Good enough
#help-19
short terrace
woven stag
Professor X, how would you have phrased it?
short terrace
The first right should be a left
But you got the idea so I said good enough and didn't focus on the semantics much
odd edgeBOT
odd edgeBOT
Available help channel!
dense temple
hello
dense temple
I have a very hard time understanding this part in calc 3
stoic cloud
Just for future reference, do you mind posting the image/question as your first message so the bot doesn’t pin greetings? This way, if the conversation continues for long, helpers don’t have to dig. 
dense temple
say i have a equation f(x,y,z) = (x^2)/3 + y^2 - z
at (3,0,3) the tangent plane is is z=2x-3
and at (3,0,3) the plane that contains the vector of the gradient is z = -x/2 + 9/2
proven harbor
Just for future reference, do you mind posting the image/question as your first ...
You can just pin messages
short terrace
He can't
proven harbor
say i have a equation f(x,y,z) = (x^2)/3 + y^2 - z
stoic cloud
You can just pin messages
I don’t have permissions to.
short terrace
You'll get there
proven harbor
@dense temple continue your question
dense temple
why is gradient
normal to tangent
like is 2d calc
its the same shit
and
look the black line is the gradient vector
how tf is that supposed to be the direction of max increase in z
quasi sparrow
are you asking why the gradient vector is normal to the tangent plane?
odd edgeBOT
@dense temple Has your question been resolved?
odd edgeBOT
@dense temple Has your question been resolved?
midnight jasper
odd edgeBOT
midnight jasper
Right now I have this triangle try to ignore the blue markings (sorry for them)
I used area of a triangle with height being 15 because 1/2bh where b is 4 and area is 30 so we know height is 15
I’m trying to solve for the slope between A and B
I figured to plug (x,15) into the f(x) equation but my issue is that I don’t want to use the quadratic formula and I feel like there’s another way to do this
odd edgeBOT
@midnight jasper Has your question been resolved?
odd edgeBOT
@midnight jasper Has your question been resolved?
midnight jasper
.close
mystic saffron
odd edgeBOT
mystic saffron
I lwk forgot how to do ts
wooden python
I lwk forgot how to do ts
Google "exponent laws"
honest turtle
$$x^{-a}=\frac{1}{x^a}$$
clever fjordBOT
Good
mystic saffron
$$x^{-a}=\frac{1}{x^a}$$
brainfuck
mystic saffron
honestly yeah I forgot how to get rid of that
blazing shuttle
wooden python
I know this but idk how on a curved bracket
Google "exponent laws"
mystic saffron
Google "exponent laws"
I did it didn't show me for a negative power on a curved bracket
wooden python
check out the yt channel The Organic Chemistry Tutor if you haven't already
it's better if you do that instead of having some random strangers yap at you
odd edgeBOT
@mystic saffron Has your question been resolved?
quasi sparrow
I did it didn't show me for a negative power on a curved bracket
,tex .exp rules
clever fjordBOT
riemann
odd edgeBOT
@mystic saffron Has your question been resolved?
safe pivot
hellooo, i need to calculate the volume of a sliced up spherical cap
small fulcrum
hellooo, i need to calculate the volume of a sliced up spherical cap
do you know the depth?
safe pivot
do you know the depth?
I need to calculate the volume between the planes
Preferably the surface area as well
and to do its as simply as possible
small fulcrum
have you learnt calculus?
safe pivot
have you learnt calculus?
only the basics 😭 I havent touched multivariables stuff
small fulcrum
i see
safe pivot
i might be having the dunning kruger effect
how hard is this?
its for a math report, im modelling the shape of an object
small fulcrum
do you know how to get the volume of a sphere through integration?
safe pivot
many classmates are modelling through rotations
small fulcrum
because if ye then you can just use that, change its limits then be done for the vol b/w the blue planes
purple*
outer peak
@small fulcrum Space is as hot as my?
small fulcrum
<@839109098980507659> Space is as hot as my?
haha
xD
i put that there like a year or two ago and completely forgot
is the light blue plane also important?
safe pivot
is the light blue plane also important?
yepppp, thats the base
its a spherical cap sliced up
let me show you what im trying to model
small fulcrum
oki
safe pivot
safe pivot
do you know how to get the volume of a sphere through integration?
let me look up an explenation real quick 😭
small fulcrum
OHHH
safe pivot
how hard is this?
?
small fulcrum
okay gotcha
not much if you know how to find the vol of a sphere through integration
what's the radius?
safe pivot
like as someone who has such limited knowladge of calc. I think if i have the fucntion that models a spherical cap, i can just take the definite integral from x=-s to x=s, where s here is d/2 and boom volume, right??
safe pivot
not much if you know how to find the vol of a sphere through integration
uff okay okay then its not that bad
safe pivot
what's the radius?
