Strunta i det som står där nere
#help-0
mental finch
Jag antar att vi inte har fått givet vart D’s x k koordinat är?
Har kallat den ”b”
Dvs. D = (b, 35)
vestal bough
what language are you guys speaking
mental finch
Kanske borde ha kallat den något annat än b lol
mental finch
what language are you guys speaking
Swedish
lone plaza
Har kommit fram till villkoren h(11)=10, h(Dx)=35, h’(Dx)=0 h’(11)=4,824
mental finch
Precis!
lone plaza
Vi kommer behöva räkna ut Dx?
mental finch
Ja
vestal bough
aslan is the lion in the movi right
mental finch
Yeah
vestal bough
i have seen all three of the movi
mental finch
Awesome!
vestal bough
the movies were good
lone plaza
Det blir då en liggande tanget. Men hur ska ja ta delta x om jag ej vet vart slutet är 😭
lone plaza
Yes
vestal bough
well sorry Interrupting
mental finch
Det gäller att skriva om steg för steg vad vi vet
vestal bough
in your study
ocean sealBOT
lone plaza
Aa kom fram till det. Men hur kan du vara anta direkt vad c är får man göra så? Förstår att c brukar typ vara start värde för y
mental finch
Jag antar inget om c
mental finch
Inga problem
lone plaza
Fyyy vad jobbigt 😭
lone plaza
Tror du att man kanske ska tänka att 1 och 3 hör ihop till ett ekvation system och 2 och 4 till ett annat
lone plaza
Dx=-b/2a tror du man ska använda de
mental finch
Jo precis!
lone plaza
Hoppas miniräknaren överlever
lone plaza
Varför skrev du 25 istället för 35
mental finch
Varför skrev du 25 istället för 35
35 - 10 =25
lone heartBOT
@lone plaza Has your question been resolved?
boreal prawn
I have a question im doing discrete maths now and i was wondering if i can say that if a|k and b|k’ then ab|kk’??
mortal trellis
a|k means that k=a*d for some integer d
b|k' means that k' = b*n for some integer n
what does that say about k*k' ?
boreal prawn
Kk’ has a factor of ab
It means its divisible by it
But the problem is that some correction mentioned that it only holds if a n b are coprime and I don’t get why is that so
boreal prawn
Its in french so..
But the goal of the ex is to prove that for p>3 where p is a prome number p^2 -1 is divible by 24
mortal trellis
Its in french so..
the math part is the same
boreal prawn
boreal prawn
One sec
I dont have the full solution but this is my main idea
In the solution they said that to be able to say 6|p(p-1)(p+1) u must mention that gcd(2,3)=1
mortal trellis
ok
so you didnt use what you wrote above
you wanted a|k and b|k => ab|k
and that indeed only works if a and b are coprime
for example 2|10 and 2|10 but not 4|10
boreal prawn
Aaa yea k is the same
boreal prawn
for example 2|10 and 2|10 but not 4|10
Ah i see thanks
Is this the reciprocal of gauss’s lemma ??
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sick tangle
can anyone
lone heartBOT
can anyone
junior kraken
i really dont know how to draw it
Yk to draw FBD ?
sick tangle
coz how am i meant to know if the box is on top of the boy
junior kraken
coz how am i meant to know if the box is on top of the boy
The boy is on top of the box 😭
junior kraken
A boy sits *
Let's not assume that the boy is spiderman, and the box is glued on top
junior kraken
NP
sick tangle
i know there is an equal and opposite force
junior kraken
i can give u markscheme if u want
It's written there
junior kraken
Yk right gravity is acting downwards
sick tangle
yea
junior kraken
And the lift is moving upwards
sick tangle
yes
junior kraken
So net, acceleration downwards is g-2
sick tangle
yes
junior kraken
That's the normal force exerted right
sick tangle
yes
junior kraken
Therefore (g-2)*weight of boy
sick tangle
i see but could u pls draw it on the diagram
sick tangle
i can zoom into the pic in the right
junior kraken
Yeah that's what you need to do
Like what to draw man !
g acting downwards
There's an upward acceleration
Therefore normal will be (g-2)*m
sick tangle
okay one sec lemme just go over everything i got the main idea
junior kraken
okay one sec lemme just go over everything i got the main idea
Yeahhh !
sick tangle
i get it now thank u
junior kraken
You're welcome
earnest geode
Which way an I supposed to do this my answers seem wrong on both, I don't know what I'm missing
earnest geode
lone heartBOT
@earnest geode Has your question been resolved?
