You're welcome
#help-0
storm ridge
fading briar
.close
lone heartBOT
lone heartBOT
Available help channel!
raw lion
I`m gonna show a pic of my answer for this question, tell me what you think of it.
raw lion
lone heartBOT
@raw lion Has your question been resolved?
lone heartBOT
@raw lion Has your question been resolved?
unborn notch
how do u calculate the ratio of 3 numbers
lone heartBOT
how do u calculate the ratio of 3 numbers
finite walrus
20/30/40
narrow kelp
3:2:4
lone heartBOT
@unborn notch Has your question been resolved?
spare birch
lone heartBOT
lavish cave
How should I go about this
try to factorise 1536
spare birch
spare birch
Ok
lavish cave
but either way it works actually
like I can recognise 512 is a power of 2
so it's 3 * 2^9
you could do the same with 32 * 48 and so on
spare birch
With the way they want me to write it
lavish cave
try to find the prime factorisations of each
lavish cave
With the way they want me to write it
yep, so the cube root of 3 * 2^9 is?
spare birch
And another number on the inside
lavish cave
yep
spare birch
Wait so I should have 3 on the outside?
spare birch
And then 2^9
lavish cave
And then 2^9
the cube root of that ye
spare birch
use the laws of indices here
Haven’t learned it yet
lavish cave
Haven’t learned it yet
really?
lavish cave
it's from tutoring?
spare birch
This stuff is from a program I signed up for that is harder than regular school
And it basically shows some stuff I don’t know how to tackle yet
lavish cave
right the laws of indices you need here are $(ab)^x = a^x b^x$
ocean sealBOT
south
lavish cave
where x = 1/3
if you multiply ab by x times
it's the same as multiplying a by x times
and then multiply that by b mutliplied x times
so $(3 \cdot 2^9)^{1/3} = 3^{1/3} (2^9)^{1/3}$
ocean sealBOT
south
spare birch
Gives us 3^(1/3) * 2^(3) = 3^(1/3)*(2^(9))^1/3
lavish cave
Gives us 3^(1/3) * 2^(3) = 3^(1/3)*(2^(9))^1/3
yeah
that's 3^(1/3) * 2^3
and 2^3 = 8
spare birch
Cube root of 3 times 8
lavish cave
yep
lavish cave
mhm
part of me wants to scream "you haven't seen difficult" but difficulty is all relative anyways
plain zodiac
lone heartBOT
plain zodiac
for this part
why are they adding pi
why not 2pi
i thought its supposed to be 2pi
so its the same angle
storm ridge
Which q
plain zodiac
i put the whole question above
long axle
That’s some crazy stylismanship
proven leaf
are you asking where they do pi/12+pi?
oh wait yes it is the whole problem, well remember what's the period of this function? :)
vapid stirrup
lone heartBOT
vapid stirrup
Does a problem like this imply that theta is less than pi/2 (or 90 degrees) ?
Symbolab gives me cos(theta) as the answer
split mantle
$cos(\pi - \theta) = - cos (\theta)$
ocean sealBOT
Good
vapid stirrup
Yes, i can see how that would happen, but thats only true if theta is less than pi/2 right?
so thats what this question is implying i guess..?
split mantle
Applying pi to an angle means to flip the angle, to its opposite angle.
If you got cos(112), which is in the 2.quadrant, and you add pi (180) to it, you would have cos(292), which is in the 4.quadrant.
split mantle
You do this question with that.
alpine sable
Are the angles around point K 90°?
lone heartBOT
Are the angles around point K 90°?
alpine sable
AK is the bisector of an isosceles triangle with the base AC. BK = AC. Prove that AK = AC
storm ridge
Are the angles around point K 90°?
If it's 90 then AK cannot be equal to AC
Coz AC is hypotenuse
alpine sable
If it's 90 then AK cannot be equal to AC
Yes i figured all that out already
Idk if they are actually 90
If so, how can we prove that?
storm ridge
I mean, if the q asks proof of why AK=AC, then it cannot be 90
To prove why it cannot be 90 we need to prove AK=AC
Using other ways
alpine sable
Using other ways
Can you please help me, i'm seriously going insane on this easy question
alpine sable
So we just ignore if they are 90°
alpine sable
AC is the base, does that mean AB=BC?
Yes
storm ridge
So we just ignore if they are 90°
For now, yeah
alpine sable
Isosceles triangle
storm ridge
Could you show from where did you get the q?
alpine sable
Could you show from where did you get the q?
That's the exact text i got from my little brother, idk
storm ridge
Oh
alpine sable
He is in grade 7 if that helps
storm ridge
Are you sure K lies on BC?
alpine sable
AK is the bisector of an isosceles triangle with the base AC. BK = AC. Prove th...
Well, if AK is the bisector and AC is the base, where else can it lie on?
storm ridge
It could lie inside the triangle
alpine sable
Does that help us?
storm ridge
Hmm
alpine sable
It is like that in his book, just in a different language
I translated and posted here
alpine sable
There are no translation errors though, i double checked the terminology
storm ridge
Oh
alpine sable
Coz it retains most of the info
It's the exact same
storm ridge
Was there a fig with that q?
alpine sable
No i asked him that too
storm ridge
Damn
alpine sable
Should i ping helpers?
storm ridge
Sure, if you want to
alpine sable
AK is the bisector of an isosceles triangle with the base AC. BK = AC. Prove th...