u can see specific measuremnts in the geogebra pic, 30.875
small fulcrum
haha im not used to using online tools
and for the base, you'd use the same method
safe pivot
yooo, yeah yeah i think im getting it
small fulcrum
and for the base, you'd use the same method
(as in integration)
safe pivot
https://www.youtube.com/watch?v=nHC92J8rNZs im looking at this proof of voluem
small fulcrum
should be fine
small fulcrum
you could always use archimedes too
but thats not math
more so physics
but thats always a less maths heavy option compared to this
use a testube or something with it to calculate the volume easily ig
safe pivot
use a testube or something with it to calculate the volume easily ig
nah i kind of need more of mathematical method 😭
small fulcrum
https://www.youtube.com/watch?v=nHC92J8rNZs im looking at this proof of voluem
anyways you can use the same method but by just using the area between the planes instead to calculate what you want then
odd edgeBOT
@safe pivot Has your question been resolved?
safe pivot
problem is still not compeletly solved
okay so looking at proofs fro the volume of a spherical cap, tehy all do it with circular disc, easiest way obsiusly
but is there a way to do it with cirucalr sectors?
how would the area of a sector be calculated?
small fulcrum
how would the area of a sector be calculated?
you would need to construct a function yes
use sectors and find it that way
safe pivot
use sectors and find it that way
yeahhh thats what im tryng to do
small fulcrum
instead of using the entire circle
safe pivot
i found a math stack exchange with the queestion https://math.stackexchange.com/questions/2135065/volume-of-part-not-necessary-the-half-of-spherical-cap?utm_source=chatgpt.com
!solved
how do i solve it lol?
small fulcrum
how do i solve it lol?
gimme a sec
odd edgeBOT
how do i solve it lol?
If you are done with this channel, please mark your problem as solved by typing .close
safe pivot
.close
odd edgeBOT
odd edgeBOT
Available help channel!
dry moon
odd edgeBOT
dry moon
whats the range guys?
odd edgeBOT
@dry moon Has your question been resolved?
odd edgeBOT
@dry moon Has your question been resolved?
glacial grove
Hi guys what does /3 rad imply? I'm taking trigo and the given for our assignment by our prof are like this, does this mean π/3? Or something else?
glacial grove
3 rad, or /3 rad?
It's /3 rad
stoic cloud
if it’s /3 rad then it’s most likely 𝜋/3 rad
glacial grove
if it’s /3 rad then it’s most likely 𝜋/3 rad
Ohh alright2 thanks
stoic cloud
anything else? Otherwise, you can use .close.
glacial grove
Last one question
stoic cloud
glacial grove
If the given is 2 rad, is it just 2 or 2π?
glacial grove
Ohhhh okok thanks very much
stoic cloud
if you are done, use .close
glacial grove
.close
light hawk
odd edgeBOT
light hawk
Here's what ive done so far:
im not sure if what i have is on the right track, but im struggling to manipulate LHS to progress
odd edgeBOT
@light hawk Has your question been resolved?
light hawk
<@&286206848099549185>
odd edgeBOT
@light hawk Has your question been resolved?
light hawk
just expand this using the entries of z, v, and D
got it, thanks
paper sentinel
i have a doubt
odd edgeBOT
i have a doubt
novel abyss
me too
paper sentinel
The answer is 16N, i solved it in a way
but the issue is if I apply 16N of force, the friction on B is 8N at its maximum, the reaction of the friction force from B is the driving force for A, the max value of friction of A is 2N, so the net force on A is 6N, so wouldn't A fall off if it keeps moving?
ik its basic stuff but has eaten up my brain.........
odd edgeBOT
@paper sentinel Has your question been resolved?
odd edgeBOT
@paper sentinel Has your question been resolved?
stray knot
Let E be a non empty subset of R. Prove that diam(E)= sup E-inf E . I took a bounded set E and from completeness property i said a = sup and b = inf.... i am into the idea of diam( E closure )= diam (E) and intuitively its known that a\in closure of E and b also but i dont get how should i write it
stray knot
.close
odd edgeBOT
odd edgeBOT
Available help channel!
blissful falcon
I got to a(x-9)/x-3
odd edgeBOT
I got to a(x-9)/x-3
vernal yacht
,rccw
clever fjordBOT
vernal yacht
lilac sandal
put the value of x as 3 as we are checking in the neighborhood of 3, soo
you will get an equation
then you can differentiate the two parts of f(x) to get the other equation
2 equations and two things to find, easy calculation forward
blissful falcon
Yes, that's what I did but I got stuck when I tried to simplify
unkempt lichen
show your work, please
lilac sandal
Yes, that's what I did but I got stuck when I tried to simplify
you will directly get the value of a when you differentiate the first and second part and equate them
then you can find the value of b further by plugging in any of the equations
blissful falcon
Im confused?
lilac sandal
Im confused?
okay answer my questions buddy
what will you get when you plugin 3 in the first part
( checking continuity first of all)
blissful falcon
3a+b?
blissful falcon
Yes
lilac sandal
you'll get 9 right ?