earnest geode
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fallow urchin
let me see
the first way u did it is how id start it
and the 5/x^2 = y seems right
earnest geode
they are the same exept in one of tyhem i multiplied by the cost
fallow urchin
the base area is 2x^2 thats right
it wants the least expensive
so i feel like you might have to form an equation for cost and differentiate
the side areas would be 6xy right
earnest geode
ye
earnest geode
i did
fallow urchin
and get 2x^2 +6/x
typo
30/x
so the cost is 10 for the base area
so 10(2x^2) = 20x^2
and the cost of the side areas is 6
so 6(30/x)
earnest geode
oh i multiply the cost after i dirive it?
fallow urchin
so you get that the cost, C = 20x^2 + 180/x
no
now you differentiate the cost
dC/dx = 40x - 180/x^2
the derivative = 0 at the minimum point right
earnest geode
fallow urchin
so you get 40x=180/x^2
earnest geode
i accidentally put 20x=180/x^2
fallow urchin
nvm
remember it wants the cost
so when you w at the minimum point you can plug it back into the equation you had for cost
lone heartBOT
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crude parrot
im confused as to why this is being marked wrong
lone heartBOT
im confused as to why this is being marked wrong
vale wigeon
$10 says it's an arithmetic error 
crude parrot
im doing the integral from 0-1, 0-1/2+y of 2x/3 + 4y/3 dxdy
crude parrot
$10 says it's an arithmetic error <:opencry:586078614865444865>
WA says its 5/6 and thats still marked wrong 😭
wait i didnt type it correctly
41/36
which is what i got originally
vale wigeon
you're supposed to integrate over only the blue region but you integrated over the blue plus the red
with the bounds you stated
vale wigeon
better would have been to compute the complement tbh
instead of trying to integrate over that mildly complicated region
crude parrot
how do i do that? i have no idea what that means i wasnt taught how to
lone heartBOT
@crude parrot Has your question been resolved?
toxic verge
how do i do that? i have no idea what that means i wasnt taught how to
Complement = (the cases out of all the possible cases, which you do not want)/(total possible cases)
(For probability).
crude parrot
Complement = (the cases out of all the possible cases, which you do not want)/(t...
how do i apply that to this problem though?
is the total possible cases 36?
lone heartBOT
@crude parrot Has your question been resolved?
lone heartBOT
<@674393799396556823> still here?
whole adder
Okay so for the first one, we have a double integral from y = 0 to y = 1 and x = 1/2 to x = 1
You're fine with that right?
crude parrot
yeah i got that one right on the first try
whole adder
Do you understand what you're doing with that one, though? It's possible to follow a procedure and get the right answer without understanding what you're doing sometimes
crude parrot
yeah i just replaced 0 with 1/2 for the bounds, and i did the integral from 1/2-2, 0-1 of f(xy) dydx
either order works since the bounds are all constant
whole adder
1/2-2?
crude parrot
sorry 1/2-1
crude parrot
that dashed line is 1/2 + y right?
whole adder
Yes
We want to integrate over the blue region this time
If you just integrate up to 1/2 + y, then you're integrating over the red region as well
crude parrot
so do i have to set up two different integrals? one for the full thing and one to subtract that red part?
whole adder
There are various ways to do that. I'll go through 2 ways and then we can check our answer as well
Well you could do it that way if you wanted to
crude parrot
i was just thinking of that way because of ap calc, from the washer method or whichever method it was called
whole adder
I was going to integrate from [y = 0 to y = 1/2, x = 0 to x = 1/2 + y] and then from [y = 1/2 to y = 1, x = 0 to x = 1]
Does it make sense why I'm doing that?
whole adder
Yes
crude parrot
okay that makes sense
forest silo
winter light
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crude parrot
the way i was saying i think i could do y from 0 to 1, and x from 0 to 1/2 + y, and subtract y from 1/2 to 1, x from 1 to 1/2 + y?
sorry i got a text from my cousin halfway through typing this i dont mean to make you wait😭
whole adder
Yep you could that if you wanted
We're doing 2 integrals either way so it doesn't matter
whole adder
Actually, I'd slightly prefer my way since we only have to deal with x = 1/2 + y once
But it's not a big deal either way
crude parrot
was it way off or close
whole adder
Close
crude parrot
lemme put my version into WA to check rq
oh i think i just messed up my algebra somewhere
it gave me 65/72
yeah i got 11/72 for my second integral but it should be 17/72
which makes sense 17-11 = 71-65
whole adder
Yeah I got 65/72
crude parrot
whole adder
My first integral is 17/72 and my second integral is 48/72
crude parrot
yeah my first was 41/36 and my second one was 17/72 (or at least it shouldve been i just did something wrong)
whole adder
-> 17/72
whole adder
And everyone is happy yay
crude parrot
always some stupid algebraic thing haha
crude parrot
integration is impeccable but i cant simplify fractions 💀
whole adder
Maybe you get complacent at that point
Let's do the other method now
P(A) = 1 - P(Not(A))
So we can integrate over the region we don't want and subtract it
What are the bounds of that integral?