<@&286206848099549185>
neat cipher
!15m
lone heartBOT
Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
storm ridge
Lol
plucky sluice
!original
lone heartBOT
Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.
plucky sluice
Your diagram shows a right angle, but you are apparently unsure if it's a right angle or not
alpine sable
Please show the original problem, **exactly as it was stated to you**, with the ...
That is the original problem
alpine sable
Your diagram shows a right angle, but you are apparently unsure if it's a right ...
Yeah we decided to ignore it and move on
storm ridge
Your diagram shows a right angle, but you are apparently unsure if it's a right ...
Ye just ignore the right angle
alpine sable
But still stuck
storm ridge
Ye just ignore the right angle
Coz if it is then we can't prove what's given in the q
alpine sable
!original
AK is the bisector of an isosceles triangle with the base AC. BK = AC. Prove that AK = AC
That is all that's given.
lone heartBOT
@alpine sable Has your question been resolved?
alpine sable
.close
lone heartBOT
alpine sable
.reopen
lone heartBOT
✅
alpine sable
AK is the bisector of an isosceles triangle with the base AC. BK = AC. Prove th...
This is the question
alpine sable
This is what i got so far. We tried solving by ignoring the 90° angle, since it would be impossible, but still are stuck
alpine sable
<@&286206848099549185>
alpine sable
Im just pure guessing but maybe prove AK = BK first by idk similarity or something... I dont see the way but there must be something
alpine sable
Im just pure guessing but maybe prove AK = BK first by idk similarity or somethi...
I don't think it's possible
I've tried already
alpine sable
Im just pure guessing but maybe prove AK = BK first by idk similarity or somethi...
Forthis try drawing a parralel to AC from K intersecring at some point On AB
alpine sable
I've tried already
Oh
alpine sable
Forthis try drawing a parralel to AC from K intersecring at some point On AB
Can you draw that?
I don't think i understand
XK || AC
Its loading
That will also be a parrallelogram, maybe use that and the Basic peoportionality theorem / Thales theorem idk
Its 2 am i cant think clearly but i have that faint memory of doing this question
Idk
Yk the thing is is that this is a problem from my 12 year old brother's math book and he would have no fucking clue what this all means
Lmao wtf
12 year old?
Exactly
What were they expecting for them to do
Then just show them it cant be 90° and hence your veryquestion is wrong
alpine sable
What were they expecting for them to do
Lol
I would love to know
Too
No way
This is stupid idk
Fr
Maybe they forgot to add some info to the question
It feels incomplete
Ye
Lemme try still
alpine sable
Lemme try still
Okay lol
AK ≠ AC
Ignore the 90°
It makes this even more impossible lol
Ye
AK≠AC
Unless special cases
See this
Alright ty
You certainly can deduce
It is
An isoceles triangle + AK≠AC
Lemme draw a circpe for you too wait. A sec
Its not the best but
Using the circle you can see
alpine sable
An isoceles triangle + AK≠AC
If AK doesn't equal AC, then we can't prove that the question is true
alpine sable
If AK doesn't equal AC, then we can't prove that the question is true
Exactly
But the questions ask us to prove that they do djeudnwnsjwnd
alpine sable
Using the circle you can see
Circle has the radius as AK and it doesnt cut at point C , AK ≠ AC
alpine sable
https://tenor.com/view/cat-insane-gif-21702784
BRO
https://virtual-graph-paper.com/MjY0OTI0ZGUyMDEx
The perfect proof
You can easily see
I took the radius as AC
Now the line
From below its exactly 45°
And from above the angle is like 30ish
Therefore it is jot the bisector
Therefore the Question is wrong
Wait wait
Maybe i did something wrong?
Actually no
😭, tell us
It is wrong
Yeah cus
Unless theres some special relation for the angles
It wont work
alpine sable
Does BK = KC
Uhh wait
if a line bisects an angle, it divides the opposite side into segments proportional to the other two sides, right?
Can we use this somehow
alpine sable
if a line bisects an angle, it divides the opposite side into segments proportio...
This true
alpine sable
Can we use this somehow
AK ≠ AC still
Is my drawing correct?
I may have did something wrong
You never sent the original question
alpine sable
You never sent the original question
AK is the bisector of an isosceles triangle with the base AC. BK = AC. Prove that AK = AC
Thats all?
Yeah😭
Yeah then your drawing is correct
Cuz
K must lie on AC
I mean
BC
Questions wrong. Period.
Why can't they just make it lay on ac
Sjebebf
alpine sable
Why can't they just make it lay on ac
Cuz K originates from A
I think it's a typing mistake
alpine sable
Cuz K originates from A
Yeah ik
Ye
Im donefor the night
Best of luck
Goodnight
Thank you, goodnight
WAIT I GOT IT I THINK
alpine sable
if a line bisects an angle, it divides the opposite side into segments proportio...
