2
#help-13
formal pasture
gusty forum
as every polynomial problem goes, sub in random values until you find a root then factorise
formal pasture
as every polynomial problem goes, sub in random values until you find a root the...
noo
im asking for the local
max and min
i dont get it
civic eagle
calculus?
white latch
max and min
Find the critical points.
set f’(x) = 0
and then evaluate these points in the function and rank accordingly
Or if you don’t have knowledge of calculus you can use polynomial remainder theorem, multiplicity, degree even or odd and find the max and min but that would be fairly complicated
But I presume one would needa know calculus for max and mins.
cedar kilnBOT
@formal pasture Has your question been resolved?
cedar kilnBOT
@unique sleet Has your question been resolved?
cedar kilnBOT
@unique sleet Has your question been resolved?
cedar kilnBOT
@unique sleet Has your question been resolved?
cedar kilnBOT
@unique sleet Has your question been resolved?
silver oxide
is the graph x^2<x+2 this
cedar kilnBOT
is the graph x^2<x+2 this
idle tusk
or is it just the domain
just the domain
idle tusk
is the graph x^2<x+2 this
this is area between 2 curves so not the same thing
violet viper
Could someone explain the notation here?
cedar kilnBOT
Could someone explain the notation here?
violet viper
My understanding this is the same as Q = nCP ΔT
Im mos5ly confused by the need for brackets and p subscript
quaint quiver
I think it want to represent the derivative here
It makes sense to write it like this
hollow minnow
i think they just want to remind you that pressure is constant or smth
because theres also the one with constant volume
probably with subscript v
quaint quiver
the same meaning. after derivative the heat Capacity Cp is the function as pressure，so it's why there is a p subscript here as the text “at constant pressure”. So what's the exact pressure value，we use p to determine.🤔
violet viper
There is but I guess im confused as in the exercise you use the the non derived formula
Physical chemistry 3rd semester in case youre curious
quaint quiver
Q refers to the amount of heat needed to absorb 1 mole of material to increase 1 degree Celsius, is the amount of heat change, deltaQ is more reasonable, so deltaQ/ndeltaT=Cp, obviously, for a small amount of temperature change dT, we also have dQ=nCpdT.
violet viper
gotcha
quaint quiver
It makes sense then in my opinion.
violet viper
How come we use the 100 twice?
quaint quiver
just like distance s=vt. For a very short time，we have v=ds/dt.
quaint quiver
No，the given heat is 1kJ=1000J
violet viper
Exactly
quaint quiver
not use 100 twice，be careful😂
violet viper
The ending there doeant add up xuz i have 100 in the numerator and it zhould be 1000
quaint quiver
yep
quaint quiver
my pleasure
violet viper
.close
nocturne oriole
To solve the inequality (\sqrt{g^2 + f^2 - c} \leq \sqrt{f^2}), let's square both sides to simplify:((g^2 + f^2 - c) \leq f^2)Now, let's rearrange the terms:(g^2 - c \leq 0)This inequality holds true for all real values of (g) and (c). Therefore, the solution is (g \in \mathbb{R}) and (c \in \mathbb{R}).
nocturne oriole
.close
bitter stag
<@&286206848099549185>
cedar kilnBOT
<@&286206848099549185>
cedar kilnBOT
<@&286206848099549185>
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.
idle tusk
<@&286206848099549185>
just ask directly first
bitter stag
ok
i have to write the numbers in order
1, 5, 9, 23, 66, 50, 16, 11
1, 5, 9, 11, 16, 23, 50, 66
idle tusk
what are you struggling with, here?
notice that in the first row, last 3 numbers are out of place
bitter stag
nvm i just relized
that was the wrong one
Factorize 16
i kinda forgot how to factorize
bitter stag
its 8
idle tusk
yep
so 2 is one of the factors (8 is a whole number)
now do it again: can you divide 8 by 2?
bitter stag
no?
idle tusk
you can
bitter stag
ok
idle tusk
then you can divide 8 by 2
yep
that means you now have two 2's as your factors
do it again: can you divide 4 by 2?
you do this process until you divide and get 1 as your results
bitter stag
you do this process until you divide and get 1 as your results
brains not braing explain please
bitter stag
do it again: can you divide 4 by 2?
its 2
bitter stag
1
idle tusk
you do this process until you divide and get 1 as your results
this is what i meant
now you have four 2's
that means that 16=2*2*2*2
that's the answer
rustic verge
Ok so this some python code i wrote for a recursive function.
this function returns x - f(f(x-1)) mean x minus output of function of output of function of x-1 (lol that sounded funny). one thing i found is that the ratio x/f(x) approached phi as x approaches infinity, can someone explain the logic behind it?
