frozen heart
Im doing some lingear algebra questions, and got this one
transelation:
Let
v1 = (1, 2, 3) och v2 = (−1, 0, 2)
be vectors in R3. which of the following vectors makes together with v1 och v2 a bas for r3.
A: (1, 0, 1)
B: (1, 0, 1, 0)
C: (0, 0, 0)
D: (1, 0, −2)
E: (0, 2, 5)
cedar kilnBOT
Im doing some lingear algebra questions, and got this one
transelation:
Let
v1 ...
@frozen heart Has your question been resolved?
frozen heart
<@&286206848099549185>
dire geode
Find which one of the choices is orthogonal to both v1 and v2
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acoustic mason
How should I think about finding the derived set A'?
For example, given A = (0, 1) U {2}: I know that 2 is not a limit point of A because there is no epsilon neighborhood around 2 that intersects other points in A, but why is it that A' = [0, 1] when 0 and 1 aren't included in A?
humble karma
Limit points need not be in the considered set.
acoustic mason
Ah, yeah, after thinking about that a bit that does make sense
haha, thanks
.close
crimson sedge
Number 5
crimson sedge
I am not sure how they got A + Bcos(2x) + Csin(2x)
Should it not be (A - [Bcos2x + Csin2x])/D ?
cedar kilnBOT
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opaque harbor
you can expand that out and rename the constants
crimson sedge
you can expand that out and rename the constants
what do you mean?
their y trial or the one i came up with?
opaque harbor
yours
$$\frac1D(A-[B\cos2x+C\sin2x]) = \frac AD - \frac BD\cos2x -\frac CD\sin2x$$
Define $A'=\frac AD, B'=-\frac BD, C'=-\frac CD$,. then you get $$A'+B'\cos2x+C'\sin2x$$
wraith daggerBOT
Edward II
opaque harbor
so their y_trial is really the same as yours
bold hinge
You choose numbers from a distribution over [0,1] 10 times and get 9 numbers less than 1/2 and 1 number greater than 1/2. What is the probability that the distribution is uniform?
cedar kilnBOT
You choose numbers from a distribution over [0,1] 10 times and get 9 numbers les...
@bold hinge Has your question been resolved?
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@bold hinge Has your question been resolved?
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@bold hinge Has your question been resolved?
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@bold hinge Has your question been resolved?
dire geode
You choose numbers from a distribution over [0,1] 10 times and get 9 numbers les...
How are you counting distributions
tropic oxide
@bold hinge i believe your question is ill-posed unless there's some finite set of potential distributions that's known in advance and based on which you could adjust your priors Bayesian-style
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viscid linden
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viscid linden
I don’t know the difference between rhombus, polygon
trail frigate
soo
a rhombus is basically
a quadrilateral
with equal sides
so like a square is a special rhombus
tropic oxide
I don’t know the difference between rhombus, polygon
a polygon is any closed shape with straight lines for sides
a rhombus is one that has 4 sides specifically, and all the sides (but not necessarily the angles) are equal
tropic oxide
also, cropping.
@viscid linden does all this answer your question of "What's the difference between a rhombus and a polygon"?
trail frigate
welp uhh
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limpid plume
well anyways fuck it I'll ask here
I'm trying to prove that a morphism u: C -> D between two chain complexes of right R-modules C and D induce the homology module functor H_n(_).
limpid plume
I see that if I can prove that u preserves n-cycles and n-boundaries, we are done
I'm having trouble proving that. Only thing I know is each block in between the chain complex sequences created by the family of R-linear maps resting inside the morphism commute, hence for any n, we have
wraith daggerBOT
Riku
limpid plume
n cycles are kernel of d_n, and n boundaries are image of d_{n+1}, for any n
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limpid plume
.reopen
cedar kilnBOT
✅
wraith daggerBOT
Riku
limpid plume
how to do the opposite ;-;
limpid plume
is this from weibel
yes
short blade
this should be some symbol pushing from my notes
short blade
**Riku**
this is saying that u maps cycles to cycles right? to make sure i’m following
short blade
i don’t think so no
limpid plume
NO WAY LMAO 😭
short blade
you just need that d(u(x)) = 0
limpid plume
😭
short blade
so then the image of the cycle is a cycle
limpid plume
okay so similarly we show (u(d_{n+1}(C_{n+1})) \subseteq d'{n+1}(D{n+1}))
short blade
yeah
wraith daggerBOT
Riku
limpid plume
i mean not similarly but yeah
wait isn't this trrivial
d_{n+1}(C_{n+1}) is in C_n
oh wait it probably is not trivial
short blade
it's trivial in that it's just symbol pushing
short blade
weibel moment
cedar kilnBOT
dire geode
no wonder timo said it was easy af
And here I thought @woven herald was just smart
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hollow storm
hello, can somebody please explain this passage?
