vague comet
a rhombus can be a
a) rectangle
b) parallelogram
c) square
d) triangle
im torn between options b and c. by definition of a rhombus, a rhombus is already a parallelogram by default. if you're asking about what a rhombus can be, then i think the correct option would be c, because rhombuses can be squares if all the angles are right angles.
amber bolt
if it can be square, it can be a) and b) as well
squares are rectangular and parallelogrammical
vague comet
hmm, true
red moat
the question seems obscure
vague comet
but then again i don't see why the option would be b because a rhombus is already a parallelogram by default
red moat
but then again i don't see why the option would be **b** because a rhombus is al...
it depends on the context of the question
the question could have been better worded
vague comet
it was an mcq i got in my exam 😭
amber bolt
don;t try to solve it assuming one option is correct
there won;t be a satisfying solution
vague comet
alright
seeing that the question itself is vague and ambiguous, i'll just close the channel
.close
calm coralBOT
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red spear
need help solving this limit, can't use d'hopital
calm coralBOT
need help solving this limit, can't use d'hopital
hollow perch
try factorising top
red spear
what now? I can write the expression in the paranthases as sin^2x but don't know if it helps
potent lotusBOT
chlamydia
calm coralBOT
lost ice
calm coralBOT
lost ice
how do i find the message length? (it is not 4)
calm coralBOT
@lost ice Has your question been resolved?
calm coralBOT
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copper kiln
Heyy, I’m having trouble figuring out why this is not divergent.
copper kiln
But I thought I was supposed to use the limit notations… how do I know when I need the limit notation and when I don’t…
I thought we use a limit notation because there is a whole at x=25
upper sparrow
Heyy, I’m having trouble figuring out why this is not divergent.
How are you getting -infinity here?
copper kiln
Well I thought that since we are taking a closest number from the left of 25, it would give us positive infinity, and then multiplied by -2 it would give us-infinity
upper sparrow
,calc 25 - 24.9999
potent lotusBOT
Result:
9.9999999999767e-5
past zinc
But I thought I was supposed to use the limit notations… how do I know when I ne...
you should get the same result wriitng the limit too
upper sparrow
Damn it calculator 
copper kiln
you should get the same result wriitng the limit too
I understand, but my math doesn’t add up 😭
upper sparrow
Well I thought that since we are taking a closest number from the left of 25, it...
But note that what's inside the square root is very close to zero, and of course, you (should!) know what sqrt{0} is
past zinc
Well I thought that since we are taking a closest number from the left of 25, it...
look, 25 minus someting very close to 25 is 0 , but your zero is not in denominator
past zinc
I understand, but my math doesn’t add up 😭
you have just zero, there, not division by zero, ok ?
copper kiln
Yes, so if it’s in numerator, it would be just 0, yes? So that whole thing is just 0 and not infinity?
And if it was on a denominator, it would have been infinity?
past zinc
Yes, so if it’s in numerator, it would be just 0, yes? So that whole thing is ju...
yes 🙂 exactly,
copper kiln
Oh okay, because the professor didn’t clearly explain when stuff goes to zero or infinity
Thank you so much for the help!
past zinc
yvw
copper kiln
🫶🏻
devout elm
calculate (3-4)+(6-7)+(9-10)+.......+(999-1000)
calm coralBOT
calculate (3-4)+(6-7)+(9-10)+.......+(999-1000)
broken adder
332, by my reckoning
it goes up in 3s from 4 to 1000
and since 333 instances of going up in three would be 999, i.e. 1 to 1000,
we know that we must have 332 instead
devout elm
so -332?
devout elm
what
pure kayak
im using arithmetic sequence equations
with a sequence 4,7,10,... 1000 would be the 333rd term
pure kayak
not by my count
pure kayak
indeed
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devout elm
calm coralBOT
devout elm
help
celest stream
!status
calm coralBOT
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
1
celest stream
divide each term individuallly by root(a/b)
devout elm
what
remote mural
what
$\frac{\sqrt{ab}}{\sqrt{\frac{a}{b}}}-\frac{\sqrt{\frac{a}{b}}}{\sqrt{\frac{a}{b}}}$
devout elm
so
potent lotusBOT
deltaG
devout elm
so the right part becomes -1 right
remote mural
yes
devout elm
how do you solve left
remote mural
do you know that $\sqrt{ab}$ is just $\sqrt{a}\sqrt{b}$ and $\sqrt{\frac{a}{b}}$ is just $\frac{\sqrt{a}}{\sqrt{b}}$
potent lotusBOT
deltaG
devout elm
yep
multiply by root b?
so then b times roota / root a?
then they cancel
so 13-1?
remote mural
right
devout elm
i get it noow
remote mural
nicee
open pine
calm coralBOT
open pine
Stuck in number 2. I'm trying to evaluate the limit
open pine
Which one?
