Available help channel!
#help-13
cedar kilnBOT
Available help channel!
forest elbow
If I want to determine if system Ax = b has a solution for all choices of b, then one way to figure this out is to check if every column in matrix A has a pivot ?
cedar kilnBOT
If I want to determine if system Ax = b has a solution for all choices of b, the...
@forest elbow Has your question been resolved?
atomic holly
cedar kilnBOT
atomic holly
How would I do this question
vestal vortex
could I have a full photo of the statement?
atomic holly
That’s all I have for this question
vestal vortex
I can't know what's next <<green slime solution>> line 2
atomic vapor
I need to prove this is correct for
cedar kilnBOT
I need to prove this is correct for
atomic vapor
no clue where to start
limits in -1 and infinity feel useless
but maybe im wrong
maybe this is better
broken temple
Do you know how to "get rid" of the ln?
And yes the second inequality is a great start
atomic vapor
Do you know how to "get rid" of the ln?
something to do with e^x?
broken temple
yes!
atomic vapor
the only question is "what" thing
broken temple
well I always think about it this way: log x = y means nothing else than 10^logx = 10^y... but 10^logx is the exact same as x
or with base e: e^ln(x) = x
atomic vapor
is this legal?
atomic vapor
maybe this is better
from here
broken temple
yes perfectly legal
broken temple
do you know how to handle exponents like you have here?
atomic vapor
maybe like this(wrong)
earnest prairie
maybe like this(wrong)
how can you do that?
atomic vapor
wait I cant
atomic vapor
so what should I do from here?
earnest prairie
i don't know.... but that step i think is illegal
limpid plume
maybe this is better
maybe we can use Lagrange's Mean Value Theorem as we know ln(1 + x) is continuous in (-1, infty)
atomic vapor
doesnt it have to be continuous in a closed segment for us to use this?
atomic vapor
maybe we can use Lagrange's Mean Value Theorem as we know ln(1 + x) is continuou...
.
limpid plume
[1, 1+x] is a closed subset of (-1, infty)
if x>0
if -1 < x < 0, then [1+ x, 1] is a closed subset of (-1, infty)
atomic vapor
I don't 100% get how does it help us 
ln x+1 is monotonic I think
Its easy to prove in [2,infinity)
but in (0,2) and (-1,0) not so much
cedar kilnBOT
@atomic vapor Has your question been resolved?
south juniper
@atomic vapor $e^{\frac{x}{x+1}} < x+1$ -- From here, you can let x+1 = X and then simplify some stuff
wraith daggerBOT
Sup?
south juniper
If you keep simplifying, you get to the inequality $\frac{e}{X} < e^{\frac{1}{X}}$
wraith daggerBOT
Sup?
south juniper
Then letting 1/X = y, then just let y be x, since it's just a variable, we get to the inequality e^x > ex
So you need to show e^x > ex for all x > 0 and x!=1
(We were given x > -1, x!=0 which is the same as x+1 > 0, x+1!=1. After x+1 = X, we have the bounds X > 0, X!=1. After y=1/X, we have the bounds y > 0, y!=1 and we just replaced y with x, so in the end you have the bounds x > 0, x!=1)
cedar kilnBOT
@atomic vapor Has your question been resolved?
south juniper
e^[x/x(x+1)] < x+1 ==> e^[(X-1)/X] < X ==> e^[1 - (1/X)] < X ==> e * e^(-1/X) < X ==> e/X < e^(1/X) ==> ex < e^x
atomic vapor
k thanks
I think I can finish it from here
thanks for the help everyone 🙂
.close
ivory veldt
Hello, so when I tried to solve this limit I get 1, like so:
$$\lim_{x\to 0^-}\left(\frac{x^2+x}{\sqrt{x^3+x^2}}\right)$$
$$\lim_{x\to 0^-}\left(\frac{x(x+1)}{x\sqrt{(x+1)}}\right)$$
$$\lim_{x\to 0^-}\left(\frac{x+1}{\sqrt{x+1}}\right)$$
$$\lim_{x\to 0^-}\left(\sqrt{x+1}\right)=1$$
But the book says the answer is -1, send help
wraith daggerBOT
Ket
cedar kilnBOT
cedar kilnBOT
Available help channel!
meager glade
Can someone help me understand these logs?
cedar kilnBOT
Can someone help me understand these logs?
meager glade
red pumice
$\log(a) + \log(b) = \log(ab)$
wraith daggerBOT
heavy
meager glade
so its, log((x+5)x) = 2 for the first part
red pumice
yes
meager glade
which is the same as, logbase6(x^2+5x)=2
but how do i further simplify that?
divide 2 by x^2+5(x)?