blissful falcon
Yes
lilac sandal
for continuity the value of all the part in neighbor of 3 should be equal so
so 3a + b = 9
this is the first equation
blissful falcon
Wait I got it now
lilac sandal
now we're done with the continuity of the function
now move on to differentiability
differentiate the first and second part then plugin the value of x ( that is 3)
and then you have another equation
lilac sandal
Wait I got it now
perfect ✨
blissful falcon
Does differentiable actually mean
narrow crypt
for single var calc purpose, derivative exists there
lilac sandal
for single var calc purpose, derivative exists there
✅
blissful falcon
When finding multiple derivatives i just keep plugging in the previous derivative right? What is this even used for
narrow crypt
usually
depends on the case
multiple derivative is used to find rate of rate of rate of ... something
unkempt lichen
acceleration is the best example
acceleration is the derivative of velocity, but velocity is itself the derivative of position/displacement
this makes acceleration the second derivative of position/displacement
blissful falcon
Im lowkey bad at factoring help pls
unkempt lichen
one quick look confirms that you have one very prominent common factor here
(amongst the remaining terms)
that being said, there is something wrong with this expansion. there is a notable lack of $t^2 h$ terms.
clever fjordBOT
fox(x, y); ∂(fox)/∂x (Flower)
blissful falcon
?? Idk what im doing
unkempt lichen
this looks more correct
now, your only term that doesn't have a h is balanced out by the -t^3 at the end
so you should be able to tell what factor is common to the remaining terms
odd edgeBOT
@blissful falcon Has your question been resolved?
odd edgeBOT
odd edgeBOT
Available help channel!
vernal yacht
. @vernal garnet post here
vernal garnet
Why there is adding root3 in 6 and root3
odd edgeBOT
Why there is adding root3 in 6 and root3
vernal garnet
Why there is adding root3 in 6 and root3
lethal spoke
Why there is adding root3 in 6 and root3
What do you mean
odd adder
Why there is adding root3 in 6 and root3
it’s called rationalizing; you multiply by sqrt(3)/ sqrt(3) ( which is essentially just 1) to get rid of the irrational number (sqrt(3)) in the denominator.
odd edgeBOT
Why there is adding root3 in 6 and root3
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
@vernal garnet Has your question been resolved?
shrewd trellis
odd edgeBOT
shrewd trellis
how do I find derivatives of exponetial fractions?
acoustic nexus
That's a bad crop 
shrewd trellis
frank tide
can we see the exponents of the e's please
shrewd trellis
Im trying to solve d
woeful briar
Im trying to solve d
Differentiate f(x) twice and see thats equal to f(x)
dawn scarab
how do I find derivatives of exponetial fractions?
Well, usually for fractions you go quotient rule, but here notice the denominator is 2, that means it‘s just a constant factor
shrewd trellis
yeah
what I tried is pulling 2 at the numerator
so it becomes
2^-1
However, I dont think thats valid since theres no x
dawn scarab
what makes you think that
woeful briar
Yes
dawn scarab
That is indeed what 1/2 equals yes
dawn scarab
noo, notice how it‘s not x to some power, it‘s e^x
so you use the "formula" for derivative of e^x
do you remember that?
dawn scarab
Right. And recall that you can move constants out of the derivative if they‘re multiplying
ie $\dv{x}\left(a\cdot f(x)\right) = a\cdot\dv{x}f(x)$
clever fjordBOT
dawn scarab
Well, right up until the second to last step you were fine
frank tide
where did you get this guy from?
dawn scarab
probably thought e^(-x) = 1/e^x (which is true) but they combined the fractions improperly
shrewd trellis
where did you get this guy from?
What’s wrong with that?
The E is raised to a negative X
frank tide
The E is raised to a negative X
shrewd trellis
So I brought it in the denominator
frank tide
you combined the fractions improperly
tacit wasp
What’s wrong with that?
$-\frac{e^{-x}}{2} = -\frac{1}{2e^x}$
clever fjordBOT
Alberto Z.
tacit wasp
**Alberto Z.**
This is correct, but it's not what you have done @shrewd trellis
shrewd trellis
dawn scarab
**Alberto Z.**
(considering the question, i wouldn‘t do that though)
frank tide
well- you cant do that with addition
tacit wasp
Awful mistake!!
frank tide
the "flipping the negative x to the denominator"
only applies when there's no addition or substraction
dawn scarab
h, you could have stopped one step before that, you were done
You just had to show it was = to f(x)
shrewd trellis
only applies when there's no addition or substraction
ohh
shrewd trellis
then thats just the answer if I cancel the last step
dawn scarab
yeah. You did what was asked
shrewd trellis
or it could be e^x/2 - 1/(2e^x)
dawn scarab
I mean, they are equal, but you wanted to show that f''(x) = f(x), so just stop when it looks like f(x) 
shrewd trellis
also if f'(x)>0 for exponentials
does it mean it will rise to the right?
if f'(x) < 0, then it will dip to the right
shrewd trellis
the confusing part is, I dont know how to graph this
I could look at e^x
and apply transofrmations
but man, this is a tricky one
dawn scarab
oh they‘re asking you to sketch this. Interesting. I‘m not sure how to intuitively find this. You could plug a few values in I guess and sketch from that
shrewd trellis
I want to know the best method
frigid canopy
uh, this is a hyperbolic trig function
dawn scarab
wai, not the time for that 
shrewd trellis
dawn scarab
I think you messed up with negative values
I suggest using the $\frac{e^x-e^{-x}}{2}$ form for your calculations as it‘s less calculator error prone imo
clever fjordBOT
dawn scarab
Yours is a bit yeah. The left side
One way to know that the function is always increasing is looking at f'(x). It‘s always positive, so f(x) is always increasing
odd edgeBOT
@shrewd trellis Has your question been resolved?
odd edgeBOT
odd edgeBOT
Available help channel!
prime falcon
Yo guys
I want an An alternative to stupid chatgpt
odd edgeBOT
Yo guys
I want an An alternative to stupid chatgpt
unkempt lichen
why do you think this server exists?
tepid pelican
Yo guys
I want an An alternative to stupid chatgpt
Have you tried stupid deepseek or stupid claude?
stoic cloud
Yo guys
I want an An alternative to stupid chatgpt
that alternative would be us
prime falcon
why do you think this server exists?