indigo gust
4-(4x-x²)
indigo gust
So limits dne
calm coralBOT
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fallow nymph
I don’t know how to set this up
calm coralBOT
I don’t know how to set this up
fallow nymph
I thought it was just asking for what x value in f’(x) you need to get 4, but that would be 6 which isn’t on here
hasty fiber
it's not quite that direct
have you been taught the derivative of the inverse function?
fallow nymph
I definitely was but I don’t quite remember it
I suppose there was a rule I forgot?
hasty fiber
i suppose so
well now's as good a time as any to bring it back
if h(x) = f^-1(x), what is h'(x)?
hasty fiber
alright then
hasty fiber
if h(x) = f^-1(x), what is h'(x)?
we can use the all-important property of the inverse function to rewrite this equation as f(h(x)) = x
fallow nymph
Oh, so then I can use chain rule?
hasty fiber
that would be wise
fallow nymph
So
fallow nymph
we can use the all-important property of the inverse function to rewrite this eq...
According to the property of the inverse function, the derivative of h(x), where h(x)=f^-1(x), Is f(h(x))=x?
It’s just like that?
fallow nymph
Ok
hasty fiber
the point is that second equation
f(h(x)) = x
is something which, if I said "differentiate both sides" is something you should be able to do
hasty fiber
differentiate both sides
fallow nymph
f’(h(x))(h’(x))=1
hasty fiber
hey look there's the h'(x) we were looking for
fallow nymph
ohh ok
hasty fiber
solve for it
fallow nymph
solve for it
I got 1/2 after I plugged in 4
hasty fiber
sounds good to me
fallow nymph
ok thanks, I’ll try to remember that property of the inverse function for next time
.close
maiden otter
How do I solve this? Ai told me to use L’hôpital’s rule but I haven’t learned it yet..
bright lagoon
How do I solve this? Ai told me to use L’hôpital’s rule but I haven’t learned it...
"AI", huh?
maiden otter
"AI", huh?
Well, photomath, chatgpt blah blah
bright lagoon
Well, photomath, chatgpt blah blah
what have you tried yourself so far
maiden otter
what have you tried yourself so far
I tried doing the conjugate and putting the fractions in the same denominator
But I got stuck while doing it
bright lagoon
I tried doing the conjugate and putting the fractions in the same denominator
ok I got it
factor the root first
or rather, factor out the GCF from the root
$\frac{2\sqrt{x+2} - 4}{\frac{1}{x+2} - \frac{1}{4}}$
potent lotusBOT
Melvin Eugene Punymier
potent lotusBOT
Melvin Eugene Punymier
maiden otter
hmm
bright lagoon
tell me what you notice
or rather, tell me what you think we should do after that.
*what you get after that
maiden otter
Not to sure, I’m still convinced that I have to do the conjugate
bright lagoon
you asked me for help and I have a solution for you, so bear with me
maiden otter
sorry
bright lagoon
can you use LaTeX?
maiden otter
What is that?
bright lagoon
nah, pick up from here, after the substitution:
$\frac{2w - 4}{\frac{1}{w^2} - \frac{1}{4}}$
potent lotusBOT
Melvin Eugene Punymier
bright lagoon
How did you jump from that step to this one?
I followed my instructions.
bright lagoon
now make the substitution
☝️
maiden otter
Right
Sorry you’ll have to be a bit patient with me because English isn’t my first language
bright lagoon
...and you are used to asking artificial intelligence for answers
maiden otter
…it gave me a method that I haven’t learned
bright lagoon
…it gave me a method that I haven’t learned
"L'Hospital's Rule" is learned later in Calculus I
you don't need it to solve this.
we are trying to make indeterminant terms cancel
..which they will
what would you do next in this situation
*could you
to make this simpler
maiden otter
Put the fractions in the same denominator?
potent lotusBOT
Melvin Eugene Punymier
bright lagoon
now what
maiden otter
Idk how to explain it, but bring the (4-w^2) with the (2w-4)
bright lagoon
Idk how to explain it, but bring the (4-w^2) with the (2w-4)
rewrite as mulitplying by the recipricol
bright lagoon
$\frac{(2w-4)4w^2}{4-w^2}$
potent lotusBOT
Melvin Eugene Punymier
bright lagoon
what else
maiden otter
Distribute
bright lagoon
Distribute
that will undo our progress
bright lagoon
what about it
maiden otter
Difference of two squares
bright lagoon
too slow
maiden otter
In French it’s called différence de deux carrées
bright lagoon
$\frac{4w^2(2w - 4)}{(2-w)(2+w)}$
potent lotusBOT
Melvin Eugene Punymier
bright lagoon
In French it’s called différence de deux carrées
ooh, fancy
maiden otter
yup
bright lagoon
what now
potent lotusBOT
Melvin Eugene Punymier
bright lagoon
now what
maiden otter
I was thinking of taking out the negative sign in the (w - 2)
potent lotusBOT
Melvin Eugene Punymier
maiden otter
Yup
bright lagoon
now what
maiden otter
how do you know we want to replace w with 2
Because the limit of x tends towards 2
maiden otter
And there’s practically nothing else to do besides replacing
bright lagoon
And there’s practically nothing else to do besides replacing
not a rigorous explanation
what was the substitution again?