rustic verge
i just used python code as representation, its a math question only (i dont want random guy to say "dont ask codin questions here")
and yeah, f(0) = 0
idle tusk
Ok so this some python code i wrote for a recursive function.
this function retu...
literally fibonacci series lol
rustic verge
literally fibonacci series lol
yeah fibonacci series also approaches phi like this- f(x)/f(x-1) right? but i cant see the fibonacci series here
fibonacci would have been f(x-1) + f(x-2) instead of x-f(f(x-1))
right?
velvet plank
wow this is interesting
idle tusk
f(1)=1-f(f(0)) = 1-0 = 1
idle tusk
f(2) = 2-f(f(1)) = 2-1 = 1
idle tusk
hold on
rustic verge
idk if the fibonacci series continues in it, lets calculate some more values
idle tusk
then the fibonacci series begins
nvm i'm wrong
rustic verge
f(4) = 4 - f(f(3)) = 4-1 = 3
rustic verge
check this out
yes i am doin this only lol
it showin big values
lemme do for small ones
velvet plank
ok i have a shitty solution but i think the gist is there
consider f(x)/x
= 1-f(f(x-1))/x
= 1-f(f(x-1))/f(x-1) * f(x-1)/(x-1) * (x-1)/x
rustic verge
ok the function is actually random sh*t
velvet plank
= 1-f(f(x-1))/f(x-1) * f(x-1)/(x-1) * (x-1)/x
if we assume f(x)->inf
rustic verge
= 1-f(f(x-1))/f(x-1) * f(x-1)/(x-1) * (x-1)/x
...
velvet plank
which yields a=1/phi
then x/f(x) approaches phi
its a really sus solution but phi does appear
rustic verge
hmm yes
rustic verge
its a really sus solution but phi does appear
yeah ig thats pretty much the way to also prove that it does approach
velvet plank
yup
cedar kilnBOT
velvet plank
np LOL
idle tusk
Ok so this some python code i wrote for a recursive function.
this function retu...
also how did you get the x->inf lol
this python code takes a couple of seconds for not so big numbers on my computer already
cedar kilnBOT
Available help channel!
autumn wolf
cedar kilnBOT
cedar kilnBOT
@autumn wolf Has your question been resolved?
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@autumn wolf Has your question been resolved?
peak drift
the straight line y=2x+1 intersect the curve y=x^2+3x-4 at the point A and b find the coordinates of A and B
cedar kilnBOT
the straight line y=2x+1 intersect the curve y=x^2+3x-4 at the point A and b fin...
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
@peak drift Has your question been resolved?
crimson sedge
Please help me solve the 11th one
cedar kilnBOT
Please help me solve the 11th one
crimson sedge
azure glade
use double angle on cos2x
write cos3x as cos(2x+x), apply addition law and double angle on ur expansion
polar mural
hello how to do these two questions？
cedar kilnBOT
hello how to do these two questions？
mild fern
hello how to do these two questions？
(a) can you bring it to the general form of (x + a)^2 + (y+b)^2 = r^2
cedar kilnBOT
@polar mural Has your question been resolved?
polar mural
(a) can you bring it to the general form of (x + a)^2 + (y+b)^2 = r^2
yes i did it and what should I do?
mild fern
now the r^2 part should always be positive
so whatever you got on the right side just solve the inequality so that its greater than 0
🫶🏼
mild fern
lol np
cedar kilnBOT
@polar mural Has your question been resolved?
cedar kilnBOT
@polar mural Has your question been resolved?
quiet salmon
which one of these rules do i use to solve for y' = 0, if y = e^(3x-x²)
cedar kilnBOT
which one of these rules do i use to solve for y' = 0, if y = e^(3x-x²)
@quiet salmon Has your question been resolved?
Available help channel!
edgy drift
cedar kilnBOT
edgy drift
I have no idea where to start
I need to add one more ecuation so that it is dependent, another one for it to be independent and another for inconsistent
edgy drift
yes
crimson sedge
Well you first start with the top equation
And find the Awnser from there you add it with the bottom
And find common factors
There should be a formula for this as well if you have one
edgy drift
i don't
crimson sedge
It’s hard to start with
But easy to end with
it’s just solve both and then delete common factors
edgy drift
this has infinitely many solutions
thats why i need to add another equation so it has one
no conditions
i thought maybe solve for x
idle tusk
I need to add one more ecuation so that it is dependent, another one for it to b...
ooh
i see
edgy drift
but then I would be just finding the answe for that sistem of equations
idle tusk
idk if you studied this but we transformed these types of questions into augmented matrices
edgy drift
I think that is the next unit i have to study
I thought maybe there would be a way to do it without matrices
edgy drift
but if not i would try with matrices idk
idle tusk
you can divide the second one on both sides by 2
edgy drift
ok
i got x=1/5
I end up solving the system which is a inconsistent
maybe i should just create another equation with the variables i got?
