@near atlas does option 3 say the first derivative or the second
#help-23
quasi bison
near atlas
option 3 is talking about the 1st derivative
sharp sentinel
for 2, just use median value theorem thrice
lime dust
And you didn't need me to answer this question, which is better you to find out.
near atlas
for 2, just use median value theorem thrice
i used Rolle's
lime dust
Tools are there to be used.
near atlas
i see. ill try to work out a proof with MVT
lime dust
MVT is much stronger theorem
Just stronger, "more stronger is incorrect".
lime dust
.close
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near atlas
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native flume
i feel like what ive done is probably wrong, i tried instead of using 7 and 4, using 2 and 1, since these are a lot easier to sketch, i then considered what the y-value is when we plug in x=1/2 into the functions, in which the y-value for the function in the integral I_1 is greater, so im assuming that i can perhaps extrapolate this for all the points 0<x<1 (not sure if this true tho would i have to prove it?) and then i can extrapolate it for the case of 7 and 4. this is likely to be wrong, how should i approach this instead? ty
safe radishBOT
i feel like what ive done is probably wrong, i tried instead of using 7 and 4, u...
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latent mountain
Hey
rugged bluff
Can I explain my approach?
yes
latent mountain
Okay so
If we expand what is given we get something like this:
x*[(1+x)^2]*[(2+x)^3]...... [(10+x)^11]
So if we write the general term for each
quasi bison
||here's a better question: what's the degree of this big product?||
latent mountain
It will look like:
x* [2Cr * 1^(2-r) * x^r] [ 3Cr * 2^(3-r) * x^r]....
latent mountain
||here's a better question: what's the degree of this big product?||
hmmm
is it 1+2+3....+11
so 66
Then?
mossy lotus
hint number 2 (following what ann said) ||how are the coefficients of a polynomial related to the factors||
mossy lotus
if you have a polynomial (x-a)(x-b)(x-c), then what is the coefficient of the x^2 term?
latent mountain
-(a+b+c)
mossy lotus
Something to do with factor theorem?
isnt factor theorem just that if x-a is factor of p(x) then p(x=a) = 0? That doesnt look not very useful here
latent mountain
Oh ur talking about sum of roots and product of roots and all that?
mossy lotus
yep, vieta's
mossy lotus
yep thats the question
latent mountain
\-1 times the sum of roots
ah yes
-b/a
we need to find roots
which is easy
0 , -1, -2 ,-3.... -10
No wait
mossy lotus
yep, those are the roots
latent mountain
So sum of those would be 55
latent mountain
Umm
mossy lotus
take a simpler example, what is are the roots of (x+1)(x+1)? what is the coefficient of x in that?
mossy lotus
yep!
latent mountain
so for this it would be 0 - 1 - 1 -2 - 2 - 2....-10 ten times
mossy lotus
mhm
latent mountain
How do you find that sum tho?
latent mountain
Its an AGP?
mossy lotus
whatever you feel easy
mossy lotus
Its an AGP?
isnt an AGP a product of terms in an AP and terms of a GP?
or am i trippin
latent mountain
isnt an AGP a product of terms in an AP and terms of a GP?
Yea I was wrong there
What if they give something like find coeff of x^34
latent mountain
I tried writing the general term for each expansion
x* [2Cr * 1^(2-r) * x^r] [ 3Cr * 2^(3-r) * x^r]....
mossy lotus
It will look like:
x* [2Cr * 1^(2-r) * x^r] [ 3Cr * 2^(3-r) * x^r]....
then I would suggest you expand this
does not make me wanna solve this, I would just skip it
latent mountain
x* [2Cr * 1^(2-r) * x^r] [ 3Cr * 2^(3-r) * x^r]....
From this
mossy lotus
so for this it would be 0 - 1 - 1 -2 - 2 - 2....-10 ten times
also this 10 would appear 11 times btw
latent mountain
also this 10 would appear 11 times btw
Oh yea mb
latent mountain
And we want 1+10r = 65
Did you get this?
mossy lotus
not really, like why do you get x^(1+10r)?
latent mountain
x* [2Cr * 1^(2-r) * x^r] [ 3Cr * 2^(3-r) * x^r]....
In this focus on the powers of x
mossy lotus
like ok, but thats just one such term, and you are not even sure you would get r such terms every time
latent mountain
you have xx^rx^r...
latent mountain
like ok, but thats just one such term, and you are not even sure you would get r...
Ohhh
mossy lotus
like for r = 5, you dont have enough number of terms from i=2 or 3 and so on
latent mountain
Yes you are absolutely right!
I took r terms for every general term
K that clears everything up then
mossy lotus
so for this it would be 0 - 1 - 1 -2 - 2 - 2....-10 ten times
I suggest you go through with this, coz I dont think anyone would ask you random coefficients like 34 or smthn
latent mountain
hmmm
mossy lotus
you would need to do massive amounts of calculations, womething no one expects you to do in an exam
mossy lotus
np
latent mountain
How do I end this?
mossy lotus
type .solved
latent mountain
.solved
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terse delta
Hello so i’m having trouble solving sutitution integrals. i can do integrals by parts but with substitution choosing an “U” is being a mess to me rn .
safe radishBOT
Hello so i’m having trouble solving sutitution integrals. i can do integrals by ...
stoic saddle
which one
terse delta
no like almost all of them
i need like a summary of where i should get U
for example someone told me if we have ln(something) and like a function the best thing is to choose all the ln(something) as u and derívate it then getting du etc etc
cobalt thunder
this sort of thing comes with experience
a general rule is if the du cancels something from the expression, then you should be on the right track
for example for (a), taking
u = x^2,
you get
du = 2xdx,
and since you have an x in your expression, that x will be swallowed by the du, so it should be good
terse delta
just did this, good )?