crude parrot
is that what i did or is that different
crude parrot
What are the bounds of that integral?
y from 1/2 to 1, x from 1 to 1/2 + y? if thats the region youre talking about
whole adder
It's different
whole adder
y from 1/2 to 1, x from 1 to 1/2 + y? if thats the region youre talking about
That's not it
That's what you did last time
We want the region that doesn't satisfy our condition
whole adder
So the entire region is y = 0 to y = 1, x = 0 to x = 1, right?
crude parrot
if we arent bounding it by 1/2+y yeah
oh i see you kinda folded the red region over
whole adder
?
whole adder
If we look at the definition of the function
It's defined between x = 0 and x = 1, and y = 0 and y = 1
crude parrot
yeah its defined on [0,1] x [0,1]
whole adder
What's the integral of the function over that region?
crude parrot
so is that 1 - the integral of the red region?
crude parrot
wait no integral y 0 to 1/2, and x 1/2 + y to 1
whole adder
Yes!
crude parrot
i see, just that white triangle space that the blue square doesnt cover
whole adder
Mmhmm!
crude parrot
that makes sense
whole adder
Let's just Wolfram that since I'm happy you can do the integration
,w 2/3 ∫[0,1/2] ∫[1/2 + y,1] (x + 2y) dx dy
ocean sealBOT
whole adder
🥳
crude parrot
thank you so much this makes so much more sense now lmao
whole adder
That's what people were talking about with the "complement" thing earlier
crude parrot
yeah i didnt understand that because i was never taught that way 😭
whole adder
The complement is Not(A)
crude parrot
i actually already took the final for this class, we never learned this part but it was on our homework
whole adder
Well... I wouldn't say it's a method in itself
It's just combining different aspects of probability
crude parrot
right but i mean we never did stuff that involved separate integrals
like taking that and applying it to probability
whole adder
P(A) = 1 - P(Not(A)) always, so it applies to density functions too
And if the probability is equal to an integral, then you can use the usual integral techniques to solve it
As we've seen here, you can look at the same region in various ways
crude parrot
yeah that makes sense
whole adder
e.g. a larger region - the extra bit, or breaking it into smaller simpler regions
All good now?
crude parrot
yes thank you so much
crude parrot
haha real, i teach math part time (obviously not this level) and i love that "aha" moment students have
whole adder
I think you can close now
lone heartBOT
naive sorrel
[
(m-1) \geq O_1 \geq O_2 - 1 \geq O_3 - 2 \geq \dots \geq O_{n-1} - (n-2) \geq 0
]
ocean sealBOT
WOWWA
naive sorrel
O_i are integers, i have honestly no clue how to solve for how many (n-1)-tuples solve this inequality
lone heartBOT
@naive sorrel Has your question been resolved?
carmine reef
Looks like a stars and bars problem
naive sorrel
i htink so too but im not sure how to set it up
carmine reef
The -1 -2 etc aren't important
naive sorrel
why not
carmine reef
Because you can just solve the version of the problem without them and then add 1 to O2, 2 to O3, etc
ocean sealBOT
WOWWA
naive sorrel
i was wondering about this as a simpler case anyways
but i dont even know how to solve this one
like i dont see a clear bijection to the stars and bars scenario
carmine reef
Think of having m-1 stars which are increments by 1
and then you have n-1 bars which are your N_1 N_2 etc
so if there are two stars between N_3 and N_4 it means N_4 = N_3 + 2
naive sorrel
so if there are two stars between N_3 and N_4 it means N_4 = N_3 + 2
would it instead be N_3 = N_4 + 2?
since the sequence is weakly decreasing
lone heartBOT
naive sorrel
.reopen
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carmine reef
would it instead be N_3 = N_4 + 2?
Yes
lone heartBOT
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sour blade
im self studying a multivariable calc book and im not sure how to approach this problem
lone heartBOT
im self studying a multivariable calc book and im not sure how to approach this ...
@sour blade Has your question been resolved?
naive valley
try considering separately the magnitude and the angle of the position vector as a function of time
hasty turtle
i need help on my highschool home work its only 2 problem can anyone help me ?
if possible i would like the the steps to
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lofty elm
First im going to get rid of some zeros and say the business man has 420, gets a total income of 26, and savings gets 2 less than the other two combined
Since savings gets two less than the other two investments and you know all 3 have to add to 26, the only two numbers that add to 26 with one being two less than the other are 14 and 12
Now that you know 12 is coming from savings and 14 is coming from the other 2, do you have an idea on how to work from there?