ok i think i got it
but thx anyway
.close
blazing hollow
how do i expand 4(x-5)^2
cedar kilnBOT
how do i expand 4(x-5)^2
dull oxide
sorta..
blazing hollow
oh wait
dull oxide
you use FOIL method
dull oxide
(4x-20)(x-5)
halfway there.
dull oxide
yep
karmic timber
can someone check if my working is correct?
cedar kilnBOT
can someone check if my working is correct?
rare vault
where work
karmic timber
my wifi is so slow
it’s not sending
there you go
the numbers in blue means the number of cases
rare vault
1.6.21?
cedar kilnBOT
@karmic timber Has your question been resolved?
karmic timber
u guys uh checked if it’s right?
karmic timber
hello?
cedar kilnBOT
@karmic timber Has your question been resolved?
worthy steppe
cedar kilnBOT
shrewd reef
!status
cedar kilnBOT
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
no
shrewd reef
do that
worthy steppe
y−4=−5x+5
y=−5x+9 is that correct?
runic garnet
Yes
shrewd reef
yes
worthy steppe
sorry i got another question for this
cedar kilnBOT
sorry i got another question for this
dire thorn
sorry i got another question for this
Do u know the slope
worthy steppe
no.
dire thorn
no.
Well the slope is ratio if how fast y changes compared to x. If you want a formula for this its (y2-y1)/(x2-x1). Choose any 2 points you want and plug it in
Alternatively you can figure it out without the formula by thinking about what slope means which is better for understanding
dire thorn
is it y=mx+b?
That is the form your final answer will take
m is slope, b is intercept, hence it being dubbed “slope-intercept form”
worthy steppe
thanks
cedar kilnBOT
@worthy steppe Has your question been resolved?
warm tinsel
Evaluate [I = \int e^{-k\omega^2t}\cos\omega x\ d\omega.]
cedar kilnBOT
Evaluate \[I = \int e^{-k\omega^2t}\cos\omega x\ d\omega.\]
wraith daggerBOT
Pheasant Plate
royal loom
Do you know eulers formula?
warm tinsel
Yeah, the issue is the omega term is squared. I've tried taking the partial derivative with respect to x and integrating by parts to use the Fourier transform of a Gaussian, but the method hasn't worked out for me since I end up with another integral that is even harder to evaluate lol
royal loom
I'd try to use eulers formula to write it into something resembling e^(-x^2)
and then use polar coordinates
warm tinsel
Using Euler's formula would give
[\frac{1}{2}\int(e^{i\omega x}+e^{-i\omega x})e^{-k\omega^2t}\ d\omega]
What are you saying your idea is from here?
royal loom
**Pheasant Plate**
cos(wx) is the real part of e^(iwx) so you can just input e^(iwx) and at the end make sure to only take the real part of your result
since you now have two exponentials you can combine their powers
I was imagining you might be able to manipulate it into something resembling e^(-x^2) where you can integrate using polar coordinates
but I'm not sure
dire geode
do you have limits on the integral?
warm tinsel
I think it should be over the positive real line
[I = \int_0^\infty e^{-k\omega^2t}\cos\omega x\ d\omega.]
wraith daggerBOT
Pheasant Plate
warm tinsel
Using Euler's formula this can be written as
[\frac{1}{2}\int_0^\infty e^{i\omega x-k\omega^2t}\ d\omega+\frac{1}{2}\int_0^\infty e^{-i\omega x-k\omega^2t}]
wraith daggerBOT
Pheasant Plate
warm tinsel
It's not immediately clear to me how that simplifies the problem. Can I combine the exponents of e^{-kw^2t} with only the real part of another exponential?
dire geode
It's not immediately clear to me how that simplifies the problem. Can I combine ...
Use completing the square method in the exponent of $\exp(-k \omega^2 t + i\omega x)$
wraith daggerBOT
riemann
warm tinsel
Ok, thank you. I think that results in:
[\int_0^\infty\exp\left(-k\left(\omega-\frac{ix}{2kt}\right)^2+\frac{x^2}{4kt}\right)\ d\omega]
wraith daggerBOT
Pheasant Plate
warm tinsel
Hmm, I tried doing a substitution of variables to get it in the form exp(-z^2) but that results in complex valued limits, which I'm not sure how to evaluate since the integrand has no simple poles.
dire geode
Hmm, I tried doing a substitution of variables to get it in the form exp(-z^2) b...