maiden otter
**Melvin Eugene Punymier**
^
bright lagoon
$\lim_{x \to 2} \left(w = \sqrt{x+2}\right) = \sqrt{2+2} = 2$
hmm..I can't do limits anymore
maiden otter
I get what you mean
potent lotusBOT
Melvin Eugene Punymier
potent lotusBOT
Melvin Eugene Punymier
bright lagoon
cool
maiden otter
Alright now there is just one thing that I don’t understand in all of this
And it’s the whole substitution part
maiden otter
All good take your time
bright lagoon
hmm...I wonder where I went awry
check out this graph
(one sec)
oh, no
I'm right
Wolfram Alpha is WRONG 😳
~neat!~
maiden otter
Gasp
bright lagoon
anyway, here's the graph
Wolfram thought there is an asymptote at x=2
but there isn't
(or maybe I goofed typing it)
maiden otter
It looks right
bright lagoon
yeah so
apparently
if you ask Wolfram Alpha DIRECTLY what the answer is to a limit in "indeterminant form" (which is what your expression is),
it may or may not get it wrong as its precision gets buggy near the limit
however, if you just ask Wolfram Alpha to GRAPH the expression, then it will draw it correctly
(usually)
Desmos worked out fine because I just asked it to graph.
maiden otter
yeah
bright lagoon
Do you remember what "indeterminant form" is?
maiden otter
For example, -inf / -inf is an indeterminant form
bright lagoon
(our situation here--yes!)
maiden otter
Right
bright lagoon
that is also the condition where "L'Hospital's Rule" will work.
...but you haven't learned that yet.
good job, @maiden otter
maiden otter
Im still confused on the substitution part though. How does the square root disappear all of a sudden?
bright lagoon
Im still confused on the substitution part though. How does the square root disa...
we replaced it
we "substituted" it
you see, when we see square roots in these nasty expressions, it's ~n i c e~ if we can find another version of the same expression in the root, but without the root
if we see that, then we can call the rooted version some variable, like w, and the version WITHOUT the root, w^2
that is,
$\sqrt{x+2} = w \text{ and } x+2 = w^2$
potent lotusBOT
Melvin Eugene Punymier
bright lagoon
it just makes things cleaner and (usually...in math homework) enables something to more obviously cancel after we finish factoring
maiden otter
**Melvin Eugene Punymier**
Specifically how this became,
maiden otter
**Melvin Eugene Punymier**
This
bright lagoon
I just SUBSTITUTED exactly like I wrote here ^
bright lagoon
**Melvin Eugene Punymier**
☝️
bright lagoon
don't you see that
potent lotusBOT
Melvin Eugene Punymier
bright lagoon
For some reason I can’t remember substituting
the subsitution I used is entirely based on noticing this ☝️
you REALLY don't understand that
$t = (\sqrt{t})^2$
potent lotusBOT
Melvin Eugene Punymier
bright lagoon
?
maiden otter
Well yes that becomes t
bright lagoon
(I mean, technically, you get the absolute value, but it's ok in this situation)
maiden otter
**Melvin Eugene Punymier**
^
maiden otter
**Melvin Eugene Punymier**
^
bright lagoon
^
that's not what I wrote.
although, you know...
$\frac{2\sqrt{x+2} - 4}{\frac{1}{x+2} - \frac{1}{4}}$
potent lotusBOT
Melvin Eugene Punymier
bright lagoon
we should technically have
nah it's good
so again, we said that
$w = \sqrt{x+2}$
potent lotusBOT
Melvin Eugene Punymier
bright lagoon
the other expression, x+2, is just the square of this. So x+2 = w^2.
$\frac{2w - 4}{\frac{1}{w^2} - \frac{1}{4}}$
potent lotusBOT
Melvin Eugene Punymier
bright lagoon
do you see?
maiden otter
I don’t really want you to try to re-explain it again and again
I’ll take in note what we’ve done and try to understand
bright lagoon
you already know how to substitute letters for numbers.
now we are just substituting letter expressions for single letters (w)
maiden otter
The w is just x right?
bright lagoon
because it is easier to write
no!
the w is sqrt(x+2)
instead of writing sqrt(x+2), we wrote w.
maiden otter
oh it makes it just simpler?
bright lagoon
that's it.
bright lagoon
oh it makes it just simpler?