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hasty turtle
Hi i need help on matrix problem (from my highschool homework)
i will really love to have the step shown so i can study it
lofty elm
You asked the same question in two channels
but either way. What have you tried so far?
hasty turtle
but either way. What have you tried so far?
does chat gpt count i cant do any math.....
lofty elm
I would probably not count chatgpt
hasty turtle
then i sadly have not tried anything
lofty elm
My first thought here is to use a system of equations, especially since we are looking to use matrices
hasty turtle
yea the teacher spesificly ask to use matrices
lofty elm
You know that the money you put in savings (s) + time deposits (t) + bonds (b) will equal 420,000,000
That can be our first equation
hasty turtle
your talking is way to advance for me
lofty elm
Sorry I can try to simplify
First thing. You are going to put all your money into either stocks, bonds, or time deposits correct?
hasty turtle
ill try that
knotty yew
Hi! Answer to this is supposed to simplify to 0 after combining trig functions, seeing it’s even, and u-subbing 1/u. Having trouble seeing how it evaluates to 0
(I u-subbed 1/u in second line, just didn’t change variable to u)
median oar
1/x is odd
Probably something about the sine as well
Something something odd function integral = 0
That’s my guess
knotty yew
It’s even because it’s a product of two odd functions
knotty yew
1/x is odd
the sin part can be written as sin((x^2-2024)/x) which is also odd
so the whole thing is even
median oar
Ugh
knotty yew
I wish that was it 😭
Answer key just says
“substituting x->1/x eventually leads to 0”
median oar
Hi! Answer to this is supposed to simplify to 0 after combining trig functions, ...
Do the sub
knotty yew
like bruh
median oar
Hi! Answer to this is supposed to simplify to 0 after combining trig functions, ...
Oh you did
lone heartBOT
@knotty yew Has your question been resolved?
tacit arch
x - 2024/x is almost odd
Try u = sqrt(2024)/x and see if you can get sin(odd function) in the integrand
jaunty olive
Try u = sqrt(2024)/x and see if you can get sin(odd function) in the integrand
No need for square root
lone heartBOT
No need for square root
jaunty olive
@knotty yew sub u = 2024/x
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@jaunty olive Has your question been resolved?
hidden flax
Could someone please help me solve this question?
5a is correct but I have no idea how to find 5b
vale wigeon
,rcw
ocean sealBOT
vale wigeon
Could someone please help me solve this question?
5a is correct but I have no ...
so you found that you need 480 mL of the weak solution and 320 mL of the strong solution for 800 mL of 61% solution, yes?
hidden flax
so you found that you need 480 mL of the weak solution and 320 mL of the strong ...
Yep
hidden flax
3/2
hidden flax
Oh yes
vale wigeon
so if we wanted to make the largest possible volume of the mixture, which bottle would we use up first -- the weak stuff or the strong stuff?
hidden flax
The weak?
vale wigeon
indeed
so if we use up the entire 1L of the weak stuff, how much of the strong stuff do we need to make the ratio
vale wigeon
how did you get that
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drifting seal
How to do?
lone heartBOT
How to do?
woeful pulsar
it's doable, just kinda need to motivate the solution... hmm
do you know power of a point? try applying it
drifting seal
no...
woeful pulsar
then try to create some congruent right triangles to exploit the length information you know
drifting seal
how?
drifting seal
no... my school only teaches us some common theorem:
angle at center twice angle at circumference
angle in semi circle is 90
angle in the same segment are equal
line from center perpendicular to chord bisects chord
line joining center to mid-pt of chord perpendicular to chord
arcs proportional to angle at center / circumference
equal arcs, equal chord and vice versa
opposite angle in cyclic quadlateral
equal chords, equidistant from center
chords equdisant from center are equal
Only these, and the question I asked is the exam question
but idk how to do
drifting seal
equidistant from center?
woeful pulsar
yeah, draw those lines in
drifting seal
ok
drifting seal
drifting seal
anything else with equal chords?
no...?
woeful pulsar
do you have anything about tangency?
oh wait
yeah we have enough power to get the answer
drifting seal
oh
woeful pulsar
now that we drawn the lines, can we mark out any angles?
drifting seal
umm I'm not sure
drifting seal
oh the right angle
woeful pulsar
yeah
woeful pulsar
great
drifting seal
oh
median flame
https://discordapp.com/channels/268882317391429632/486841085210132490/1382393213553475615
In this question I was told that we should not take limits to parts of the expression. But in the question (approach 2) we multiply and divide by x to remove the tanx term. (This reduction of sinx or tanx by multiplying and dividing by x is done in a lot of limit questions) -> Which shows that we are applying limit to a part of the expression only (as applying the limit to the whole expression may result in an inderminate form).
toxic verge
https://discordapp.com/channels/268882317391429632/486841085210132490/1382393213...
That's because in the second example x^2*(tanx/x) is of the form f * g where the limits can be evaluated individually (given they exist).