cobalt thunder
so you just kind of try random stuff and watch out for whether anything gets canceled; eventually you'll notice patterns but there's so many patterns that they can't really be taught
cobalt thunder
just did this, good )?
yeah, this looks good
terse delta
now i’ll do this . will be back in a secs
so should i choose cos 2x as u ? @cobalt thunder
sorry for ping
and then the derívate is -sen 2x and i put the - to the other side and it is -du = sen 2x
cobalt thunder
yeah, exactly!
cobalt thunder
for example for (a), taking
u = x^2,
you get
du = 2xdx,
and since you have an x...
in this case you can even choose 1+cos(2x), just like for (a), you could have taken 1+x^2, since adding a constant term does not change du
cobalt thunder
and then the derívate is -sen 2x and i put the - to the other side and it is -du...
btw the derivative is -2sin(2x), don't forget the chain rule!
terse delta
oh fuck forgot that
i’ll do it again
so u
1 +cos 2x
du= -sen 2x * 2
-du/2 = sen 2x
that’s ok ?
@cobalt thunder
sinful thicket
sorry to interrupt, i just never seen sen in trigonometry 😭😭
oh is it just made up value
cobalt thunder
that’s ok ?
yep
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@terse delta Has your question been resolved?
verbal vector
why do they seperate the letters with bars? what does that achieve?
rain stratus
TANJANT KOTANJANT
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@verbal vector Has your question been resolved?
tardy mango
why do they seperate the letters with bars? what does that achieve?
Separate into a's, b's, c's, d's
exotic anvil
TANJANT KOTANJANT
Please don't shit post in help channels.
verbal vector
.close
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coarse sky
hello! I have three questions i need to get done for homework tomorrow but I'm struggling. Its algebra/geometry?? simultaneous equations basically. I'd appreciate if someone could show how to do it with some small explanation notes, i already have the awnser but how i get it is what i struggle with. this is the first question i need help with! : 3x - 2y = 8
x + y = 6
safe radishBOT
hello! I have three questions i need to get done for homework tomorrow but I'm s...
quasi bison
,rccw
flat frigateBOT
quasi bison
@coarse sky have you learned elimination and/or substitution methods?
if both, is there an instruction to use a specific one for this question in particular?
coarse sky
I dont think so, maybe that's why i struggle with it. I know formulas partly
quasi bison
what language do you study in
coarse sky
if both, is there an instruction to use a specific one for this question in part...
Nope, but the awnser is in coordinates. Its: (4,2)
quasi bison
coarse sky
what language do you study in
Irish / Gaeilge
quasi bison
.. ok i don't speak that
latent mountain
https://youtu.be/oKqtgz2eo-Y
This channel is gold
quasi bison
still give this video a watch
coarse sky
not alot of ppl do🥹 its so hard to learn things online bc of it
coarse sky
https://youtu.be/oKqtgz2eo-Y
Idk if i watched this already
woven fjord
Multiply eq (2) by 3 u get:
3x+3y=6 call this eq (3)
Then subtract eq (1) by eq (3)
Eg
Eq (1) - Eq (3) gives:
-5y=-10
Y=2
Sub y= 2 into eq (1) or eq (2) or eq (3) and find x
[NOTE subbing into eq (3) is dumb because its equivalent to eq (2)]
For example sub y=2 into eq (2) giving us
X+2=6 so x=4
As a row vector the solution to this simultaneous eq is:
(4,2)
This process is the elimination method
normal moss
Multiply eq (2) by 3 u get:
3x+3y=6 call this eq (3)
Then subtract eq (1) by eq ...
!nosols
safe radishBOT
Multiply eq (2) by 3 u get:
3x+3y=6 call this eq (3)
Then subtract eq (1) by eq ...
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.
normal moss
Nobody learns math if they just read what to do
safe radishBOT
@coarse sky Has your question been resolved?
coarse sky
Wait
spring hill
?
woven fjord
Nobody learns math if they just read what to do
Oh i mean its just ine question
They said they have 3
normal moss
I don't understand your point
woven fjord
I don't understand your point
Learns how to do the first question via a solution
normal moss
One equation is more than enough to teach them how to solve these systems in general
I disagree.
woven fjord
Then he can do the ither 2 himself
woven fjord
One equation is more than enough to teach them how to solve these systems **in g...
I gave my solution so now he knows
normal moss
You showed him how to solve this specific system, by showing every step. But they get no insight into why we did any of the steps
And that is by far the most important part in math
woven fjord
You showed him how to solve this specific system, by showing every step. But the...
Its kinda obvious why we do the steps if u follow the solution
normal moss
And while it seems intuitive to you, not everyone understands it, especially those dealing with it for the first time
woven fjord
Ok well sorry mb
woven fjord
Multiply eq (2) by 3 u get:
3x+3y=6 call this eq (3)
Then subtract eq (1) by eq ...
To simplify all i did was multiply eq 2 by 3 because multiplying a single equation does not affect the solution
Then i subtracted to get rid of the second variable
This is now simply a equation in one variable which is easy to solve if u can't solve this i suggest u go back and learn elementary algebra
After solving i can sub that value in for any of the equations and solve for the second variable
For completeness check ur answers via re subbing in to every equation
woven fjord
Nobody learns math if they just read what to do
Also this is a false statement
I learnt maths by following a worked solution
So lets not lie
coarse sky
Everyone learns different
💕
Thanks for ur help! And sorry if i diddnt understand some words, i dont learn math in English so some things are a little confusing ^^
normal moss
Also this is a false statement
Well.
Reading solutions is known as passive learning. The learner doesn't make decisions, try to reason or experiment. Research proves that active learning is what builds actual understanding.