yeah, it's much easier to re-factor single variables and square variables than square roots
bright lagoon
you can do all this (technically) without substituting
but I've been doing this for years
and I wouldn't have noticed right away
unless I made the subsitution first
maiden otter
Yeah I get it now
bright lagoon
good luck interpretting a square root expression as a difference of squares!
maiden otter
But I don’t think my teacher would let me do it
bright lagoon
But I don’t think my teacher would let me do it
you already did this.
you just forgot
bright lagoon
$\text{factor: } f(x) = x + 2\sqrt{x} + 4$
potent lotusBOT
Melvin Eugene Punymier
bright lagoon
you did this
y = sqrt(x)
so then
y^2 = x
and then
f(y) = y^2 + 2y + 4
...which is a "perfect square trinomial"
f(y) = (y + 2)^2
...and so f(x) = (sqrt(x) + 2)^2
...but it was easier to see that with the substitution 🙃
bright lagoon
ok, that all?
maiden otter
I think so!
bright lagoon
ok, goodnight
fluid yew
Let A be an ordered integral domain. Prove that $a^2+b^2+c^2 \geq ab+bc+ac$. This is possibly trivial, but I got to $2a^2+2b^2+2c^2 \geq 2ab+2bc+2ac$. Am I allowed to multiply by 1/2 here, and if so, why? How do I know the LHS/RHS is still in A if I multiply by 1/2?
potent lotusBOT
Fuzzy_Alpaca
calm coralBOT
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barren nymph
what is the logic behind this? btw it's asking to solve the inequality
pure kayak
you can expand it to look a bit easier
-1<(x-1)/(x+1)<1
barren nymph
nvm I got it, sorry
calm coralBOT
Available help channel!
cosmic hill
Can someone explain how this step came?
calm coralBOT
Can someone explain how this step came?
cosmic hill
cos(2a) is a constant with respect to t
Oo yess
cosmic hill
C1 is just a dummy name for a constant
Then the last line C=acos2a +C1
What does that mean?
leaden thunder
C is a constant wrt t
calm coralBOT
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vale mantle
can someone please help me with question b?
calm coralBOT
can someone please help me with question b?
@vale mantle Has your question been resolved?
vale mantle
<@&286206848099549185>
vale mantle
.close
calm coralBOT
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rose depot
Layla has a coin that has a 60% chance of showing heads each time it is flipped. She is going to flip the coin 5 times. LetX represent the number of head she gets.
What is the probability that she gets more than 3 heads?
prime ingot
I need some help with Surface Area of revolutions. Having a tough time figuring out what to pick as my radius.
icy ingot
I need some help with Surface Area of revolutions. Having a tough time figuring ...
2пr out of the integral
calm coralBOT
2пr out of the integral
prime ingot
r in this case we needed to pick a radius
I did some reading and it turned out r=x which makes a lot of the practice questions I have give weird solutions. So ill talk to my prof for help
calm coralBOT
@icy ingot Has your question been resolved?
spark adder
Guys the function inside is odd right? therefore the integral is 0?
torn gorge
do you know odd function's definition ?
spark adder
f(-x) = -f(x)
torn gorge
does this function satisfies that property ?
spark adder
well yes?
(-x^3 - 3sin4x) cosx^3
torn gorge
hence your function is odd
calm coralBOT
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maiden solstice
i want to find the gradient of this
calm coralBOT
i want to find the gradient of this
calm coralBOT
@maiden solstice Has your question been resolved?
maiden solstice
.close
remote mural
<@&286206848099549185>
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upper drum
Hello please help me establish the order of convergence of the sequence obtained from the bisection method
upper drum
In the text we have only established that this condition is necessary but not sufficient for linear convergence
How do we conclude that p_n converges linearly?
calm coralBOT
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proven junco
I need help with 12 b)
calm coralBOT
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@proven junco Has your question been resolved?
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@proven junco Has your question been resolved?
remote mural
calm coralBOT
marsh valley
Have you tried anything?
remote mural
Wdym
I'm not sure how to do this kind of problem at all I'm failing my math class 😭😭
marsh valley
Consider the triangle you obtain by drawing a horizontal line where the slanted part starts.
Try and find the sidelengths with the information given to you.
remote mural
The side lengths are given to me right
marsh valley
Consider the triangle you obtain by drawing a horizontal line where the slanted ...
(Or the triangle missing that would make the shape a rectangle)
remote mural
I'm so confused
marsh valley
Have you tried drawing the triangle I'm talking about?
marsh valley
You should draw it.
remote mural
6.4?
calm coralBOT
@remote mural Has your question been resolved?