If we set AB and BC to x, and AC to y, we can write it as
AK/BK = AB/BC
AK/y = x/x
AK=y
So AK = AC
storm ridge
WAIT I GOT IT I THINK
K was on BC all along eh?
alpine sable
K was on BC all along eh?
I think so?
storm ridge
Damn
alpine sable
If we set AB and BC to x, and AC to y, we can write it as
AK/BK = AB/BC
AK/y...
I guess this is correct
Fuck this question though
alpine sable
If we set AB and BC to x, and AC to y, we can write it as
AK/BK = AB/BC
AK/y...
@subtle birch
subtle birch
If we set AB and BC to x, and AC to y, we can write it as
AK/BK = AB/BC
AK/y...
you basically used similarity
storm ridge
I guess this is correct
Glad you got it
subtle birch
though that appears to be provable by similarity, the triangle so formed is quite contradictory
alpine sable
Alright, i can finally close this channel after like 3 hours of opening it
Time to explain this to my 12 year old brother
Thank you to everyone that helped me with this, actually can't thank you guys enough 🙏
.close
lone heartBOT
lone heartBOT
Available help channel!
upbeat wraith
lone heartBOT
upbeat wraith
how is this solved?
tacit arch
do you know the definition of surplus
upbeat wraith
yes
tacit arch
what is it
tacit arch
I find s(q)=119, but how do I find the surplus
Use the definition
lone heartBOT
@upbeat wraith Has your question been resolved?
upbeat wraith
.close
past rain
If a probability problem says that it has been observed that historically, test scores follow a standard distribution of 30.9, that is σ instead of s, right?
gusty gorge
I mean technically it's a t distribution with the number of degrees of freedom as historical observations - 1
but typically, we have a lot of history, so it converges to the normal distribution
past rain
so then that value of standard deviation is of the whole population, right?
Not s from just a sample?
gusty gorge
it's a really large sample, since you haven't actually observed the whole population
but since the sample is really large, you just use the normal distribution
past rain
so, in a sample of 23, with an average of 249.1, and a historic 30.9 standard deviation
with a confidence of 94%
The upper limit of the average would be 261.2?
gusty gorge
I have no idea; I'm far too lazy to calculate it
but confidence of 95% is just +/- two standard deviations, where the standard deviation is of the sample mean
lone heartBOT
@past rain Has your question been resolved?
past rain
.close
lone heartBOT
lone heartBOT
Available help channel!
flat cloud
lone heartBOT
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
1
sour dove
Plurality method just means the letter has the most 1st place votes
so sum up the the total number of A, B, C, D 1st choice votes. Whomever has the most is the winner
For example D = 8 + 10 = 18
do the rest and compare results
flat cloud
thank you, how do I do pairwise?
lone heartBOT
@flat cloud Has your question been resolved?
lone heartBOT
@flat cloud Has your question been resolved?
lone heartBOT
@flat cloud Has your question been resolved?
flat cloud
.close
waxen turtle
lone heartBOT
waxen turtle
When I graph to it, it seems like (x-1)^2+(y-2)^2=6.25
But I get =25 when I do it myself
Oh wait
It's in half units
.close
ebon meadow
2 popular answers for this: 1/2 and DNE.
lone heartBOT
2 popular answers for this: 1/2 and DNE.
ebon meadow
Rewrite to [sqrt(1+x) - 1] / x
yes but isn't this ignoring sqrt(x^2) which is abs val of x?
lone heartBOT
@ebon meadow Has your question been resolved?
limpid turret
yes but isn't this ignoring sqrt(x^2) which is abs val of x?
You are right on the money here.
ebon meadow
You are right on the money here.
how do i continue though
limpid turret
how do i continue though
Piecewise the limit for x<0 and x>0
wooden jewel
lone heartBOT
wooden jewel
I dont understand why we can just find the normal of the vector (5,2,2) and then plug it in the equation of the plane
while making sure it passes through (2,-6,1)\
lone heartBOT
@wooden jewel Has your question been resolved?
wooden jewel
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granite holly
i have a sequence $a_1 = 1, a_{n+1} = a_n + (-1/2)^n$ (which is indeed a geometric series, but pretend i didnt know that).
how can i find $\lim_{n \to \infty} a_n$? i tried the method where i say $\lim_{n \to \infty} a_n = \lim_{n \to \infty} a_{n + 1} = L$ but when i subsititute my $a_{n+1}$, $L = \lim_{n \to \infty} a_n + (-1/2)^n$ i get $L = L + \lim_{n \to \infty} (-1/2)^n$ which is just $L = L$. what am i doing wrong?
ocean sealBOT
nufflee
lone heartBOT
@granite holly Has your question been resolved?
granite holly
<@&286206848099549185>
lone heartBOT
@granite holly Has your question been resolved?
tough dawn
I’m working on partial fractions and I need to solve this with a matrix.
jagged cobalt
progress?
lone heartBOT
@tough dawn Has your question been resolved?
tough dawn
progress?