there's a couple ways to show it's just equal to the usual gaussian integral, pick one method you're more comfortable with
opal kiln
cedar kilnBOT
torpid panther
lemme have a think bout that
torpid panther
try drawing a diagram to help u better understand
opal kiln
these are the diagrams but i am not sure abt it
thats the ans i got but i don't think thats correct
cedar kilnBOT
@opal kiln Has your question been resolved?
cedar kilnBOT
@opal kiln Has your question been resolved?
cedar kilnBOT
@crimson sedge Has your question been resolved?
random raptor
I got 41 m for h can someone verify this
cedar kilnBOT
I got 41 m for h can someone verify this
@random raptor Has your question been resolved?
wraith daggerBOT
sly abyss
Can u send ur work
sly abyss
Pretty sure height is
406.87697
m
I mean that answer makes a lot more sense than 41m
sly abyss
Then you just use law of sines or cosines to find x and y
simple totem
I am le stuck once again
pls ping if ur gonna help
cedar kilnBOT
I am le stuck once again
pls ping if ur gonna help
simple totem
ping?
stark quest
I am le stuck once again
pls ping if ur gonna help
be careful when you distribute. what is cos theta * sec theta?
simple totem
be careful when you distribute. what is cos theta * sec theta?
cot
stark quest
I am le stuck once again
pls ping if ur gonna help
this should be right.
stark quest
maybe they want you to write it in terms of tan?
so instead of sinx/cosx
theyre looking for tanx?
simple totem
maybe they want you to write it in terms of tan?
nope they said
sinx cosx
bruh deleted lmao
stark quest
oh okay no clue then
plucky owl
nope they said
sinx cosx
Show your work
simple totem
Show your work
I didnt do any dawg
I did it in my head
plucky owl
That doesn't help
plucky owl
you wanna check how i'm wrong then?
That would be ideal
plucky owl
Or you can send your work
simple totem
Or you can send your work
dawg
I DONT HAVE ANY WORK
I cnt figure out why im wrong thats why i need help
plucky owl
Then write it down
simple totem
Then write it down
either help out or leave the channel please
I don't need you telling me to write it down or not
plucky owl
I am trying to help. I'm trying to help by checking your work
simple totem
<@&286206848099549185> any other helpers?
plucky owl
So send your work
simple totem
I am trying to help. I'm trying to help by checking your work
alright then wait for me to write it down
plucky owl
nope they said
sinx cosx
Are you sure you were looking at the right problem/answer when you said this?
simple totem
Are you sure you were looking at the right problem/answer when you said this?
yeah dude
they asked us to write it in terms of sine and cosine
need more proof?
plucky owl
Can you screenshot the answer that was shown to you?
plucky owl
Who showed you that answer?
plucky owl
Then how do you know if sinxcosx is the correct answer if it didn't show you the answer?
simple totem
I didnt say that
simple totem
i was talking about this
plucky owl
Yeah you did
plucky owl
nope they said
sinx cosx
You said it here
simple totem
they said phrase it in sinx and cosx like in terms of sine and cosine
I meant that
i phrased it wrong
can we move on?
plucky owl
Then you weren't clear on that part, because it looked like you were saying the answer was sinxcosx
plucky owl
What does it say after the comma?
simple totem
What does it say after the comma?
heres the full question for you
plucky owl
It wants you to simplify that more so it's not a fraction
simple totem
It wants you to simplify that more so it's not a fraction
so that becomes
cos^2 theta - Sin^2 theta / sinthetacostheta
plucky owl
Your work looks fine, that question statement doesn't really make any sense with the "simplify that no quotients appear" since you can't really a simplify that to not have a fraction
simple totem
Your work looks fine, that question statement doesn't really make any sense with...
EXACTLY 😭
im so annoyed
plucky owl
But the first step does say to write each expression in terms of sine and cosine so maybe it's a multiple part question where you were suppose to convert those terms into sin and cos first and input that into the box?
simple totem
But the first step does say to write each expression in terms of sine and cosine...
nope
it always asks for the final answer
plucky owl
Then I suggest you should ask your teacher what it expects
Or submit it and see what the answer it wants is
simple totem
the teacher doesnt reply to emails because ofcourse
so ill just have to submit and see
thanks for trying to help
.close
deep thorn
can i get some help on this question
cedar kilnBOT
can i get some help on this question
deep thorn
cant wrap my head around to what the series might be
cedar kilnBOT
@deep thorn Has your question been resolved?
olive radish
cedar kilnBOT
olive radish
Can someone check my work
shut tapir
You might need to calculate f''(x) and show that f' '(-3)>0 to show that the critical points is a minimum
olive radish
cedar kilnBOT
@olive radish Has your question been resolved?
cedar kilnBOT
cedar kilnBOT
Available help channel!
deep cloak
does anyone know how to find basic reproduction number in stochastic sir models?
cedar kilnBOT
does anyone know how to find basic reproduction number in stochastic sir models?