In the first example however, you have applied the limit only to the numerator in a f/g form, hence resulting in the limit becoming infinity- this partial insertion of limits isn't allowed since if we consider f* 1/g, the limit of 1/g (which is 1/x) does not exist (in a finite form) at x=0.
lone heartBOT
@median flame Has your question been resolved?
median flame
I see. So in general, tanx or sinx can be multipled and divided by x to remove the term, although the expression may not be determinate yet and would still need solving?
toxic verge
I see. So in general, tanx or sinx can be multipled and divided by x to remove t...
Provided that the limit (trig function)/x exists at that particular x (which it usually does), yes
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median flame
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toxic verge
Just to be clear, while applying lhopitals you did differentiate a^x as a^x * lna correct?
(Btw I'm assuming the answer you got by the second approach is the correct one, i haven't checked it).
median flame
yeah, the second approach is correct
I think I have the problem in differentiating, lemme send a photo
,rotate
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toxic verge
Yeah this differentiation is incorrect
You need to individually differentiate both the num and the den. Also, the differentiation of (a^x-1)/x is not lna
median flame
what I did was the I took the lim(x -> 0) (a^x - 1)/a = lna, which becomes a constant, whose differentiation becomes 0
toxic verge
Try applying the quotient rule and deriving it yourself
toxic verge
what I did was the I took the lim(x -> 0) (a^x - 1)/a = lna, which becomes a co...
Oh you took the limit not the differentiation
median flame
what I did was the I took the lim(x -> 0) (a^x - 1)/a = lna, which becomes a co...
this is the part which I think is the problem, but I don't understand what is it
toxic verge
Well it's the same problem again then isn't it, you evaluated just the limit of f from f*1/g
Partial limit evaluation will not give you correct answers
median flame
but what I don't get is why this problem doesn't happen in tanx/x or sinx/x, why are we able to seperate them, but not this?
deft sparrow
im failing math and a single math problem could help me pass
but i have no ideea how to solve it
and the translation in english is kinda ass
toxic verge
im failing math and a single math problem could help me pass
!occupied
lone heartBOT
im failing math and a single math problem could help me pass
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median flame
but what I don't get is why this problem doesn't happen in tanx/x or sinx/x, why...
I get that this is very subtle, pardon me for going in circles
toxic verge
but what I don't get is why this problem doesn't happen in tanx/x or sinx/x, why...
Because then you evaluate the limit of tanx/x as a whole not just the limit of tan x from tanx * 1/x
Is that understandable
median flame
yeah, now that you mention tanx/x and tanx*(1/x) I am kinda starting to get this
toxic verge
If you have some other example problems i can help you understand with those
median flame
basically here we try to eval the numerator, and get something finite (0) but the problem lies with 1/x which is going to infinite?
toxic verge
Yep
You can only evaluate lim f*g as lim f * lim g if the limits of both those functions exist and are finite
median flame
and if we had some other expression f(x) instead of 1/x which we could solve further, we would have done that, but not here since we get infinite * 0 indeterminate form?
toxic verge
and if we had some other expression f(x) instead of 1/x which we could solve fur...
Yep
median flame
finally this makes sense.
toxic verge
Pog
median flame
thanks a lot
toxic verge
Yw
median flame
.close
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deft sparrow
help?
toxic verge
help?
Open a new help channel... go to #❓how-to-get-help
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hot vale
For ii), is the answer e-1
lone heartBOT
For ii), is the answer e-1
lone heartBOT
@hot vale Has your question been resolved?
hot vale
<@&286206848099549185>
rustic coral
e-1 makes no sense because e-1>1 yet the region is a subset of the unit square
hot vale
oh true
hot vale
i basically used this
@rustic coral is this working out correct?
i think i did the algebra wrong then
lol i keep getting e-1
ik its wrong though
lone heartBOT
Show your work, and if possible, explain where you are stuck.
hot vale
@rustic coral is this the answer
i realised the integral of lnx is not 1/x, the derivative is lol
thats why i kept getting the e-1
rustic coral
<@560122149126275093> is this the answer
,w (integral of e^(x-1) from 0 to 1)-(integral of (1+ln x) from 1/e to 1)
ocean sealBOT
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heavy viper
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runic basin
Okay so can you tell what kind of transformations have happened here?
heavy viper
like ik for the first one, there is a vertical reflection and then vertical translation since the horizontal asymptote is moved 6 units up
heavy viper
but how do i tell if theres vertical dilation, horizontal dilation or horizontal shift
heavy viper
okay so what does that do to the equation of 2^x
-2^x+6
runic basin
but how do i tell if theres vertical dilation, horizontal dilation or horizontal...