cedar kilnBOT
hello, can somebody please explain this passage?
crimson sedge
uh you want someone to explain euler's equation?
hollow storm
uh you want someone to explain euler's equation?
uh just this passage, why by negating the exponents you negate the arguments
sonic cradle
uh just this passage, why by negating the exponents you negate the arguments
set for example $\phi = -\vartheta$
wraith daggerBOT
bruhh
sonic cradle
then $e^{i\phi}=\cos\phi+i\sin\phi=\cos(-\vartheta)+i\sin(-\vartheta)$
wraith daggerBOT
bruhh
sonic cradle
no, its about what were inputting into the function
instead of inputting $\vartheta$, were inputting $-\vartheta$
wraith daggerBOT
bruhh
hollow storm
ohhh ok gotcha
sonic cradle
suppose $f(\phi)=e^{i\phi}$. then $f(-\phi)=e^{-i\phi}$
wraith daggerBOT
bruhh
sonic cradle
yeah
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sly roost
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slate notch
Well do you know a/b can be written as
1/(b/a)?
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@sly roost Has your question been resolved?
nova echo
x^2+x-1
show that the equation above has exactly one root
cedar kilnBOT
x^2+x-1
show that the equation above has exactly one root
idle tusk
exactly one root $\iff$ discriminant = 0
wraith daggerBOT
artemetra
idle tusk
or just find the roots
slow jewel
Idts x²+x-1 has only one root
idle tusk
yeah must be a typo
slow jewel
Ye
idle tusk
x^2 + 2x + 1 has one root
slow jewel
Ye
idle tusk
x^2+x-1
show that the equation above has exactly one root
are you sure you wrote the question correctly?
cedar kilnBOT
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still barn
For a whole complex function f(z) we have:
f(z) (less than or equal to) (ln|z|)^2023 , for all |z| > 9. Show that f(z) is a constant function.
For this exercise I was thinking of using Liouvilles Theorem which states that if f(z) is a whole function where f(z) (less than or equal to) M, then f(z) is constant. I am not quite sure how to apply L.T. here though, since (ln|z|)^2023 is a function of z, and not just some constant M. Perhaps (ln|z|)^2023 is bounded?
cedar kilnBOT
For a whole complex function f(z) we have:
f(z) (less than or equal to) (ln|z|)^...
@still barn Has your question been resolved?
viscid linden
a _rhombus_ is one that has _4_ sides specifically, and all the sides (but not n...
Thank you
viscid linden
a diamond like this
/\
/ \
\ /
\/
is a rhombus
Thanks again
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delicate atlas
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stark frost
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stark frost
Hi, what mistakes I had made?
nimble mulch
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dull basin
dull basin
Calculate the area of the region of the plane enclosed by the graphs of functions
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thick tiger
what does "y el eje de abscisas" mean?
you didn't give a full translation
but i'm guessing the exercise is asking for this region:
in that case, you'll want to use integration; i recommend you split the integral
glass sky
if the latus rectum of an ellipse be equal to half of its minor axis , then its eccentricity is
granite panther
any1 know answer?
glass sky
any1 know answer?
sorry mate channel already in use , consider using #help-41 or #help-21｜아리스킨충1
granite panther
my bad
glass sky
np, happens
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hardy tiger
hello
hardy tiger
i need help w linear algebra
flint plinth
what's the question?
hardy tiger
how do u solve this
flint plinth
well there are probably a number of ways, but the straightforward way is to find the eigendecomposition of A^t A and AA^t
cyan wyvern
Yo
hardy tiger
how do u solve for the eigendecomposition?
flint plinth
i.e. find eigenvalues and eigenvectors of A^t A and AA^t
hardy tiger
what do u do after u find the eigenvectors?
flint plinth
probably easiest if you just read up on how to do it, rather than me just paraphrasing the instructions 😁
cedar kilnBOT
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stable sundial
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astral bay
...i'm not really sure what mistake you're referring to?