To add on, just following the steps teaches procedures, as I mentioned before, not concepts. They might learn to multiply both sides of an equation by (-2) in an example but won't have any clue when, how, or why to do it in an another one.
This also taps in our memory. Reading the steps can overload our working memory because of too much information (symbols, words, equations, and no sense of logic or organization). If we don't think about the why, much of that information is deemed "useless" to us and does not move to long-term memory (very dumbed down).
Also, there are two massive downsides.
- No error-based learning: making mistakes and correcting them is crucial for learning. You know the saying "we learn from our mistakes". Solved solutions do not allow this.
- Just reading solutions can create a very false sense of understanding. They might think they get it because they got to the end and the steps made sense, but they won't be able to reproduce or apply the process elsewhere themselves.
Yes, when it comes to relatively 'basic' things like this system of equations, just learning through the solved example may suffice. But if you count on it too much, I guarantee it is not enough for higher level maths (even if you don't decide to pursue math later, in late highschool). It's much harder to fix a problem that becomes apparent later, when it could have been fixed relatively easily sooner (like here).
And I mean this with no disrespect whatsoever. But ask any professor, they will tell you that the why is fundemental.
woven fjord
And I mean this with no disrespect whatsoever. But ask any professor, they will ...
Idk mate ive been using worked solutions and learnt everything pretty easily
Especially elementary algebra watching a worked solution is easier to learn imo
main musk
what works for u might not work for someone else tho 
woven fjord
what works for u might not work for someone else tho <:kot:636591995611250709>
I said imo
And obviously i was refuting him bc he said worked solutions dont help at all
Which is in fact false as it depends on the person such as me ive learnt elementary algebra very easily just by watching tons of worked solutions
main musk
I said imo
yes I understanding im just saying mine too
normal moss
Which is in fact false as it depends on the person such as me ive learnt element...
Well, see, your success here doesn't necessarily disprove the principle I mentioned. Some people are naturally more intuitive in math. You can look at a worked solution and automatically infer the underlying concepts without needing explicit explanation, especially in areas like elementary algebra. You might generalize from examples better than most, be better at spotting patterns and reasoning principles that others would miss ...
But this is far from the norm - most people need guidance, reasoning, and active engagement to truly understand and retain the material
woven fjord
Well, see, your success here doesn't necessarily disprove the principle I mentio...
U never mentioned some tho
Thats the issue here
U just said "Nobody learns math if they just read what to do"
normal moss
Yes, my original sentence was phrased poorly. "nobody" was not appropriate
I apologize for that
I didn't mean it as absolute nobody, but obviously you can't read my thoughts 😅
"Nobody learns math if ..." sounded better in my head than "most people don't learn math if ..."
woven fjord
Yea ic sorry for being mean i just got annoyed lol cuz the sentence sounded a bit aggressive :( 😖
(also ill avoid giving sols from now on unless theres like 10 questions then ill give a sol for 1)
normal moss
Yea ic sorry for being mean i just got annoyed lol cuz the sentence sounded a bi...
Yes, I understand
You can think about it this way: say we have 2x - 4 = 8. We want to solve for x. Of course you can just tell them: move 4 to the right side, we get 2x = 12. divide by 2, we get x = 6.
But then they stumble upon 1/5x + 2 = 12. again, this seems intuitive to me and you, but that's because we have learned way past this by now. Right, they will remember we moved the 4, so I guess we move the 2. We get 1/5x = 14. you would be surprised by how many people would add two instead of subtracting But then they'd get stuck with 1/5x = 14. What do we multiply by? But if we explained why we can add/subtract the same amount of both sides, because it preserves equality and explained that we want to isolate x (which means undoing the operation), and we do that by multiplying/dividing both sides, they would understand the principle, not just the steps. They would think "oh, I need to isolate x -> so I will first subtract 2 on both sides, because I can do that and I know why, working towards my goal to isolate x -> now I have 1/5x, and to isolate x, I need to undo the operation, so I need to multiply both sides by 5 to undo 1/5 ... and so on
And so this becomes kind of a "tool" that flows from understanding, having an idea of what they are trying to work towards, not just doing random steps, not knowing why
This is just a quick example I made up, but I hope it's understandable
So they move from thinking "I move the 4, then divide by 2" into "I'm trying to isolate x, so I'll need to reverse the operations that were applied to it, one at a time"
safe radishBOT
@coarse sky Has your question been resolved?
true cypress
safe radishBOT
hardy lion
cal compon
de then fin
true cypress
bruh
hardy lion
trig ratios are defined using SOHCAHTOA
you cant gain information by using the x axis as a reference, so you use the y axis
imagine rotating the image 90 degrees counterclockwise
,rotate 90 ccw
flat frigateBOT
hardy lion
now you look for the horizontal component
true cypress
you cant gain information by using the x axis as a reference, so you use the y a...
can you elaborate on this?
hardy lion
you cant gain information by using the x axis as a reference, so you use the y a...
you cant gain information because the angles given based on the angle to the y axis in the original image
hardy lion
you would need to know the angle a vector makes to the x axis
whoch is possible, but it requires some extra work
true cypress
so cant we imagine 3v and 65 degrees attached to x axis?
hardy lion
no, because the 65deg measures the angle between the two vectors
not V1 and the x axis
true cypress
i see, so basically what you are saying is, there is insufficient information for us to use the x axis
so it would be beneficial
to use the y axis
hardy lion
there is sufficient information, its just more work
true cypress
im going to try them both
so from what i understand
if the vertical distances are equal
we can evenly split 115 degrees on the top end of 3v
and lower end of 5v
or wait nvm
idk why they gave such a confusing diagram
hardy lion
yes, we know theta' and theta sum to 115
true cypress
so if we are rotating it clockwise and the dashed line is basically the length
if we know that those lengths are equal
cant we say the angle of theta and theta'
are the same
hardy lion
no
true cypress
ok i get it now.
do uk any resources
with problems of this level
this the only one the prof assigned
hardy lion
no, sorry
safe radishBOT
Available help channel!
hot stone
whats the domain of log(12+sqrt(x))
safe radishBOT
whats the domain of log(12+sqrt(x))
hot stone
don't i just do
12+sqrt(x) > 0
sqrt(x) > -12
x > 144
lime dust
What?