red pumice
$6^{\log(x^2+5x)} = 6^2$
wraith daggerBOT
heavy
red pumice
$6^{\log(x^2+5x)} = x^2+5x = 6^2 = 36$
wraith daggerBOT
heavy
red pumice
log base 6 everywhere of courese
wraith daggerBOT
heavy
red pumice
so then also $6^{\log_6(x^2+5x)}=6^2$
wraith daggerBOT
heavy
red pumice
therefore $x^2 + 5x = 36$
wraith daggerBOT
heavy
meager glade
Okay
i understand so far i think
But when i have this, do i simplify? or is this the simplest form
gusty notch
cedar kilnBOT
gusty notch
cedar kilnBOT
@gusty notch Has your question been resolved?
gusty notch
<@&286206848099549185>
cedar kilnBOT
@gusty notch Has your question been resolved?
wispy marten
Hi I'm so confused how to find symmetric and reflexive but I tried it
cedar kilnBOT
Hi I'm so confused how to find symmetric and reflexive but I tried it
@wispy marten Has your question been resolved?
cerulean sail
Symmetric is saying that if $(a, b)$ is in the relation if and only if $(b, a)$ is (i.e. $a$ is related to $b$ if and only if $b$ is related to $a$)
Reflexive is saying that $(a, a)$ must be in the relation for any $a$ in the set (i.e. for any $a$ in that set, $a$ is related to itself)
wraith daggerBOT
chartbit
cerulean sail
You're right with reflexivity and you're almost there with symmetry
Why do you think that (3, 3) needs to be there for symmetry?
cerulean sail
I'm confused on this part
Alright, what made you think that (3,2) was needed for symmetry?
wispy marten
Alright, what made you think that (3,2) was needed for symmetry?
Because (2,3) implies (3,2)?
I'm just guessing
cerulean sail
And why (2,3) is also reflective ?
Ehhh, for reflexivity you just need that (a, a) is in the relation for all a in the set (in this case, {1, 2, 3})
Reflexivity doesn't care about the elements of the form ("something", "different thing")
It just says that for the original set $A$, for all $a\in A$, you have $(a, a)$ in the relation
wraith daggerBOT
chartbit
cerulean sail
Because (2,3) implies (3,2)?
And that's the idea behind it, yep! Note that you have (2, 3) in the relation, which if you see the quote I made, means that you must have "the other way round" (so that means you need (3,2) in there too)
Note that for the others, because they're of the form (a, a), they're already enough to be symmetric (you end up saying (a, a) is in R if and only if (a, a) is in R, which is quite clearly true)
cerulean sail
So these are comparing the 4th pairs?
Basically, yea - you have those three pairs, and one additional one will make you symmetric, while another one will make you reflexive, and they want you to find those ones
Which one's needed for reflexivity, and which one's needed for symmetry?
wispy marten
Which one's needed for reflexivity, and which one's needed for symmetry?
(3,2) for symmetric ?
(3,3) for reflexive
I'm so bad at relations
cerulean sail
I'm so bad at relations
Awww, well you just have to work on them really(!) 
But does that all make sense though as for why?
cerulean sail
Is (2,3) also reflexive ?
(2, 3) is irrelevant for reflexivity 
reflexivity is about elements of the form ("something", "same something") if that makes sense?
cerulean sail
So relations are just comparing something?
In a way yep, they're a way of comparing elements in some way (for example, equivalence relations are a way of saying things are "the same" in some form)
cerulean sail
Sorry for keep asking
Don't be sorry at all! 
better for you to ask and then understand than to not ask and stay lost!
cedar kilnBOT
cedar kilnBOT
Available help channel!
crimson sedge
Hello people. I need help about how i should solve in
5^(N+1) / N + 1 > 1000
The result of N is 5 but i cant seem to know why or how its made.
clear berry
Using a graphing calc like desmos is the easiest
crimson sedge
How?
clear berry
You can see this is true for the range highlighted in red
Since, we want natural numbers, the smallest one to satisfy it is 5
clear berry
Hello people. I need help about how i should solve in
5^(N+1) / N + 1 > 1000
...
Another way is to guess and check
Guess when would 5^(n+1) > 1000(n+1)
crimson sedge
and what would be efficient way to solve?
use log or ?
like
log (5^(n+1)) > log(1000(n+1)) ?
clear berry
That should also work but in any case you'll need some form of computation
clear berry
and what would be efficient way to solve?
On desmos it doesn't matter, for writing code also it should matter unless it's very complicated
crimson sedge
i meant i dont need to use any software or smth,i just need to figure it out as in plain paper + calculator
clear berry
Then log should work better although, be a it careful as you'll need to adjust for bases also
Like with log base 5 you'd have gotten n+1 > log(1000(n+1)), but otherwise you'd use base e or base 10
clear berry
Usually by default, the base is e or 10. To check, find log(10). If it gives 1, the base is 10 otherwise it should be e
crimson sedge
Usually by default, the base is e or 10. To check, find log(10). If it gives 1, ...
okay then what would be format?
log_10(5^(n+1)) > log_10(1000(n+1)) ?