neither of those equations are true
stable sundial
with cube root
astral bay
ok well that's still false
if 128 was equal to 4*cbrt(2), then cubing both sides, you would get that 2,097,152 = 128 and those are obviously different
so i'm still not sure what the mistake is here
chrome karma
cedar kilnBOT
tropic oxide
what do you think it should be instead
chrome karma
I thought it was C originally
tropic oxide
how did you get C
chrome karma
change in velocity over change in time, 13.4-12.2 over 2.0-1.0
but i guess the question asks at t=1 so how would you find that
drifting marlin
wraith daggerBOT
Result:
1.6
civic eagle
you were on the right track, but you should've used [1.0, 1.5] not [1, 2]
tacit spade
Was having a think about Cauchy sequences: so a sequence is Cauchy if for all ε > 0 |an - am| < ε for all n, m >= N, so if we fix m = m1 >= N, do we get that for all ε > 0, |an - am1| < ε for all n >= N?
tacit spade
i thought the issue here might be that we can't fix m but I can't exactly see why that'd be the case
flint plinth
Was having a think about Cauchy sequences: so a sequence is Cauchy if for all ε ...
yes, you do
tacit spade
but then if you fix m = m2 don't you get (an) converging to a different limit?
flint plinth
well if you fix both of them then you no longer have a sequence, just a pair of numbers
astral bay
for all ε > 0 |an - am| < ε for all n, m >= N
this isn't quite the actual definition, you're missing a quantifier
for every eps > 0, there is some N such that, for all n,m >= N, |an - am| < eps
astral bay
so you don't actually get that the sequence converges to a_m for any particular m
flint plinth
all you get is that all of your a_n's (for n sufficiently large) within epsilon of a_m
if you make epsilon smaller, you generally have to pick a bigger m
astral bay
for some sufficiently small epsilon, N might be larger than m, and then you don't have that the rest of the sequence is within eps of a_m
astral bay
for instance the sequence {1, 1/2, 1/4, 1/8, ...} is cauchy
if you pick the element 1/8 and say "well the sequence must converge to 1/8 then!"
i ask "ok so for eps = 1/64 when does the sequence become within that of 1/8"
but the cauchy sequence only stays within 1/64 after the term 1/64, which is after the 1/8
tacit spade
yeah that makes sense
astral bay
so the proof doesn't work, which makes sense because this sequence does in fact not converge to 1/8
smoky ore
cedar kilnBOT
smoky ore
Hii, my understanding is that for real-valued functions, the Hessian is the jacobian of the gradient
so we differentiate gradient wrt theta to get Hessian
in this context the function g is the sigmoid/logistic function, so g'(z) = g(z) (1 - g(z))
my question is, how did they go from the gradient to H?
because like, X^T is n x m, g(Xtheta) is a vector (m x 1), 1 - g(Xtheta) also another vector m x 1, but we're probably doing element wise multiplication there, but then X is m x n, so
we have n x m x m x 1 x m x n, how does it even multiply properly?
cedar kilnBOT
@smoky ore Has your question been resolved?
smoky ore
<@&286206848099549185> Hii i hope someone can help me... thank you in advance
tender geyser
this is quite an advanced question which I know nothing about, yet. What you can do is ask it in a specific channel in #advancedmathematics
tender geyser
<@&286206848099549185> Hii i hope someone can help me... thank you in advance
you will get better help there
waxen fiber
im confused with what i am doing wrong?
cedar kilnBOT
im confused with what i am doing wrong?
waxen fiber
the common factor is removed, but idk what to keep as the Q?
cerulean sail
What are the P, Q R being referred to? what comes before step 1? 
waxen fiber
simplification?
sorry this is a new formula my teacher threw in
so im trying to find it online
cerulean sail
As in can you share a screenshot of the whole page?
cerulean sail
not particularly clear with what they mean, unless P is supposed to represent 6x^2 - 41x - 56 and Q is supposed to be that 6x^2 + 37x + 35
waxen fiber
its ok im just so confused
cerulean sail
Oh I think I know what they mean - it's so poorly expressed
cerulean sail
<:catFone:849254980812013639> not particularly clear with what they mean, unless...
it's not this
But they basically wanted you to notice that for any general P, Q, and R, you can multiply the numerator and denominator by the same thing (as long as it isn't zero) and it doesn't change the expression
cerulean sail
Basically, if you multiply the numerator and the denominator of P/Q by the same (nonzero) thing, you don't change the fraction
What do you think they multiplied the numerator by? What would you have to multiply the denominator by to have it being equivalent?
(the answer they want will be in terms of P, Q and R - maybe not all of those mentioned!)
waxen fiber
would they multiply by R?
or since the denom is (x+5)
and cant equal -5? u multiply that??
im still confused
cerulean sail
would they multiply by R?
