so their voltage is negative
#help-49
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last slate
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last slate
I am not able to understand why the potential measured according to the potentiometer(I.e phi L1) is equal to the emf of the cell
Could someone explain it
9:39
Please do ping me
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forest jackal
I am not able to understand why the potential measured according to the potentio...
the galvanometer is moved on the wire till we reach a point where it shows no deflection
if it shows no deflection then that means no current passes through it
last slate
Oh,I do understand that
forest jackal
no current passes because the potential difference across the galvanometer is 0
last slate
I understand how a potentiometer works
Here, how is the reading of the voltmeter equal to the emf of th3 cell?
forest jackal
one minute please
forest jackal
Here, how is the reading of the voltmeter equal to the emf of th3 cell?
this situation is not the same as the potentiometer
last slate
In both cases we are measuring the potential ?
forest jackal
there are 2 cells connected in parallel in a potentiometer
in a potentiometer we are just trying to find emf/internal radius of unknown cell with respect to the known cell
last slate
I am not able to understand why the potential measured according to the potentio...
Since there is no current passing through the resistor here, there won't be a potential either, thus the potential across the battery is the same as it's emf
Am I right?
@forest jackal
forest jackal
yeah, its convincing
viral dagger
$\sum_{n=1}^{\infty}\frac{n^3}{7^n}$
midnight plankBOT
$\sum_{n=1}^{\infty}\frac{n^3}{7^n}$
grand pondBOT
Skill_Issue
ivory crescent
What is the question?
zealous schooner
**Skill\_Issue**
Try writing a general binomial expansion and differentiating it
viral dagger
idfk what you said lmao
ivory crescent
Are you trying to prove convergence, or find the value of the expression, or something else?
viral dagger
im pretty sure there is a simpler method, i just wrote it like that so that i can generalize it and not write it
viral dagger
Are you trying to prove convergence, or find the value of the expression, or som...
find the value
zealous schooner
im pretty sure there is a simpler method, i just wrote it like that so that i ca...
Nope
There isn’t an easier way
How would you do it if the power in the numerator was 1 instead of 3?
viral dagger
use the geometric sum formula?
sinful trout
geometric sums have a common ratio
but since the numerator changes as well
i.e. 1/7 -> 2/49 -> 3/343
zealous schooner
This is called an Arithmetico-Geometric series- a series of fractions where the numerators are in an AP and the denominators are in a GP
However the problem you have is even more complicated due to the third power
sinful trout
^
viral dagger
i.e. 1/7 -> 2/49 -> 3/343
uh i make it like A=that sum then i make A-A/7=1/7+1/49+...
zealous schooner
uh i make it like A=that sum then i make A-A/7=1/7+1/49+...
Sure that works for the first power
You can try smth like that for the third power but I doubt it works
zealous schooner
my tracher told me to do exactly that
Okay well I’m not sure if that works but go for it
You’d have to do it repeatedly
viral dagger
uh i got 7/18
blissful ether
the final answer?
neon rune
oogy boogy
zealous schooner
,w sum from n=1 to infty of n^3/7^n
grand pondBOT
zealous schooner
uh i got 7/18
Wrong
blissful ether
oogy boogy
yes
neon rune
Okay well I’m not sure if that works but go for it
that works
you can end up with a form that's AP/GP
zealous schooner
you can end up with a form that's AP/GP
But you have to do the same thing multiple times right?
neon rune
yes
zealous schooner
Probably thrice
neon rune
and that's no pain
zealous schooner
Yeah makes sense
zealous schooner
and that's no pain
True
I like the binomial expansion method though, feels more neat
midnight plankBOT
shell wigeon
Time to define some variables and set up some equations
Here are some quantities to name and to relate to each other:
- the fastest race time (what the question is asking)
- the total time of each person
- the walking time of each person
- the biking time of each person
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round marlin
Hi, I can’t figure out how they result in that expression, when I plug it in I get something different
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Hi, I can’t figure out how they result in that expression, when I plug it in I g...
errant isle
What do you get, step by step?
round marlin
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scarlet arch
Hi, I can’t figure out how they result in that expression, when I plug it in I g...
what's sigma?
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round marlin
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novel herald
what the sigma
novel herald
NO CAP BUSSIN TACO LITERALLY HITTING THE GRIDDY, BRUH SUSSY KIRBY IT TUMMY BE ALL GLITCHY CIRNO FUNKY DANCE! SKIBIDI TOILET CHUNGUS LIKE METAL PIPE FALLING, GOOFY AHH OPPENHEIMER DAIRRHEA DRIPPIN' NONSTOP! WHAT THE SIGMA. GYATT GOATED CHAD!
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flat spire
NO CAP BUSSIN TACO LITERALLY HITTING THE GRIDDY, BRUH SUSSY KIRBY IT TUMMY BE AL...