or how you should solve about 5^(n+1)
clear berry
log is an increasing function so, the inequality would remain preserved
You can try $\log_b 5^{n+1} > \log_b 1000(n+1)$
wraith daggerBOT
numbpy
clear berry
Or $(n+1) \log_b 5 - \log_b 1000(n+1) > 0$
crimson sedge
okay but how i am supposed to solve about 5^(n+1)??
thats where i am stuck with that part
wraith daggerBOT
numbpy
clear berry
okay but how i am supposed to solve about 5^(n+1)??
use the properties of log
clear berry
say we have base 10, then, we'd have
$(n+1) \log_{10} 5 - \log_{10} 1000 - \log_{10} (n+1) > 0$
wraith daggerBOT
numbpy
clear berry
Or $(n+1) \log_{10} 5 - \log_{10} (n+1) > 3$
wraith daggerBOT
numbpy
crimson sedge
wait where is that 3? xd
clear berry
Then try different values of n till this happens
crimson sedge
im so confused
clear berry
wait where is that 3? xd
$\log_{10} (1000) = \log_{10} {10}^3 = 3 \log_{10} 10 = 3$
wraith daggerBOT
numbpy
clear berry
Does this make sense now
crimson sedge
**numbpy**
it should be 5 * log_10(n+1) - log_10(n+1) > 3 and then it would be like 4 * log_10(n+1) > 3
right?
clear berry
it should be 5 * log_10(n+1) - log_10(n+1) > 3 and then it would be like 4 * log...
How did you get 5?
crimson sedge
clear berry
That's log_{10} 5, not just 5
clear berry
That's log_{10} 5, not just 5
Turns out $\log_{10} 5 = 0.6989700043360187$
wraith daggerBOT
numbpy
crimson sedge
the solution would be like
i meant
the question would bel ike this
Using the error bound associated with Leibniz's theorem, obtain the value of necessary for the error made when approximating the exact sum of the series
clear berry
I don't have much idea about that
crimson sedge
lets start from begin
you said that it would be right format
5^(N+1) > 1000(N + 1)
I have thought about that and it would be like 5^(N+1) > 1000N + 1000
or i am wrong about that?
clear berry
hardly makes any difference
clear berry
As in, this won't help to find the value of n
crimson sedge
5^N + 5^1 is equivalent to 5^(N+1)
no? why is that
If there is such case, how you would be able to solve like 5^N > 100 ?
clear berry
Computationally any simplification won't be of much help, log-wise it's now harder to take log
clear berry
If there is such case, how you would be able to solve like 5^N > 100 ?
Just take log
clear berry
5^n > 100 => log(5^n) > log(100) => n log5 > 2 (assuming base 10). Thus, n > 2/log5
log5 = 0.6989700043360187. So, 2/log5 = 2.8613531161467862
crimson sedge
okay
clear berry
ie n > 2.8613531161467862. Hence, n >= 3
crimson sedge
but how would you solve 5^(n+1) > 1000(n+1) ?
What i understood by the far that would be like
N + 1 > log5*1000(n+1) then
N + 1 > log1000(n+1) / log5?
clear berry
yeah, that's kinda it. The issue is that here we can't separate the n completely one
clear berry
Yeah but it's not clean, you don't get a value of N. There's N on both sides of the inequality
crimson sedge
so what are you suggesting me to do ?
clear berry
The easiest is to just put it in desmos, otherwise you can guess and check
crimson sedge
The easiest is to just put it in desmos, otherwise you can guess and check
no way,i cant do that
clear berry
For example here, you can remember that 5^4 = 625. So, 5^5 > 1000
So, 5 is a good starting guess
just check if 5^5 > 5*1000
If not, try 5^6 > 6*1000
and so on...
crimson sedge
oh
i see
so you need to guess and check if that N can reach and is greater than 1000
holy fk
so hard calculations and stuff have gone for nothing LOL
clear berry
Yeaah, if you have a calculator. It makes it much easier
clear berry
cause anything bigger will also work
crimson sedge
i see
how i can close this help or smth?
now i can say that my doubts are solved
cedar kilnBOT
cedar kilnBOT
Available help channel!
clever rock
I've lost my mind and can't remember how to do the product rule for counting, grateful for any help 😢
clever rock
Question is: Work out how many 5-digit odd numbers can be
formed using the digits 1 3 4 6 8 with no
repetition of any digit
Pondering on whether it's just a simple factorial of 54321, but I can't remember and can't find the mark scheme
Oops, 5x4x3x2 I mean
tropic oxide
you want the number to be odd
mighty drift
First express the constraint in a more useful way
tropic oxide
take that into account
clever rock
O wait so
I have 3 odd digits
Not 3
Reading the wrong thing lmao
2 odd digits
So, 43212?
tropic oxide
2 * 4! yes
clever rock
E, 4x3x2x1x2 I mean?
severe void
just a quick clarification question: if i'm looking to determine whether or not a space curve r(t) lies in a plane, do i just plug in and find points to create 2 vectors, then cross them, find the normal and use one of the points and the normal to find the equation of the plane?
