It is very much needed in mathematics and itwill be very useful to u if you learn it.

]]>Related problem (III)

2 circles A and B both with radius 1 unit rotate freely and randomly

outside a circle E also with radius 1 unit on its circumference .

Find the expected value of the overlapping area of A and B .

Can you clarify the question. Are the centers of A and B on the circumference of E or does each of them just intersect with E at one point ( circumference to circumference)?

]]>Find the area bounded by the curve y=x^3-4x and the x axis

Also we have an earlier post about factorising quadratics. Putting these together, I think the expectation is (1) factorise the quadratic (2) identify the area formed by the curve and the x axis (3) use integration to determine this area.

There are several plots already in this thread showing this curve.

Usually an additional piece of information is given, such as x > 0, which would make the interval [0,2]

But without that, taking two intervals [-2,0] and [0,2] seems reasonable.

What you mustn't do is

as the negative part will exactly cancel the positive part, giving an incorrect answer of zero.

Better to do

Bob

]]>Use the lesson learned from the last problem. http://www.mathisfunforum.com/viewtopic … 91#p396691

Look for some right angle triangles and add.

Remember, that if a teacher poses a problem there must be an answer and a method to it, a simple one at that. He/she is there to teach not to confound. That limits the complexity of questions they can give. So, if the question is given to you on the day you are studying right triangles what do you think the solution is going to use? Let me know what you get?

]]>bob bundy wrote:SA = 10/3

From the second pair SA/SD = AQ/RD

=> RD = 1 x (5+10/3)/(10/3) = (15+10)/10 = 25/10 = 2.5

Can't we just say SA/SD=2/5=AQ/RD, so since AQ=1, RD=5/2?

I was thinking the exact same way. Why not use the slope of the line, and the height it gains as it crawls along the edge of the cube, rather than a big long solution that I partially didn't understand? This is my reasoning:

PA = 2, and AQ = 1, so line PQ has a slope of 1/2. Therefore, when the line QR, which is just a continuation of PQ, goes 5 units laterally, it climbs 2.5 units. Therefore, DR = 2.5.

Q.E.D.

]]>2) Is there a function with uncountably many strict extremal points?

No, there cannot be. The following is a proof, which I found on the internet, is for maximas. We could produce a similar proof for minimas and then union them to get the same result.

I cannot believe that I actually found a solution to this problem that I understood. I thoroughly remember having this conversation here on this forum two years ago, it still feels like yesterday. I remember the sequences of events that followed.

And now, here I am fully (well, at least much better) being able to comprehend this. It does turn out I have learnt *something*.

Welcome to the forum.

Whenever I teach fractions, I start with diagrams.

example: http://www.mathisfunforum.com/viewtopic … =17631&p=6

Bob

]]>I've never heard it called that but, as you will see from this link, I did know this:

http://www.mathisfunforum.com/viewtopic … 92#p368592

Bob

]]>LATER EDIT: Had a brain-wave about how to search for it and here it is (many solutions)

http://www.mathisfunforum.com/viewtopic.php?id=20628

Bob

]]>I suggest you to read through my thread " An algorithm to generate primes " .

You will find our similarity and difference .

A soccer ball is constructed using 32 regular polygons with equal side lengths. Twelve of the polygons are pentagons, and the rest are hexagons. A seam is sewn wherever two edges meet. What is the number of seams in the soccer ball?

Number of hexagons = 32 - 12

Each hexagon has 6 sides and each pentagon has 5. Before the ball is sewn together work out how many sides in total. To make the ball pairs of sides are sewn together so halve this total.

If you post your working I'll check it over.

Bob

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