Math Is Fun Forum

Sorry for not being clearer.
I meant there are more conditions, if satisfied; the two equations will have one solution too.

I am afraid that many books are also incorrect about many other things (while many other books are correct).
We like it or not, this was always the case, for one reason or another. And it will be so till the end of time.

Therefore, the best thing that one can do is to present, as possible, what he has as 'new knowledge' without expecting any positive reaction... with the hope that his 'new knowledge' doesn't oppose, in any way, the interests of some powerful rich groups which are based on 'old knowledge'.

I guess you both know now that, to let this exercise have a solution, the sum 95 could be multiplied by 10 for example (and the missing 0 was simply a mistyping).

Good question. Here are two ways, I think of, to answer it:

[1]
x=0.12 could also be written as 0*y = 1*x - 0.12
And let us assume that the value '0' here is actually very close to 0 [not exactly 0], like 1/1,000,000,000,000 for example.
We get:
y*1/1,000,000,000,000 = 1*x - 0.12
or
y = 1*x*1,000,000,000,000 - 0.12*1,000,000,000,000
As we see, we have now m=1,000,000,000,000 and c=-120,000,000,000
In other words, we can simplify this process by saying that m=infinity and c=-infinity [while the ratio of their infinities is m/c=-1/0.12]

[2]
As you know, 'm' is the slope of the line, which is defined by the linear equation. Therefore, m = dy/dx.
Since the line is vertical on the x-axis (x=0.12 for any value of y), dx is zero for any value of dy.
m = dy/dx = dy/0 = infinity [as you know, a number divided by zero is equivalent to a very big number, infinity]
Also, 'c' is where the line intercepts the y-axis. Since both, the y-axis and the equation's line, are on the same plane and vertical on the same straight (x-axis), they are parallel. Therefore, they intersect at infinity. Again,'c' here is equal to infinity

Kerim

Well, this is what I discovered too but I thought it was just me.
In brief, Wikipedia is for 'old knowledge' only. And its rules are made so that it can, when necessary, be biased legitimately about 'any topic', very clever.

I guess we all know that 20x+25y=1000 is equivalent to:
y = -20x/25 + 1000/25
y = -4x/5 + 40 [m=-4/5 and c=40]

But this equation is of a special case. Its 'y' and 'x' have to be positive integers or zero only. That is not all points of the straight line which this linear equation represents are valid as a solution.

Any idea?

Even at age 75, I am still learning. I am also making many mistakes before I solve the problems I am interested in.
I simply don't give up whenever I face a well-defined math problem (usually related to my designs).

On the other hand, having no interest in doing something has no remedy at all, even in the case of the most intelligent humans.

But I am afraid that the crucial starting point is self-trust. In other words, the unlimited power of the human's brain is limited by its owner only and to how far he believes it can help him. Unlimited/Limited trust results unlimited/limited intelligence (this is the practical meaning of the greatest advice said 2000 years ago).

Kerim

Although you used the diameters instead of radiuses, I noticed you used the identity:
a^2 - b^2 = (a+b)*(a-b)
This is a clever step that usually helps to simplify the calculation.
I think you will be very good in math.

Kerim

From my rather long experience, I ended up realizing that 'new knowledge' could be welcomed (assuming it is understood by some people) if it makes direct money only (or the like).

Anyway, speaking practically, 'new knowledge' in any field has to be useful to the one who needed it in the first place. For example, about forty years ago, I needed to connect my house and workplace (3 km distance) via RF voice inks. For about 5 years, I achieved this connection/communication by using a novel technique so that my RF links (on MW band then on FM band) couldn't be noticed by the radio listeners or authorities. Even in these days, this technique is supposed non-existent, at all universities around the world.

I am 75. I was fortunate that, since I was teen, I have enjoyed the most every time I had difficult math problems to be solved (numerical and logical). For example, while the boys and girls played together around the swimming pool, I enjoyed solving new math problems instead

Naturally, this helped me be an independent professional designer in electronics (hardware and software), right after finishing my high studies. Since then, I design and produce various electronic controllers which are needed by the local consumers in every period of time.
This is how I was able to gain my daily bread (and of my few assistants) while working independently.
(Please note that working independently may not be possible for engineers living in some other countries).

Kerim

This is how I understand truncation:
6.20 to 6.2499999 gives 6.2
6.25 to 6.2999999 gives 6.3

Therefore, my answer is:
6.2 ≤ x < 6.25

For instance, the answer [ 6.2 ≤ x < 6.3 ] refers to int(x).

Kerim