Math Is Fun Forum

After simplification they are both ln2 (log2) !!!

I admit my method is wrong, because the trapezoid fails to approximate even

So is the answer ln2 instead? It depends on whether (sint)[sup]n[/sup]/t[sup]n+1[/sup] can be treated as 1/t.

Mikau, do you love movies? I think a philosophical movie would be a good start.

IT IS A GOOD QUESTION!!!

It's a question about coords, combination of derivatives, and vector calculus altogether.

It's about expressing the original combination of derivatives in another co-ords, usually orthogonal curvy ones. For example, polar co-ords are curvy, and dr and dθ at any given point are orthogonal to each other.

It's usually explained in a vector calculus book or a calculus book for physicians. Untill now, I haven't got a satisfactory explaination for this kind of transfer in any books.

However, I do find a particular solution for your coords and your case.

Define

After substition,

According to Chain Rule

Thus you can compute the right of your equation and use cos²θ+sin²θ=1 to prove it equates the left.

If two objects' projecture on a surface are equal, while their angles against the surface are equal, they are equal, too.

yes the formula you use is correct
for
85/3    +85/3    +85/3 =    85
1st mon 2nd mon 3rd mon 3months altogether

(H0) If the (original )coefficient of holidays is 0, while its sample standard deviation is 0.0975, then according t distribution for degree of freedom being 10 (Samples Size)-2 (Coefficient Amount)=8, -1.425/0.0975 should be at the very tail of the bell curve. Thus the probability for a sample observation of a 0 coefficient, -1.425/0.0975, to occur is very low. Usually they integrate PDF before -1.425/0.0975 and double it for symmetricity of t distribution to demonstrate how low the "altogether" probability is and say it's an almost imposible event.

Since its probability is too low under the assumption that the coefficient is 0, we have enough reason to doubt the very assumption. This is like what cops do-yes the victim can die of an accident but the situation is unnormal and the probability for an reasonable accident in that situation is too low, thus a further investigation should be compulsory.

Refusing 0 assumption= admitting non zero= admitting that there is a correlation between AbsentDays and Holidays-we can interpret it as lack of Holidays being cause and absent behavior being effect. And -1.425Holidays is called statistically significant.

Initially I used excel (tools-data digging-regression, load vb before first using) to do the regression of absent days to 3 other variables (grades turned into wages), but 2 of the 3 independent variables doesn't pass the 0 test-their integrated probabilty is more than 10%. Then I used only the remaining independent variable, also the significant variable Number of Holidays to do the regression and get post #5, with R²=96.4%, virtually as same as the previous R²=97.6%. So I could say this new function with variable amount reduced to 1, can explain as much dependent variable, the amount of absent days, as the previous function with 3 variables, why not choose the new one? Both my econometric textbook author and I believe in Occum's Razor, and I give you the simple function(formula).

This should be a geometry problem, but I've forgotten all the theorems.:(

I totally agree with your idea. Sometimes it's really difficult to apply math by just referring to a formula (Or else everybody could escape from math lessons through keeping a handbook). Yet introducing the whole system would be like authoring a new book and unrealistic.

So my idea is to set a Theory Piece Section, to allow people to explain and dig difficult, fundamental  ideas or whatever he/she thinks important to a math learner, in Existing math theories.

But that won't be too much help.
It's like proposing a Euclid post. Can you imagine a bunch of formulas or theorems can express the whole system, or at least the majority of?

What job can we do if you put all the tricks online ????

:d :d