Haven’t made it anywhere
Oh wait let me try something
Ok so to start would it look something like this?
jagged cobalt
it would
jagged cobalt
multiply by 2x(x+1)^2
jagged cobalt
no, idk what you just did
$\frac{5x^2+20x+8}{2x(x+1)^2}=\frac{A}{2x}+\frac{B}{x+1}+\frac{C}{(x+1)^2}$
ocean sealBOT
AℤØ
jagged cobalt
multiply by 2x(x+1)^2
jagged cobalt
both sides of the equation...
tough dawn
So like for example a would be what? 2Ax or something?
tough dawn
Because the x+1 cancels
tough dawn
Oh
jagged cobalt
B(2x)(x+1)
jagged cobalt
it would be
tough dawn
Ok
So to make them equations I would do A(x+1)^2=5? Then do the same kind of thing for B and C?
tough dawn
Then how do I make them a system of equations to turn it into a matrix
jagged cobalt
choose values of x to sub in to make equations purely in terms of A, B or C
ig if you wanted to go wild, you could expand the brackets and compare coefficients to make your equations
either is fine
tough dawn
Ok so if I had x=1 A would be 4A right?
jagged cobalt
indeed
tough dawn
Alright so the equation for that would be 4A = 5?
jagged cobalt
no
thats not how it works
you have more than one term
if i say 3+12=7+8 that doesnt mean 3=7
thats what youre doing rn
tough dawn
Oh
I thought you did them one at a time. That’s why there’s a, b ,and c. X^2, x, and the constants
jagged cobalt
you sound like you want to compare coefficients
but you also did an x substitution
so i really dont know
which one are you doing
tough dawn
I don’t know what I’m doing either bruh
jagged cobalt
tough dawn
I just need to get this into a system of equations so I can make a matrix
jagged cobalt
fine lets say youre letting x=1 like you wanted
then you have 5+20+8=4A+4B+2C
multiple terms
tough dawn
Ok
ocean whale
I just need to get this into a system of equations so I can make a matrix
If you were doing this way, I think the more ideal way is to expand 5x^2+20x+8=A(x+1)^2+B(2x)(x+1)+C(2x)
then compare coefficients to make equations
tough dawn
If you were doing this way, I think the more ideal way is to expand 5x^2+20x+8=A...
That sounds more familiar. How do I do that?
ocean whale
Expand the right side
tough dawn
So Ax + A^2 would expand A right?
ocean whale
Not sure what exactly you are doing
tough dawn
Expanding
ocean whale
Like starting with this part here, A(x+1)^2
Expand (x + 1)^2
tough dawn
x^2 + 2x +1
ocean whale
So now it's A(x^2 + 2x +1)
Distribute the A to all the terms
Repeat with B(2x)(x + 1)
ocean whale
Yes
tough dawn
Yes
ocean whale
On the right side, group up all the x^2 terms, all the x terms, and constants
Like rewrite that right side so all the x^2 terms are next to each other, and so on
ocean whale
Now notice how you can factor the common term. Like Ax^2 + 2Bx^2, the common term is x^2, which is why you grouped the terms like that. So Ax^2 + 2Bx^2 = (A + 2B)x^2
Do you see that?
tough dawn
Yes
ocean whale
Can you do the same with the rest terms?
ocean whale
No, you should leave it
ocean whale
5x^2+20x+8 = (A + 2B)x^2 + (2A + 2B + 2C)x + A
Do you agree?
tough dawn
Yes
tough dawn
(A + 2B)x^2 = 5x^2?
tough dawn
Oh ok
ocean whale
Do the same for the rest of the coefficients
tough dawn
So it would look like A + 2B = 5
ocean whale
So it would look like A + 2B = 5
Yes
ocean whale
Yep
tough dawn
Ok so now I can use a matrix
ocean whale
You now have your equations
A + 2B = 5
2A + 2B + 2C = 20
A = 8
From there you can make your matrix and solve for A, B, and C
tough dawn
Yes this looks like what my professor showed
Alright I think I understand how to solve these types of problems now
ocean whale
You now have your equations
A + 2B = 5
2A + 2B + 2C = 20
A = 8
I mean from this, you don't really need to do the matrix
Because by observation, you have A = 8 already
Then you know what A is, so you use the first equation, plug in A, the solve for B
Then you know A and B, and just use the second equation to find C
tough dawn
Yea I could solve it by hand. I noticed that too but my professor wants us to get comfortable with matrices
Thank you for helping me. I’m not the easiest to help when it comes to this
.close
obtuse folio
hello, does P({1,2,3}) mean just the set {1,2,3}? prob not... because P(x) represents a power set, no?
obtuse folio
also, "given by inclusion" means that it is a set with finite elements?
<@&286206848099549185>
lone heartBOT
@obtuse folio Has your question been resolved?
limpid turret
hello, does P({1,2,3}) mean just the set {1,2,3}? prob not... because P(x) repre...