severe void
(assuming i can't use torsion or whatever, prof said we aren't learning it)
<@&286206848099549185>
flint plinth
just a quick clarification question: if i'm looking to determine whether or not ...
what 2 vectors would you use?
probably you would want to check if the so called velocity vector (dr/dt) is always orthogonal to the plane's normal vector
severe void
i was more so thinking i plug different values of t into the components of r(t) and create vectors based on the outputs of that. would it be easier if i just took the derivative of r(t)?
flint plinth
(and you'd want to check that r(t) is in the plane for at least one t)
i don't think it would suffice to just form a few vectors by plugging in values of t
it has to be true for all t
so yeah, check r'(t)
if it's always orthogonal to the plane's normal vector then r(t) is always parallel to the plane
and if additionally some point of r(t) is in the plane, then all of r(t) is in the plane
severe void
once i get r'(t), what would i do in order to check it
flint plinth
take its dot product with N
where N = normal vector to the plane
you want the dot product to always be zero
cedar kilnBOT
cedar kilnBOT
Available help channel!
gentle perch
cedar kilnBOT
gentle perch
i dont know why the answer is 0 and 1
i know it has to do something with the number 6 but i dont know how you get a 6
grand forge
i know it has to do something with the number 6 but i dont know how you get a 6
what makes you say this?
coarse blaze
but thats honestly so overkill
grand forge
ahhh
gentle perch
so square root mean 1/2?
grand forge
than your left with $x^{\frac{1}{6}} = 1$
wraith daggerBOT
Mortta
gentle perch
so you just do 1/2 mutiply 1/3?
coarse blaze
Since they are dividing, you would subtract
gentle perch
but why is there a 1 left
wraith daggerBOT
dp
coarse blaze
and that's how you get the $x^{1/6} = 1$
wraith daggerBOT
dp
coarse blaze
Because we divided both sides by x 1/3
gentle perch
aren't you supposed to minus both sides x 1/3
coarse blaze
you could, but that wouldn't be useful for this problem, so we divide
(or it maybe could be, I just think dividing is easier)
wraith daggerBOT
dp
coarse blaze
$\frac{a}{b} = 1$
wraith daggerBOT
dp
coarse blaze
yes
but 3 ≠ 2 so in your example it doesn't work, but in general yesm
do you understand how we got $x^{1/6}$?
wraith daggerBOT
dp
gentle perch
kinda
coarse blaze
and by doing this division we realised x = 0 is a solution
because before dividing you must calculate x=0
so you understand how we got x = 0?
olive heart
cedar kilnBOT
olive heart
how do u solve this
ik the diagonals are congruent
$(2)(x)=(y+1)(3) and (2)(x+y)=(x-y)(7)$
wraith daggerBOT
Hehehehaw
olive heart
any1 help
zenith sail
**Hehehehaw**
In this form they are just linear equations
You can solve the same way you'd solve any system of equations
with substitution or elimination
olive heart
how do u set up the equations
zenith sail
with substitution or elimination
Do you know what I mean by this?
olive heart
yea
is it
like
wait nvm dont listen to me
ik what they mean
but how do u set them up
zenith sail
I mean just distribute the constants to get rid of the parentheses first
Like the first one is 2x = 3y+3
zenith sail
No problem 👍
zenith sail
yep that's all
olive heart
.close
mortal fiber
May I please get help factoring polynomials I forgot how to do it, the question is 4z^2+4z-3
mortal fiber
.close
ornate salmon
did i error in this procedure? the answer to z seems a bit peculiar
muted bear
,rotate
wraith daggerBOT
ornate salmon
eg?
muted bear
5-12-y~x-5-z
odd badger
Hi, can someone explain the logic here?
cedar kilnBOT
Hi, can someone explain the logic here?
cerulean sail
Also notice that the integral they mentioned is a lot like the form $\frac{f'(x)}{f(x)}$ but scaled
wraith daggerBOT
chartbit
odd badger
😵💫
odd badger
the only way they can is to make the numerator "usub-able"
Can you explain the process on how it became "u-subable"?
muted bear
thats what they explain in words
odd badger
So I picked up that they let u be the denominator
And differentiating it gives (2x-2)dx
And it gets factored
Monkey brain of mine sees that there's x-1 in the numeartor here
But can't seem to see how the "1" came from
cerulean sail
x = x - 1 + 1
odd badger
Add by zero shoulda known
cerulean sail
Added zero then split the fraction
cedar kilnBOT
cedar kilnBOT
Available help channel!
prisma root
what is the mass of an alloy consisting of 24% copper and 152 g of tin?
Pls help, How to solve this mathematical problem?😭
fading hazel
Does it only consist of copper & tin?
prisma root
Does it only consist of copper & tin?
yes
fading hazel
If so what could you say about the % of the alloy that contains tin?
prisma root
If so what could you say about the % of the alloy that contains tin?