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novel herald
so true bestie
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craggy yew
why
glacial slate
if both the insides are positive, then you can just remove the abs
since |n| = n for positive n
craggy yew
ohh
glacial slate
and if both are negative, then you put a minus on both sides
and it's the same thing after multiplying by -1
the solution is badly worded
subtle blaze
A more geometric approach to this perhaps is to first consider what |x| looks like on a graph
glacial slate
it should really say x-1 and x-2, and not |x-1| and |x-2|
subtle blaze
Then notice that |x-a| is the same graph but shifted a to the right
So you have 2 copies of |x| shifted various amounts, and you want to find the intersection
craggy yew
and in the second part of the solution, why does it simplify to x-1=2-x
visual tiger
if both x-1 and x-2 are positive for example, then their absolute values are the same numbers
so |x-1| = x-1 and etc
if both are negative, then both signs are swapped when taking absolute values, so -(...) = -(...) and simplify -
visual tiger
and in the second part of the solution, why does it simplify to x-1=2-x
because in this second case, only one of them swaps sign when taking absolute value
so either -(....) = (...) or (....) = -(...)
craggy yew
yes but why is it x-1=2-x
visual tiger
yes but why is it x-1=2-x
x-1 = -(x-2) (only x-2 swaps sign when taken absolute value)
x-1 = 2-x
craggy yew
why is only the rhs given the neg sign
visual tiger
why is only the rhs given the neg sign
since the LHS is positive
craggy yew
cant the lhs do the same?
visual tiger
cant the lhs do the same?
no, as was stated, we're in the case where only ONE of them is positive
so only the OTHER will swap sign
craggy yew
so why cant like
craggy yew
since x-1 > x-2, we deduce easily which one is the one that swaps...
we can?
visual tiger
even if we had -(x-1) = (x-2)
just multiply by -1
x-1 = -(x-2)
boom, x-1 = 2-x still
so it don't matter
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last slate
I have this question: "A recipe needs ingredients in the following proportions: 3-parts flour, 2-parts sugar, 1-part butter. Assume you want to make a batch with a total of 12 cups of these ingredients combined. How many cups of each ingredient will you need?" I'm told it's unsolvable but wouldn't you just do 3 + 2 + 1 = 6, 12 / 6 = 2 cups per part, then 3 x 2 = 6, 2 x 2 = 4, 1 x 2 = 2 for flour, sugar, butter respectively?
midnight plankBOT
I have this question: "A recipe needs ingredients in the following proportions: ...
short kettle
okay lets determine the parts
Flour: 3 parts
Sugar: 2 parts
Butter: 1 part
So you have 6 toal parts
and you want 12 cups
wait a sec
last slate
I can't tell if the question is worded weirdly or if it's legit illogical
last slate
yeah that's what I thought but my professor said there shouldn't be an actual solution
so I wanted to see if someone else saw it or not lol
thank you for checking it out man, appreciate it
.close
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plush palm
how can i find the intersection point between the straight line given by the curves gradient vector and the curve?
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how can i find the intersection point between the straight line given by the cur...
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Jill ♡
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plush palm
.reopen i think im just misunderstanding something
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plush palm
**Jill ♡**
how can i find the gradient vector of this function?
tribal tartan
take the partial derivative with respect to x and y
tribal tartan
oh z is just the same as f(x,y)
it’s just what they’re calling the function
so like would want to find $\pdv{z}{x}$ and $\pdv{z}{y}$
grand pondBOT
y0shi
tribal tartan
wrong order oops
plush palm
im trying to map the gradient to any point on the function
using two constants a and b
i have define the vector v as the gradient
$v=\left(-e^{-a^{2}-b^{2}}\cdot2a,-e^{-a^{2}-b^{2}}\cdot2b,e^{-b^{2}-a^{2}}\right)$
grand pondBOT
Jill ♡
plush palm
this doesnt seem right though
tribal tartan
oh yeah the gradient should only have two components
you don’t need the last bit
oh wait
i see
nvm
you’re trying to give it that z component too
plush palm
hold on
its not pointing in the right direction
and idk what i did wrong
i think i have to find the intersection between this vector and the curve
$i=\left(-e^{-a^{2}-b^{2}}\cdot2a,-e^{-a^{2}-b^{2}}\cdot2b,1\right)$
grand pondBOT
Jill ♡
plush palm
but idk how to do that
i think i should make a new ticket since i doubt anyone will be able to understand what im trying to figure out
oh i have an idea
tribal tartan
oh it’s cuz your c was defined as b,a
it should be a,b for the x and y
cuz you used a as the x and b as the y
plush palm
cuz you used a as the x and b as the y
i found the mistake..
its negative a and b
because of the output
tribal tartan
wait you want to make the vector normal to the curve?
plush palm
wait you want to make the vector normal to the curve?