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leaden thunder
.close
onyx quiver
sorry but why was he allowed to turn x^3 - 64 to x - 4 ?
dull wagon
they didn't
onyx quiver
ohh ok
dull wagon
difference of two cubes identity
devout elm
calm coralBOT
devout elm
can someone explain how
quaint sphinx
first
draw segment between two points of intersection of the shapes
this might help you see what to do
empty quail
!15m
calm coralBOT
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.
devout elm
oh
devout elm
first
draw segment between two points of intersection of the shapes
this might...
i did it i don't know what to do nex
nvm
found out
.close
calm coralBOT
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Available help channel!
half raven
calm coralBOT
half raven
not sure how to start
calm coralBOT
not sure how to start
viscid ice
start with a substitution of u=1/x
half raven
okay
half raven
start with a substitution of u=1/x
look right so far?
viscid ice
spot on
dull wagon
a few notation errors
half raven
wat
dull wagon
missing dx in the original integral
and missing () around the -x^2 when converting to du
viscid ice
what's the integral of that
well you can move the minus to the front of the integral so its just integration e^x and thats pretty simple
dull wagon
don't forget the + c
viscid ice
but otherwise yes correct
calm coralBOT
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Available help channel!
half raven
how do i get the integral of something to the x power
calm coralBOT
how do i get the integral of something to the x power
potent lotusBOT
jacks
blazing coyote
$\int a^x = \frac{a^x}{ln(a)}$
potent lotusBOT
Why am. I here
blazing coyote
I encourage you to ponder why
blazing coyote
What? Why it's $\frac{a^x}{ln(a)}$
potent lotusBOT
Why am. I here
half raven
i see but like i just can't visualize where it comes from
blazing coyote
what are you unable to understand? I'm unable to understand what you can't understand?
upper sparrow
is it sort of like the chain rule
You can write $a^x = e^{x\ln(a)}$ for example, and note that $\ln(a)$ is a constant
potent lotusBOT
@upper sparrow
upper sparrow
Are you happy with integrating something like $\int e^{kx} \dd x$?
potent lotusBOT
@upper sparrow
glacial pecan
does this seem right and if it does do i combine 2x^4 and x^4
glacial pecan
the equation
kindred estuary
does this seem right and if it does do i combine 2x^4 and x^4
Yes
glacial pecan
so itd be 3x^4?
kindred estuary
Yes
calm coralBOT
feral totem
https://i.imgur.com/aKJZFbA.png
Hey I'm usually p confident with inequalities and interval notation, I'm a little confused on why this is incorrect?
calm coralBOT
https://i.imgur.com/aKJZFbA.png
Hey I'm usually p confident with inequalities an...
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).
feral totem
ah
little brook
https://i.imgur.com/aKJZFbA.png
Hey I'm usually p confident with inequalities an...
??
For the first inequality $x-1 \leq 2-2x$, we add $2x$ to both sides to get $x + 2x - 1 \leq 2$, which simplifies to $3x - 1 \leq 2$. Then we add 1 to both sides to get $3x \leq 3$. Finally, we divide both sides by 3 to get $x \leq 1$.
For the second inequality $3x+5>2$, we subtract 5 from both sides to get $3x > -3$. Then we divide both sides by 3 to get $x > -1$.
we are looking for the values of $x$ that satisfy both $x \leq 1$ and $x > -1$. This is the interval $(-1, 1]$.
potent lotusBOT
Flamey
little brook
https://i.imgur.com/aKJZFbA.png
Hey I'm usually p confident with inequalities an...
@feral totem I think you did good
calm coralBOT
Available help channel!
tepid glacier
How do i solve coordinate/ordered pair composition of function
calm coralBOT
How do i solve coordinate/ordered pair composition of function
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plush spoke
trail ingot
lolll what is that asking
plush spoke
Idk
broken anvil
Is that the whole question??
plush spoke
Yea
calm coralBOT
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calm coralBOT
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jade wyvern
how to calculate the minimum,maximum and zeros for the function : 2cos(x/4 -π/3) -1
jade wyvern
because when i calculate the second zero it says it is 8kπ but i have 8π+8kπ. HELP
leaden thunder
because when i calculate the second zero it says it is 8kπ but i have 8π+8kπ. HE...
Factor out 8π from your expression
Then find the k+1 that is the second zero
jade wyvern
no cuz i ran it through photomath and it says the 8π is zero because the closest positive coterminal angle is zero?
jade wyvern
Factor out 8π from your expression
?
jade wyvern
yes but the equation is x=8π+8k so that does nothing
jade wyvern
no cuz i ran it through photomath and it says the 8π is zero because the closest...
could u help me understand this?
jade wyvern
yes the answer is x=8kπ but i have x=8π +8kπ. When i put in the origrinal function into photomath it transforms x=8π +8kπ into x=8k because apperently the closest coterminal angle is zero
jade wyvern
?
leaden thunder
Factor out 8π from your expression
Then do this
leaden thunder
Then find the k+1 that is the second zero
And this
You can check photo math after you find your k
jade wyvern
the x-es are zeros the k is there only to signify the fact that the function repeats
<@&286206848099549185>
leaden thunder
the x-es are zeros the k is there only to signify the fact that the function re...