100%
fading hazel
But 24% of the alloy is copper
If 100% of the alloy was tin it would have no copper
prisma root
The alloy is composed of copper & tin
prisma root
If so what could you say about the % of the alloy that contains tin?
O-ops, I was wrong
prisma root
**what is the mass of an alloy consisting of 24% copper and 152 g of tin?**
Pls ...
But the task sounds exactly like this, I was not mistaken in this
fading hazel
If the alloy is 24% copper and the rest of the alloy is tin, what % of the alloy would be tin?
prisma root
If the alloy is 24% copper and the rest of the alloy is tin, what % of the alloy...
This task is about knowing how to solve percentages.
There is no need to know the percentage of tin
prisma root
It'll help you calculate the mass of the alloy
152% of tin
fading hazel
where did you get that?
I think you'd be getting somewhere if you divided that number by two
The idea is that the percentage of each element in the alloy should add to 100%
Then if you find that x% of the alloy is y grams you can calculate the mass of the alloy
prisma root
🤔
tidal heart
I have a combinatorial problem. I’m trying to identify all the possible sequences of 4 objects arranged in a 2x2 grid. The combinations must all be unique so spinning the board would be considered a duplicate (1,2,3,4 is effectively the same as 4,1,2,3 3,4,1,2 or 2,3,4,1)
tidal heart
Is there a name for this, how do I solve it, and what’s the solution?
tidal heart
They are hexagonal wheels with matching symbols on each side. They are each unique and there’s only 4
fading hazel
In that case the answer is just 6
think of it this way
there are 4 spots to put the first object in
then 3 for the second
two for the third
then one for the fourth
so you have created 4 * 3 * 2 * 1 configurations
But each configuration can be rotated to form another configuration (that we've already account for)
In fact, we see that we can group these configuration into groups of four, as we can rotate a configuration 3 times to get 3 others
So we have (4 * 3 * 2 * 1)/4 unique configurations
fallen moat
so, like
a_1=1+4
a_2=1+4+8
a_3=1+4+8+12
...
a_n=1+4+8+12+...+4n
is that what you are saying?
yea, that's what we called arithmetic series
,w arithmetic series
wraith daggerBOT
fallen moat
do you know the quick way to find
1+2+3+...+100?
ohhhh
if you are interested, you can read this 🙂
crimson sedge
How would I find all the roots?
cedar kilnBOT
How would I find all the roots?
crimson sedge
Would I just replace the (x-2) with whatever it gives me on each choice, and then just do synthetic division
obsidian coral
Use the remainder theorem, whatever that is
crimson sedge
im not sure how that can help find multiple numbers though
oh wait no im such a dumbass
it says one of them is (x-2), not to divide by it 🤦♂️
thanks anyway
.close
cedar kilnBOT
soft owl
plug in the values of x
if f(x) = 0 =>x is a factor
else isn't a factor
crimson sedge
Ok thanks ill do that
soft owl
Ok thanks ill do that
anytime
cedar kilnBOT
Available help channel!
vestal mason
I need help
cedar kilnBOT
I need help
vestal mason
Ok
so
I know this is minecraft lol
but
I am really struggling on this
listen
stop with the reactions
anyway
grand forge
Brah
vestal mason
its a sort of sudoko thingy
when you flick a lever
both the numbers above
andbelow are activated
grand forge
My friend is an expert in red stone if u need his help
vestal mason
so
vestal mason
My friend is an expert in red stone if u need his help
this isnt redstone
so
you need to add it up
so that
the top makes a certain number which is 17
and the bottom makes 29
which combination do I put in
vestal mason
yea
vestal mason
AND yo ass be cheating
well
the game is kinda broken
because the door opened
while I fired lol
but the code was wrong
and I need help getting the code
violet night
grand forge
I got it
vestal mason
what is it
grand forge
No
vestal mason
by default the're up
grand forge
Leave them pointing up
vestal mason
that works I think
grand forge
Put the rest down
grand forge
All g
vestal mason
bad map
Oh hell no you guys can help me find x, y and z I dunno what the hell it is
crystal raptor
its a sudoku
vestal mason
ik
crystal raptor
it gives you contradictory answers for x,y,z
zenith sail
But there are two X's in the third row
crystal raptor
definitely sudoku related though
crystal raptor
check your head for a button
cedar kilnBOT
@vestal mason Has your question been resolved?
tawny moon
I need help
cedar kilnBOT
I need help
fading hazel
You should elaborate otherwise it's hard to answer
cedar kilnBOT
@tawny moon Has your question been resolved?
tawny moon
You should elaborate otherwise it's hard to answer
i need help with quadratics
test tomorrow and I know literally nothjing
tawny moon
can you send me something that covers the entire quadratic relations unit
i tried searching for something helpful but everything is trash
tawny moon
quadratics relation
fading hazel
tawny moon
like parabolas quadratic formulas and discriminant
fading hazel
A good skill to learn is finding these things yourself
fading hazel
but theyre all trash
I feel like you're making an excuse to not watch them
they're definitely good enough
rotund dagger
hi can someone please explain to me where they got 3.6 from? For question d
rotund dagger
<@&286206848099549185>
half forge
phythagoras theorem
s is the altitude of the face of this square based pyramid
green line is s
and the length of the yellow line is 3.6
rotund dagger
ohhh
I thought 7.2 was the yellow line 😅
and i got really confused
ty
.close
half forge
np
elder elm
cedar kilnBOT
elder elm
I could be overthinking this, and should probably understand it, but for the first question, does 7 days include both day 0?