no i want them all to have the same length
oh wait ye
i gotta devide it by its length
next step will be to add the plane to which the gradient is the normal vector
.close
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stable mirage
im having trouble understanding part 2
midnight plankBOT
im having trouble understanding part 2
long sleet
Looks right
stable mirage
part one might be wrong but i think its right
ok then how does epsilon get on there
long sleet
you chose delta = epsilon/5
i think its just plugging that in
5 delta = 5 (epsilon/5) = epsilon
stable mirage
but there is no relationship between x-2 and delta/epsilon
long sleet
5|x-2|<5 delta right
stable mirage
yes'
long sleet
and then choosing delta = epsilon/5 would do the trick, so it becomes 5 (epsilon/5) = epsilon
stable mirage
oh wait i didnt realize it ended with just epsilon
i guess my question is more about how the prompt reached 5(epsilon/answer)
long sleet
just replacing delta with epsilon/5 without simplifying anything
long sleet
ye limit definition is hard to wrap your head around at first
stable mirage
fr
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kindred torrent
So I was practising for a math olympiad, when I came across this question... I can't seem to get my head around the solution.
Let $S_1, S_2, S_3, \ldots , S_{2011}$ be nonempty sets of consecutive integers such that any 2 of them have a common element. Prove the there is an integer that belongs to every $S_i, i = 1, 2, 3, \ldots, 2011$.
midnight plankBOT
So I was practising for a math olympiad, when I came across this question... I c...
grand pondBOT
everything_addict
runic hamlet
your question seems to imply that you know the solution so it would help if you actually posted it so people could try explaining it. instead of having to solve it themselves
kindred torrent
your question seems to imply that you know the solution so it would help if you ...
alright.
My friend sent this solution: Define s as the number that is the element of the most number of sets. Our job is to prove that s is inside all sets.
Let us split our group of sets into two groups: ones that contain s and the ones that do not. Now, we notice that s might have different possible values: if the sets that contain s are …, then the possible values of s are in the intersection of all those sets. Call this intersection A.
Since the rest of the set do not contain s, they do not contain any of the elements in A (since then if at least one element is in A then s can be adjusted such that it becomes a element of those sets too.)
Now, we prove that A is a set of consecutive integers. (Try yourself!)
For all our sets to not contain anything that is already in A, both their smallest and largest number must be below or above A on the number line.
Now, let us consider one set that does not contain A. Call it C.
We prove that at least one set that contains s has a smallest number same that of the set A. (Try yourself) Same for the largest number.
Now, if the set C is above A in the number line, then that set with the same largest number as A does not have a common element with C. (Prove!)
Same for if C is below A in the number line.
Thus, C doesn’t satisfy the condition. By contradiction, C ( and all other sets) must contain s.
I'm completely lost in this
<@&286206848099549185>
The official solution is:
Let $a_i = $ max $S_i$, $b_i = $ min $S_i$ and suppose that $t_1 = $min${t_i}$. For each $j$, if $S_1\cap S_j \neq \emptyset$ then $a_1 \geq b_j$. Therefore $a_1 \in S_j$.
grand pondBOT
everything_addict
runic hamlet
the first solution is not very well written and I am not sure if its even correct
the second one is what I would have done
kindred torrent
the first solution is not very well written and I am not sure if its even correc...
well... its technically not a solution
hes trying to explain it
but i dont get it
runic hamlet
well frankly (1) his explanation is not good and (2) I am not sure if its correct
kindred torrent
well frankly (1) his explanation is not good and (2) I am not sure if its correc...
wdym not good tho
kindred torrent
**everything\_addict**
also for this, what would t mean
runic hamlet
The official solution is:
Let $a_i = $ max $S_i$, $b_i = $ min $S_i$ and suppos...
only focus on this
kindred torrent
also for this, what would t mean
pls?
runic hamlet
try it for 5 sets first
fleet moss
pls?
basically the idea is you take the set of maximum values of each set, and then take the minimum of that set and call it a1. since every minimum value b is <= a1 and every maximum value a >= a1, a1 is in every set
normal moat
wdym not good tho
1st of all its hard to read and he messes up notation. Because of this it’s hard to clearly see if the arguments actually makes sense.
kindred torrent
1st of all its hard to read and he messes up notation. Because of this it’s hard...
well, thats valid
as i said, its not a solution, but rather an explaination to help us craft a solution
i dont get the solution tho
pls walk me through
grand pondBOT
esca (@ with reply)
fleet moss
then let A be the set of all $a_i$
grand pondBOT
esca (@ with reply)
fleet moss
do you follow so far
fleet moss
alright now let $a_1= \min(A)$
kindred torrent
what i dont get is the t given in the solution
grand pondBOT
esca (@ with reply)
kindred torrent
**esca (@ with reply)**
so we assume such?
fleet moss
what i dont get is the t given in the solution
its probably a typo, dw about it. replace t with a
fleet moss
seriously
i think so yeah. the soln makes sense if you do so, at least to me and denascite
kindred torrent
i get the second last statement
fleet moss
so we assume such?