@deep cloak Has your question been resolved?
valid yacht
vivid grove
hi
pure tulip
The last transposition leaves 4 fixed/untouched.
vivid grove
i don't get it
pure tulip
So first we apply (2 5 1 3) to 1 and we get 3. Then we apply (1 3 4 2 5) to 3 and get 4. Then we apply (1 2) to 4 which leaves it fixed, so we get 4.
pure tulip
yeah
humble peak
How do I solve these 2 equation with the elimination method
cedar kilnBOT
How do I solve these 2 equation with the elimination method
amber ridge
10 < 15
solid magnet
How do I solve these 2 equation with the elimination method
U basically need to multiply both sides of both equations with numbers so that the coefficients of any variable (j or c) are same in both equations. Then subtract them to get a linear equation in one variable. After getting the variable, substitute it in either equation to find the other variable
humble peak
U basically need to multiply both sides of both equations with numbers so that t...
can you go thru the problem with me
solid magnet
Kk
humble peak
thx
humble peak
j
solid magnet
K
So basically u gotta ensure that the coefficient of j is same in both equations
Which it is not here
In one equation the coefficient is 3 and in the other it is 5
So basically u gotta make both coefficients the same
In order to do that you gotta find lcm of 3 and 5
humble peak
so multiply?
solid magnet
Yes
Multiply the first eqn by 5 and the second by 3
Both sides ofc
And tell me what do you get
humble peak
alr
crimson sedge
so if coeff is same then yu can eliminateit
crimson sedge
no i know i was telling him
solid magnet
Oops sry
crimson sedge
np
solid magnet
I got 15j+35c=24
And do the second one too
solid magnet
Yes
solid magnet
Yes and find c
humble peak
Yes and find c
Wait 17/5.1
Or
I use one of them to divide both sides
@solid magnet
amber ridge
How do I solve these 2 equation with the elimination method
first of all can you show the problem as well?
humble peak
amber ridge
,rotate
wraith daggerBOT
amber ridge
ok
amber ridge
btw strictly speaking, your variable names are wrong here
amber ridge
no
humble peak
Yea
solid magnet
C for pounds of carrot and j for gallons of juice
humble peak
Wait 17/5.1
@solid magnet I'm confused
amber ridge
J isn't just "juice", it is "cost per gallon of juice"
similarly, C should be "cost per pound of carrot"
the problem here is pretty simple so it's not a big deal, but it's a good idea to be careful with what your variables represent for more complicated problems
amber ridge
C for pounds of carrot and j for gallons of juice
C and J represent the price, not the items themselves
amber ridge
Does it really matter tho? Or now
the math should still be the same but I'm saying just be careful
humble peak
C=0.3
humble peak
the math should still be the same but I'm saying just be careful
Alr
humble peak
Yea
humble peak
now just plug it back
Is it j=5.4
solid magnet
C and J represent the price, not the items themselves
Yea
humble peak
plug both variables back in
Idk
amber ridge
idk what
humble peak
I think I'm wrong
crimson sedge
$$3g+7p=4.80$$
$$5g+6p=6.30$$
wraith daggerBOT
Sparking
crimson sedge
$$15g+35p = 24$$
$$15g+18p = 18.9$$
wraith daggerBOT
Sparking
crimson sedge
$$35p-18p=24-18.9$$
wraith daggerBOT
Sparking
crimson sedge
$$17p=5.1$$
wraith daggerBOT
Sparking
crimson sedge
$$ i pound carrots = 0.3 dollars $$
wraith daggerBOT
Sparking
crimson sedge
@humble peak
humble peak
Yes I got that part
Ty
I'm lil more confused on the 2nd equation @crimson sedge
Cuz
18*0.3
=5.4
crimson sedge
$$3g+7p = 4.80$$
$$ substitute-p=0.3$$
$$3g+7*0.3=4.80$$
$$3g+2.1=4.80$$
$$3g=4.80-2.1=2.7$$
$$g=2.7/3=0.9$$
wraith daggerBOT
Sparking
humble peak
5g+6p=6.30
crimson sedge
$$5g+6p=6.30$$
so
$1.5+6p=6.30$
$6p=6.30-1.5$
$6p=4.8$
oh shoot
@humble peak
humble peak
Uh...
crimson sedge
i substituted wrong one
humble peak
Damn all good
wraith daggerBOT
Sparking
crimson sedge
5g......
humble peak
Don't need to rush
crimson sedge
$5g=4.5$
wraith daggerBOT
Sparking
crimson sedge
$g=0.9$
wraith daggerBOT
Sparking
humble peak
Alr
cedar kilnBOT
The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.
humble peak
Thank so much
crimson sedge
np
humble peak
.close
mint raft
Hi can someone please help me with this
cedar kilnBOT
Hi can someone please help me with this
tulip crane
ok
mint raft
Thanks
tulip crane
Alright so first the paralellogram question
Obviously ABCD is a ||gm meaning AD(or AE if you want to call it that) is parallel to BC
EC is a transversal to these two lines
By law of transversal, you can say that Angle BCE is equal to Angle CED
So you can say that CED is 74 degrees.