P means power set, yes
So P({1, 2, 3}) is the set of every subset of {1, 2, 3}
obtuse folio
so {/0,{1},{2},{3},{1,2},{1,3},{1,2,3}}
limpid turret
In general, for any set $A$, $C\subseteq A\leftrightarrow C\in P(A)$.
ocean sealBOT
SWR
limpid turret
so {/0,{1},{2},{3},{1,2},{1,3},{1,2,3}}
You're missing one subset
limpid turret
For any finite set A of cardinality n, the cardinality of P(A) is 2^n
obtuse folio
What is cardinality
limpid turret
number of elements in the set
obtuse folio
ah ok
does "given by inclusion" mean that it is a powerset/set with finite elements?
statement is consider a partial order R on P({1,2,3}) given by inclusion of sets
honest folio
Any1 can tell me why my answer is incorrect?
lone heartBOT
Any1 can tell me why my answer is incorrect?
sour verge
The antiderivative of ln(x) is not 1/x.
storm ridge
Also it would be better to take ln x as the first function
lone heartBOT
@honest folio Has your question been resolved?
honest folio
The antiderivative of ln(x) is *not* 1/x.
Thx
honest folio
Also it would be better to take ln x as the first function
Would I still get the correct answer if I dont?
storm ridge
Would I still get the correct answer if I dont?
I think you would but you would've to integrate ln x as the second function
Which would be quite tedious
honest folio
I think you would but you would've to integrate ln x as the second function
Ah ok, thanks for the help
lone heartBOT
storm ridge
Np
lone heartBOT
Available help channel!
alpine sable
Hello
alpine sable
a test contains 6 MCQs each having 4 options and only one option is correct. the number of ways a cadidate can answer all six questions such that exactly 4 of the answers are correct. in how many ways can this be done?
.close
half flicker
$2^2x = 7 \cdot 2^{x + sqrt(x - 1)} + 8 \cdot 2^{2sqrt(x - 1)}$
half flicker
$2^{2x} = 7 \cdot 2^{x + \sqrt{x - 1}} + 8 \cdot 2^{2\sqrt{x - 1}}$
ocean sealBOT
Yanek
half flicker
i tried substituting $2^x = t$
ocean sealBOT
Yanek
half flicker
but i how do you find $2^{\sqrt{x - 1}}$
ocean sealBOT
Yanek
half flicker
$2^{x-1} = \frac{t}{2}$
coarse marlin
try taking logarithm on both sides
ocean sealBOT
Yanek
coarse marlin
it'll help bring the exponent terms of x to algebraic terms
velvet smelt
If you want, you could also split the 1st term on the right side of the equal sign into 2^x • 2^sqrtx-1
Then divide both sides by 2^2x
It becomes a quadratic actually
coarse marlin
If you want, you could also split the 1st term on the right side of the equal si...
you mean the first term?
velvet smelt
Oh sorry yes
Then after dividing by 2^2x, you could let 2^(sqrtx-1)-x be equal to a variable like p, then you'll get a quadratic that you can solve very easily
It's up to you tho, multiple ways of solving this
coarse marlin
Then divide both sides by 2^2x
well actually you'll still have 2^sqrt(x) to deal with.
not to mention, the second term will get even more complicated cuz there'll be x in the denominator of the exponenet
coarse marlin
I meant 2^2x
hmm. now i think it'll be quite easier. cuz all the exponents will be the same
right
velvet smelt
Exactly
If you have any trouble with it, please ask
Oh I just realised that you're not even the one that posed the question
north perch
that is +8 or .8
ocean sealBOT
Yanek
north perch
what was the original question
half flicker
**Yanek**
@north perch and i took log_2 of both sides
and i have $2x = \sqrt{x - 1} - \log_2(7 \cdot 2^x + 8 \cdot 2^{\sqrt{x-1}})$
ocean sealBOT
Yanek
north perch
u didnt have to take log this early
u can have 2^x=a and 2^(x+1)^1/2=b
so a^2=8b^2+7ab
(a+b)(a-8b)=0
so a=-b or a=8b
now substitute the value of a and b and take log
lone heartBOT
@half flicker Has your question been resolved?
fallen raptor
I need help with this question
lone heartBOT
I need help with this question
vivid minnow
I need help with this question
could you write it here?
fallen raptor
Sure
Show that curve r = b cuts the curve r^2 = a^2 cos2theta + b^2 at an angle tan^-1 (a^2/b^2)
lone heartBOT
@fallen raptor Has your question been resolved?
lone heartBOT
@fallen raptor Has your question been resolved?
fallen raptor
<@&286206848099549185>
lone heartBOT
@fallen raptor Has your question been resolved?
lone heartBOT
@fallen raptor Has your question been resolved?
lone heartBOT
lone heartBOT
Available help channel!
toxic hound
How would u do part a to this question
lone heartBOT
How would u do part a to this question
carmine reef
Separation
rearrange to get something of the form f(x)dx = dt and integrate both sides
toxic hound
rearrange to get something of the form f(x)dx = dt and integrate both sides
yes but im confused how to intergate this
mark scheme isnt helpful
upper sonnet
lone heartBOT
upper sonnet
find
upper sonnet
sum of double partial derivative wrt to x and y
carmine reef
yes but im confused how to intergate this
Substitute u=x-6
carmine reef
sum of double partial derivative wrt to x and y
$f_x+f_y$?
ocean sealBOT
thewizardofOU
upper sonnet
no
ocean sealBOT
thewizardofOU
carmine reef
Are you having trouble finding the partial derivatives individually?