yeah i mean this is kinda subtle, but we choose the indexing $i$ such that $a_1$ gives us the minimum of A. we can do it because the indexing set is finite
grand pondBOT
esca (@ with reply)
fleet moss
honestly that part doesnt really matter
fleet moss
kindred torrent
but now, how would we think of it
fleet moss
wdym
kindred torrent
as in the though process
fleet moss
like how would you come up with it yourself?
kindred torrent
ye
fleet moss
uhh good question 
honestly idk if i could come up with that one myself
but i think maybe if we reasoned about it by first considering the constraints given to us
kindred torrent
its like so random
fleet moss
namely:
- the elements are consecutive
- no two sets have a null intersection
then i think it wouldnt be too hard
in fact you can actually change the problem statement to talk about ranges on the real number line without changing the solution
maybe that would help you visualize a little better
the consective elements constraint is captured by just making the sets ranges of $\mathbb{R}$
grand pondBOT
esca (@ with reply)
kindred torrent
wait
yeah i get that now
then its a matter of presenting the solution succinctly
fleet moss
yep exactly
fleet moss
then think about what it means for two ranges to have a non empty intersection
this leads you to thinking about maxes and mins
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What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
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status 3
are the 4 100 notes identical or nnot?
A)3×5^3
B)5×3^5
C)3^6
D)None of these
options
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spice scroll
can someone do a one-direction proof for me? I want to get the concept down (as in, LFS is subset of RHS direction proof)
midnight plankBOT
can someone do a one-direction proof for me? I want to get the concept down (as ...
fallen galleon
cartesian product
fallen galleon
i mean you still have to prove it rigorously
spice scroll
there needs to be a rigorous proof you see
nope, regarding the concept of how to proof these
fallen galleon
can someone do a one-direction proof for me? I want to get the concept down (as ...
is this an if then statement or if and only if
spice scroll
is this an if then statement or if and only if
if and only if
fallen galleon
and you want to forward proof it?
spice scroll
and you want to forward proof it?
forward? i want to show RHS is subset of LHS, and vice versa
I just never saw a proof using <x,y> ∈ set*
I don't know how to Google math proofs, half the time it's completely different theorems
yes it should, I'll try that
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twilit field
if $A_1$ and $A_2$ are two AMs and $G_1$ and $G_2$ are two GMs between a and b, find $\frac{A_1+A_2}{G_1 G_2}$
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if $A_1$ and $A_2$ are two AMs and $G_1$ and $G_2$ are two GMs between a and b, ...
grand pondBOT
ƒ(Why am. I here)=I don't Know
twilit field
what do they even mean by $A_1$ and $A_2$ here
grand pondBOT
ƒ(Why am. I here)=I don't Know
sage helm
a, A1, A2, b form an AP
grand pondBOT
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sage helm
uh no
the arithmetic mean of two numbers would be that yes
and you'll notice the mean and the two numbers form an AP
twilit field
yes
sage helm
you can insert multiple means similarly
twilit field
ah
sage helm
here the word mean doesn't have the same intonation as "average" as we're used to
im sure you can tell what G1 and G2 would be now
sage helm
yes
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candid charm
Can someone help me with this, i am stuck
midnight plankBOT
Can someone help me with this, i am stuck
candid charm
so far i have gotten to here
but i am unsure how to get to sin?
and i am unsure how to get the values 3 and 2?
i tried integrating these into the equation but my whole thing is very messy
would love some guidance
shy hearth
Can someone help me with this, i am stuck
it isn't telling you to differentiate the thing
candid charm
yea but im using the differentation to check my answer
im stuck on the limit part
its not matching
shy hearth
you can't
scratch that, you're doing it wrong if you're trying to apply l'hopital
what do you think f(x) is here @candid charm
candid charm
cosx - 1/2 / x- pi/3 ?
shy hearth
why?
let's say that f(x) = cos(x) @candid charm
it would look like this, right? $\frac{f\left(x\right)-f\left(a\right)}{x-a}\to\frac{\cos\left(x\right)-\cos\left(a\right)}{x-a}$
grand pondBOT
Combustion
candid charm
👍
shy hearth
and let's say that a = pi/3
$\frac{\cos\left(x\right)-\cos\left(a\right)}{x-a}\to\frac{\cos\left(x\right)-\frac{1}{2}}{x-\frac{\pi}{3}}$
grand pondBOT
Combustion
candid charm
whats the difference between these two
candid charm
so im doing the whole thing wrong pretty much
candid charm
so far i have gotten to here
sorry but how is this part wrong ?
shy hearth
you're differentiating $\frac{\cos\left(x\right)-\frac{1}{2}}{x-\frac{\pi}{3}}$
grand pondBOT
Combustion
shy hearth
rather than correctly differentiating cos(x)
candid charm
sorry i do not get this limit differentiation method
i have watched yt videos but their expressions for examples are more simpler
shy hearth
i have watched yt videos but their expressions for examples are more simpler
alright
do you see the lower limit?
candid charm
yea
shy hearth
do you understand how f(x) = cos(x) and a = pi/3 in our case?