Yep, that's it - and your denominator was originally Q, so...
cerulean sail
so it would be QR?
Yep, that's what I expect they want from you!
waxen fiber
it worked ! :)) ty
waxen fiber
tyy
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summer lintel
cedar kilnBOT
summer lintel
ca anyone hlep out
humble karma
Compute the left side and the right side of the equation and make sure they match.
Or compute the first one and make it look like the second one.
summer lintel
yh i know
humble karma
In both cases, you'll have to compute the cross product
summer lintel
I meant like how
humble karma
Are you able to compute a cross product?
If so you have the coordinates given to you for all vectors.
The vector w+x shouldn't be too hard to manage either.
summer lintel
its just like this?
you multiply the terms along the diagonals from left to right and subtract the product of terms along the anti-diagonals from right to left
right
humble karma
Should be it. I always prefer the determinant trick with I,j,k, but this works, especially since it's a formula so you can directly apply it to your problem.
summer lintel
yh i,j,k trick should work as well
i was just thinking if you had a smart way to do it
or if i had to compute it all
humble karma
It's the proof for a fairly basic property, so I think brute force is mostly the way here.
humble karma
Yeah you could split the top but more explicitly into the two added vectors, but that's it
summer lintel
would this be correct?
or if all entries are 0
Or if you have a zero vector in one of them
summer lintel
Yeah you could split the top but more explicitly into the two added vectors, but...
I suppose i could
v×w=0⟺either v or w=0 or v and w are parallel
If they are parallel
and if they are perpendicular
vocal quarry
Hi i was just wondering how do you know if a function is derivable at a certain point?
vocal quarry
Or if its not why?
I know it has to do with the tengent no being the same on both side
Damn i just answered my own question
.close
open crest
hello! we're doing table of signs for the inequality stuff, and i wanted to ask if the circled part in blue is correct? [1] seems to satisfy the condition, but i'm not quite sure how to format the answer.,
Also, my teacher said not to include [1], but i'm really confused why. is there something i'm missing?
open crest
(i'd also greatly appreciate if there are any mistakes in the other parts of the problem pointed out! thank you again)
<@&286206848099549185>
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nimble stone
Girlfriend is taking a quiz and has until midnight.
Gibbs free energy calculations, if anyone has any help with what she's doing incorrectly would be greatly appreciated.
nimble stone
read the <#486128019652476939> , no quiz help
Had hardships this semester and professor refuses to help.
That's fine, the quiz changes every time we resubmit. I can give a set that was done and practically expired.
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dark berry
I'm trying to prove the underlying mathematics behind RSA, where did I go wrong?
dark berry
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dark berry
<@&286206848099549185>
dark berry
Prove what statement exactly
That you can find P if u know d
dire geode
That you can find P if u know d
Section 5.10
https://www.cis.upenn.edu/~jean/RSA.pdf
dark berry
Section 5.10
https://www.cis.upenn.edu/~jean/RSA.pdf
is there anything wrong with mine? i based it off of this https://brilliant.org/wiki/rsa-encryption/ and https://math.stackexchange.com/questions/20157/rsa-in-plain-english
dark berry
i dont understand what i did wrong here
dire geode
i dont understand what i did wrong here
Your work just looks circular
Maybe it's just the way you structured it
dark berry
Your work just looks circular
I’m trying to get p =p but idk how
dire geode
Yea it's definitely a structure problem
dire geode
You have everything = P on the right side starting in the second equation
That's confusing
dark berry
You have everything = P on the right side starting in the second equation
I see but if the first 2 equations hold I should still be getting P=P at the end right
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signal vault
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signal vault
<@&286206848099549185>
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river topaz
cedar kilnBOT
wraith daggerBOT
river topaz
B is the one above D
slow jewel
For B, have you found angle BAC?
river topaz
no
slow jewel
You can use a property of circles to find it out
river topaz
which one
slow jewel
Angle subtended at the center by a chord is twice the angle subtended at any other part or smth
In this case that chord is BC
slow jewel
In this case that chord is BC
There would be other ways too but I just said what I found
slow jewel
alr what about C
In triangle OAB, OA=OB
What does it say about the angles?
slow jewel
The center is O
slow jewel
Cuz it's the radius
slow jewel
Yes
river topaz
what is it then
slow jewel
But yes it's 110⁰
river topaz
i mean B*
slow jewel
Angle subtended at the center by a chord is twice the angle subtended at any oth...