I don't want make you tired 😇
stoic cloud
I don't want make you tired 😇
!nogpt
unkempt lichen
I don't want make you tired 😇
you know the server has close to 300k people?
odd edgeBOT
I don't want make you tired 😇
Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).
stoic cloud
they’re all dumb
prime falcon
Ok then i have question
stoic cloud
post it an let a helpful pin it
acoustic nexus
Yo guys
I want an An alternative to stupid chatgpt
try alphageometry for Euclidean Geo
prime falcon
I want to find the solution of
|x+2|>|3x+5|
To find the solution we need to assume that predicate is true right?
plucky eagle
what predicate?
prime falcon
P(x): |x+2|>|3x+5|
plucky eagle
I don't know why you're bringing logic into an algebra question, but sure I guess?
prime falcon
I don't know why you're bringing logic into an algebra question, but sure I gues...
Gpt said no
unkempt lichen
!original
odd edgeBOT
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.
unkempt lichen
when I use that command, I'm usually asking for a picture of the question
prime falcon
Just find x
plucky eagle
Gpt said no
then what the hell are we supposed to do with the fact that GPT said no? said no to what? what was the original context of the question?
and what did you prompt GPT with?
plucky eagle
we want the values of x that makes it true
of course this inequality is not true for literally every x (just try x = 1)
prime falcon
we want the values of x that makes it true
And to get x we need to suppose it true?
plucky eagle
in a way yes, I suppose? you can keep the inequality sign and suppose that it's true, and if you get a contradiction later, then you can conclude that no value of x makes the inequality true
(assuming you didn't bomb the algebra)
prime falcon
in a way yes, I suppose? you can keep the inequality sign and suppose that it's ...
To solve every inequality we must do that?
plucky eagle
I don't like the concept of "assuming it as true", but yes, I suppose
prime falcon
I don't like the concept of "assuming it as true", but yes, I suppose
You mean the concept isnt correct ?
plucky eagle
I won't say it's entirely incorrect as per how I think you are viewing it. I just won't even think of this as a logical statement
prime falcon
Explain please
plucky eagle
or rather, I won't be thinking of truthiness when it comes to solving inequalities, because that's unnecessary
I mean, how do you solve an equation?
if I have an equation, say, x + 5 = 4
how would you solve it?
prime falcon
Using connectors
plucky eagle
...what are "connectors"?
prime falcon
x+5=4 => x=5-4
plucky eagle
not sure again why logic is coming into algebra, but sure
but you have to make this implicit assumption that the equation you started with is true in the first place
prime falcon
not sure again why logic is coming into algebra, but sure
But all mathematics concepts built as logics
plucky eagle
and that's a universal assumption across algebra
if you started with a "false" equation then what's the point
prime falcon
No sense
plucky eagle
But all mathematics concepts built as logics
ok, but doesn't mean that we have to overcomplicate an algebra problem
prime falcon
The same with inequality?
plucky eagle
the same with everything that you want to solve for. what's the point of solving for a known false statement? you know it's false!
prime falcon
ok, but doesn't mean that we have to overcomplicate an algebra problem
I want to understand mathematics more abstractly.
prime falcon
the same with everything that you want to solve for. what's the point of solving...
So we suppose to be true
plucky eagle
sure. abstract algebra it is then. overcomplicating regular algebra problems is still not my recommendation
(not gonna say you can't do it though)
prime falcon
sure. abstract algebra it is then. overcomplicating regular algebra problems is ...
So then
Where do you think I can use logic?
prime falcon
(and, well, logic itself of course)
You mean what did i send not supposed to be statement we want to prove it?
plucky eagle
I never said your original question was a proof
that's why I recommended against using logical concepts here
your original question was a simple algebra question
prime falcon
your original question was a simple algebra question
Look honestly i want to understand logic, i know how to solve this simple inequality but i want to know if the steps which I'm doing to solve this is correct logically
plucky eagle
show your work then
jaunty hollow
so what seems to be the problem here?
plucky eagle
also, you don't have to ping with every reply
prime falcon
plucky eagle
I don't know why that > 0 is there from the start, and I presume that interval is French notation for (-7/4, -3/2)
if my presumption is correct, your answer is as well, but the right side of line 2 is a clusterfuck and I can't see most of the things towards the end
prime falcon
I don't know why that > 0 is there from the start, and I presume that interval i...