Yea so find the k in your formula then evaluate the x at those points
calm coralBOT
@jade wyvern Has your question been resolved?
cobalt cave
what i am doing wrong here?
calm coralBOT
what i am doing wrong here?
upbeat venture
what i am doing wrong here?
Arg(z) = pi/4 does not necessarily mean |z| = sqrt(2)
take z = 5 + 5i for example
cobalt cave
it means k x sqrt(2) ?
upbeat venture
I mean sure, but k could be any real number, so that's not very helpful
upbeat venture
Arg(a+bi) = arctan(b/a)
cobalt cave
Arg(a+bi) = arctan(b/a)
wait why arctan though
isn't it jsn't it just tan?
isn't arg supposed to mean tilt angle of z?
upbeat venture
Arg(z) represents the angle z makes with the real axis. from trig, you know tan(Arg(z)) = b/a, if z = a+bi
cobalt cave
Arg(z) represents the angle z makes with the real axis. from trig, you know tan(...
would you mind to show me solution to this problem? it would help me to understand it better
<@&286206848099549185>
ok i got it
calm coralBOT
calm coralBOT
Available help channel!
silent oar
Use the shell method to find the volume of the solid generated by revolving the shaded region about the y-axis.
silent oar
$\int_0^32\pi{xf(x)}:dx = 2\pi\int_0^3\frac{18x^2}{\sqrt{x^3+9}}:dx$
potent lotusBOT
ryan
leaden thunder
,w 18 * int 0 to 3 of x^2/(x^3+9)^(1/2)
potent lotusBOT
leaden thunder
i got my final answer as 72pi but its wrong apparently...?
Then your setup is wrong
You should be taking 3 - curve as your shell
Solve for x in the equation for y
calm coralBOT
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worn light
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remote mural
this is false right
calm coralBOT
this is false right
remote mural
or am i just stupid
because if you let m = n + 1, this clearly isnt true lol
but im convinced i just read this wrong
and am being stupid
torn gorge
n=0?
torn gorge
every number divide 0=0 times what ever
frank gull
i just have to prove this is true when n = 0
tbf depending on who you ask they may or may not include 0 in the seet of the naturals, lol
remote mural
tbf depending on who you ask they may or may not include 0 in the seet of the na...
in my class they do
frank gull
bugt since y'all do then yeah it's totally valid
remote mural
but like why tf would they ask this
thats so stupid
i dont have to show that it only holds for 0 and not any other n right
remote mural
any advice...
ive been trying to practice a lot
to overcome my reading comprehension struggles
frank gull
i dont have to show that it only holds for 0 and not any other n right
yeah correct. You're trying to prove some n exists, which you did 🙂
frank gull
to overcome my reading comprehension struggles
I hate to say it but just practice. Find extra problems where you can find a solution to it and practice, practice, practice.
Also come here and ask people to help read your proofs 🙂
Make sure that you have all of the availalble data
remote mural
btw
do u have a good text book rec
the supplemetal materials they gave us are not enough i dont think
frank gull
what always tripped me up was forgetting some small detail like "a natural number n that is prime". The key to the proof was that it was prime, but I forgot that fact
which class is this for?
frank gull
I'm not a big DM person from here if that's alright. Keep work and pleasure separate, ya know?
how about you react? lol
Intro to adv math
number theory
remote mural
thats fair
frank gull
discrete math
remote mural
no
frank gull
oh I don't think I had a class before discrete math for that topic, lol
for me that was calculus 2 but they're separate fields
frank gull
I recall our course used The Book of Proof by Richard Hammack
it provides solutions for odd problems and each chapter has a large sample of practice problems
remote mural
so you would say it is good
frank gull
yeah I enjoyed it personally
remote mural
im not going to lie, i really hate this math, but i really am trying to change my mindset
but it is hard
frank gull
that's fair. I say this as someone who loves math, not everyone feels that way. But that's also because our education system kinds of fails us because the way we teach it is not very efficient
I really enjoyed some more "off the beaten path" math courses like abstract algebra
and that came after proofs
remote mural
yeah its true, but my major is math adjacent
and proofs are important, even if i dont want to admit it
frank gull
I'm guessing CS?
remote mural
yes
frank gull
100% Proofs are what make math math. It's why it's so strong. Without proofs, we can't truly prove any statement, even if it seems obvious
I was a CS major too
currently a software engineer
remote mural
but like, my brain doesnt work to use proofs
remote mural
currently a software engineer
yeah thats what i want to do
well i want to do ||compiler development||
but yeah
frank gull
||compiler construction||
remote mural
Love that book
yeah anyways so
and its the only thing holding me back
from doing what i like
which is why i hate this class
frank gull
I guess DM the specific course
I'm still not clear on what this particular course subject is lol
remote mural
wait r u american by any chance
remote mural
sounds accurate
frank gull
ok yeah that textbook I recommended should help a ton then
it's a gentle approach of proofs and holds your hand through the first concepts.