Never seen anything like this before eh?
slow jewel
Let's say you have a chord AB in a circle with center O
Angle AOB is the angle subtended by chord at center
And let's say C is any other point on the circle above AB
Then ACB is angle subtended by AB on the circle
river topaz
what doe subtended mean
slow jewel
Have you read the above messages?
river topaz
subtended means angle at the center?
slow jewel
It's angle at a point
If it's at point O, then it's at the center
river topaz
alright then
slow jewel
Angle subtended at the center by a chord is twice the angle subtended at any oth...
Maybe you've seen the same thing but in a different version
river topaz
you know what
this question wont be in the exam
imf ine
thanks alot for the help
.close
cedar kilnBOT
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grim urchin
I have these points:
x=-0.37 y=-1
x=2.72 y=1
I want to get the slope. I tried with m=(y2-y1)/(x2-x1). That gives me 0.65.
-0.37 x 0.65 = -0.23
2.72 x 0.65 = 1.76
I know that I haven't added the independient term, but I think that it is weird that the initial value is just a bit off from the correct value -0.23 vs -0.37 while the final value is very different 2.72 vs 1.76. This is lineal, so the difference should be the same in both (initial and final), right?
floral arrow
"pendiente" is "slope" in English
grim urchin
Thanks
dire thorn
I have these points:
x=-0.37 y=-1
x=2.72 y=1
I want to get the slope. I tried wi...
The difference is the same for the output (y values). This is not the case for the x values. Think of a line like y=2x. At x=0 y=0, the difference is 0, but as we get further away from 0 the difference gets bigger
grim urchin
Right
dire thorn
Ur m is fine though
floral arrow
You are comparing -0.23 to -0.37 and 1.76 to 2.72 but you should be comparing -0.23 to -1 and 1.76 to 1
grim urchin
Thank you
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nimble mulch
Let f:A->B be uniformly continuous with A,B subsets of C (complex)
nimble mulch
And some sequence x_n whose values lie in A
then if lim(x_n) lies on bound(A), does that imply lim(f(x_n)) lies within B or bound(B)?
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livid tundra
Hello
livid tundra
Can someone explain to me how to find the bounds
I did sketch the line x= 1 and y=x
Slow wifi 😅
There are 2 methods
@uncut veldt
anyoneee
???
<@&286206848099549185>
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wanton wigeon
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visual socket
For this problem I need to find the first five terms in the sequence. I know how to do that but this problem has some new things I haven’t worked with
visual socket
I’m not sure what to do when the left side is a_1 instead of a_n. The second thing I’m not familiar with is the 3,
frail glen
since we start at 1, we would then go on to find n = 2, and go on.
thick tiger
I’m not sure what to do when the left side is a_1 instead of a_n. The second thi...
the comma only serves to present the two statements next to each other, it has no special meaning in this context
thick tiger
right, you can think of it as simply being equivalent to
wraith daggerBOT
lifefuel
strong nexus
@dire geode
strong nexus
I forgot to close the old channel, my bad
dire geode
<@261933205387477002>
Maybe try multiplying top and bottom by the rational conjugate
strong nexus
Maybe try multiplying top and bottom by the rational conjugate
I actually did already do that, I guess I need to recontrol
Gimme a sec
strong nexus
trig sub also works
Tried it, it gets quite long
subtle harbor
nah
strong nexus
I did put ${x\over4}=\sin t$
subtle harbor
sin(t) is better choice
wraith daggerBOT
Leo, ze FluffBøt
subtle harbor
you just have to some clever +-=0 trickery
strong nexus
I get the interval between $0$ and $\pi\over2$ so I get $\sin x=\sqrt{1-\cos^2x}$ and viceversa
wraith daggerBOT
Leo, ze FluffBøt
subtle harbor
integrand gets down to $\frac{4\cos(\theta)}{\sin(\theta)+\cos(\theta)}$
wraith daggerBOT
Moosey
strong nexus
Here I go for $u=\tan{\theta\over2}$ I suppose
wraith daggerBOT
Leo, ze FluffBøt
subtle harbor
no need for another trig sub
note that $\cos(\theta)=\frac{1}{2}\left(\cos(\theta)+\sin(\theta)+\cos(\theta)-\sin(\theta)\right)$
wraith daggerBOT
Moosey
strong nexus
I see
subtle harbor
we do this because if we let u=sin(theta)+cos(theta), du=cos(theta)-sin(theta)
strong nexus
**Moosey**
I do really appreciate it, I actually never thought about this use
From now on I suppose I can go on my own with the resolution
@subtle harbor @dire geode Thank you guys very much for the help! Really appreciated it ^^
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crimson sedge
cedar kilnBOT
edgy quarry
n + 1 numbers are chosen from the series of natural numbers 1,2,3...2n. Show that in these n + 1 chosen numbers there are two numbers such that one divides the other.