That doesn't make sense.
Read what you wrote.
Sqrt(x) is never < 0
and in R is only defined for x>0
since sqrt(x) is always positive...
what would be the domain then?
hot stone
right
i thought i would set up the domain of log as (___) > 0 just like how log(x+1) is set up as x+1 > 0
i forgot that it's different with this problem because there's a square root in there
.close
frozen quarry
Hi, what’s the difference between “equal axis of symmetry” and just P?
frozen quarry
Equal axis of symmetry is just the line from the vertex?
blazing swallow
that is the axis of symmetry, yes
what is P in this case?
safe radishBOT
@frozen quarry Has your question been resolved?
sleek agate
Those are symmetrical?
Axis of symmetry is the line through the vertex of the parabola
The person above asked what are u saying “P” represents
I don’t see it anywhere on there either but I also don’t read Icelandic
lean otter
Can someone help me understand what it means when it says 0,1 or 1,0 or even like 2,1
safe radishBOT
Can someone help me understand what it means when it says 0,1 or 1,0 or even lik...
timid escarp
those are coordinates on the grid. (0, 0), the reference point, is at the intersection of the x/y-axes (the two lines on the grid that are darker).
lean otter
I get where X and y axis are but I don’t understand when it says about (0,-1)
timid escarp
do you first know where (0, 0) is?
empty sky
what the heck mn
safe radishBOT
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pearl ruin
help, can' t understand, my simplification brings me to the answer 30p - 45
gritty pasture
help, can' t understand, my simplification brings me to the answer 30p - 45
Hey
pearl ruin
yeah
gritty pasture
you don't add 1 and 4, because it's not in brackets together
pearl ruin
why, do we not add them.
gritty pasture
you're essentially doing 1 + 4 * (6p - 9)
mossy lotus
help, can' t understand, my simplification brings me to the answer 30p - 45
remeber your bodmas/pemdas
pearl ruin
yeah.
ok.
so what do i do i multiply 1 with 6p than with -9
then i do with 4 the same thing
help me someone.
gritty pasture
hi
fierce nimbus
so what do i do i multiply 1 with 6p than with -9
then i do with 4 the same th...
Multiply 1?
gritty pasture
@pearl ruin you do 4(6p-9) first
you don't add the 1, because it's not in brackets
fierce nimbus
Not only are u wrong about the second part but what would multiplying by 1 do
Ignore the 1 and evaluate the multiplication first
If it was 7+4(6p-9) you’d evaluate 4(6p-9) then add ur answer with the 7
safe radishBOT
pearl ruin
.reopen
safe radishBOT
✅ Original question: #help-23 message
pearl ruin
yeah, so why am i wrong now??
pearl ruin
no i did.
gritty pasture
check again
gritty pasture
what's 2(2+8k)
gritty pasture
lol dw
fresh birch
For this problem here, I don’t understand why I keep getting that as my acceleration
safe radishBOT
For this problem here, I don’t understand why I keep getting that as my accelera...
fresh birch
I have to solve for a and T
gritty pasture
hello
fresh birch
Hi
fresh birch
so masses are 8, 2, and 8?
Yes
fresh birch
and mu is 0.2?
Yes, miu sub k
fresh birch
the tension?
Yeah, acceleration and tension
fresh birch
Thank you
gritty pasture
For this problem here, I don’t understand why I keep getting that as my accelera...
I believe it's because 9.8 is positive?
fresh birch
I believe it's because 9.8 is positive?
Right, but why?
gritty pasture
fresh birch
I’m taking upward as positive
gritty pasture
in here you wrote one g as -9.8, and the other as 9.8
fresh birch
Not downward
Right, so
My q is
If it’s already - f sub f
And downward is negative
Do I still make that g negative?
gritty pasture
you should make g negative
because
you're subtracting that in the first place, because it opposes the force of the 8kg mass
fresh birch
Right, so
fresh birch
Do I still make that g negative?
Is the answer to this yes?
gritty pasture
yes
fresh birch
Even if it’s already - f sub f?
gritty pasture
I didn't solve for the tension
but put the 2 and 8 kg masses individually, and label the forces on them to calculate the tension
fresh birch
but put the 2 and 8 kg masses individually, and label the forces on them to calc...
But is my equation correct?
Nvm
Got it
.close
safe radishBOT
gritty pasture
what was your answer
safe radishBOT
Available help channel!
hoary seal
safe radishBOT
hoary seal
what did I do wrong with c
gritty pasture
hi
timid escarp
what did I do wrong with c
you misinterpreted the question.
she does run 750m more per week, but only up to a max of 10km per week.
gritty pasture
yeah
timid escarp
you assumed that she was gonna keep running 750m more every week.
gritty pasture
you do it up to 13 weeks then add 130
timid escarp
could have let OP try to figure that out, but okay.
safe radishBOT
@hoary seal Has your question been resolved?
near atlas
Find n if n is the number of real roots of the equation \
$e^{4x}+2e^{3x}-e^{x}-6=0$
safe radishBOT
Find n if n is the number of real roots of the equation \\
$e^{4x}+2e^{3x}-e^{x}...