Now, since BEC is an icoseles triangle, The angles 1 and 3 are equal
(I can't see clearly which is 1 and 3, basically the 2 angles inside the triangle BEC marked with numbers are equal)
Now we know one of those angles is 74 degrees
The other obviously has to be 74
Now the sum of these two angles is 2 times 74 which is 148
Consider the triangle BEC, the sum of all angles inside should be 180
So the third angle is, 180-148=32
Now the second question.
Notice how the triangles ALS and NLE are similar
You can use the law, $\frac{LS}{LE}=\frac{AS}{EN}$
wraith daggerBOT
diaas_(yt)
wraith daggerBOT
diaas_(yt)
tulip crane
2x+8=3x+6
mint raft
I am following along
cedar kilnBOT
cedar kilnBOT
Available help channel!
fast sundial
(x^2+x-3)^2
cedar kilnBOT
(x^2+x-3)^2
fast sundial
i got x^2-5x^2-6x+9 but there's meant to be a -2x^3???
umbral dew
!xy
cedar kilnBOT
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.
wraith daggerBOT
!Yajat!
fast sundial
don't you isolate -3?
cedar kilnBOT
fast sundial
oh hiow do you draw the line of best fit?
there's no exact question but it's coming on my test tomorrow
fast sundial
on a scatter plot
its like a type of regression line that goes onto a scatter plot to determine the median or etc
my teacher says to eyeball it but ther'e s gotta be a mathematical solut
cedar kilnBOT
Available help channel!
grand heath
cedar kilnBOT
grand heath
Hi I would like to ask how can I find 40.5p from part C stock =1
I tried to do by at stock =1
when demand =0 profit =-45 with prob 0.1
when demand =1 profit =50 with prob 0.2
expected return of profit when stock=1 = -45(0.1) +50(0.2) but the answer wont be 40.5p
<@&286206848099549185>
cedar kilnBOT
@grand heath Has your question been resolved?
grand heath
<@&286206848099549185>
grand heath
<@&286206848099549185>
grand heath
@crimson sedge
cedar kilnBOT
@grand heath Has your question been resolved?
cedar kilnBOT
@grand heath Has your question been resolved?
fast sundial
Hi I would like to ask how can I find 40.5p from part C stock =1
is that the answer?
cedar kilnBOT
cedar kilnBOT
Available help channel!
junior bluff
i have a question
cedar kilnBOT
i have a question
still beacon
i have a question
send it here
junior bluff
if you have a function that has a defined point, its function is continuous at that point, is that enough to show that the limit exists at that point?
oscillations im thinking now so maybe not
well nvm cause oscillations are a discontinuity
floral arrow
If a function has a limit at a point and its value is equal to that limit, then it's continuous at that point
junior bluff
If a function has a limit at a point and its value is equal to that limit, then ...
so the converse must also be true?
meaning defined, and continuous so theres a limit
floral arrow
If it's continuous at a point then yes it has a limit at that point equal to its value
It's pretty much the definition of continuity
junior bluff
would this idea be a good method of knowing if a limit in multivariable functions exists (not proving)
for ex, if a surface is continuous everywhere and it has a defined point, so that point must also be the limt
yes
floral arrow
That seems correct, but you need to word that better
A limit is a value (or -inf +inf in some contexts)
If the function f of a surface is continuous at a point A then the limit of f at A is its value at A
cedar kilnBOT
cedar kilnBOT
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radiant stream
Hi all! first question here, hope this is the right place for it. I was reading this Math SE https://math.stackexchange.com/questions/456552/integrating-2-form question on the evaluation of double integral of a 2-form, and I was wondering what is meant by the inclusion $\iota : M \to \mathbb{R}^3$ and was sent down a rabbit hole, and now I'm confused. Let's say I have a manifold $S^2$ in $\mathbb{R}^3$ which is the unit 2-sphere $x^2 + y^2 + z^2 = 1$, what would the inclusion map $S^2 \to \mathbb{R}^3$ look like? I was following along Vincent Bouchard's Calc IV notes https://sites.ualberta.ca/~vbouchar/MATH215/section\_surface\_integrals.html and I didn't see an explanation about the inclusion
wraith daggerBOT
euwbah
radiant stream
cedar kilnBOT
@radiant stream Has your question been resolved?