Please heelp
crimson sedge
Uhm I think I posted my question before but I'll let you have the channel, so just repost your question @edgy quarry ig
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crimson sedge
Alright this is not the type of question you usually get here
crimson sedge
But
If the first linear algebra class and the first discrete math class kicked my butt, am I doomed to suffer immensely throughout my entire upper level math journey if I take it?
did u study hard
slate lintel
not necessarily, but it may be worth examining what was so difficult about them
and how much practice you did
crimson sedge
did u study hard
I wrote an entire 10-page review document and went through every HW of the year
crimson sedge
I wrote an entire 10-page review document and went through every HW of the year
you may want to learn how to study efficiently not just studying hard
so I’m a comp sci major but
math would be my focus area
if you didnt already know, there is a lot of research in the past few decades about how learning works and how to study efficiently
but idk with all the classes after cal 3 I’ve felt so discouraged
could physics be viable too? if it’s just a ton of hard calc i could probably handle it
crimson sedge
you may want to learn how to study efficiently not just studying hard
yes but @crimson sedge dont give up what you want until you try this
i mean
what I want is my comp sci degree but i have to focus in an area too
slate lintel
linear and discrete are often very computation heavy. I wouldn't give up on it until you take something like an intro to proofs, intro to advanced math, mathematical reasoning, something like that
crimson sedge
fair
yk what
I should minor in astrophysics that sounds cool
I’ll look into that
thanks for life advice I’ll def look into learning strategies
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cedar kilnBOT
crimson sedge
thanks for life advice I’ll def look into learning strategies
search higher order learning or metacognition
crimson sedge
@pale lake since its with replacement i think every time you catch a fish it's a 1/2 cod, 1/5 sole and 3/10 mullet, then u can have for example p(X = 3, 0, 0) = 1/2 * 1/2 * 1/2
pale lake
<@1183753255919038505> since its with replacement i think every time you catch a...
i see i see
ok lemme have another go
tranquil nymph
2 + 2 pls
upper garnet
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cedar kilnBOT
tranquil nymph
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uneven pagoda
Is there a continuous function R to R that is not lipschitz continous for any interval D in R?
foggy merlin
Is there a continuous function R to R that is not lipschitz continous for any in...
welp, if a function is lipschi, there is uniform continuity I guess
And uniform continuity implies continuity
🤔
uneven pagoda
original question?
solid juniper
Is there a continuous function R to R that is not lipschitz continous for any in...
ok this one still sounds weird to me then
is D something fixed?
uneven pagoda
D is interval in R and f: D to R is Lipschitz-continuous
So i guess D is not fixed
e.g. i can show that x^2 is not lipschitz for x > 2C-y but what if this x is not in D
solid juniper
no that does not make sense
uneven pagoda
e.g. i can show that x^2 is not lipschitz for x > 2C-y but what if this x is not...
the task or this?
solid juniper
e.g. i can show that x^2 is not lipschitz for x > 2C-y but what if this x is not...
this
uneven pagoda
Why
|x^2 - y^2| = |x+y||x-y| <= C|x-y|
|x+y| <= C
for x = 2C - y the inequality doesn't work
solid juniper
like... yes what you're saying is kind of relevant
but you have choice over f, D, x and y
you want to show there is no C
i can see you've chosen f
D is also something you get to pick
solid juniper
then one way to proceed is to show that for every C > 0, there is an x and y in D such that this inequality fails
that says there is no C such that the inequality holds for every x,y in D
uneven pagoda
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cedar kilnBOT
cedar kilnBOT
Available help channel!
flint sapphire
Do you think I could use
cedar kilnBOT
Do you think I could use
cedar kilnBOT
@flint sapphire Has your question been resolved?
cedar kilnBOT
cedar kilnBOT
Available help channel!
sour crow
im not really sure how to finish this question can someone help? it's linear approximations calculus
sour crow
i thought i would just need to substitute in sqrt(3.9) into the x in a) but that didnt work
gentle flower
do you know the formula for linear approximation?
sour crow
L(x) = f(a) + f'(a)(x-a)
pinging just to let you know i responded, sorry @gentle flower
crystal raptor
sqrt(3.9) = f(what?)