flat frigateBOT
T&C
gritty pasture
hi
near atlas
my steps: \
Let $f(x)=e^{4x}+2e^{3x}-e^{x}-6=0$\
Let $e^{x}=t$ such that $t>0$ (as the range of $e^{x}$ is $(0,\infty)$ )\
now, let $g(t)=t^{4}+2t^{3}-t-6$
vagrant ice
all good so far
quasi bison
ain't that the same one you came with yday
vagrant ice
thanks for the warning Ann
quasi bison
btw \infty
near atlas
ain't that the same one you came with yday
yeah i couldnt solve it with calculus
gritty pasture
$\infty$
flat frigateBOT
lifehealer
gritty pasture
I gotta learn latex
quasi bison
0 is a single point. even if it were to turn out a solution, you could just discard it.
flat frigateBOT
T&C
quasi bison
@near atlas this is your official permission slip to extend the domain of g by that one point
in the name of making your life easier
and allowing yourself to consider g as a polynomial function in its own right
being aware of its connection to the original question but NOT binding yourself with absolute rigidity to it
near atlas
well then, with that there's only one root, between 0 and 1 but can you explain why we can do such a thing
quasi bison
because there are no gods
[INSERT DEITY NAME HERE] won't smite you with lightning for allowing yourself to extend g to be defined also at x=0
near atlas
it still doesn't sit right with me tho
quasi bison
it's a function YOU define
near atlas
okay okay
quasi bison
it still doesn't sit right with me tho
you have nothing to lose but your chains
it is a QoL thing
near atlas
tysm for your help. yesterday and today ❤️
quasi bison
even if g(0) turned out to be 0, corresponding to a bogus solution,
you could have enough human awareness to discard it
near atlas
ahh i see, because im concerned with where the function crosses the x axis not with its domain. got it
thank you
.close
safe radishBOT
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✅ Original question: #help-23 message
vagrant ice
- f(0) is negative, so that point is below the x-axis
- the end behaviour of the function as $x \to \infty$ is $+\infty$
flat frigateBOT
south
vagrant ice
or did Ann not tell you this
safe radishBOT
safe radishBOT
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ocean path
M
gritty pasture
M
ocean path
Someone please explain: The following Diagram shows 2 triabgles OBC and OBA on a set of axis. Point C lies on the Y axis and O is the origin
the area of AOB is 3 times the area of OBC
Di find the area of triangle OBC in terms of a
Dii find the area of triangle AOB
Diii find the X coordinate of point A
gritty pasture
,rotate
flat frigateBOT
gritty pasture
the area of AOB is 3x the area of OBC
what's the question@gimmi
@ocean path
are all of them questions?
ocean path
Js explain part d to me
The following Diagram shows 2 triabgles OBC and OBA on a set of axis. Point C lies on the Y axis and O is the origin
the area of AOB is 3 times the area of OBC
Di find the area of triangle OBC in terms of a
Dii find the area of triangle AOB
Diii find the X coordinate of point A
gritty pasture
is this also a statement?
the equation of the line BC is y = 4
or is that an assumption for another question
and this
ocean path
I js need to check wether I got Di and Dii correct
also Dii is supposed to be in terms of a aswell 1 more thing I got no clue how to find the x coord of A for Diii
gritty pasture
so point B is at (a, 4)
so I would assume the area is gonna be 2a
is that what you got?
and AOB is triple so just 6a
@ocean path you got the same?
2a and 6a for the triangles
ocean path
so I would assume the area is gonna be 2a
Yea
gritty pasture
ok
and you need help solving Diii
so the x coordinate of point A is just gonna be the length of OA, since O is 0, 0 at the origin
and we know that the area of triangle OAB is 6a
so the base (AO) x height x 1/2 = 6a
flat frigateBOT
lifehealer
gritty pasture
So which of these variables do we know?
We're trying to figure out the length of the base, AO
ocean path
<@904157647475978291> you got the same?
Yay I got the same
ocean path
So which of these variables do we know?
Mb I’m multi tasking uh height is 4
gritty pasture
yep correct
so 6a = 0.5(4)(AO)
you see where all this is coming from right
the x coordinate of A is just gonna be the length of AO
since A is a horizontal line starting from the origin
safe radishBOT
@ocean path Has your question been resolved?
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trail otter
Find an entire function ( f ) such that it's real part is
[
u(x,y) = x^4 - 6x^2y^2 + y^4 + 2xy
]
and ( f(0) = 2i. )
so far i got here
[\frac{\partial u}{\partial x}= 4x^3-12xy^2+2y=\frac{\partial v}{\partial y}\implies v= 4x^3y-4xy^3+y^2+C(y)]
[\frac{\partial u}{\partial y}= -12x^2y+4y^3+2x=-\frac{\partial v}{\partial x}\implies v= 4x^3y-4xy^3-x^2+C(x)]
what should i do next?
flat frigateBOT
Slowaq
safe radishBOT
@trail otter Has your question been resolved?