cedar kilnBOT
@radiant stream Has your question been resolved?
cedar kilnBOT
@radiant stream Has your question been resolved?
radiant stream
.close
torpid urchin
cedar kilnBOT
torpid urchin
what is the thinking to solve for c here?
sharp lotus
well key word is the function needs to be continuous
so you need to make sure that the two pieces "match up"
torpid urchin
right
so will i want to plug in 0 and 9 and find the value for which they are both 0?
sharp lotus
i.e. make sure that $\lim_{x\to0} c(9x-x^2)=0$
sharp lotus
as x-> from the right, i forget the latex notation
torpid urchin
so why x approaches 0?
wraith daggerBOT
Soosh
torpid urchin
and similarly why dont i care about approaching 9 from the right
sharp lotus
because you have f(x) = 0 using the second piece of the function
sharp lotus
in "simple english terms" you pretty much just need to make sure the two pieces match up. what that means in math speech is, well continuity is defined by function value and limit matching up for any x where f is continuous
sharp lotus
so i wouldnt want limit for approaching 9 from the left either?
f is not defined at x = 9?
torpid urchin
well f(x) is just 0 at 9 isnt it
torpid urchin
im just trying to understand the reasoning behind checking the limit of only one side
ok
sharp lotus
that was just me misreading
royal finch
I have no idea why you need to calculate a limit at all here
You need to integrate this
sharp lotus
I have no idea why you need to calculate a limit at all here
i mean you can just think of it as making sure the values matchup but im just explaining it conceptually that's what definition of continuity is based on
torpid urchin
thanks for the help regardless lol
royal finch
Yes
torpid urchin
ok cool
oh its a density function
that probably shouldve given it away
i thought it was a pmf for a second lol
royal finch
and note that you still have to write down F(x), not f(x) once you have it all
signal nymph
cedar kilnBOT
signal nymph
i am unsure on how to show commutativity and associativity with these types
what do i use as 'c' for commutativeness
associativity is just ba+1 ?
crimson delta
thats the wrong way around
crimson delta
well c is just some other number
you need to show (a*b)*c=a*(b*c)
by plugging in the definition of * on both sides
twice each
and yes for commutative its just a*b=ab+1=ba+1=b*a
torn anchor
If im understanding correctly both these questions will have me multiplying the 2 main numbers and taking the result x and then doing xmod (subscript on modifier)
cedar kilnBOT
@torn anchor Has your question been resolved?
torn anchor
<@&286206848099549185>
nimble veldt
If im understanding correctly both these questions will have me multiplying the ...
it depends how the meaning of "+" with subscript is defined. it is not a common used notation (at least in my region).
torn anchor
Yea Ive been having trouble finding information about all this
I thiiiiink Im doing it the way he wants it but I wanted to see if anyone here knew
crystal raptor
I think that's the most likely interpretation of the notation yes
cedar kilnBOT
@torn anchor Has your question been resolved?
cedar kilnBOT
cedar kilnBOT
Available help channel!
bleak mulch
How would I write 8^x/3 in the equivalent general form y = ab^x?
bleak mulch
I tried to solve it like this
hollow minnow
thats right
bleak mulch
Really? It doesn't matter if there's no a?
hollow minnow
well a = 1
bleak mulch
.close
junior thorn
I really don't understand what "onto" means and how to solve ii.
cerulean sail
Given any element of P_1, can you find something that f maps to it?
junior thorn
what does it mean to be "f maps to it"?
cerulean sail
E.g. take something like pt + q, can you find an [a,b,c] such that f([a,b,c]) = pt + q?
cerulean sail
Yep that works 
junior thorn
does that mean the function f is onto?
cerulean sail
In that case, you're surjective, because for any element of P1, you can find an element of R3 that "corresponds" to it
junior thorn
ohhhh
cerulean sail
For an example of something that isn't surjective (onto), e.g. consider $f: \bR \to \bR, f(x) = e^x$, where $e^x = b$ has no solutions if $b\leq 0$
wraith daggerBOT
@cerulean sail
junior thorn
then... if another question asks like
Let : T: V -> W be a linear transformation defined by blah blah...
then I have to pick any elements in W and find if an element in T corresponds to it?
cerulean sail
Basically yeah: if you have that T, then either find some element w of W that doesn't have a corresponding v in V such that T(v) = w (for non-surjectivity), or show that no matter what w in W you pick, you must have some corresponding v in V such that T(v) = w (which shows surjectivity)
There are some theorems when it comes to linear maps that can make your life somewhat easier in that regard
cerulean sail
No problem 
have a good one!