Dont care about the right side
plucky eagle
also, if you want to use $\Rightarrow$ to denote a new step, that's a good thing, but make sure each $\Rightarrow$ is on a new line
prime falcon
Look i know that my solution right
clever fjordBOT
Tairin
prime falcon
But logically, is that true?
plucky eagle
in this case, you're not looking for logical truth. you're looking to see if the steps are algebraically correct
yes, the steps are indeed algebraically correct, except for that > 0 that has plagued the first three steps
prime falcon
Well keeping thinking about this makes me confused
I know it's a wrong way of thinking, but for me it's the way to understand mathematical steps and if they're right.
Like i said mathematics concepts all built as logic
plucky eagle
if that's how you wish to view algebra, sure I guess.
prime falcon
if that's how you wish to view algebra, sure I guess.
It’s perfectionism i guess
signal yacht
I know it's a wrong way of thinking, but for me it's the way to understand mathe...
turns out math doesnt give a fuck about what you think is correct
signal yacht
I want to understand mathematics more abstractly.
take higher math classes
prime falcon
turns out math doesnt give a fuck about what you think is correct
What
prime falcon
How it doesnt give a fuck
stray arch
this logic is good to learn before you really dive into proofs, since your different proof strategies rely on understanding basic logic (and doing a proof is just a series of steps)
signal yacht
writing stuff like this is just obtuse and weird for solving an inequality
and if you wanna do higher math then you should learn the basics therein first
prime falcon
this logic is good to learn before you really dive into proofs, since your diffe...
So am I on the right road?
graceful viper
i think the op is just trying to understand the hypothesis of the theorems disguised in logic which isnt wrong at all
stray arch
personally i think you should once you pick up basic logic, start looking at set theory and writing the basic proofs there
signal yacht
personally i think you should once you pick up basic logic, start looking at set...
this.
prime falcon
i think the op is just trying to understand the hypothesis of the theorems disgu...
Yeah that’s it
I want to know what happens logically
graceful viper
I want to find the solution of
|x+2|>|3x+5|
To find the solution we need to ass...
anyways no, we dont assume the predicate is true. we are actually finding the set of solutions for which the inequality is true
devout hedge
we want the values of x that makes it true
^
graceful viper
now suppose the question was if |x+2| > |3x+5| then show that
|x+2| +3 > |3x+5| + 2
then u do assume that the predicate (the original inequality) is true and prove the next statement
prime falcon
anyways no, we dont assume the predicate is true. we are actually finding the se...
And to find that we use implication connector
Which we need to assume P to be true
graceful viper
yeah if P(x) is the original inequality and Q(x) is the following statement then u'd want to prove P(x) -> Q(x) for all x in domain
prime falcon
.close
magic dome
why am I able to scale them like this?
My calculator and answer just say 2, 6, 1
when doing rref
late dust
Can you post the original question as well?
magic dome
Linear depedence and Linear Independence of Vectors
Express vector t as a linear combination of the vectors u, v , and w.
- $\vec{t} = (0,0,19) , \vec{u} = (1,4,3), \vec{v} = (-1,-2,2), \vec{w} = (4,4,1)$
I wrote this as see image to start
clever fjordBOT
smeagol
magic dome
Since
$a \vec u + b \vec v + c \vec w = \vec t$
clever fjordBOT
smeagol
stray arch
oh your mistake is on the 2nd step
you said 2 - 3*(-1) = -1 when it's 5
one thing i'd really recommend doing out of habit is saying where your reduction is going since then it's harder to follow
magic dome
you said 2 - 3*(-1) = -1 when it's 5
it's -2 - 3(-3) though
stray arch
no on R3 - 3R1
magic dome
ooh
stray arch
you should write this as R3 - 3R1 -> R3 i think
like it's just easier for someone else reading it to follow, they don't have to look at the resulting matrix to figure out where you're sending it
and if you're reading your own work later on
magic dome
gotcha
late dust
Yeah, even if it seems obvious to you that R3 - 3R1 is working on R3, it's not good notation
magic dome
thank you!
stray arch
especially if you're doing multiple steps at one time like the first one
late dust
If you know a bit of programming, you might have encountered a -= operator; R3 -= 3R1 would be ok assuming the reader knows about that symbol
magic dome
I prefer that over
R3 = R3 + R1
R3 += R1 (better imo)
magic dome
My teacher did it confusing to me where he lined them up in the same row
stray arch
you should write this as R3 - 3R1 -> R3 i think
we were taught this in my linear algebra course
late dust
Oh yeah that's kinda ugly
magic dome
Thank you both for advice, I gotta eat lunch now -- I'll redo the second half in a bit
.close
fast bolt
ive only just started a levels so i havent been taught this but i want to give it a go anyways, I started expanding and googled u have to take the derivative but i think i made an error in expanding and even after that im not sure what to do 😭
fast bolt
pls help
tepid glen
use chain rule for derivative instead of expanding
fast bolt
use chain rule for derivative instead of expanding
i dont know what that is sorry
stoic cloud
use chain rule for derivative instead of expanding
…CP server tag… 
woeful briar
Chain rule tells you how to take a derivative of a composite function
fast bolt
erm
woeful briar
Chain rule tells you how to take a derivative of a composite function
If y=f(g(x)), then chain rule is that
y'=f'(g(x)) * g'(x)
brazen hare
were you not taught the chain rule before?