long axle
Show ur work
upper sonnet
Show ur work
wait a min
long axle
,rotate
ocean sealBOT
long axle
Well first show what u got for the first derivatives
upper sonnet
(6x^2-2y^2) that term
long axle
?wdym
long axle
I’m not allowed to
long axle
If u just wanna check ur answer why not use an online derivative calculator
long axle
Fire
lone heartBOT
@upper sonnet Has your question been resolved?
tall pebble
For question 13 part B in this guys solution why does he divide -3x^2 by 2?
tall topaz
thats just how you do integrals
$\int x^n , \mathrm{d}x= \frac{x^{n+1}}{n+1} + C, n \neq -1$
wild umbra
bad font
ocean sealBOT
Pure
tall topaz
what r u typing bro
wild umbra
nothing?
storm ridge
Ye
wild umbra
i am not typing anything
lone heartBOT
tall topaz
lone heartBOT
Available help channel!
alpine sable
I neeed help with discrete random variable
lone heartBOT
I neeed help with discrete random variable
plucky sluice
what kind of picture is this? Are the questions photoshopped on to a picture of a mostly blank page?
alpine sable
what kind of picture is this? Are the questions photoshopped on to a picture of ...
i translated it so u could understand
plucky sluice
Anyway, you will have better luck if you focus on one question at a time and show your work for that question
!show
lone heartBOT
Show your work, and if possible, explain where you are stuck.
alpine sable
Anyway, you will have better luck if you focus on one question at a time and sho...
can u help me tho?
plucky sluice
Yes, if you show your work for one question and explain exactly where you get stuck
alpine sable
Yes, if you show your work for one question and explain exactly where you get st...
what if i dont know where to start?
also i dont rlly think these are questions u can show ur work in
plucky sluice
Honestly, both of those usually mean you haven't done the min. amount of studying on your own to be able to start the problem
alpine sable
i have i saw like 6 youtube videos
plucky sluice
These certainly have work that can be shown, and if you can't write down anything for any of the problems, then you should read your textbook, go over your lecture notes
Mimic some example, etc.
I could try to walk you through, but if you are so far behind, you will probably not learn much.
My advice is to try your best to make some progress on one of these problems. Then you'll have enough context to learn from the help you'll get, and the helper will know what you don't understand
For instance, for the first question, what do these $\Omega$ answers mean?
ocean sealBOT
Xenophon
plucky sluice
I could tell you, but it's such a basic thing that I would be haphazardly trying to teach you an entire course.
alpine sable
omega?
plucky sluice
yeah? what do they represent conceptually?
alpine sable
the number of elements in a set
plucky sluice
no
plucky sluice
the number of elements in a set
I really recommend reading your textbook/notes and trying these problems on your own
lone heartBOT
@alpine sable Has your question been resolved?
faint salmon
when solving a differential equation by separating its two variables
faint salmon
how come the +c doesn't cancel out?
if we have dy/dx = 2x/3y^2
i can separate the variables and get
3y^2 dy = 2x dx
integrate both sides to get y^3 + c = x^2 + c
junior vigil
how come the +c doesn't cancel out?
the c's combine in a sense. Since they can be any value, each one need not be the same as the other
cinder thicket
And yes they could be 0 also
faint salmon
ah, so instead of thinking about it algebraically and just assuming the c's cancel out you can just take them as one unknown vertical translation
junior vigil
uhhh
weak plinth
You can think of it algebraically, it is algebraic. The cs are just different variables
Like
weak plinth
integrate both sides to get y^3 + c = x^2 + c
This is wrong
Bc u wrote the same number is added to both sides
junior vigil
instead of thinking of +c and +c
faint salmon
y^3 + c1 = x^2 + c2
weak plinth
Yeah exactly
alpine sable
why was my help channel closed?
faint salmon
and our final result would be y = cubicroot(x^2+c3)
weak plinth
Idk if your teacher cares tho, maybe they're fine with it being implied they're different
junior vigil
yes
faint salmon
c3 being c2 - c1
weak plinth
Usually teachers let you use the same symbol
junior vigil
but its easier to just think of it as its own constant
rather than have multiple constants
rose igloo
Hi I'm struggling with this problem. I probably need to apply Bayes' theorem, but not sure how. I came up with this so far but it doesn't work: A = event that a person voted party X. B = event that a person claims they voted party X. p(A|B) = (p(B|A)*p(A))/p(B). But p(B|A) and p(A) are not given so this cannot be right
lone heartBOT
Hi I'm struggling with this problem. I probably need to apply Bayes' theorem, bu...