Like, do we take into account day 0 as a day based off of the table? So day 7 would infact be day 6?
cedar kilnBOT
@elder elm Has your question been resolved?
elder elm
Please? Anyone? @lusty birch
dire geode
i can't see the problem its to small
Probably a screenshot of a screenshot of a screenshot
cedar kilnBOT
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cedar kilnBOT
woven storm
how does this work
e^5 + e^6 != e^(5 - 6)
cedar kilnBOT
how does this work
e^5 + e^6 != e^(5 - 6)
woven storm
.close
cedar kilnBOT
woven storm
nvm typed the wrong number in my calculator
cedar kilnBOT
Available help channel!
sick bronze
cedar kilnBOT
@sick bronze Has your question been resolved?
cedar kilnBOT
@sick bronze Has your question been resolved?
sick bronze
<@&286206848099549185>
cedar kilnBOT
@sick bronze Has your question been resolved?
ripe raft
cedar kilnBOT
ripe raft
If anybody could help me with initial process.
cedar kilnBOT
@ripe raft Has your question been resolved?
fallen moat
is the answer in terms of x?
ripe raft
is the answer in terms of x?
Nope.
fallen moat
hmmm
wraith daggerBOT
Nikhil Kumar
ripe raft
I'm tagging for the last time: <@&286206848099549185>.
fallen moat
well, you don't have to...
ripe raft
Okay.
sonic oyster
Lol dude what's the question
pearl galleon
$\left(\sqrt{a^2-3a}-2\right)=\dfrac{a^2-3a-4}{\sqrt{a^2-3a}+2}$
wraith daggerBOT
SAKUUN
pearl galleon
and $a^2-3a-4=(a-4)(a+1)$
wraith daggerBOT
SAKUUN
ripe raft
Yes.
ripe raft
Needed is the set of values of 'a' that satisfies the given equation with the given conditions.
sonic oyster
$\left(\sqrt{a^2-3a}-2\right)=\dfrac{a^2-3a-4}{\sqrt{a^2-3a}+2}$
Woww how u did it????
ripe raft
The original question is this.
pearl galleon
Woww how u did it????
mmmmm a rule ....$a-b=\frac{a^2-b^2}{a+b}$ and the a here is $\sqrt{a^2-3a}$ and $b=2$
wraith daggerBOT
SAKUUN
sonic oyster
$\y=$dfrac{a²-2a-1}{5y+4}
ripe raft
$\y=$dfrac{a²-2a-1}{5y+4}
Edit. Put '$' at the end.
sonic oyster
Not working
pearl galleon
u should resend the msgs
wraith daggerBOT
FeelingGood
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
ripe raft
I'll take a leave at 21 00 hours UTC+5:30 and rejoin at 21 30 hours UTC+5:30.
long arrow
$y=\frac{34y-4}{2e+r}$
wraith daggerBOT
Modus
FeelingGood
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)
sonic oyster
$y=\frac{3r-7t}{4d+8m}$
wraith daggerBOT
FeelingGood
ripe raft
I'll am taking a leave at 21 00 hours UTC+5:30 and will rejoin at 21 30 hours UTC+5:30.
sonic oyster
Of this
ripe raft
Initial step(s) of method of solving.
wraith daggerBOT
FeelingGood
sonic oyster
Trigo one side, and other stuff on other side
Then make graph of Tanx
And rough graph of RHS function
And see all domain where your function is less than than Tanx
ripe raft
That's not an easy task anyway I think.
sonic oyster
Yeah lol
pale stone
Im trying to understand how to solve the following recurrence relation (IMG1) but i struggled so i looked at th "model ans" and i cant understand how/why its doing what its doing. Orange highlite is the problem child(IMG2). I havent gotten to the pink part yet but ill probably need help with that too unless somethign magicaly clicks
short blade
they factored the quadratic
after that, it’s in the form a * b = 0, so either a = 0 or b = 0
thus x-8 = 0 or x+3 = 0
cedar kilnBOT
@pale stone Has your question been resolved?
pale stone
okokok i understadn wht i was confused by the 1st part i get that now
but how does (x-8)(x+3)=0 end up as x=8 or x=-3.
am i just missing algebra knowlege ?
wait....
i get it now
i think
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
distant fox
Have I done this correctly?
cedar kilnBOT
Have I done this correctly?
half forge
yes
empty vapor
cedar kilnBOT
empty vapor
can someone explain how to do this?
half forge
You can find the roots of f'(x)=0 and use it to sketch y=f'(x)
and after you sketch f'(x) you can find the intervals when the slope of the tangents in f'(x) is negative
zenith sail
Where f''(x) < 0, the graph of f is concave down
You can just visually estimate this from the graph you're given
viral lark
Hey there! I'm trying to figure out an efficient strategy for obtaining the result to this problem. I've tried factorisation based on the following constraints : every value is between 1 and 9 and only one occurence of each value is allowed. (i.e. 9x9 is not allowed).