fast bolt
were you not taught the chain rule before?
im 16 we started like a week ago
im fresh out of gcse
tepid glen
basically just do power rule and times it by the derivative of the inside of the bracket
brazen hare
this is taught before a level stuff at least for me
tepid glen
theyre actually ttrolling you if they didnt teach chain rule and giving u that question
💔
fast bolt
this is taught before a level stuff at least for me
probably further maths i only locked in a week before gcse
fast bolt
theyre actually ttrolling you if they didnt teach chain rule and giving u that q...
im cooked ngl
so wait
i would do
4 times that thing
anf make the ^3 a ^2
fast bolt
yes
tepid glen
and then you times it by the derivative of (x-2)
which is 1
so the answer is just 4(x-2)^3
fast bolt
why do i do the derivative of (x-2)
tepid glen
because the chain is y' = f'(g(x)) * g'(x)
fast bolt
thx twin
tepid glen
no thats ur m
fast bolt
frick
tepid glen
thats like ur gradient
fast bolt
okay yeah
tepid glen
u need to find what y is when x = 0
fast bolt
omg im an idiot
fast bolt
ohhhhh
tepid glen
do u know how make
tepid glen
theres like
fast bolt
-32x
tepid glen
a formula
tepid glen
y = -32x + 16
tepid glen
do u know point gradient formula
fast bolt
do u know point gradient formula
nope
tepid glen
or point slope
fast bolt
no 🥺
tepid glen
y-y1 = m(x-x1)
fast bolt
why did my teacher give me ts
tepid glen
idk
fast bolt
y-y1 = m(x-x1)
ive never seen that before
brazen hare
ur teacher sucks
maybe it's just a difference in curriculum 
fast bolt
am i going to fail
tepid glen
they troll u
brazen hare
am i going to fail
do you have notes on this topic?
everything should be in your notes
fast bolt
do you have notes on this topic?
no i started last week all we have done is uhmmm quartics
tepid glen
maybe it's just a difference in curriculum <:sully:651816820122189834>
well how does she do those types of questions without knowing chain rule or point gradient bruh
its gonna be so tedious
if she has to expand allat
brazen hare
well how does she do those types of questions without knowing chain rule or poin...
y - y_1 = m(x - x_1) is technically not necessary
you can use y = mx + c
tepid glen
?
tepid glen
i mean i guess
brazen hare
but y - y_1 = m(x - x_1) is just faster tho
tepid glen
yeah
tepid glen
i give u practise question morri
fast bolt
yes
fast bolt
5(3x-1)^4 * 3
brazen hare
my notes is just graphs 🥺
btw in general for most functions $f(x)$ the derivative
[\dv{x}[f(x)^n] = nf'(x)f(x)^{n-1}]
clever fjordBOT
fast bolt
ok so trying to be fancy
brazen hare
ok so trying to be fancy
what derivatives and integrals do you know rn?
fast bolt
what derivatives and integrals do you know rn?
idk what an integral is and i taufht myself an hour ago how to do derivatives
😅
tepid glen
integral is like opposite of derivative
brazen hare
idk what an integral is and i taufht myself an hour ago how to do derivatives
do you know all of these already?
tepid glen
but u prob dont need to know now
fast bolt
do you know all of these already?
i dont know any of them
brazen hare
i dont know any of them
well you know the last one, don't you ;)
tepid glen
u know power rule
fast bolt
🧍♂️
tepid glen
yes
fast bolt
oh yeah
fast bolt
sowwy
tepid glen
dude i hate quotient rule
brazen hare
quotient rule is pretty easy
fast bolt
why is it so long im going to ksm
brazen hare
$\dv{x}[cf(x)] = cf'(x)$
clever fjordBOT
tepid glen
derivative
north sparrow
another notation for the derivative
fast bolt
okay so the derivative of that
is the same as putting an apostrophe
like in front of its x
im so tuff
what do i do with that though
brazen hare
$f'(x)$ and $\dv{x}[f(x)]$ both mean the same thing
tepid glen
bro what
clever fjordBOT
tepid glen
oh yeah
fast bolt
yeah thats what i meant pal
tepid glen
and y'
brazen hare
what do i do with that though
you can differentiate something like $f(x) = 6(7x + 3)^4$
clever fjordBOT
fast bolt
with chain?
brazen hare
with chain?
chain and product
fast bolt
chain and product
product?
brazen hare
idk what an integral is and i taufht myself an hour ago how to do derivatives
bro have you had to self-study your math class like all year 😭
north sparrow
example of the constant multiple rule: $\dv{x}{5e^x} = 5 \dv{x}{e^x}$
you can put the 5 "outside" of the derivative operator
fast bolt
im confused sorry
north sparrow
but the formating hates me
fast bolt
😭
fast bolt
but the formating hates me
u could write on paper and send photo
brazen hare
but the formating hates me
$\dv{x}[5e^x] = 5\dv{x}[e^x]$
clever fjordBOT
brazen hare
third time's the charm
fast bolt
what is the e
brazen hare
what is the e
do you know the mathematical constant $e$?