sour crow
i think i get what you mean
like finding x that would be the approximation of sqrt(3.9)? via L(x)
crystal raptor
sqrt(3.9) = f(what?)
no just literally think about what the "what?" is
if f(x) = sqrt(2+x) then sqrt(3.9) = f(what?) ?
gentle flower
what value of x would give you sqrt(3.9) ^
sour crow
im trying to think, im just kinda lost sorry
gentle flower
if you’re adding 2 to x, what operation would you have to do to get x back?
gentle flower
so whats the value of x when you have sqrt(3.9)?
gentle flower
and what’s the linear approximation of f(x) at 2?
sour crow
3/2+1/4x?
gentle flower
L(x) = f(a) + f'(a)(x-a)
.
sour crow
well if i went with the same structure of the formula it'd be like L(x) = 2 + (1/4)(x - 2)
gentle flower
now use 1.9 as your a value and 2 as your x value
sour crow
OH
i think i get it now
i did L(x) = f(1.9) + f'(1.9)(2-1.9) thats how im supposed to approximate sqrt(3.9) right?
gentle flower
yes
sour crow
i think im doing it correct but im not sure where im messing up
when i plug in f(1.9) into f(x) i get f(1.9) = sqrt(2+1.9) = sqrt(3.9)
gentle flower
is it webwork?
sour crow
yeah
🤷♂️ maybe webwork is just bugging, or rather i could be inputting it incorrectly?
i'd like to point out that it is practice questions just to let you know im not like cheating or something
sour crow
tried, came back as incorrect, since the question asks for 6 decimal places as well it just takes the first 6
well what's more important is that im, doing it correctly
so as long as I know it's correct i dont really mind
oh what
sour crow
no its alright lol
sour crow
i took a look and was like, i guess i should try this it makes a bit of sense
gentle flower
yeah i completely forgot that you’ll substitute 1.9 as the x value
well good job on figuring that out
sour crow
thank you two for pointing me in the right direction in general though! @gentle flower @crystal raptor
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fickle maple
need help with this. I dont understand.
cedar kilnBOT
need help with this. I dont understand.
fickle maple
subtle harbor
!status
cedar kilnBOT
crimson delta
dull oxide
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
!showwork
cedar kilnBOT
Show your work, and if possible, explain where you are stuck.
fickle maple
```
What step are you on?
1. I don't know where to begin.
2. I have begun but go...
1
I dont know where to start
subtle harbor
cedar kilnBOT
@fickle maple Has your question been resolved?
cedar kilnBOT
cedar kilnBOT
Available help channel!
scarlet pasture
cedar kilnBOT
scarlet pasture
number uhh
59
i tried to make a ratio
but idk if thats the right direction im going in
subtle harbor
Let $x=$The price of the cheaper flour per kg
scarlet pasture
ok
wraith daggerBOT
Moosey
subtle harbor
**Moosey**
the units of x are $/kg
scarlet pasture
the first equation is x+.15=y
uhh yes
and then ill uhh figure out the second one
subtle harbor
the first equation is x+.15=y
er almost
subtle harbor
i would let y be the price
subtle harbor
price overall
subtle harbor
both prices are the same (she's spending the same amount of money)
subtle harbor
she's spending the same amount of money on different amounts of flour
scarlet pasture
wait what
it says she finds that if she buys some cheaper costing 15 cents less per kg
subtle harbor
i am reading the question wrong???
scarlet pasture
she can buy 2 1/2 kg more for the same amount
yes
shes spending less money
she gives you a rate
subtle harbor
yes
scarlet pasture
in which it tells you what it would be if
subtle harbor
spending the same amount of money
cerulean sail
shes spending less money
less per weight, but same amount overall
scarlet pasture
what am i misunderstanding the question?
she buys some cheaper flour
tho
its 15 cents less
subtle harbor
yes, but she's buying more of it
subtle harbor
ok
think about it in terms of units
let P be the amount of money she is spending
$
right?
scarlet pasture
oh waitttt no i think i get it
less per kg
im stupid
so same money but more kg?
subtle harbor
the first equation is x+.15=y
and you're forgetting to multiply by kg up here
subtle harbor
we DO
scarlet pasture
oh wait uhh
she can buy 34.5 kg more flour for x
or wait no
we cant
its uhhh
for some other value
we dont know
subtle harbor
ok. x+.15 is the $/kg of flour for more expensive one
subtle harbor
and how many kg did she buy of the expensive one
scarlet pasture
32
subtle harbor
yes
scarlet pasture
so x + 0.15 = 32?