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@trail otter Has your question been resolved?
trail otter
<@&286206848099549185>
main mural
**Slowaq**
you have that y^2 + C_1(y) = -x^2 + C_2(x)
also note that the first C function isn't (necessarily) the same as the second one
main mural
you have that y^2 + C_1(y) = -x^2 + C_2(x)
this is possible for all x,y if both sides ||are constant||, i.e. ||C_1(y) = -y^2 + c, C_2(x) = x^2 + c, where c is some complex number that is the same for both functions||
from this you get v=||4x^3 - 4xy^3 + c|| and then you simply proceed by plugging in the initial condition into f=u+iv
also kinda crazy how i literally just covered this in my complex analysis lectures a couple of days ago lol
safe radishBOT
@trail otter Has your question been resolved?
main mural
@trail otter what's wrong with my answer? do you need more clarification?
safe radishBOT
@trail otter Has your question been resolved?
trail otter
<@461113398915104769> what's wrong with my answer? do you need more clarificatio...
no sorry i didnt respond
it's great ive got it now
thanks a lot
raven heart
you have that y^2 + C_1(y) = -x^2 + C_2(x)
I don't think what slowaq wrote is correct in the first place
if you have dv/dy = 4x^3 + ..., then v can be 4x^3y + ... + C(x)
main mural
oh yes
raven heart
cause it's the pure x functions that get killed when differentiating by y
@trail otter
atomic sedge
Wtf is this pattern
safe radishBOT
Wtf is this pattern
flat frigateBOT
Ann
quasi bison
i looked up the denominators on OEIS
safe radishBOT
quasi bison
Hmm how was i supposed to guess that lol thanks
no fucking idea tbh. it's p much impossible to guess
lime dust
Taking the differences gets you to a constant of 96 in the forth step
that leads you to a sequence generated by a forth-deg polynomial
safe radishBOT
Available help channel!
midnight spindle
I’m not sure where to go from here, how to prove
safe radishBOT
I’m not sure where to go from here, how to prove
plucky elk
for the first one you just need 1 <= 1 + x^2
for the second you need x^2 <= 1 for x in [-1, 1]
plucky elk
why is the intergral dropped
It's not dropped
You plug the inequalities into the integral
plucky elk
I’m not sure where to go from here, how to prove
See the list of properties of integrals you were taught
plucky elk
not seeing anytthing that rings a bell
show the list
midnight spindle
1 moment
its not in a list form
but more like notes
this would be the relevant one then right?
because sqrt(1+x^2) is continuous on [-1,1]
burnt notch
this would be the relevant one then right?
Not this
last wren
If $f(x) \geq M > 0$, then $\int_a^b f(x) dx \geq \int_a^b M dx = M(b-a)$
flat frigateBOT
Doaby
midnight spindle
more like something like this
so this is applying 3 in reverse
plucky elk
no it's exactly applying 3
plucky elk
your m is incorrect
you're also plugging the thing you're trying to prove into the inequality in 3
but what you should be doing is finding the things in 3 to conclude the inequality at the end of the problem
start by identifying f(x)
plucky elk
how did you find m and M?
plucky elk
Your m and M do look correct but i don't see how you got it from your work
midnight spindle
1 moment
I found the critical point
then checked that along with the end points
so this should give me the min/max of this interval
plucky elk
yea you almost got it then
plucky elk
your last two lines just need integral from -1 to 1 in the middle
plucky elk
sorta like this except your m and M were wrong here
safe radishBOT
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ebon spire
safe radishBOT
cedar widget
🍜
ebon spire
i have shown that their direction vectors are not a multiply of a scalar of each other so they skew or intersect
but i aint sure how to find the point of intersection
cedar widget
you want a value for t where the two functions defining the lines are equal
ebon spire
ik so i did this:
@cedar widget
i just stopped once i got that t=8 and 7t=1
@cedar widget
cedar widget
what I suspect is that there is a mistake in this exercise
ebon spire
what I suspect is that there is a mistake in this exercise
last quesiton of my h.w.
cedar widget
mb, the two t's don't need to be the same
and then the way you did is right
just a small modification
ebon spire
just a small modification
ok lemme try thx
safe radishBOT
@ebon spire Has your question been resolved?
worldly crypt
Integrate $sin(x)$ from 0 to $\pi$ using riemann's sum.
safe radishBOT
Integrate $sin(x)$ from 0 to $\pi$ using riemann's sum.
flat frigateBOT
Mystic
split kayak
We are probably missing some info here
worldly crypt
We are probably missing some info here
wat sort of info
split kayak
Oh, i was thinking about approximating it using riemann sum, mb
worldly crypt
are these steps correct
visual kraken
I'm wondering about your second step, how did you convert the sum of all those sins into the product of just 2?
worldly crypt
I'm wondering about your second step, how did you convert the sum of all those s...
oh my professor told me about that formula
its like $\sin{\frac{first angle + second angle}{2}} \sin{\frac{difference}{2}}$
flat frigateBOT
Mystic
visual kraken
Okay sure sure
Hmmm... something definitely feels wrong about your 2nd line though, since I'm pretty sure the limit of that is 0
split kayak
Yeah, i was thinking about that. My greatest idea is that its comes from Lagrange's Identity.
somehow
Still, im not too sure it can be truly used here given the lower bound near 0
just in case:
visual kraken
Yeah I'm looking at that too
That does seem useful, since that's basically the 1st line
split kayak
we have to let theta limit to 0 and n limit to infinity though
visual kraken
But n*theta = pi doesn't it?
worldly crypt
guys havent yall ever solved this in your college times
visual kraken
Oh probably something like this
worldly crypt
or is it only my professor who is this cruel
split kayak
not my case, im in STEM, we just learn the integral, lmao
visual kraken
Integral calculus is usually a pretty rough topic
worldly crypt
Do you have the formula your prof told you about written down anywhere?
its the same as i sent
thats the only thing i hv
is this not a common formula?
visual kraken
Well it looks like a mix of a few common formulas
Like one of these
These work for adding/subtracting 2 trig functions, but not necessarily adding a bunch of them
worldly crypt
yea that is what i used in the later steps
can you check my work after I used that special formula
loud ember
What is the size of angle x when AB is diameter of circle?
safe radishBOT
What is the size of angle x when AB is diameter of circle?
north raven
What is the size of angle x when AB is diameter of circle?
!xy
safe radishBOT
What is the size of angle x when AB is diameter of circle?
Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.
plucky elk
is there a picture coming?
loud ember
plucky elk
you should try to use:
https://www.mathsisfun.com/geometry/circle-intersect-secants-angle.html
loud ember
There are no sufficient angles
safe radishBOT
@loud ember Has your question been resolved?
lime furnace
?
noble mango
There are no sufficient angles
Are you sure? (Whats the measure of arc AB?)
loud ember
There are two possible arcs from that
noble mango
There are two possible arcs from that
Not sure what the other guy is saying, but it actually doesn't matter which arc AB you find, because AB is a diameter.
lime furnace
각 CDO는 67도지요..?
loud ember
이등변삼각형이니까 맞네요
lime furnace
각DAO를 아무 미지수로 둔 다음 다른 각도들을 쭉 풀어보면
닮음꼴이 나오지 않을까싶네요
보시면
각 DAO로 잡으면
ADO도 동그라미
그럼 2동그라미는 각 DOB라서
각 COB는 2동그라미-46
변 CO랑 BO랑 같으니까,
각 BCO가 113-동그라미
아까 말씀드렸다시피 각 CDO,DCO가 67도니까 각각
각 EDC가 113-동그라미,
각 ECD는 동그라미면
그럼 x값 나왔네요
만약 제가 실수한거나 잘못한게 있다면 알려주세용
loud ember
하나같이 방정식을 세울수 없게 돼있어요
safe radishBOT
@loud ember Has your question been resolved?
safe radishBOT
@loud ember Has your question been resolved?
hoary seal
I got this wrong
safe radishBOT
I got this wrong
timid escarp
,w (2/3)^8
flat frigateBOT
timid escarp
,w (1 - (256/6561))/(1/3)
flat frigateBOT
timid escarp
ok, now I don't trust your marking, so show me the answer please.
hoary seal
timid escarp
....
hoary seal
I got it right but it wasnt in exact value
timid escarp
please, at least take the time to verify your answer. I don't know where you got the decimal expansion from, presumably a calculator. if you did, you could have told the calculator to express it as a fraction and you would have not had this trouble.
timid escarp
?
show me what you entered in your calculator, together with the result.
(in a picture.)
hoary seal
I pressed SD
It didn’t turn it into a fraction
also from our previous conversation, is this allowed?
or it only has to be addiiton and subtraction
then after you can use multiplication or division
my course asks for exact values often
timid escarp
just got back, but have you tried pressing the S <-> D button here?
timid escarp
also from our previous conversation, is this allowed?
what context?
safe radishBOT
@hoary seal Has your question been resolved?
safe radishBOT
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Available help channel!
half perch
help
median vigil
what have you tried so far?
safe radishBOT
@half perch Has your question been resolved?
half perch
whats the formula
rigid yoke
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balmy shale
can somebody explain what this means
safe radishBOT
can somebody explain what this means
open wedge
can somebody explain what this means
Okay
When you say something like: a person's height is around 1.5m-1.6m, how would you understand it?
open wedge
When you say something like: a person's height is around 1.5m-1.6m, how would yo...
Here, i updated it
open wedge
When you say something like: a person's height is around 1.5m-1.6m, how would yo...
Here 🙏
errant bison
Like max is 1.6
balmy shale
i don’t understand the question
i round up if there in that range and above 155cm to 1.6m?
open wedge
i don’t understand the question
When you hear someone saying: He is around 1.5m to 1.6m tall, how would you understand it. Relate how would you understand it in REAL LIFE
balmy shale
i know how tall that is compared to me
open wedge
When you hear someone saying: `He is around 1.5m to 1.6m tall`, how would you un...
Get that mathematics thought out of your mind for now
balmy shale
like i’d say he’s up to my shoulder
open wedge
like i’d say he’s up to my shoulder
So his height is between 1.5m and 1.6m right?
balmy shale
yeah
open wedge
can somebody explain what this means
And in this case is the same
balmy shale
oh so 0 is lower bound and 20 is upper
open wedge
oh so 0 is lower bound and 20 is upper
Nice
balmy shale
okay
we never got told how to do that
or what it means
so maybe it’s just common sense lol
open wedge
so maybe it’s just common sense lol
Lol
open wedge
so maybe it’s just common sense lol
Yeah it's common sense
balmy shale
Yeah it's common sense
if my data isn’t continuous
how do i find the mean
midpoints?
open wedge
how do i find the mean
Isn't the mean the same as the average?
open wedge
i have a non continuous data set
You still do it the same on how you do averages
safe radishBOT
@balmy shale Has your question been resolved?
gray verge
I got stuck on the following problem: A wall is decorated with vases, an awful lot of 'em, we know that they are disposed in rows, on the first row there is 4 vases, and in the next one there is 3 more. The pattern repeats. Determine the number of rows, knowing that there are a total of 531 vases.
safe radishBOT
I got stuck on the following problem: A wall is decorated with vases, an awful l...
flat frigateBOT
ℕ∈ℝD ALERT: Gonçalo Gonçalves
flat frigateBOT
left gyro
you need to be more specific when throwing things into wolfram alpha
first and foremost its just a calculator, it cant solve math for you
gray verge
yeah sorry+
left gyro
you have to describe exactly what it is you need calculating
in this case it wont help you out
left gyro
**ℕ∈ℝD ALERT: Gonçalo Gonçalves**
can you be more specific on where this formula is from
gray verge
in this case it wont help you out
forgot to specify u_1 and u_n, I just need to know if it was an algebra problem
gray verge
can you be more specific on where this formula is from
it's the sum of all the terms
from the first
to the nth term
then I solve for n
opps
hold it
$$\frac{u_1 + u_n}{2} (n+1) = 531$$
flat frigateBOT
ℕ∈ℝD ALERT: Gonçalo Gonçalves
flat frigateBOT
ℕ∈ℝD ALERT: Gonçalo Gonçalves
compact plover
might wanna step back and think what the sum of u_n actually does
compact plover
have u observed any patterns?
