Math Is Fun Forum

There may be more than one way to solve it.

My first step was to write the area's formula of a triangle ABC.
S = base * height / 2
I chose:
base = AB
height = CM (from C to AB, M on AB)
So,
S = AB * CM / 2

Now, we have two rectangular triangles ACM and BCM (or CMA and CMB, if you like).
The second step was to find at its end:
AB = f(CM,A,B)

...

Based on this definition, you mentioned, you are totally right.

I just added what I know because in my designs, if I ended up with the equation:
x^2 - 9 = 0 
X^2 = 9
x = sqrt(9) = ±3
I had to consider both results.

But in case you believe that I do wrong, and I have to ignore always the negative result, please accept my apology.

As you know, to compare two solutions, one just needs to find each of them first.

But in the case of someone who didn't hear yet the solution (root’s formula) of a quadratic equation, the proof will be much longer.

For instance, I forgot the math trick by which the root’s formula was found (when I was at school about 60 years ago), so now I needed to search “How to find the quadratic equation formula” to remember it

May I add...

sqrt{(a + b)^2} = ±(a + b)

like sqrt{(1 + 2)^2} = sqrt(9) = ±3

So far, it seems there is no continuous function for f(x) whose curve could be made somehow close to the breaker's one.

I guess, a practical solution in this timing case could be the use of a piece-wise function.

Regards,
Kerim

I am 74. Lately, I write an MCU code (actually for ATmega8). And one of its algorithms is about emulating the response of a mechanical breaker (to cut a current when overload).

I thought I may gain time in asking for help. But I also understand that it may not be an easy exercise to most members.

For instance, I used to ask for technical help to also stimulate my brain's cells while some others may think with me about it (much like creating a virtual race... in which I may be the only racer).

So far, it is somehow obvious that f(x) here should have (x-1) in its denominator. And it should have two parameters, in the least, whose values let its graph be close to the breaker's response one.

I will be back when I will find a good f(x), unless someone will do it faster than me.

Good luck

The answer is:
The maximum quantity of fuel that could be delivered at the second city is 2400 litres.

I agree on what you said because it also describes reality as seen by many people.

But in my case and since my graduation, it was (still is) a shame for me if I have to work by following directions of some others (getting a good job as you said). I had no choice but to start a small business (with a capital of about $100) as a private designer of electronic controllers that the local consumers/market may need in every period of time.

It happens that the process of thinking (to discover new things; scientific and else) gives my body all pleasure it needs. So I, unlike all persons I knew, didn't have a real interest in having sexual pleasure with anyone. Naturally and since I also wasn't interested in being rich (hence not running after money and s_x), my family wasn't proud at all of me Even my uncle, a Catholic priest living in Paris, couldn't imagine that it is possible for a person to live without s_x!

For instance, the main reason for which it is out of question for me to have a wife is that marriage needs a third party that represents a certain authority in order to confirming it. In other words, in the conventional marriage, true love and trust come second (at best ). After all, true love and trust can exist between two real free/independent persons only who are usually rare in the world I personally cannot live and/or work with another if our relation has to be supervised by a law (a formal contract for example).

My first crucial question in my life (when I was teen and which I had to answer) was "What is the end purpose of being forced to exist (me), though temporarily, in this universe?". Only after I discovered the answer I have had a rather stable balanced life with myself and all others; no matter if one's role is to play the friend or enemy.

Sorry for not being clear about how using certain non-existent (abstract) objects could help know better some real things.

To simplify solving the equations of an electronic filter for example, I use complex numbers (real + imaginary) to model its real elements (resistors, capacitors... etc.). If the solution is right, all deduced results (giving the values of the real elements) will end up to be real numbers only (the imaginary numbers were just a temporary tool as the temporary wooden structure to build a concrete house).
Of course, one could solve such problems without using the notion of the imaginary number SQRT(-1), but the work would be somehow harder to do.

To me in the least, defining something not real doesn't imply - for sure - it cannot be useful in feeding better one's real knowledge in some respects.

But, concerning the above example, let us be rational. Millions (if not billions) of people around the world don't need including the concept of this imaginary SQRT(-1) in their logical reasoning.

I mean, if a "certain" concept (notion) of an unreal thing doesn't interest many rational intelligent people in the world, this doesn't mean it has to be so to all other rational intelligent humans

Sorry, I try my best not to go further since here is a math forum.

I heard of this problem in early 80’s from a person returning from France. He told me that it was a question in a context TV show (French) that couldn’t get an answer. After about 40 years, I am not sure what its original numbers were but I still remember how I solved it. Its few equations have each one variable (unknown) of the first degree.

For instance, when I was a student and before starting a math exam, I noticed a colleague in my classroom trying, in vain, to solve an exercise that was expected to be given in the exam. I thought that helping him is a good thing. So I reminded him the basic hint by which the exercise in question could be solved rather easily. He looked at me and said: “Who asked you for help? I bet you are happy now for proving you are smarter than I”. So I apologized, but since then I fully understood the famous saying “Ask and you will be given” which also means “Give if you are asked... otherwise don’t blame the other side for any unexpected reaction”

M #385

If the perimeters are equal

Ss = Sc * π / 4

where:
Ss = the area of the square field
Sc = the area of the circular field

Therefore:
Ss= 3850 * (22/7) / 4 = 3025 square meters