candid charm
yea
shy hearth
and do you understand that this is the derivative of f(x) (which is cos(x)) at x = a (which is pi/3)
candid charm
cos(x+h) - cos(x)/h ?
candid charm
okay i kinda see what your saying, that 1/2 isnt apart of f(X)
shy hearth
yep! it's cos(pi/3) aka f(pi/3)
candid charm
will try it out again, ty
shy hearth
good luck!
candid charm
i tried integrating these into the equation but my whole thing is very messy
at that point do i use my sum trig identities?
shy hearth
yep
candid charm
okie ty
Cos(pi/3)cosh - sin(pi/3)sin(h) - cos(pi/3) //h
sorry idk how to use latex
do i factor out cos and sin from the first two terms?
candid charm
am i wrong to assume my final answer should look like this? if i just do the quotient rule derivation
shy hearth
remember that you got this when you tried to differentiate the whole thing
instead of just cos(x)
but you should just get a number in this case
shy hearth
sorry idk how to use latex
all good
candid charm
instead of just cos(x)
oh yea thats true
shy hearth
Cos(pi/3)cosh - sin(pi/3)sin(h) - cos(pi/3) //h
just put the actual value of cos(pi/3) and sin(pi/3)
aka 1/2 and sqrt(3)/2
candid charm
what do i do with the h
shy hearth
so you have this right now, right? $\frac{\frac{1}{2}\cos\left(h\right)-\frac{\sqrt{3}}{2}\sin\left(h\right)-\frac{1}{2}}{h}$
grand pondBOT
Combustion
candid charm
yep
shy hearth
let's factor out (1/2)
candid charm
you are so fast with latex damn
candid charm
oh
shy hearth
after factoring out 1/2
$\frac{1}{2}\left(\frac{\cos\left(h\right)-\sqrt{3}\sin\left(h\right)-1}{h}\right)$
grand pondBOT
Combustion
shy hearth
do you know the basic limits such as sin(x)/x as x approaches 0?
and (cos(x)-1)/x as x approaches 0
candid charm
similar i assume?
shy hearth
not really
you need them to solve this
you'll need to use these
(remember, h here approaches 0)
candid charm
h = theta?
shy hearth
sure, but keep it as h
candid charm
$\frac{1}{2}\left(\frac{\cos\left(h\right)-1}{h}-\frac{\sqrt{3}\sin\left(h\right)}{h}\right)
shy hearth
dollar signs before and after
shy hearth
nice!
candid charm
thank you man, sorry if it was annoying helping step by step!
shy hearth
thank you man, sorry if it was annoying helping step by step!
nah all good, well done 
candid charm
my brain turns off when its sin/cos involved in limits
shy hearth
haha
torn temple
hi what is the angular momentum of an atom ?
midnight plankBOT
hi what is the angular momentum of an atom ?
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grand pondBOT
ƒ(Why am. I here)=I don't Know
dull yoke
desimplify 3sqrt(2)
grand pondBOT
ƒ(Why am. I here)=I don't Know
twilit field
this is
\log_{\left(18\right)^{\frac{1}{2}}}\left(18\right)^{\frac{5}{4}}=\frac{1}{2}\cdot\frac{5}{4}$
$\log_{\left(18\right)^{\frac{1}{2}}}\left(18\right)^{\frac{5}{4}}=\frac{1}{2}\cdot\frac{5}{4}$
grand pondBOT
ƒ(Why am. I here)=I don't Know
twilit field
is that right?
cobalt roost
no
dull yoke
nah
cobalt roost
it should be 5/4 x 2
twilit field
wait, what
dull yoke
$\frac 54 \log_{\sqrt {18}} 18$
grand pondBOT
grand pondBOT
ƒ(Why am. I here)=I don't Know
dull yoke
and whats b
twilit field
working on that rn
weak cairn
You have to first solve log
grand pondBOT
ƒ(Why am. I here)=I don't Know
grand pondBOT
twilit field
ok, so I can use that I guess
dull yoke
no need to do any factorization
weak cairn
6^3 x 5 =1080
twilit field
yup
dull yoke
**ƒ(Why am. I here)=I don't Know**
what did u get after turning this into ^(1/6)
twilit field
ah
dull yoke
cuz u dont need to factor at all
twilit field
read it wrong
oops
$\log_{5^{-\frac{1}{6}}6^{-\frac{1}{2}\left(6^3\cdot5\right)}}$
grand pondBOT
ƒ(Why am. I here)=I don't Know
dull yoke
lol bruh
grand pondBOT
dull yoke
$0.5\log_{[(1080)^{-\frac 16}]} 1080$
grand pondBOT
dull yoke
and then that log is just -6
twilit field
$\log_{5^{-\frac{1}{6}}6^{-\frac{1}{2}\left(\left(5^{-\frac{1}{6}}\cdot6^{-\frac{1}{3}}\right)^{-6}\right)}}$
grand pondBOT
ƒ(Why am. I here)=I don't Know
twilit field
$\log_{5^{-\frac{1}{6}}6^{\left(-\frac{1}{2}\right)\left(\left(5^{-\frac{1}{6}}\cdot6^{-\frac{1}{2}}\right)^{-6}\right)}}$
grand pondBOT
ƒ(Why am. I here)=I don't Know
midnight plankBOT
twilit field
-3 im p sure
thanks a lot
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Available help channel!