compact plover
yes
gray verge
the 4 is u_1
compact plover
mhm
gray verge
I just substituted
now, I'm gonna see if it was an algebra problem
,w \frac{4 + 1 + 3n}{2} (n+1) = 531
flat frigateBOT
compact plover
n needs to be an integer value
gray verge
yeah
compact plover
if yes, you should know how to calculate 3+6+9+12+15+...
if you can do that, then you can do 4+7+10+13+...
left gyro
ngl that is a surprisingly quick way to get the same formula
you can do it this way because theres less room for error
its always good to get the same answer through two different methods
gray verge
but I did the formula, I
left gyro
it would help to know how many numbers are being added
left gyro
but I did the formula, I
you only did one formula
when Im in this situation, Id look for another
see if that lines up too
gray verge
sorry, I did an enter by accident, I didn't mean to send that
compact plover
dw about being wrong, its just learning
gray verge
dw about being wrong, its just learning
dw?
left gyro
Im not focusing on this problem rn but I wouldve literally just added the numbers together directly with a calculator to see that this lines up
compact plover
cant remember how many times i got math wrong at this point
left gyro
dw stands for "dont worry"
gray verge
figured it out?
yeah, for that one I know the deduction
do I send that out
or just the formula
compact plover
if you already understand the deduction, just send the formula
gray verge
$$\frac{u_1 + u_n}{2} \times (n+1)$$
flat frigateBOT
ℕ∈ℝD ALERT: Gonçalo Gonçalves
gray verge
if you already understand the deduction, just send the formula
this is it right?
compact plover
let me wrack my brain if this can be used for u_n as well
gray verge
in this case it would be: $$\frac{1 + n}{2} \times (n+1)$$
flat frigateBOT
ℕ∈ℝD ALERT: Gonçalo Gonçalves
gray verge
since $u_n = n$
flat frigateBOT
ℕ∈ℝD ALERT: Gonçalo Gonçalves
compact plover
ack slow internet
compact plover
**ℕ∈ℝD ALERT: Gonçalo Gonçalves**
pretty sure this isn't right
there are n terms
you are adding the sum of two opposite terms
(u1+un)
you can only do this n/2 times
so
(u1+un)n/2
gray verge
pretty sure this isn't right
there are n terms
you are adding the sum of two op...
allr sorry
give me a sec
yeah
nop
you're right
it's $\frac{u_1 + u_n}{2} \times n$
flat frigateBOT
ℕ∈ℝD ALERT: Gonçalo Gonçalves
gray verge
sorry
at least it's what my texbook says
I'm gonna go lunch, I didn't expect it to be ready this soon, I'll go over why I though it was n -1 in a sec ok?
compact plover
k lil bro
safe radishBOT
@gray verge Has your question been resolved?
gray verge
k lil bro
allr
I'm back
so I though it was n -1 because the last term was not included, which is wrong
winged flare
at least it's what my texbook says
yes the one you sent now is the correct one
gray verge
I just noticed that
gray verge
yes the one you sent now is the correct one
let me try to apply the formula now
,w 3n^2 + 5n -1062 = 0
flat frigateBOT
compact plover
never knew there was a formula like that
tbh i just did 3(x)(x+1)/2+x=531 and solved stuff
gray verge
tbh i just did 3(x)(x+1)/2+x=531 and solved stuff
how did u get to that
compact plover
how did u get to that
black magic
just the sum 3x+1 split into 3x and 1
repeated 3+6+...+3n=3(n)(n+1)/2
1 is repeated n times
so, n+3n(n+1)/2
safe radishBOT
safe radishBOT
Available help channel!
native flume
have i gone wrong somewhere in where i circled red, since when i desmos the two curves i get different things😭
safe radishBOT
have i gone wrong somewhere in where i circled red, since when i desmos the two ...
native flume
timid ridge
how did you get 1 from (e^x - e^-x ) / (e^x + e^-x)
desert pasture
Let $\abs{G}=120$. Find all isomorphism classes, given there are 3 elements of $G$ of order $2$.
safe radishBOT
Let $\abs{G}=120$. Find all isomorphism classes, given there are 3 elements of $...
flat frigateBOT
wai
desert pasture
If there are 3 elements of $G$ of order $2$. there must be 3 elements in the direct product of order $2$
flat frigateBOT
wai
desert pasture
$120 = 2 \times 2 \times 2 \times 3 \times 5$
flat frigateBOT
wai
desert pasture
Beyond this I'm lost
astral glacier
What's an isomorphism class
desert pasture
Oh, I got an idea
desert pasture
What's an isomorphism class
An isomorphism to an abelian group written as a direct product of Z_ns
astral glacier
Is that standard terminology
desert pasture
astral glacier
First time I'm hearing of it
Anyway
Do you want help or do you wanna try out your idea first
desert pasture
I'll try mine
cedar widget
First time I'm hearing of it
Just equivalence classes under isomorphism
astral glacier
No I get that
It's just the first time I've heard it referred to as an isomorphism class
astral glacier
Expand the second half of that statement
Are you saying there is 1 element in Z5 with order 2?
Cuz if so that's incorrect
astral glacier
Let's do this systematically
120 = 2 x 2 x 2 x 3 x 5
The 3 and 5 cannot contribute an element of order 2
And if you want three elements of order 2, you gotta keep the 2's separate
With me so far?
desert pasture
yes
astral glacier
Good
desert pasture
oh, I get it now
astral glacier
So what are your options now