remote mural
i should really practice every day
im not even kidding i have nightmares about this class
my calc 3d class is 10x easier for me
frank gull
Yeah for sure. If you can manage it, what I used to do was like 10 theorems a day for the chapters of studying concepts, I would try to re-write them on my own, then do like 5-10 practice problems
takes in total like an hour a day if you can spare that
remote mural
one thing i want to avoid is like, memorizing proofs
frank gull
it's practically impossible to do, imo. Unless you have an eidetic memory, you'll trip up small details.
proofs is like learning a new language
you have to also understand the structure of your proof, make sure that your claims have validity (this is where things like axioms or previous proofs come into play)
however, I will say (and I really hate to admit this) but depending on which CS branch you go, you may or may not need that much math
the most math I use in my job is for figuring out subnets in networks
I like math so I do it on my own, but yeah I use very little of my math degree in the day to day job
your primary focus should be on bit masking, manipulation, inversions, etc. This is all math related, but you learn more about that in an actual compiler/OS course than in any related math topics.
Most people who get CS degrees and don't like math just survive the math part until they're done with it, much like I did with government courses
I hated them, I made a C and moved on with my life
remote mural
however, I will say (and I really hate to admit this) but depending on which CS ...
this is true
for me
but
i dont know
its not a good excuse to not learn it well, it used to be, ive changed my mind
remote mural
your primary focus should be on bit masking, manipulation, inversions, etc. This...
but even compilers / systems use math
remote mural
I hated them, I made a C and moved on with my life
yeah im trying to stop doing this
remote mural
proofs is like learning a new language
i think part of me believes ill never be good at them
even despite the practice
frank gull
practice makes perfect 🙂
fwiw I failed most of my math courses in HS, then years later I started back at algebra 1 and got my math degree
compared to other helpers here I'm absolutely trash at math
but I still managed. Persistence and practice trump natural abillity
if directly comparing the two
(tortise and the hare, etc)
remote mural
but I still managed. Persistence and practice trump natural abillity
i wish i could have this mentality
its really unmotivating
i feel like im the bottom of my class
forest walrus
T_A and T_B are linear transformations, with standard matrices respectively A and B [as shown in image].
Find standardmatrix C for the composite transformation T_A ∘ T_B.
forest walrus
I don't know where to start from here. I'm going through these chapters before we go through this in class. Could someone teach me some fundamentals here? What does "T_A ∘ T_B" mean basically?
Wait... is this supposed to be a dot product? ∘ is a weird symbol.
forest walrus
lmao I got the correct answer by just multiplying both matrices
Was it the right approach? x)
forest walrus
first apply T_B then apply T_A
ah, understood.
glass heart
yes the point is that composition of linear maps is the same thing as multiplying their corresponding matrices
forest walrus
yes the point is that composition of linear maps is the same thing as multiplyin...
Got it, makes sense 
thank u 😄
.close
calm coralBOT
calm coralBOT
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west merlin
hey can you verify my explanation as I'm trying to understand the intuition of how to use 'unless' in logic.
q unless not p means that when not p is the case then not q which is the same as p then q
(q unless not p) = (not p then not q) = p then q
west merlin
im trying to come up with my own blurb to remind me of the intuition why q unless not p = p then q
clear delta
q unless not p
q if p
if p then q
west merlin
i see the advantage of this one to for the symmetry is mine correct too tho?
Ill use both if mine is correct to help me remember
in particular this:
q unless not p means that when not p is the case then not q which is the same as p then q
clear delta
"unless not" would annoy me in most writing
unique jackal
yeah i prefer the "q unless not p" means that "if not p is true, then not q is true"
but i dont like unless not anyways
unique jackal
i hate it its so confusing
i have never heard someone use "unless not" outside of an introduction to logic so you may be fine to forget about it afterwards
west merlin
i thought so too but id just get mad if i didnt get it lmao
you have no idea how happy this has made me lmao
ive been thinking about it all day
calm coralBOT
Available help channel!
glad sinew
Ok, so I wasn't there when ta explained the question.. I'll share the notes but I have no idea what Im looking at
glad sinew
I'll try deciphering the notes and figure it out
Im already stuck on the first statement
why (x-eps, x+eps) intersect A
oh man its so over
upbeat venture
this guy's handwriting sucks
upper sparrow
why (x-eps, x+eps) intersect A
The definition of dense?
upper sparrow
this guy's handwriting sucks
[yea, also the pictures aren't clearer when I zoom in on them 
]
upper sparrow
The definition of dense?
