Skip to main content

[Community Question] Algebra-Precalculus: working with traded numbers

One of our user asked:

A man want 762 by a number, but he trade it and its quotient result 13 and its rest was 13. What the quotient and rest of the original number? $$ q = ?; r=? $$ $$ 762 = q \cdot \overline{ ab } + r $$ $$ 762 = 13 \cdot \overline {ba} + 21 $$

Another way to write this is: $$ \frac{762-r}{ \overline{ba}}=r $$ $$ \frac{762-21}{ \overline{ba}}=13 $$


Labels:

Comments

Post a Comment

Popular posts from this blog

[Community Question] Linear-algebra: Are linear transformations between infinite dimensional vector spaces always differentiable?

One of our user asked: In class we saw that every linear transformation is differentiable (since there's always a linear approximation for them) and we also saw that a differentiable function must be continuous, so it must be true that all linear operators are continuous, however, I just read that between infinite dimensional vector spaces this is not necessarily true. I would like to know where's the flaw in my reasoning (I suspect that linear transformations between infinite dimensional vector spaces are not always differentiable).
Post a Comment
Read more

[Community Question] Calculus: prove $\int_0^\infty \frac{\log^2(x)}{x^2+1}\mathrm dx=\frac{\pi^3}{8}$ with real methods

One of our user asked: I am attempting to prove that $$J=\int_0^\infty\frac{\log^2(x)}{x^2+1}\mathrm dx=\frac{\pi^3}8$$ With real methods because I do not know complex analysis. I have started with the substitution $x=\tan u$ : $$J=\int_0^{\pi/2}\log^2(\tan x)\mathrm dx$$ $$J=\int_0^{\pi/2}\log^2(\cos x)\mathrm dx-2\int_{0}^{\pi/2}\log(\cos x)\log(\sin x)\mathrm dx+\int_0^{\pi/2}\log^2(\sin x)\mathrm dx$$ But frankly, this is basically worse. Could I have some help? Thanks.
Post a Comment
Read more