brazen fractal
I'm very confused on how to do this problem, i know i need to use an inductive proof and properties of nCr but i dont know how to apply them together
brazen fractal
and the answer on the math stack exchange doesnt explain enough
I proved it for k=1, cause n choose 1 is n, but i dont know what to eve write for P(n+1)
midnight hatch
P(n+1) : " C(n+1,k) <= (n+1)^k/2^(k-1)
Then idk if that will get you anywhere
But you can try to use newton's binomial
To get a combination out of (n+1)^k
brazen fractal
P(n+1) : " C(n+1,k) <= (n+1)^k/2^(k-1)
right but i dont understand how to prove that
midnight hatch
Then idk if that will get you anywhere
could try this
These formulas might also prove useful
brazen fractal
P(n+1) : " C(n+1,k) <= (n+1)^k/2^(k-1)
i think the inductive step has to be C(n, k+1) because if i use n as the inductive variable then i'm stuck with proving 1 choose k ≤ 1^k/(2^(k-1)) which im not sure is easy
and the basis step is n choose 1 ≤ n^1/2^(1-1) which is true
midnight hatch
sure you could do it with k i think
but then the redaction is different
cuz that's a finished induction
basically you're not doing it on all of N
brazen fractal
ok then how would I do it with n
midnight hatch
You can do it with k
i dont find anything about it in english
but basically
just fix n
and take k in 1,...,n
And then just do a regular induction
Since the property always starts at 1 you won't have any problem
brazen fractal
ok i think i have an idea
crimson sedge
Im not sure if it works, but if you replace n with n+1 for the induction step you can equate the left side in the 3rd formula of the picture that was sent earlier
And you already have those two terms in you induction hypothesis
cedar kilnBOT
@brazen fractal Has your question been resolved?
brazen fractal
Im not sure if it works, but if you replace n with n+1 for the induction step yo...
i got here but im not sure how to get to the final P(n+1)
brazen fractal
i got here but im not sure how to get to the final P(n+1)
<@&286206848099549185> i got here but im not sure how to finish the proof
midnight hatch
<@&286206848099549185> i got here but im not sure how to finish the proof
compare n^k+2n^(k-1) and (n+1)^k
you just have to show that n^k+2n^(k-1) < (n+1)^k and you're finished
brazen fractal
you just have to show that n^k+2n^(k-1) < (n+1)^k and you're finished
right but im not sure how to show that 
midnight hatch
right but im not sure how to show that <:clueless:1040718011176341554>
(n+1)^k = n^k+C(n,1)*n^(k-1)+.......
We essentialy want to know if C(n,1)>2 then
However C(n,1)=n
So for any n>=2 your inequality is working
And it's also working for n=1 since you verified it with the base step
midnight hatch
So for any n>=2 your inequality is working
You might want to change the reasoning a little bit then
Add a 2nd base step
with n = 2
brazen fractal
yknow what my brain hurts im just gonna write that its less than the n+1 step and turn it in and myabe ill get points
.close
thin junco
How would u rewrite this in the form of q(x)+r(x)/b(x)
cedar kilnBOT
How would u rewrite this in the form of q(x)+r(x)/b(x)
@thin junco Has your question been resolved?
cedar kilnBOT
@thin junco Has your question been resolved?
cursive crystal
hey guys, i shall proof that the n-th root of a constant c converges to 1. We were given a hint to look at the series c^(1/(2n)) but what does that help us with? i could show c>1 pretty easily but i am stuck at c<1.
gusty forum
assume c in [0, 1). show that c^(1/k) is bounded above by 1 for any natural k
hollow minnow
a slight correction that c != 0
cursive crystal
yeah c!=0 is already given.
cursive crystal
assume c in [0, 1). show that c^(1/k) is bounded above by 1 for any natural k
But where do i need c^(1/(2n)) for?
I mean i can easily proof c<1 with 1/c>1, the solution itself isnt a problem but i dont comprehend how i shall include the other series.
I could argue purely without that.
hollow minnow
not sure tbh seems like simple binomial would do the trick
cursive crystal
yeah. But our prof said:
Hint: use monotony and this other series.
gusty forum
seems a little out of place
it might be sandwich but that seems redundant
if you just covered sandwich i guess do that
cursive crystal
Yeah, we covered sandwich. But then i need to show that this other series converges to 1 and how should i do that?
gusty forum
modify your current argument for c^{1/n} so that it applies to c^{1/2n} ig lmao
cursive crystal
hahaha
gusty forum
a lot of things work such as the binomial stuff as suggested by pure
cursive crystal
yeah i did c>1 with binomial and c<1 with lim (1/n-th sqrt(c))=1/lim(n-th sqrt(c)) which is just saying that 1=1/x and thus x=1
crimson sedge