(basically they're saying that whatever real number, call it x, you pick, you can always find an element of A as close to x as you desire)
glad sinew
From my understanding, if you have an interval there's always an x in between the two bounds. So rationals and irrationals are both dense in the reals
but yea I dont really understand the solution
I'll try writing everything out and I can send what I wrote
upper sparrow
I'll try writing everything out and I can send what I wrote
Yes please!
Also what do the curly brackets {} represent? Like closest integer or?
glad sinew
glad sinew
Also what do the curly brackets {} represent? Like closest integer or?
I have no idea, this is my first time looking at this
set notation?
maybe
upper sparrow
Would seem strange, it appears as if they're treating them as numbers e.g. here
If e.g. it were the floor/ceiling, it would explain this part here (if they were the same, the difference between them would be strictly less than 1, which would force m = n) wait nope
glad sinew
upper sparrow
Actually no I think it might be the fractional part of the relvant number
That would explain them being in [0, 1)
glad sinew
I dont understand this proof at all
I dont understand the solution
oh my friend replied
its floor
the decimal part only
upper sparrow
the decimal part only
Thought so(!)
upper sparrow
~~If e.g. it were the floor/ceiling, it would explain this part here (if they we...
I modify this then: if the fractional parts were equal, then that would force $m = n$, as then
[
\alpha m - \alpha n = \alpha (m - n) = \floor{\alpha m} - \floor{\alpha n}
]
and as the rightmost term is integer, if $m \neq n$, you get an irrational equal to a rational
potent lotusBOT
@upper sparrow
upper sparrow
I dont understand this proof at all
Are you at least happy up until the statement I just made, that this bit is true?
glad sinew
what do you mean you get irrational equal to rational. Also, m doesnt have to equal to n? cause you can have floor m= 3.63 and floor n= 3.32 for example and the floor of m and n are equal
if fractional parts are equal, you can still have 6.63 and 4.63 for example
upper sparrow
You assumed $\alpha$ was irrational, but $m \neq n$ gives that $\alpha = \frac{\floor{\alpha m} - \floor{\alpha n}}{m - n}$, a ratio of integers with a nonzero denominator
potent lotusBOT
@upper sparrow
upper sparrow
And of course 3.63 and 3.32 are rational: the point was more that if you had an irrational number, you can't have two integer multiples of it having the same floor or fractional part
glad sinew
Im sorry Im very confused. So alpha is an irrational, multiplying by n an integer and m a natural number, and two integer multiples cant have the same floor??
or fracional part??
what why
Im so lost here
upper sparrow
both
upper sparrow
~~If e.g. it were the floor/ceiling, it would explain this part here (if they we...
If you had $\alpha$ irrational, and $m, n$ integers (for ease, let's assume $m \neq n$, and for ease, that in particular $m > n$) such that $\floor{\alpha m} = \floor{\alpha n}$, you're saying that both round down to the same thing, which means that $\alpha m - \alpha n = \alpha (m - n) \in [0, 1)$
potent lotusBOT
@upper sparrow
upper sparrow
But as alpha is irrational, it's not zero, so we can divide by it safely and find an integer strictly between 0 and 1, or -1 and 0, not possible
upper sparrow
<@788085606483361802>
As for the fractional parts not being able to be the same, note that for any number $a$ you can write it as $a = \floor{a} + { a }$ and so as per here...
potent lotusBOT
@upper sparrow
upper sparrow
Actually wait, ignore the floor part for now, reasoned it wrong
The fractional part still holds tho
glad sinew
yup, fractional part makes sense, its floor + its decimal part, makes up alpha
but fractional part is {a}
why not have the same
upper sparrow
As before, noting that ${ a } = a - \floor{a}$ for any number $a$, then ${\alpha m } = {\alpha n }$ means that
[
\alpha m - \floor{\alpha m} = \alpha n - \floor{\alpha n}
]
and so
[
\alpha m - \alpha n = \floor{\alpha m} - \floor{\alpha n}
]
factorise $\alpha m - \alpha n = \alpha (m - n)$, and if you had $m\neq n$, you get
[
\alpha = \frac{\floor{\alpha m} - \floor{\alpha n}}{m - n}
]
Now, $m, n, \floor{\alpha m}$ and $\floor{\alpha n}$ are all integers, and $m - n \neq 0$, and $\alpha$ was assumed irrational, i.e. not a fraction of integers with nonzero denominator...
potent lotusBOT
@upper sparrow
upper sparrow
[also as a note I was wrong about the "floors not being equal", e.g. alpha = sqrt{2}/4 is such that there are different integer multiples with the same floor, dummy moment 
]
calm coralBOT
@glad sinew Has your question been resolved?
upper sparrow
oop mistyped lol
upper sparrow
<@788085606483361802>
I meant the fractional parts at the top
potent lotusBOT
@upper sparrow
round tusk
limpid flame