I imagine there must be a faster way to get the correct result without going through each scenario. I'd appreciate any input!
viral lark
crimson delta
there aren't that many options. 6*7*8 is too small, so you need to include a 9
if you divide 373 by 9 you get 40 something, so the other two numbers have to multiply to something around there
viral lark
So your go to is to first try 6x7x8 first everytime?
I guess my question is what made you decide to test with that set of numbers?
half forge
6 * 7 * 8 is the largest number you can get without using 9
but that value is much to small to become 373, so they just proved that 9 has to be included
viral lark
And why not use 9 straight away?
half forge
to narrow the number of cases
viral lark
Ok
half forge
if you know that 9 must be included, it becomes much easier
viral lark
OK but if I have 160 you would start with 4x5x6?
half forge
4x5x6=120
crimson delta
yes that would tell you that you need at least one number bigger than 6
meanwhile 5*6*7=210 is way too big so you would also need a number smaller than 5
viral lark
That's a pretty good technique!
crimson delta
that doesn't get you as good as information as in the 373 case but still pretty usable
half forge
meanwhile 5\*6\*7=210 is way too big so you would also need a number smaller tha...
This won't work if the number is between 1 and 9
like, if you're looking for 160, you can have 4x5x8
oh
crimson delta
which has one number smaller than 5
crimson delta
I hear sleep helps
half forge
insomnia :'(
hoary charm
v
hoary charm
How do I find the solution for this ODE?
I'm not sure how to deal with step functions and the hint says to solve it as if H was continuous
This is what I tried doing, but I'm not sure if this is even correct
I factored out h(t) because it's a constant in both parts of the step function
dire geode
you solve the differential equation piecewise, then stitch it together at t=1
$y' + y = 0$ if $t<1$
wraith daggerBOT
riemann
dire geode
$y' + y = 1$ if $t\ge1$
wraith daggerBOT
riemann
dire geode
you should have boundary conditions at t=1
dire geode
yea so set them equal when t=1
dire geode
sure
hoary charm
Im a bit lost, is this so I can find C3 and C4?
dire geode
read the problem again and see what you're supposed to do
hoary charm
Im supposed to find the general solution to the IVP y(0) = 1 right
dire geode
yes
hoary charm
So is the solution also a step function for values of C3 and C4 that satisfy y(0) = 1?
@dire geode
dire geode
you're probably supposed to use the bottom equation to eliminate one variable in your general solution
dire geode
this is not specific enough. you should not have any C
hoary charm
but is the general solution supposed to be a step function?
hoary charm
this is not specific enough. you should not have any C
also im not sure what you mean, in the last image I no longer have the C variables
dire geode
$1+e^{-t} (1-C)$
wraith daggerBOT
riemann
hoary charm
o
dire geode
oh is that an e?
dire geode
yea then your IVP solution is good
hoary charm
Ok cool, thank you.
cedar kilnBOT
@hoary charm Has your question been resolved?
stuck crag
Could someone help me sove this problem? It goes as follows:
persons A B C and D each pick one random card from a standard deck of cards (52 cards) and lay them out in front of them on a table. A fifth person E looks at the cards and takes away one of them. A sixth person F comes in and by looking at the 3 other cards he is able to determine what sort the 4th card is (so not its number, but like heart, spades, clubs and diamonds). You can asume that person E and F agreed on a strategy before the situation starts.
I have thought about this for a long time and i can't figure the strategy out. Someone able to help?
dull oxide
Ask yourself this: What would happen if person E came in and saw one heart, one spade, and one diamond? What strategies could you develop around this scenario?
The reason I ask is because, if there were one of each card, then this kind of scenario must exist.
stuck crag
Well i have written down the odds what the 4th card could be is in ths scenario but that only leaves my wondering how he can ever know it for certain
like, i cant seem to understand how he can know it for sure and not pick the option which has the highest chance
cedar kilnBOT
@stuck crag Has your question been resolved?
stuck crag
Shouldn't they have agreed on some sort of code?
where E leaves a piece of information by picking a specific card to take away
and F is able to read this information
cedar kilnBOT
@stuck crag Has your question been resolved?
fair geyser
i think you misunderstood the problem
or like misexplained it
he also sees the empty spot
cedar kilnBOT
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cedar kilnBOT
cedar kilnBOT
Available help channel!
