, and slow down toward the end.

You could think of the list of integers as a lookup table, so that x0 ouputs y0,

x32 outputs y32, but incrementing in-between is not a linear output.

I wouldn’t expect the output...

Reverse a function from a Plot?]]>

Vin is a 240Vrms sine wave.

Vout is a half-wave rectification of Vin (with no voltage losses due to rectification).

(actually the negative portion of Vin rectified - but that has no bearing on the result)

What is the rms voltage of the Vout waveform?

Suggest you calculate your answer before revealing what others have posted.

View attachment 150424]]>

how can solve δ2?]]>

sine wave with sqrt(3) times the amplitude of either of it's contituent parts, but when doing the same for pulses

the resultant is twice as large as either constituent part. It seems the harmonics traveling with the pulse [as

in Gibbbs phenomena] add 15% to the amplitude of...

Vector Sum and Gibbs phenomena]]>

I just need help with the calculations. Once I know how to do the calculations I can just translate that into java code.

View attachment 148331]]>

On the way back to the table, the waiter ponders on how he is going to split $5 three ways.

No problem, he thinks. "They think the total...

Another math problem (fun)]]>

Math is fun again.]]>

Since at any given point in time the filtered signal is the weighed average of many previous points, whatever change the amplitude of a constant frequency signal is irrevocably lost.

For instance, if I filter a simple sine wive that is within my passbound limits, I still get the same wave as a result. Okay. But if the signal is, say, one period...

Demodulating a filtered signal]]>

If the following input signal (which is made up of 2 components) is applied to the low pass filter:

Using superposition the out signal can be determined. If we assume that ,

Multiply input directly to the tranfer function/frequency response]]>

Solve for Y = 0 with proof.

Rules:

Don't post the answer if you already know it. The challenge is to figure it out from scratch. Who will be first ?

It will be interesting to see how different people approach the problem.

WARNING

Those of faint heart best not indulge.

This puzzle is way harder than it looks.

It was first solved in the 1600's and considered one of the greatest achievements.

I started looking at it 5 years ago, with a few clues, and only worked it...

Cubic Solution Puzzle]]>

Not surprisingly, the more games that constitute a match the greater the likelihood that the better team will win the match. But if the teams are almost evenly matched, it can take a large number of games before the likelihood that the better team will win the match becomes...

How many games should be in the match [rec puzzle]]]>