Yeah so the way you can tell that here is because we have notches on the axes we can read off some points our function passes through
For exponentials a nice fact is that horizontal shifts are the same thing as vertical dillations
So you're looking at something like f(x)=6-a2^{bx}
and to work out the values of a and b you can just plug in points on the graph
heavy viper
so like id have to equations and i do substitution or something?
heavy viper
For exponentials a nice fact is that horizontal shifts are the same thing as ver...
so i can either do -2^b(x-c) + 6 or -a2^bx + 6
runic basin
yeah
heavy viper
yeah
but i think the a one is easier, so does that mean u cant have a vertical dilation and a horizontal shift together?
heavy viper
is there a reason why?
runic basin
[b2^{a(x-c)}=b2^{ax-ac}=2^{-ac}b2^{ax}]
ocean sealBOT
lance
runic basin
That 2^{-ac} is a constant
so its like we've secretly just vertically dilated by b*2^{-ac} the whole time
runic basin
nw!
alpine sable
fuck ur math
heavy viper
nw!
quick question
could there be multiple answers for these types of questions
i did a and got the right answer, and looked at the answer for b but it has a horizontal translation
is it the same if i write the horizontal translation in terms of a vertical dilation
runic basin
quick question
Yeah there can be multiple correct answers
A good way to check your work is to open up something like desmos and graph your equation and see if it looks the same
heavy viper
yea thats true lemme try part b real quick
lone heartBOT
@heavy viper Has your question been resolved?
heavy viper
heavy viper
A good way to check your work is to open up something like desmos and graph your...
is there a way to see if theres a better time to use the horizontal translation vs the vertical dilation
i tried doing it with the dilation but im getting a different answer
runic basin
Do they both give you the same graph?
runic basin
is there a way to see if theres a better time to use the horizontal translation ...
Not really, I personally just use the dilation factor approach since it’s usually easier on the algebra
runic basin
i tried on desmos, they are different
Check the points you plugged in
heavy viper
and i used points (-4,0) and (-6,4)
runic basin
Does the graph of the equation in the book pass through those points?
heavy viper
Does the graph of the equation in the book pass through those points?
the book answer passes through (-6,6)
but the graph they gave doesnt look like that
heavy viper
but my answer doesnt pass through (-6,4) as well so i think i did something wrong too 😅
heavy viper
Assuming you mean part b
yes part b
runic basin
but my answer doesnt pass through (-6,4) as well so i think i did something wron...
Ah yeah then your algebra must’ve been a bit off
heavy viper
Ah yeah then your algebra must’ve been a bit off
i just redid it but now my equation matches the answer in the book, even though both of them dont pass through -6, 4 and i used -6, 4 as a point 😭
runic basin
Send your working
heavy viper
ok 1 sec
This is what I did
I used -4,0 as a point then once I got a=(2)^1-4b I plugged it into the next equation
And got b= 1 ( I used -6,4) for that one
And b=1 gives me a= 1/8
runic basin
Sorry if I'm reading this right you have
\begin{align*} 6&=2^{1+2b} \
6&=2^1+2^{2b}
\end{align*}
ocean sealBOT
lance
runic basin
Wait it's supposed to be times
yeah exactly
heavy viper
Oh so 3= 2^2b?
heavy viper
I haven't been taught how to do questions where u can't make the bases the same my teacher said we can't use logs
U can't make the bases the same in this case right ?
runic basin
Yeah you can't
so I'm assuming this question had a typo in it
and it was meant to pass through (-6,6)
heavy viper
I think if I were to get a question like this, I would just stop here
heavy viper
and it was meant to pass through (-6,6)
Yea I think they just graphed it wrong
runic basin
If you get a question like this you raise you hand and ask your teacher if they made a mistake :p
heavy viper
Alr but all my steps were correct up until that right ?
heavy viper
If you get a question like this you raise you hand and ask your teacher if they ...
Yea lol
runic basin
Yeah excluding that mistake about + instead of times I didn't see anything
runic basin
you too :)
heavy viper
.close
lone heartBOT
scenic stream
How the hell do I stop being so superficial? I make mistakes on almost any problem I solve, whether its just from just copying the task from my pc to paper, missing minuses/numbers... HOW, PLEASE
opal jolt
paying attention to what you're doing, probably.
vale wigeon
make a habit of doing things slowly.
and one thing at a time.
maybe you could show us some of your rushed/error-filled work
for more precise diagnosis
idle rose
Guys, I need help identifying the set of functions.
scenic stream
Guys, I need help identifying the set of functions.
go to #help-4
scenic stream
for more precise diagnosis
I'm good, I just rush too much probably
but ignored the problem
until now
thanks guys ❤️
.close
lone heartBOT
white spire
Hey, can someone help me with infinitesimal calculus?
lone heartBOT
Available help channel!