sterile pecan
cedar kilnBOT
red pumice
the line does not connect
so the left hand limit is not the same as the right hand limit
therefore the limit ...
sterile pecan
Does not exist!
cedar kilnBOT
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sterile pecan
.close
crimson sedge
f(x)=x^3-64
cedar kilnBOT
f(x)=x^3-64
scarlet garnet
f(x)=x^3-64
I agree
so what do you ask
scarlet garnet
i am not sure where to start
what exactly do you want to do
crimson sedge
hold on one sec
crimson sedge
how do i find B
soft owl
b³ = 64 = 4³ so b = ?
crimson sedge
b^3=64 b=?
dire geode
b^3=64 b=?
do you know what cube roots are?
crimson sedge
kinda
dire geode
b^3=64 b=?
take the cube root of both sides in your first equation
crimson sedge
hold on
ok so i think i got the answer
but i need one more question done
and this one i know pretty much nothing about it
f(x)=2x^2+5x-9 quadratic formula]
cedar kilnBOT
@crimson sedge Has your question been resolved?
cedar kilnBOT
@crimson sedge Has your question been resolved?
wraith daggerBOT
ilegosking
Heres what i know about them, if $\lfloor x\rfloor=n$ then $x\lfloor x\rfloor=nx$ and we have the inequality $n^2 \le nx < n^2+n.$ So, for $f(x)=1,$ we know that $nx=1$ so we have $n^2 \le 1 <n^2+n$ then we check for different values of $n, n=0,1,2,3...$ and we find that $1\le n < 2$ are the values for $n$ here, but how do i make it so this inequality shows the range of $x?$
cedar kilnBOT
sour hollow
Heres what i know about them, if $\lfloor x\rfloor=n$ then $x\lfloor x\rfloor=nx$ and we have the inequality $n^2 \le nx < n^2+n.$ So, for $f(x)=1,$ we know that $nx=1$ so we have $n^2 \le 1 <n^2+n$ then we check for different values of $n, n=0,1,2,3...$ and we find that $1\le n < 2$ are the values for $n$ here, but how do i make it so this inequality shows the range of $x?$
wraith daggerBOT
ilegosking
modern compass
Note that n is an integer. So if 1<= n <2 then n = 1
Since n is the floor of x, then n <= x < n+1
cedar kilnBOT
Available help channel!
woven turtle
hi, how can I do this pls ?
cedar kilnBOT
hi, how can I do this pls ?
woven turtle
I tried to take the integral from 22 to 30 but it seems im wrong
since they said after 22 months
short blade
that probably means the want the population at 22 months
woven turtle
that probably means the want the population at 22 months
Apparently, I should've added +12 to my first result
I wonder why
short blade
total population = pop change + initial pop
grim token
its such utter fucking bullshot
cedar kilnBOT
its such utter fucking bullshot
grim token
how do i find 2 numbers that multiply to 70, but add up to -19?
7x^2−19x+10=0
Solve the following quadratic equation by factoring.
I'm spending 3 hours on every assignment that normally takes 20 minutes to finish
short blade
how do i find 2 numbers that multiply to 70, but add up to -19?
you can solve this as a system of equations
but if you want to generally factor something like that, i would try a few simple numbers and see what you get
crimson sedge
7 is a prime number
so you have to see
if 10 is made up of two negative factors
what factor of 10 multiplied by 7 + the other factor = -19
crimson sedge
-2x7-5x1 = -19
crimson sedge
$x^3 - 3x^2 + 4x - 12 = 0$
cedar kilnBOT
$x^3 - 3x^2 + 4x - 12 = 0$
wraith daggerBOT
AllUtility
crimson sedge
$x^2(x-3) + 4 (x-3) = 0$
wraith daggerBOT
AllUtility
crimson sedge
$(x-3) (x^2+4)$
wraith daggerBOT
AllUtility
dull oxide
✅
crimson sedge
$\sqrt{x^2} = \pm\sqrt{-4}$
wraith daggerBOT
AllUtility
crimson sedge
what do I do now ?
vagrant elbow
i
vagrant elbow
$\sqrt{-1} = i$
wraith daggerBOT
NEONPerseus
vagrant elbow
**AllUtility**
Also you only add the plus-minus after you take the square root, just saying
crimson sedge
**NEONPerseus**
what is this
dull oxide
what do I do now ?
what is the question?
crimson sedge
**AllUtility**
where do i go from here
dull oxide
What was the original question you were trying to solve?
crimson sedge
**AllUtility**
.
crimson sedge
What was the original question you were trying to solve?
.
vagrant elbow
I think he meant to ask about what were you meant to find
The solutions, real solutions, just factor?
cedar kilnBOT
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cedar kilnBOT
cedar kilnBOT
Available help channel!
jaunty bronze
cedar kilnBOT
jaunty bronze
i need help breaking this down into the solution
vagrant elbow
What do you mean by solution exactly
jaunty bronze
not really solution, i guess i should say simplify