dull yoke
@weak cairn what didnt u get about this
midnight plankBOT
<@828993726051123271> what didnt u get about this
dull yoke
i thought u were confused cuz u reacted with ? on the message
if i did anything wrong, lmk
.close
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midnight plankBOT
last slate
hello
bleak pier
Helew
last slate
im not sure, but try calculating the lcm of (70,42,66,286,130,170)
last slate
why
yeah i see now why
actually
@bleak pier it works.
just a bit huge number
that's how you do it.
feral sedge
Hints please
start by adding the fractions that look like they have big common factors in their denominators
bleak berry
you could also approximate them and guess
bleak pier
Like how?
dreamy lichen
start by adding the fractions that look like they have big common factors in the...
add the fractions one by one, dont try to do them all at once
bleak pier
start by adding the fractions that look like they have big common factors in the...
I didn't understand it
dreamy lichen
you could also approximate them and guess
this is quite a good hint too actually
if you know that at least one of the options is correct
@bleak pier are you allowed to approximate and guess?
feral sedge
if they're having trouble adding the fractions i don't think approximating is gonna do them any good
sage helm
1/66 and 3/286 have 11 as a common factor
start from there I guess
the weird ones you know
dreamy lichen
then approximate each
dreamy lichen
if they're having trouble adding the fractions i don't think approximating is go...
but i agree with this
dreamy lichen
So 3/7 will be 0.42
approximating it in terms of 1/85 is def more useful than decimals
like 1/42 should be fairly similar to 2/85
3/70 could be like 3.5/85
etc
gloomy blade
Hello
bleak pier
Helew
gloomy blade
@everyone
gloomy blade
can you tell me the pythagoream theorum
dreamy lichen
can you tell me the pythagoream theorum
stop it
dreamy lichen
asking stupid questions
"what is pi times quadratic equation"
if you have an actualy question, go to #❓how-to-get-help
feral sedge
can you tell me the pythagoream theorum
the <@&268886789983436800> can tell you
dreamy lichen
I can't really decipher that
dreamy lichen
(1/7 - 1/10) + (1/6 - 1/7) + ...
bleak berry
consecutive ones seem to work out nicely
dreamy lichen
(1/7 - 1/10) + (1/6 - 1/7) + ...
interesting solution, but its not something id come up with tbh
midnight plankBOT
@bleak pier Has your question been resolved?
formal blade
Sorry there was a spammer I was going to mute but they left and/or were banned before I muted them. You can just ignore that.
midnight plankBOT
@bleak pier Has your question been resolved?
gloomy scaffold
@bleak pier put them all into their prime factors
midnight plankBOT
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stable mirage
midnight plankBOT
stable mirage
i already tried the 3rd option (composition of functions) and none of these didnt work either
and i know it's continous in all its domain
because (-inf,inf) is correct
so it could be rational or polynomial
and i got one attempt left
gleaming spear
I would think that it is B, rational function, but I may be wrong
gleaming spear
ayy
midnight plankBOT
@stable mirage Has your question been resolved?
shy valve
I need help with this problem. It is very tricky. I have tried converting the equation to a different form but had no success. I also tried finding example values of a, b, and c but nothing was helping me write the proof. Help would be nice!
midnight plankBOT
I need help with this problem. It is very tricky. I have tried converting the eq...
@shy valve Has your question been resolved?
midnight plankBOT
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half meteor
midnight plankBOT
feral sedge
I get 0, but integral calculator says 2. What did i do wrong?
e^u evaluated from 0 to 1 is not e
half meteor
.close
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valid hare
need help with composite functions
midnight plankBOT
need help with composite functions
valid hare
I understand them, just not solving them so...
twilit field
show us an example
valid hare
(f-g)(x)=(1/x+2)-(2/x-1)
this is the one from my homework yet the video my professor gave us doesnt really tell us muh
much*
slender walrus
what are you being asked to solve exactly
slender walrus
for that consider the domain of f(x) and g(x) individually
and then determine their intersection
valid hare
alr
ok so
like when combining functions im not actually combining equations or anything, im just finding the domains of the two equations then and finding where they overlap?
like I found the domains of the two seperate equations, im just confused on this, and this assignment is due at midnight so
chat
slender walrus
for addition/subtraction, yeh
for stuff like f(x)/g(x) you'd have the additional condition that g(x) can't be 0
(so exclude such values)
and for f(g(x)) you'd want the intersection of domain of
f(g(x)) (potentially simplified)
and g(x)
valid hare
so how exactly would I do this problem, I found x=/=-2 and x=/=1
so
idk Im rushing this since I didnt get home until 10 and barely had time to watch all this and do all this
would love to look more into it but i dont have the time and im more of a demonstrational learner
valid hare
so the domain is just (-oo,-2)U(-2,1)U(1,-oo)?
slender walrus
yeh
valid hare
thanks
slender walrus
also use () to clearly indicate numerators and denominators of fractions as needed when comminicating in text
valid hare
alr thanks
ok for multiplication
and if I have fractions
I just combine the numerators and then factor a common denominator etc etc
chat
.close
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severe glade
I’m watching a Khan academy video on factoring and in this video (picture taken at the end) he says he uses the SQUARE OF SUM BINOMIAL method.
