What was the Percentage of Discount given?
23.5 % profit was earned by selling an almirah for rs 12,350.
If there were no Discount,the earned profit would have been 30%
The cost price of the almirah was rs 10,000
for these Question option are
only I and II
only I...
Hello all, need help here. Im given a hint on a difficult question on midterm, it says "know how to construct an initial value problem for ODE using Picard Lindelof theorem".
If a,b,c,d,p are different real numbers such that $$(a^2+b^2+c^2)p^2-2(ab+bc+cd)p+(b^2+c^2+d^2) \leq 0$$ then $a,b,c,d$ are in A.P, G.P, H.P or A.G.P ? Try this @DHMO ! (Meanwhile I'm having a look at your sum)
https://en.wikipedia.org/wiki/Kato_theorem Quantum chemistry theorem which in order to understand the proof, requires knowledge in functional analysis and real analysis. I wonder if this guy is secretly a mathematician
I solved this question $\int \frac{ 1 }{\displaystyle\sqrt {1 - 36x^2}} = \frac{ 1 }{6}arcsin(6x)$ but apparently he wants me to evaluate it using trig substitusion so this is not the right answer, but isn't this supposed to be trig sub?
@TimTheEnchanter I think I should be using $\displaystyle\sqrt {a^2 - x^2} \ {\text{let}}\ {x = asin(theta)} {\text{ and}} \displaystyle\sqrt {a^2 - x^2} = acos(theta)$
@someone I don't know mate. Everything you've done is correct. The only possibility I can think of is that your prof expects you to explicitly write down the substitution $x=sin( \theta )$ and work from there.
@TimTheEnchanter If I did not use the above shortcut formula and used trig sub shouldn't one side of the triangle be $\displaystyle\sqrt {1 - 36x^2}$ ?
because if $x=sin(theta)$ then the adjacent side is $\displaystyle\sqrt {1 -x^2}$
The solution should be the construction of a matrix. If you write down the first and last couple of columns, the pattern should be clear enough to anyone who would be reading the answer.
@Balarka $\pi_1(\Sigma_2)=\langle a,b,\alpha,\beta\mid \alpha\beta\alpha^{-1}\beta^{-1}=aba^{-1}b^{-1}\rangle$, we did Seifert-Van Kampen's yesterday and I computed this, not sure whether it is correct (I also don't recognize it as a "nice" group)
@DHMO There are some known results about representation numbers in the form $\sum\limits_{i\in I} a_i$. See here for a few references. You can probably find much more.
@DHMO You asked about uncountable sums. In this way you can define the sum only for $I=\mathbb N$. If you want to see a more general definition (i.e., sumation for arbitrary index sets) have a look at the links I posted above.
@DHMO I think I just did. (Even though I do not see any "question about definition".)
of course, finding a uncountable sum which converges is presumably not too hard, since one can arrange for cancellation of positive/negative terms in the general case.
If you have a look at the link, there is a rather standard definition. You take sums over finite sets, and take a net defined on the directed set $[S]^{<\omega}=\{F\subseteq S; F\text{ is finite}\}$.
Note: For the purpose of this question, $\Bbb N$ does not include $0$.
I have a function $f:\mathscr P(\Bbb N) \to \Bbb R$ defined by:
$$f(I) = \sum_{n \in I} \frac 1 {n!}$$
This is essentially a transformation from binary sequences of $\Bbb N$ to a number in $\Bbb R$.
I would like to prove th...
It starts: Claim:If $(x_\alpha)_{\alpha\in A}$ is a collection of real numbers $x_\alpha\in [0,\infty]$ such that $\sum_{\alpha\in A}x_\alpha<\infty$, then $x_\alpha=0$ for all but at most countably many $\alpha\in A$ (A need not be countable).
@DHMO You know I suck at series, it will took me quite a deal of background reading before I can even have some idea on how to compute them (thus unlike all other problems you gave me before, where I at least have some idea what to do). Generating functions, however seemed to be a good start
What was the Percentage of Discount given?
23.5 % profit was earned by selling an almirah for rs 12,350.
If there were no Discount,the earned profit would have been 30%
The cost price of the almirah was rs 10,000
for these Question option are
only I and II
only I...
Note: For the purpose of this question, $\Bbb N$ does not include $0$.
I have a function $f:\mathscr P(\Bbb N) \to \Bbb R$ defined by:
$$f(I) = \sum_{n \in I} \frac 1 {n!}$$
This is essentially a transformation from binary sequences of $\Bbb N$ to a number in $\Bbb R$.
I would like to prove th...