subtle harbor
no...
scarlet pasture
ok
scarlet pasture
ye ok
subtle harbor
so what should we do with x+.15 $/kg and 32 kg to get to $
scarlet pasture
uhh x+.15/32?
subtle harbor
how do we get $/kg to become just $
scarlet pasture
oh multiply
subtle harbor
(don't think too hard about it)
scarlet pasture
srry
subtle harbor
yes
so we multiply 32 with (x+.15) to get the amount she spends on the expensive flour, i.e. 32(x+.15)=y
scarlet pasture
ohh
subtle harbor
do you know what the equation would be for the cheaper flour then?
subtle harbor
yesss
scarlet pasture
okk
subtle harbor
so we can set 34.5x=32(x+.15)
scarlet pasture
okk
subtle harbor
do you understand why we set them equal though? because she's spending the same amount
the same amount of $
scarlet pasture
19.2 is x right>
scarlet pasture
do you understand why we set them equal though? because she's spending the _same...
yes i simplified it to that actually
cuz if like
a=c
and b=c
a=c
so u just put the two systems together
scarlet pasture
SAME THING
😭
bleh yes
im just bad at uhh saying it
lol
ia ht;io4jwaprejareapio;anepo;irejwarea
so uhh
19 dollars and 20 cents right?
subtle harbor
,calc 32*.15
wraith daggerBOT
Result:
4.8
$34.5x=32x+4.8$
wraith daggerBOT
Moosey
scarlet pasture
ye
subtle harbor
$2.5x=4.8$
wraith daggerBOT
Moosey
subtle harbor
,calc 4.8/2.5
wraith daggerBOT
Result:
1.92
1 dollar and 92 cents
cedar kilnBOT
cedar kilnBOT
Available help channel!
queen jungle
can someone pls help?
clear umbra
@queen jungle what have you tried
cedar kilnBOT
@queen jungle Has your question been resolved?
weary rock
What do I do here?
clear umbra
@weary rock close this channel
weary rock
how do I do that
clear umbra
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weary rock
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cedar kilnBOT
wraith daggerBOT
Maladroit
cedar kilnBOT
wraith daggerBOT
Maladroit
wraith daggerBOT
Maladroit
clear umbra
do you mean like why two negatives multiply to a positive or?
fiery valley
do you mean like why two negatives multiply to a positive or?
its more like
vestal hedge
**Maladroit**
-1^2 is - 1*1
vestal hedge
^2 only works for the number it is on
fiery valley
why is (-1)^2 = -1*-1
vestal hedge
Here it is on 1
fiery valley
^2 only works for the number it is on
wdym by this
vestal hedge
In the first case it is on -1
vestal hedge
wdym by this
1^2 is 1*1
fiery valley
2 times 1^2 is 2 times 1 times 1
yes
vestal hedge
-1 times 1^2 is -1 times 1 times 1
You indiciate what you want to square by brackets. If it says -1^2 without brackets then ^2 is only for 1 and not the - sign
If it was (-1)^2 then it would work for the whole thing
fiery valley
You indiciate what you want to square by brackets. If it says -1^2 without brack...
then what does -2^2 indicate
vestal hedge
-4
fiery valley
^2 is only for positive 2?
vestal hedge
^2 is only for positive 2?
Yes
So you square the two and put the minus before it
Because the brackets tell us to do so
-10^2 is -1 x 10 x 10 which is -100
(-10)^2 is -10 x -10 which is 100
fiery valley
then what does -2^2 indicate
wouldnt it make sense if its like this, since ^2 is for positive 2
$-x^2 = -x(|-x|)$
wraith daggerBOT
Maladroit
fiery valley
or smthing idk
vestal hedge
You are overcomplicating it
fiery valley
You are overcomplicating it
mb
vestal hedge
(ab)^c = a^c times b^c
fiery valley
(ab)^c = a^c times b^c
yeah distributive property
vestal hedge
-2 is -1 times 2
cedar kilnBOT
Available help channel!
raven smelt
point P (4,b) is on terminal arm of an angle, *, in standard postion. If cos & = square root 5/5, and tan & is negative, what is the value of b
cedar kilnBOT
@raven smelt Has your question been resolved?
dire geode
,rotate
wraith daggerBOT
dire geode
ok so basically, how do I solve this???
Do you know inverse trig functions
cedar kilnBOT
@raven smelt Has your question been resolved?
languid bison