Is this similar to the perfect square formula ?
It looks like he turned the a^2 + 2ab + b^2 into the (a+b)^2 but the final answer has subtraction in it ? (a-b)^2 ??
midnight plankBOT
I’m watching a Khan academy video on factoring and in this video (picture taken ...
split coral
yes
because ax^2+bx+c can also be written as 2x^2-5x-4 as an example
take the bx in the case above
really -5x is +(-5)x, hence +bx... the b here is really the -5
if you get what i mean?
severe glade
I don’t really understand
So he’s using the perfect squares formula right?
If so, Why does he call it square of sum binomial method then?
split coral
its just the way they call it lmao
well you can take -1 as an example as really +(-1)
theres a plus in everything
split coral
your question is why its (5x^2-3) when the formulae is (x+b)^2 right?
if you look at the -3
-3 is the b value
and 5x^2 is the x value
so really what we have is (5x^2+(-3))
severe glade
You mean a?
severe glade
Ohhhh
split coral
so really what we have is (5x^2+(-3))
can you see the plus?
thats why
theres a plus in every subtraction
we just dont write it
cause plus minus will give minus
but for us to see the form this is the way to see it
severe glade
So technically instead of
(5x^2 - 3)
You can write it as
(5x^2 + -3)
Which would make it equal to (a+b)^2?
split coral
yes
severe glade
So technically for the perfect squares formula you can do (a+b)^2 or (a-b)^2 right..?
severe glade
But if it’s a subtraction then it would still work tho?
Because then you can just add the negative instead of subtracting a positive
So I’m just curious why they specify (a+b)^2
split coral
its just the form most commonly used
severe glade
Ok
split coral
its like why its
ax^2 + bx + c is not written as ax^2 - bx - c
i cant assure you that using (a-b)^2 is the exact same as (a+b)^2
there may be cases so just use (a+b)^2
severe glade
So just to confirm , he’s using perfect square formula in the video
And (5x^2 - 3)(5x^2 - 3) is still ok for perfect square formula?
?
<@&286206848099549185>
Can I get help with my original question, just want to make sure because I want to understand it deeper!
last slate
Whats the question
severe glade
It’s above
I just didn’t want to repost everything and spam the chat
Picture is a bit up there
..?
<@&286206848099549185> still haven’t gotten help
hollow bridge
Can I get help with my original question, just want to make sure because I want ...
If you want to, you can remember that ax^2 - 2ab + b^2 = (a-b)^2
As the person above said, the reason why that is true is because you can think of ax^2 - 2ab + b^2 as equal to ax^2 + 2a(-b) + b^2 which itself is equal to ax^2 + 2a(-b) + (-b)^2 (does that make sense so far?)
So now you can use your normal formula if you think of the b as (-b) instead, and you know that thing will be equal to (a + (-b) )^2 = (a-b)^2
severe glade
Ohhh so it can be either of the equations above
I found this in google
I thought it was just one
hollow bridge
Yep, but fundamentally it is the same. It can be useful to remember both so you can readily use them
severe glade
Okay got it. And is the method in the picture above using the perfect squares formula? Cause he called it something different @hollow bridge
He called it square of sum binomial but it looked similar to the perfect squares formula
hollow bridge
He called it square of sum binomial but it looked similar to the perfect squares...
Yea that’s just a different name. A “sum binomial” is something that looks like a+b, so that’s why it’s called “square of a sum binomial”
Both names are valid
severe glade
But it’s the same thing as the perfect squares formula right
I was jw if it’s the same or if it’s a new method I need to learn
severe glade
.reopen
midnight plankBOT
✅
severe glade
@hollow bridge sorry I just want to confirm they’re the same thing before I close
hollow bridge
But it’s the same thing as the perfect squares formula right
Yep, it’s the same thing
twilit field
$\sum_{i=1}^{100}n2^{n-1}$
midnight plankBOT
$\sum_{i=1}^{100}n2^{n-1}$
grand pondBOT
ƒ(Why am. I here)=I don't Know
twilit field
so this is essentially $1+22+32^2...$
grand pondBOT
ƒ(Why am. I here)=I don't Know
sage helm
,ti @hard shard
grand pondBOT
The current time for garlicbredfries is 11:54 PM (PDT) on Fri, 21/06/2024.