@rose igloo Has your question been resolved?
rose igloo
<@&286206848099549185>
lone heartBOT
@rose igloo Has your question been resolved?
blissful hound
.close
north perch
I had a problem but suddenly the solution clicked when I got the help channel
wild umbra
I had a problem but suddenly the solution clicked when I got the help channel
this was ur 3rd time
one more time
and banned
north perch
north perch
this was ur 3rd time
What 3rd time
3rd time of what
Asking smth in help channel
Or some offense which I don't know about
tacit arch
and banned
Wrong. Don't lie
tacit arch
Asking smth in help channel
!msgdel
lone heartBOT
Asking smth in help channel
The original post of this help channel has been deleted, and it will abruptly close and possibly lock. (This is irreversible.) Please claim a new channel, and don't delete the first message of any future channel you claim.
wild umbra
Wrong. Don't lie
lmao ok
tacit arch
No
lone heartBOT
Available help channel!
gilded olive
Hello! Can you please help me a little with the solution to this problem, because I solved it, but the compendium I got it from doesn't have the answers and I'm not sure if I worked the right way
Given a pyramid ABCDM with base rectangle ABCD, the lengths of all surrounding edges are equal. The lengths of the base edges are AB = 4 cm and BC = 3 cm, and the angle between two surrounding edges not lying in a wall is 2 alpha. Find the volume of the pyramid and the distance from point A to the plane (BDM).
north perch
Thats just half of the volume of pyramid
gilded olive
Thats just half of the volume of pyramid
The final answer for the volume will contain tan(alpha)?
north perch
I can't understand what alpha really is
gilded olive
Angle can't be found
north perch
So I can't tell
Which 2 walls are they talking about when they say 2alpha is angle between them
north perch
Ohk
gilded olive
i tnink angle AMC=2 alpha
lone heartBOT
@gilded olive Has your question been resolved?
gilded olive
do u need to know how to do this or there is no need
How much did you calculate it?
north perch
There was basic integration
Nothing complex
Suppose there is triangle in a plane that's parallel to auc plane
It's base is x
And the angle at top is 2alpha
It's width is dx
Since it's an isosceles triangle,when we cut the triangle into 2 parts we can get a right triangle of base x/2 and the top angle is alpha. Now use some trigno to get area in terms of x and then integrate with limit from 0 to 5 as the max value of x is AC which is 5
lone heartBOT
@gilded olive Has your question been resolved?
hybrid pilot
Hello, I am attempting a problem in which I must find the taylor series expansion at point 0 of a function similar to the form of (3x^3)/(1-x) using known . Online solvers are telling me to use the known geometric expansion (first image) and then just multiply in the 3x^3 within the summation. Why does this work? When is just multiplying in another part of the expression into to the known expansion okay? for another example, when solving for the expansion of (1-x)(ln(1+x)), could I just multiply (1-x) into the known expansion of ln(1+x)? Thanks
cursive badger
[f(x)\sum\g(i)=\sum(f(x)g(i))]
ocean sealBOT
Astral
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
cursive badger
so long as something is not dependent on the summation variable it can be moved in and out of the sum as if it were a constant
ie
[a^2\sum_{n=1}^{∞}\frac{1}{n^2}=\sum_{n=1}^{∞}\frac{a^2}{n^2}]
ocean sealBOT
Astral
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)
cursive badger
in this case x^n, x is constant in the function, n is the summation variable
so while you can't move f(n) terms outside the sum, you can move terms that are constant (relative to n) in and out
hybrid pilot
I'm a bit confused on what you mean by f(n) terms, can you elaborate on what those would be in the (3x^3)/(1-x) situation?
cursive badger
Hello, I am attempting a problem in which I must find the taylor series expansio...
so yes, in this case you could just multiply every term in the expansion for ln(1+x) by 1-x and it would work, because as far as math is concerned you just multiplied every term in a sum by a constant before adding them instead of after
it would be x^n
how do I put this
[g(x)=\frac{3x^3}{1-x}]
[g(x)=3x^3\sum_{n=0}^{∞}x^n]
[g(x)=3x^3\sum_{n=0}^{∞}f(n)]
within the function, x is a constant, it's not dependent on n
ocean sealBOT
Astral
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)
cursive badger
true, g(x) depends on x
but the sum depends solely on n, as far as it's concerned x is unchanging
hybrid pilot
I see I think I get it
I think my follow up question would be besides my list of known taylor polynomials, how do I know that the other part of the equation that I'm treating as a constant doesn't end up relying on n?
cursive badger
what do you mean?
hybrid pilot
uhh sorry i think my knowledge is just lacking but
cursive badger
it relies on n if it is a summation term that cannot be extracted, ie infinite sum of xn you can factor out an x from all the terms to get x * infinite sum of n
but infinite sum of 3/4^n you can turn into 3 * infinite sum of 1/4^n, but you can't take out 4s because while the 3 is common to all the terms, each term inside the sum does not share all the same number of 4s
in 3x^3/(1-x) you can multiply all the terms by 3x^3 before or after summing them together
but you can't take out "x" terms from the x^n because not all the terms have the same number of "x"s
ie the first term at n=0 has no x, it's just 1
you can compensate, ie get x * infinite sum of x^n-1
but that's less simplified
hybrid pilot
i think the gap in understanding im having is why 1/(1-x) becomes x^n and by extension reliant on n
while 3x^3 stays as just that without any reliance on n
cursive badger
i think the gap in understanding im having is why 1/(1-x) becomes x^n and by ext...
