Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

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Bob wrote:

My first attempt at every post is usually full of typos. After I've read it through and corrected a few times I think I've got an error free post. Let me know if you discover this statement is false.

Bob

Same is here. I never write something new without editing it several times.

So, at work, I see myself having a good luck if I can end up writing an error free code (for MCU) after correcting 50 bugs, not 500's, if not more, which happened sometimes

Bob wrote:

hi KerimF

Didn't spot you were on line too. Looks like we both saw the same thing

Bob

Off topic, after I realized, at school, that I can't avoid doing typo mistakes (not only in math), I used after finishing an exam (or the like) to revise what I did but as if I were a bad rival of Kerim who insisted to show him (Kerim) the many mistakes he did. By doing this seriously, it was possible for me to get the highest grade in most exams.

Kerim

FelizNYC wrote:

x^2 - 2x + 1 + y^2 + 4y + 4 - 9 = 0

x^2 + y^2 - 2x + 4y + 1 + 5 - 9 = 0

x^2 - 2x + 1 + y^2 + 4y + 4 - 9 = 0

to

x^2 + y^2 - 2x + 4y + 1 + 5 - 9 = 0

It is actually:

x^2 + y^2 - 2x + 4y + 1 + 4 - 9 = 0

Your typo was 5 instead of 4.

I recall how, me too, I did this type of mistake in some math exams (when I was a student many decades ago). I even failed in one of them because of a silly typo I did.

FelizNYC wrote:

(x - 1)^2 + (y + 2)^2 = 9

...

x^2 + y^2 - 2x + 4y - 3 = 0

(x - 1)^2 + (y + 2)^2 = 9

Let us assume x=1:

(1 - 1)^2 + (y + 2)^2 = 9

(y + 2)^2 = 9

y + 2 = 3

y = 3 - 2

y = 1

Now,

x^2 + y^2 - 2x + 4y - 3 = 0

Let us verify if this final form is also satisfied for x=1 and y=1

1^2 + 1^2 - 2*1 + 4*1 - 3 = 0

1 + 1 - 2 + 4 - 3 = 1 ≠ 0

I am afraid that you did a typo somewhere.

FelizNYC wrote:

In that case, the equation should be

x^2 + y^2 + 10x + 4y - 20 = 0

Yes?

Yes.

The general form of Q1 is:

x^2 + y^2 - 9 = 0

Perhaps he meant the surface area of a sphere which is 4*pi*R^2.

a) 4

b) 10/4 = 2.5

c) 2.5 + 4 = 6.5

d) 6.5 / 2 = 3.25

a) 3.25

b) 10/3.25 = 3.077

c) 3.077 + 3.25 = 6.327

d) 6.327 / 2 = 3.163

...

Bob wrote:

You can get around this problem by restricting the domain of the inverse so that only one input exists.

Thank you.

In other words, in the full definition of a function, the domain in which it is valid is also specified.

I wonder how we can see this case:

An event occurs whenever Time = arcsine (0.5) is satisfied.

Perhaps we need to differentiate between a function and its inverse.

So, as you found out already, we can't have small boxes or medium ones whose number is not natural, even if the ratio 2:5 is satisfied.

Just a thought:

The matter in our universe (level 0) is formed by the universe of atoms (level -1).

This could lead us to also say that the matter in the atomic universe (level -1) is formed by the universe of sub-atoms (level -2).

And the matter in the sub-atomic universe (level -2) is formed by the universe of sub-sub-atoms (level -3).

etc.

In the opposite direction, our huge universe (level 0) could be seen by a much bigger universe (level 1) as a small piece of matter in it... the same view applies between (level 1) and (level 2)... etc.

Long ago, humans were aware of Earth as being the center of Existence.

Then, humans became aware of the huge universe (level 0)

Lately, humans became aware of the atomic universe (level -1)

Will humans exist long enough to be aware of the upper universe (level 1) and/or the next lower one (level -2)?

After all, it is just a thought.

Kinetic energy = K.E. = m*v^2/2

Potential gravitational energy = P.E. = (m+M)*g*h

Based on the energy conservation, we can write (since the exercise is about an ideal situation):

m*v^2/2 = (m+M)*g*h

therefore:

h = m*v^2/(m+M)/g/2

I have usually insisted to find the key to a locked door which looks related to my life and whose key is assumed out of reach. Then, I simply opened it and looked for another one to open.

Unfortunately, at age 74, I can't find more locked doors (unanswered crucial questions related to my existence and the real world) to also find their hidden keys

Being rational, math's door was among the easiest ones to open and gave me the chance to enjoy playing on its yard since I was teen till now.

I guess this speed is also assumed constant (no friction).

My broken calculator knows how to divide.

It knows how to multiply.

But it knows how to add 1 only.

(30,160/13+1)*13 = (2320+1)*13 =30,173

**KerimF**- Replies: 0

Hearing of a set of formulas is not bad and it could be an important first step.

But only knowing when and how these formulas is useful to solve a problem in an easier and/or faster way lets someone be scientific and professional in certain fields.

In fact, the origin of every formula was the need of a simpler and/or faster way to solve a repeated problem in certain applications.

You did very well

a+(√5)/(b) = (5+√5)/(5) = 5/5+(√5)/(5) = 1+(√5)/(5)

After graduation, I was able to start a private business as a designer in electronics for the local consumers (I am 74). And since then, I used to follow at work what pleases me only

3^c = 1 / √3

3^c = 1 / 3^(1/2)

3^c = 3^(-1/2)

c = -1/2

3^b = 9√3

3^b = 3^2 * 3^1/2

3^b = 3^(2+1/2)

3^b = 3^(5/2)

b = 5/2

Perhaps you mean the following method:

3^a = 1/9

3^a = 1/(3^2)

3^a = 3^(-2)

a= -2

It seems no one around here recall well the first definition of parallelism he heard of at school It was:

Two straight lines are said parallel if they **don’t** intersect.

Kids see this **wrong** definition as being true because they see the geometrical figures on their sheets of paper only or on any other planes.

Only when these kids will grow up and start to see them (geometrical figures) in space, they will know it is wrong and it needs to be updated as:

Two straight lines are said parallel if they **don’t** intersect and are on the same plane.

As long they will not need to learn the perspective geometry, the second definition is all what they need to know about how parallelism is defined.

But those who will need learning it (the perspective geometry), they will hear the complete definition of parallelism which is:

Two straight lines are said parallel if they **do** intersect at infinity.

I guess, it is out of question introducing parallelism to kids using its third and best definition, right?

Similarly, introducing the fact of Creation to the kids of humanity, our very old ancestors, by unreal tales was very important at those early times, as the first definition of parallelism is also wrong but important for the kids at elementary school.

So now, I don't need to hear any tale to know that there is a supernatural Will/Power that let me (actually forced me to) exist temporarily in a realm which is defined/limited by time and space. Fortunately, like any other human, I was also given, by design, a human brain in which I used to trust its power to no limit (equivalent to trusting its maker to no limit). It helped me discover, with time, the logical answers to all important/crucial questions, related to my own existence and the real world on earth, which I was looking for.

Kerim

Your remark is interesting.

As you know, a line is formed by dots (geometrical dots).

And by definition, a geometrical dot has no dimensions; actually, this means that it could be given any dimensions.

To answer your questions (confusion), we can assume that the dimensions of the dots forming the arms and the vertex of an angle are infinitesimal small (close to zero, though they are not in our drawings using a pen). This makes all definitions, you presented, be equivalent to each other, at least in theory (speaking geometry).