clever fjordBOT
fast bolt
no 😭
north sparrow
oh boi
brazen hare
i mean
fast bolt
frick
brazen hare
you'll get there 😭
fast bolt
idk pal
brazen hare
@fast bolt try this:
differentiate $\frac{3}{x} + \sqrt[3]{x} + \sqrt{2}$ with respect to x
clever fjordBOT
brazen hare
1.5x + 1/3x
no..
fast bolt
what the hell
tepid glen
yeah
fast bolt
-3x + 1/3x
tepid glen
huh
fast bolt
3x^(-1) + x^(1/3) + sqrt2
brazen hare
3x^(-1) + x^(1/3) + sqrt2
now use your power rule to differentiate each term
brazen hare
-3x^(-2) + 1/3x^(-2/3)
very good :)
fast bolt
thanks
brazen hare
now simplify
brazen hare
if you remember your exponent rules, it should be easy to simplify
btw im not asking you to simplify for fun, in exams (at least, a levels i think) , the final answer must be simplified
fast bolt
btw im not asking you to simplify for fun, in exams (at least, a levels i think)...
yeah my teacher said that
im stuck sorry
im eating my dinner at the same time 😭
waitr when i have
tepid glen
1/3x^2/3
brazen hare
$\frac{1}{3} x^{-\frac{2}{3}} = \frac{1}{3} \times \frac{1}{x^{\frac{2}{3}}}$
pls compile
tepid glen
what the heck
fast bolt
so 3 to the power of 3/2
clever fjordBOT
brazen hare
$x^{\frac 23} = ?$
fast bolt
3x^(3/2)
clever fjordBOT
brazen hare
so $\frac{1}{3} x^{-\frac{2}{3}} =$ ?
clever fjordBOT
brazen hare
did i mess up
yes
fast bolt
where 😔
brazen hare
why are you turning the -2/3 into 3/2
fast bolt
i was taught to flip everything to remove the negative
so 1/3 becomes 3/1
and -2/3 becomes 3/2
brazen hare
nono the power of -2/3 applies to only the x not the 1/3
brazen hare
$\frac{1}{3 \sqrt[3]{x^2}}$?
clever fjordBOT
fast bolt
yes
brazen hare
that's correct ✅
fast bolt
are you sure ur not saying that to make me feel better
brazen hare
lol ez 3 marks amirite
clever fjordBOT
brazen hare
still the same concept of power rule, just with another twist
brazen hare
8x^(1/2) + 3x^(3/2
close, but not quite
fast bolt
oh where did i mess up
brazen hare
8 and 3x are being divided by sqrt(x)
fast bolt
oh 😭
brazen hare
if they were being multiplied by sqrt(x), you would be correct
fast bolt
i’m not sure where to start then
i’m trying to do it in my head because i don’t have paper rn 😭 this is hell
wait
8/sqrtx + 3x/sqrtx
so 4x^(-1/2) + 4.5x^(1/2
brazen hare
so 4x^(-1/2) + 4.5x^(1/2
hmm not quite
brazen hare
no, but close
fast bolt
where did i mess up 😔
north sparrow
where you are
brazen hare
$\frac{3x}{\sqrt x} = 3x^{1-\frac{1}{2}} = 3x^{\frac 12}$
clever fjordBOT
brazen hare
where you are
from here you can just apply power rule
brazen hare
simplify that?
fast bolt
-4 times 1/x^3/2
and then
-4/sqrt of x cubed
plus
1.5 x 1/x^1/2
so 1.5/sqrt of x
i’m cracked
u guys should become tutors
brazen hare
you can also write that as $\frac{3}{2\sqrt{x}}$
clever fjordBOT
brazen hare
$1.5 \times \frac{1}{\sqrt x} = \frac{3}{2} \times \frac{1}{\sqrt x}$
clever fjordBOT
brazen hare
1.5 = 3/2
brazen hare
loll of course not
the full expression is $-\frac{4}{\sqrt{x^3}} + \frac{3}{2\sqrt{x}}$
clever fjordBOT
brazen hare
@fast bolt here's another question, this time more in tune with the style of an exam: \
Find the gradient of the curve $y = \frac{x-1}{x^2}$ at the point where the curve crosses the $x$-axis.
clever fjordBOT
fast bolt
i have to go can i add you and dm my answer later 😭
my dad is making me play a board game
odd edgeBOT
odd edgeBOT
Available help channel!
glad kestrel
Please help I got E and the answer is D
odd edgeBOT
Please help I got E and the answer is D
exotic bobcat
How are we supposed to help when you aren't telling us how you got to E?
glad kestrel
sorry
I drew triangles ORQ and POQ next to eachother and used cosine rule to find the straight line that connects P to the midpoint of OR
exotic bobcat
that's a path right through the pyramid though. Not along the outer surface of the pyramid, which is what the exercise asked for
late dust
I drew triangles ORQ and POQ next to eachother and used cosine rule to find the ...
Can you show your calculation
glad kestrel
this is what i drew
late dust
that's a path right through the pyramid though. Not *along the outer surface of ...