ah, you are simply rewriting as an infinite sum
hmm how to put this
hybrid pilot
im sorry my understanding of taylor series is definitely not there
cursive badger
we are not changing 3x^3's form, it does not rely on anything but x
1/1-x does not rely on anything but x, but our problem is we want a series
so we rewrite 1/1-x as a series, getting an equivalent form, an infinite sum where each term is dependent on n and x
however, 3x^3 is untouched, it's not dependent on n and can be moved in and out of sums
if you know calculus, it's like how you can't move f(x) out of $\int{f(x)dx}$
ocean sealBOT
Astral
cursive badger
because n is a "temporary" variable, it only exists to make the sum, just like how here x only exists to integrate f across a domain
hybrid pilot
ohhhh i think im understanding now, its not that 1/1-x needs to be related to n its that we want it to be so we can form a series?
cursive badger
yup
mint tundra
lone heartBOT
mint tundra
why is this =0
vernal snow
It is an odd function
echo socket
It's an odd function integrated over a symmetric interval
lone heartBOT
keen karma
math yhelp please
A business executive travels 1120 miles in a corporate jet and then travels an additional 60 miles by
car. The plane ride took two hours longer than the car ride. The jet travels 8 times the speed of the
car. Find the total time for the 1180-mile trip.
.open
A business executive travels 1120 miles in a corporate jet and then travels an additional 60 miles by
car. The plane ride took two hours longer than the car ride. The jet travels 8 times the speed of the
car. Find the total time for the 1180-mile trip.
lone heartBOT
Available help channel!
vale rivet
how to evaluate this limit to infinity
lone heartBOT
how to evaluate this limit to infinity
hushed locust
squeeze theorem
vale rivet
uh
hushed locust
aka sandwich theorem, etc
naive sorrel
well
vale rivet
huh
naive sorrel
since n is approaching infinity
the denimjnator in the second term is approaching infinity at a faster rate than the numerator
the answer is just 2 bc the denominator grows faster than the numerator
vale rivet
thank you but i need to prove it
naive sorrel
prove it waw
vale rivet
like develop it
hushed locust
the (-1)^n term alternates between -1 and 1. so the expression is always less than or equal to the same but with 1 in place of (-1)^n and greater than or equal to the same but with -1 in place of (-1)^n
naive sorrel
yea
hushed locust
the (-1)^n term alternates between -1 and 1. so the expression is always less th...
so if you can prove that both of these limits converge to the same limit, the overall limit converges to that as well, by the sandwich theorem
limpid turret
Have you learned squeeze theorem?
vale rivet
no
vale rivet
ok
limpid turret
Does this theorem sound familiar to you at all? If not, we can do your problem without it.
vale rivet
without it
limpid turret
Okay
So, it's good to start with the definition of a limit to infinity. Do you recall it at all?
limpid turret
i can solve 1 indeterminate form but there's two here
Can you show me what you have so far?
limpid turret
Let's start with the definition of limit then
vale rivet
ok
limpid turret
You are trying to show that $\lim_{n\to\infty} \frac{(-1)^n}{n}=0$.
ocean sealBOT
SWR
vale rivet
yes
limpid turret
By definition, that you means that, $$\forall(\varepsilon>0)\exists(N\in\mathbb{N})\forall(m\in\mathbb{N})\left(m>N\to\abs{\frac{(-1)^n}{n}-0}<\varepsilon\right)$$
vale rivet
uh
ocean sealBOT
SWR
limpid turret
with me so far?
vale rivet
no
limpid turret
where did I lose you?
limpid turret
which part do you not understand?
What is the definition of a limit, in your words?
vale rivet
but it's not about proving that it's 0, it's more like just evaluate it and find that it gives 0
limpid turret
If you're in calc 2 you should have absolutely learned squeeze theorem by now
vale rivet
What is the definition of a limit, in your words?
it's when you approach a number without touching it
limpid turret
Ah I see you are still using the very weak standard of proof for limits.
limpid turret
the denimjnator in the second term is approaching infinity at a faster rate than...
Then this was the proof wording explanation for your limit. No better way to put it in calc 2 terms.
vale rivet
ok but I need numbers
limpid turret
i need to calculate it
You already did. You found out it was zero.
vale rivet
no
limpid turret
!xy
lone heartBOT
Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.
vale rivet
ok basically i need to make the indeterminate forms disappear by developing it somehow so I can solve it
limpid turret
Oh. You are using lhopital I think.
vale rivet
ok
limpid turret
This is just a simple x/∞=0 limit. It really isn't any indeterminate form'
I'm not sure how else to help you other than...
!xy
lone heartBOT
Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.
vale rivet
-1^infinity is not defined?
limpid turret
It is not. But it is bounded
Which is why everyone is telling you to use squeeze theorem
limpid turret
Do you have the original problem?
vale rivet
.close
vapid shuttle
Technically that is undefined
jagged cobalt
it being -inf is basically saying it doesnt exist, but it just goes down forever
vapid shuttle
But
jagged cobalt
not exactly
vapid shuttle
Yes
Kind of
The idea is that the thing on the bottom is becoming really small
And the top is negative
Dividing by something really small gives you something really big, but negative because of the top
So they write -infinity
But really the limit DND
DNE*
The other ones are completely different
If you apply the reasoning, it doesn’t make any sense?
So that’s why
Well
If you multiply by something
And then divide by that same thing
You’re doing nothing at all
So the terms cancel