neonperseus is 9 hours ahead, at 08:54 AM (CEST) on Sat, 22/06/2024.
hard shard
anyway, what have you tried?
twilit field
I was thinking of shifting it by 1 , and then subtracting
hard shard
good idea
sage helm
assuming after multiplying by 2
twilit field
spoliers !
hard shard
thats how to shift by 1 yes
twilit field
so $2S=2+2\cdot 2^2+3 \cdot 2^3....$...
grand pondBOT
ƒ(Why am. I here)=I don't Know
twilit field
now what?
sage helm
you said it
last slate
I was thinking of shifting it by 1 , and then subtracting
this
grand pondBOT
ƒ(Why am. I here)=I don't Know
twilit field
so S= $\sum_{i=1}^{100}2^{n-1}-1$
grand pondBOT
ƒ(Why am. I here)=I don't Know
twilit field
,w $\sum_{i=1}^{100}2^{i-1}$
grand pondBOT
sage helm
lol
twilit field
but is the answer right?
hard shard
id write it as 2^99-2
quiet hinge
Your method is corrwxt
twilit field
thanks everyone!
midnight plankBOT
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viral dagger
in the list {1,2,3,...,n}, take n numbers (if can be fhe same)
a.find the probability that you pick exactly (n-2) diffrent numbers
b.find the probability you pick exactly (n-3) numbers
midnight plankBOT
in the list {1,2,3,...,n}, take n numbers (if can be fhe same)
a.find the proba...
midnight plankBOT
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Available help channel!
last slate
This is how i did it
Assuming $B^-1AB = X$
And applying DET on both sides
I would be left with $"IAI=IXI"$
midnight plankBOT
This is how i did it
Assuming $B^-1AB = X$
And applying DET on both sides
I woul...
grand pondBOT
Cnidarian
last slate
if X was skew symmetric so would be A
And if X was symmetric,A will also be the same
Now that gave me the Correct answer
but
is this a proper method ?
last slate
**Cnidarian**
$I.I$ mean det btw
grand pondBOT
Cnidarian
last slate
and $(b^,)$ means b inverse
grand pondBOT
Cnidarian
twilit field
$let B^TAB=M$
grand pondBOT
ƒ(Why am. I here)=I don't Know
twilit field
$\implies AB=B^{-T}M$
last slate
its inverse
grand pondBOT
ƒ(Why am. I here)=I don't Know
last slate
nvm
they didn't mention if its inverse or tranpose
lets just consider that its inverse
twilit field
now $A=B^{-T}MB^{-1}$
grand pondBOT
ƒ(Why am. I here)=I don't Know
last slate
isn't it $A=BMB^{-1}$
grand pondBOT
Cnidarian
twilit field
or that if you're not taking the transpose
twilit field
ok, let's start from $B^{-1}AB=M$
grand pondBOT
ƒ(Why am. I here)=I don't Know
grand pondBOT
ƒ(Why am. I here)=I don't Know
last slate
yes
twilit field
now $A=BMB^{-1}$
grand pondBOT
ƒ(Why am. I here)=I don't Know
twilit field
yes?
last slate
$A^,$ means A tranpose
grand pondBOT
Cnidarian
last slate
nvm that
could you confirm if my method is correct
if it was inverse instead of tranpose
twilit field
what is $A'$
grand pondBOT
ƒ(Why am. I here)=I don't Know
twilit field
transpose?
last slate
https://www.toppr.com/ask/question/prove-that-the-matrix-bab-is-symmetric-or-ske...
tranpose in this case and the in the question i asked
twilit field
the same logic applies
last slate
but lets just say A^, is inverse
last slate
could you confirm if my method is correct
^
last slate
Then you can't come to any conclusion
Are you saying that when A^, is inverse we can't come to any conclusion
last slate
what did the test assume ?
transpose
twilit field
I feel so
last slate
hmm
twilit field
**ƒ(Why am. I here)=I don't Know**
we can't come to any conlusion from this
last slate
oh
twilit field
afaik
last slate
but there aren't any mistakes in my the method ?
^
last slate
**Cnidarian**
its here
twilit field
$\det{ X}= \det{M}$
grand pondBOT
ƒ(Why am. I here)=I don't Know
grand pondBOT
Cnidarian
twilit field
that doesn't mean that $X=A$
grand pondBOT
ƒ(Why am. I here)=I don't Know
last slate
yes , but we can predict the nature of those matrix right ?
symmetric or skew symmetric
twilit field
I don't think so, ping helpers to confirm
cobalt swan
What is the problem?
last slate
The question or my doubt ?
cobalt swan
Ur doubt
last slate
if X was skew symmetric so would be A
And if X was symmetric,A will also be the...
if X was skew symmetric so would be A
And if X was symmetric,A will also be the same
is this a proper method
Someone copied your name lol
simple field
<@&286206848099549185>
A = A' => B' A B = B' A' B = (B' A B)'
in words B' A B is symmetric if A is symmetric
i dont understand what it was you were trying to show with DET and etc