It's not, he is correct
glad kestrel
i think maybe i assumed the angle is 120 when its not
but i just cant visualise it or something
late dust
No, it is 120º
late dust
Can you show your calculation
.
glad kestrel
yes 1s
glad kestrel
.
ah wait nvm
sorry i just did the wrong value of cos
i thought cos 120 was -sqrt3 / 2
when it was -1/2
exotic bobcat
It's not, he is correct
the straight line that connects P to the midpoint of OR
no such thing exists in the sketch above. Not unless you have a really interesting definition of straight lines in 3d space or pass through the pyramid
glad kestrel
i drew 2 faces of the net of the pyramid
late dust
> the straight line that connects P to the midpoint of OR
no such thing exists i...
along the outer surface
You can definitely define straight lines on surfaces, even of a polyhedron
odd edgeBOT
@glad kestrel Has your question been resolved?
mystic saffron
i keep get stuck on these kind of questions, maybe it's the tiredness but please someone help
worn saddle
i keep get stuck on these kind of questions, maybe it's the tiredness but please...
hmm imo in such cases check when the term is free from the variable
then add the values of those terms
signal yacht
i keep get stuck on these kind of questions, maybe it's the tiredness but please...
!status
odd edgeBOT
i keep get stuck on these kind of questions, maybe it's the tiredness but please...
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
all of the above uhhh 1.
worn saddle
hmm imo in such cases check when the term is free from the variable
...
stray arch
So what does the constant term mean? It means that the xs cancel out
Try to find where $x^n \cdot (\frac{1}{x^3})^{12-n} = 1$
clever fjordBOT
Crackhex
mystic saffron
right
worn saddle
Try to find where $x^n \cdot (\frac{1}{x^3})^{12-n} = 1$
hmm how do i use this bot
stray arch
Once youve done that you reduce your answer down to two choices, and then remembering the sign rule for binomial distribution will give you one option left
mystic saffron
i got to (12 C k ) (2^(12-k))(x^-4k) (-5^k)
and now i have no idea what
stray arch
**Crackhex**
I flipped this accidentally I meant it to be $x^{12-n} \cdot (\frac{1}{x^3})^{n} = 1$
Can you solve for n here?
clever fjordBOT
Crackhex
stray arch
I stripped the constants away for the moment because theyre entirely unimportant to the fact the xs cancel out in the constant term
mystic saffron
n = 12
righhhhhttttt..........??????
no
what am i on
am i stupid??
well i know n = 9 but i am trying to justify it
no
n = 3
what am i on
stray arch
N=3 yes
mystic saffron
but how
mystic saffron
can i use ln(x) to find this
stray arch
No need, just exponent laws: $(\frac{1}{x^3})^n = x^{-3n}$, then $x^{12-n} \cdot x^{-3n} = 1 \implies x^{12-4n}=1$, thus $12-4n=0$ and $ n=3$
clever fjordBOT
Crackhex
stray arch
So now we know n=3, calculate the third term in the expansion
And see which answer you get
odd edgeBOT
@mystic saffron Has your question been resolved?
mystic saffron
one more thing; i did this
and i got the right answer
but in the wrong way
is this valid to keep doing it like this since i can't see what i did wrong
worn saddle
ye
you removed A and B since K is a positive integer
C gives a valid value for K so C has a constant term for it
mystic saffron
you removed A and B since K is a positive integer
whatever i did i dont think it was intntional
worn saddle
whatever i did i dont think it was intntional
hmm so what you did here is check wether a constant term exists
or to say if any term gets free of x
worn saddle
**Crackhex**
or to say if this happens for any value of n
now here n is a positive integer acc to the binomial theorum
so whenever we dont dont get a value of n thats a positive integer , hence we dont satisfy the condition , hence we dont have a constant term
and when something doesnt exist it means its coefficient is 0 or to say it is 0
wheat magnet
losing my mind over part 3!
sturdy cape
!xy - that can't be the full question, surely
odd edgeBOT
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.
Available help channel!
wary tide
this is a physics question but it has math involved so
my question is how did get the equation sb + sc-sb
odd edgeBOT
this is a physics question but it has math involved so
my question is how did ge...
@wary tide Has your question been resolved?
odd edgeBOT
@wary tide Has your question been resolved?
rustic maple
I am meant to find the vector and parametric equations of the line R^2 that passes through the origin and is orthogonal to the vector v, where v = (-2, 3)
rustic maple
Here's what I tried. Book said it's wrong
yes, I know that that would make the line parallel to v, not perpendicular like it wants of me
(I cannot use cross products because they haven't been taught to us)
nvm, I just used the fact that the normal u is -1/slope of v with (0, 0) as the starting point for both vectors
.close
odd edgeBOT
odd edgeBOT
Available help channel!
worthy root
how can i prove that AB, DM, EN converge at K
Given two parallelograms ABCD and ABEF not lying in the same plane.
odd edgeBOT
@worthy root Has your question been resolved?
acoustic nexus
how can i prove that AB, DM, EN converge at K
Given two parallelograms ABCD and ...
Ehhh, what is this
!original please