modest robin
<#490557019623915520>
sterile ruin
lone heartBOT
lone heartBOT
Available help channel!
median oar
what's the difference between a function that is lipschitz, and a function that is continuous + every secant has finite slope
median oar
or do i need it to say the set of all slopes of secants is bounded
then the set of all slopes of all secants will have a maximum, and i can set L to be that for the lipschitz number
keen plinth
most secants have finite slope...
median oar
oh true
i guess the lipschitz is just saying this maximum exists
or minimum same thing
placid zinc
The bounded part is important. Namely, e^x is not lipschitz
median oar
i think neither is like x^2 then
placid zinc
Oh yeah true. Tough condition
median oar
i suppose it says something about uniform boundedness
it looks kinda like uniform convergence but for slopes and not really convergence
so just the uniform part 
interesting so ln(x) is lipschitz on [a, inf) for a > 0
so the function (can) go to infinity, it's just that the slope can't
keen plinth
x is lipschitz
median oar
so if f is differentiable then you just need f' to be bounded
if f is between differentiable and continuous then it's cringe
keen plinth
lone heartBOT
Available help channel!
wild horizon
Unable to visualize. Can someone help?
lone heartBOT
Unable to visualize. Can someone help?
vale wigeon
Unable to visualize. Can someone help?
the questions are divided into three types:
- known, correct answer
- guessed, correct answer
- guessed, wrong answer
(there would also be "known, wrong answer" but we assume that doesn't exist)
wild horizon
right
vale wigeon
of all the correctly answered questions, 1/6 are guessed
and of all the guessed questions, half are correct and half are wrong
wild horizon
ok yes
vale wigeon
of all the *correctly answered questions*, 1/6 are guessed
this means that known : guessed-correct = 5:1
vale wigeon
and of all the *guessed* questions, half are correct and half are wrong
and this means guessed-correct : guessed-wrong = 1:1
vale wigeon
so this kinda directly gives you that the ratio of questions by category is 5:1:1
vale wigeon
no
lone heartBOT
lone heartBOT
Available help channel!
jovial sierra
Translation : Find the dimension, equations and a base of the subspace
jovial sierra
I don't seem to get how to find whats being asked
fierce moss
Translation : Find the dimension, equations and a base of the subspace
could you give some context, in what chapter of your math book is this?
vale wigeon
this is definitely a linalg book.
fierce moss
it looks you need to create a matrix
jovial sierra
it is linalg
jovial sierra
it looks you need to create a matrix
yes, indeed, i understand that. I tried making a matrix then using gauss for the range of the matrix, but im unsure wether the range is the same as dimension
fierce moss
yes, indeed, i understand that. I tried making a matrix then using gauss for the...
try reducing the matrix to a row echelon form
so
jovial sierra
yes, by gauss i mean row echelon form
that's just how its taught in spanish
i guess
fierce moss
so where did you get stuck?
fierce moss
hm you'll have to look it up if you want the full def but I think they mean how many directions can the given vectors go in
jovial sierra
alright, ill look into it. But how do i find the equations and the base?
fierce moss
so once you have your final echelon form you can form the system and you'll have your equation
if you get x y z you have 3 dimension if you only get x and y your answer will be 2 dimensions
lone heartBOT
@jovial sierra Has your question been resolved?
lone heartBOT
lone heartBOT
Available help channel!
alpine sable
the answer should be 0 but I got what did I do wrong?
lone heartBOT
the answer should be 0 but I got what did I do wrong?
alpine sable
how do I differentiate between floor and greates integer value?
sorry for the stupid question
proud obsidian
[] is the integer less than
proud obsidian
how do I differentiate between floor and greates integer value?
huh😭
alpine sable
I meant how do I know if the question want the floor or the greatest integer value
lmao
thanks
.close
lone heartBOT
proud obsidian
I meant how do I know if the question want the floor or the greatest integer val...
same thing, its just notation ig
alpine sable
same thing, its just notation ig
Thank you for the help.
lone heartBOT
Available help channel!
static wagon
how do i do b?
lone heartBOT
how do i do b?
stark crater
Consider what you would do with standard divison. If you do 59/7 which has a remainder of 3 what would you do to make 59 divisible by 7
static wagon
Consider what you would do with standard divison. If you do 59/7 which has a rem...
minus 3 from 59?
stark crater
yeah do same idea here
gritty bramble
-5
stark crater
then wouldn’t you have to subtract 5 from b?
where are you getting 5
stark crater
Consider what you would do with standard divison. If you do 59/7 which has a rem...
The point of this is to show the quotient doesn't really matter once you have the remainder
In that example we subtracted 3 from 59, none of these numbers are the quotient
static wagon
true
stark crater
The end goal is to force the remainder to be 0
static wagon
then 12 - 13x = 0?
static wagon
so we equate ax + b to the original polynomial
gritty bramble
yes
static wagon
and then
stark crater
Yeah basically just subtract the remainder from the orignal polynomial
Like we did in the 59/7 example
alpine sable
$\frac{sin(x)}{x}+cos(x)$ is the LHL and RHL of this function equal at x=0
ocean sealBOT
17
alpine sable
i got LHL as cos(x)-1
wait thats 0
lhl as 0
and rhl as 2
because its 0^-
then sin(x) can be written as -sin(x)/x right
and sin(x)/x would be 1
and it becomes -1
-1 + cosx
cos(x) becomes 1
tribal verge
because its 0^-
then sin(x) can be written as -sin(x)/x right
It cannot be written like that
alpine sable
and we get 0
tribal verge
sinx/x as x approaches 0 is always 1 irrespective of the direction you approach it from
alpine sable
but the angle is indeed negative right
tribal verge
but the angle is indeed negative right
sin is also negative then and signs cancel
alpine sable
sin is also negative then and signs cancel
uh ? :(
tribal verge
do you know the infinite series of sinx?
When you divide by x on both sides, you will be left with even powers of x in rhs
So sign does not matter
When you perform the limit, everything except 1 in the rhs approaches 0
vale wigeon
$\lim_{x \to 0} \frac{\sin(x)}{x} = 1$
ocean sealBOT
Ann
vale wigeon
this is two-sided
(so both one-sided limits exist and agree)
maybe that's easier even if OP doesnt know the taylor series for sine
lone heartBOT
@alpine sable Has your question been resolved?
alpine sable
do you know the infinite series of sinx?
yes
alpine sable
When you divide by x on both sides, you will be left with even powers of x in rh...
ohhh
tysm people 😌
i understood it
languid bolt
I have no idea on what and how to approach this question, i’m posting this in hopes someone can explain how to do this, my brother has been stuck in this question for days and i’m trying to help him
median oar
what's the covariance defined as
vale imp
small lance
Cool
lone heartBOT
@languid bolt Has your question been resolved?
languid bolt
sorry, just got back
lone heartBOT
languid bolt
i think he solved it 🙏
lone heartBOT
Available help channel!
delicate prawn
lone heartBOT
vale wigeon
delicate prawn
Nothin'
vale wigeon
!nosols
lone heartBOT
As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.
lone anvil
delicate prawn
I am not doing homework
lone anvil
Okay
vale wigeon
server policy still applies, we do not give out answers
delicate prawn
No need to worry about @lone anvil
vale wigeon
anyway there is one rather obvious root
delicate prawn
server policy still applies, we do not give out answers
Ohh
lone anvil
vale wigeon
if you write the equation as x^2 + x - (p^2 + p) = 0
there is one root that is very directly visible
delicate prawn
I am seeing it
vale wigeon
ok can you tell me what this obvious root is
delicate prawn
ok can you tell me what this obvious root is
Wait a sec
vale wigeon
do not overthink it
unique dune
front and back terms look similar...👀
delicate prawn
front and back terms look similar...👀
What?? How? What u talkin' about?
unique dune
delicate prawn
do not overthink it
The root u talkin about is that a number
ancient temple
they are hinting, that x^2 + x and p^2 + p look similar, and they are subtracted, so x = ? is an obvious root
unique dune
front and back terms look similar...👀
this is the hint for that root😭
vale wigeon
it is a number but it's not a raw number
literally just
god ok you ARE overthinking it im sorry
ok
let me try to make it even more on the nose for you
delicate prawn
With variable
delicate prawn
x=p²+p-x²
vale wigeon
no
overthinking it
dont do that
dont do any algebra
x^2 + x = p^2 + p
just stare at it
what can x be to make this true
no algebra no numbers no calculations NOTHING just stare at this
delicate prawn
Common
delicate prawn
Cancel the squares
unique dune
compare the terms
vale wigeon
no algebra no numbers no calculations NOTHING just stare at this
what can x be to make this true
delicate prawn
What do u mean by true
vale wigeon
like to make the equation true
you know what the word "true" means right...
look idk how else to say this without just revealing it and making you facepalm
cause i promise this IS the kind of obviousness to induce a facepalm
vale wigeon
ok
im gonna set a timer
@delicate prawn aight your two minutes are up
have you come up with the obvious root for x^2+x=p^2+p as i tried making you
delicate prawn
Still doing it
vale wigeon
ok no
that's too long
cut
since you're DEFINITELY overthinking it
im just gonna tell you
listen closely
for the equation x^2 + x = p^2 + p,
the obvious root, the one you can see with zero extra calculations... is p.
delicate prawn
Is that so how?
vale wigeon
literally look at the thing like