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#help-17
vocal sleetBOT
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slender thicket
I'm struggeling with asymptotes. I'm trying to learn it and wrap my head around it, but I just can't seem to get the hang of it. I can kinda understand the easy questions to some degree, but I'm struggeling quite a bit with this one example in my book. Can someone maybe give a "dumbed down" version?
Translation:
You're making a cake and bake it at 225 °C. A model of the temperature development of the cake after it leaves the oven is given with f (t) = 205e^-0,455t + 20. f (t) is the temperature in °C t minutes after the cake is taken out of the oven.
a) What is the horizontal asymptote of f when time moves forward.
b) give a explenation of the y-value to the asymptote
vocal sleetBOT
I'm struggeling with asymptotes. I'm trying to learn it and wrap my head around ...
honest flame
Yo
bronze osprey
e^(0.455 * 100000000) for example will be a very big number
in fact e^(0.455t) will go to +infinity
slender thicket
oh, and hope it's alright to ask here, but is there any form of vc help here? Like any dedicated channels..?
bronze osprey
so when we divide a finite number by something going to infinity, the limit is 0
bronze osprey
oh, and hope it's alright to ask here, but is there any form of vc help here? Li...
ehh no, sorry
slender thicket
¯_(ツ)_/¯
slender thicket
so when we divide a finite number by something going to infinity, the limit is 0
that makes sense :)
honest flame
Asymptotes can be tricky, but I'll break it down in simpler tA horizontal asymptote is a line that the graph approaches as x (or t, in this case) goes to infinity.
For your cake fn ,
As t increases , the term 205e^(-0.455t) approaches 0. Hence
f(t) ≈ 20 right?
slender thicket
ah, I see
honest flame
Are you catching my view of approach for this problem or struck?
slender thicket
no I get it :)
bronze osprey
I'm struggeling with asymptotes. I'm trying to learn it and wrap my head around ...
great, so part b is just remembering what the question was all about
the temperature of the cake is f(t)
so we can't really have infinite time, but we can say that the cake will remain at a stable temperature of nearly 20 degrees Celsius after a long time
slender thicket
thanks a lot
honest flame
Let me know so that I can continue typing
honest flame
thanks a lot
Don't mention it btw.
bronze osprey
great, so part b is just remembering what the question was all about
the temper...
more accurately, the cake is always cooling, but it cools slower and slower
slender thicket
I got the b part 
bronze osprey
and the limiting temperature is 20 C
honest flame
I got the b part <:ThumbsUp:825328287282626584>
Yep it's 20
slender thicket
so it'll level at 20 for a pretty long time :)
honest flame
Yeah
slender thicket
"room temperature"
bronze osprey
so it'll level at 20 for a pretty long time :)
yeah that's what happens in practice, in a science experiment for example
vocal sleetBOT
bronze osprey
more accurately, the cake is always cooling, but it cools slower and slower
mathematically though it's this
in a perfect world
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iron parrot
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junior notch
Idk but my guess is get a ruler and measure PQ. Compare it to AC and QC and choose a reasonable answer
vocal sleetBOT
@iron parrot Has your question been resolved?
worthy tartan
Idk but my guess is get a ruler and measure PQ. Compare it to AC and QC and choo...
get a ruler is hilarious 😂
junior notch
get a ruler is hilarious 😂
Which is also a no.1 rule you should never follow but this question is an exception
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bitter kettle
Can someone please check my work here? I know it’s a lot but it’s explained in detail so it should make sense. Thanks!
vocal sleetBOT
Can someone please check my work here? I know it’s a lot but it’s explained in d...
vocal sleetBOT
@bitter kettle Has your question been resolved?
bitter kettle
maybe you can simplify a bit?
This is supposed to be like a explain the problem type of thing
We also don’t need to simplify our final answer
onyx night
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onyx night
<@&286206848099549185>
heady vine
!status
vocal sleetBOT
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
Could you show you work ?
onyx night
Could you show you work ?
it's all over the place really
can you just show me how I'm supposed to go about doing this
heady vine
First of substitute the values of a,b,c
heady vine
Ok
heady vine
Isn’t c = x-1 ?
quick crag
I'd start by manipulating the fraction into a proper fraction. i.e. no smaller fractions on top/bottom. Then substitute in a,b,c and solve further.
sterile swift
just substitute in the last form and divide
the (b-c)/bac+b
polynomial division i mean
heady vine
just substitute in the last form and divide
Where did that green b(ac+1) come from ?
quick crag
Or, just assume 1 - (a + 1/b) / (a + 1/c) equals 1/( px^2 + qx ), expand, simplify, and match like terms to solve for p and q.
sterile swift
Where did that green b(ac+1) come from ?
i just did 1 as b(ac+1)/b(ac+1)
heady vine
i just did 1 as b(ac+1)/b(ac+1)
oooooh I see
quick crag
lots of the terms should cancel when you simplify XD
onyx night
heady vine
just substitute in the last form and divide
Now that I look at it yeah the polynomial below would be 2nd degree
onyx night
idk honestly
sterile swift
don’t substitute immediately it just makes it more annoying and longer try to simplify it as much as possible then plug in the numbers
onyx night
Oh okay then let me try
the other approach
Okay so I got to b(ac+1) - c(ab+1) / b(ac+1)
now what
@sterile swift
sterile swift
Okay so I got to b(ac+1) - c(ab+1) / b(ac+1)
you will see that bac and -cab cancel
quick crag
Okay so I got to b(ac+1) - c(ab+1) / b(ac+1)
Should be 1 - c(ab+1) / b(ac+1)?
onyx night
Should be `1 - c(ab+1) / b(ac+1)`?
Idk man
sterile swift
Should be `1 - c(ab+1) / b(ac+1)`?
yeah i just let 1 be b(ac+1)/b(ac+1)
sterile swift
yeah
quick crag
$$\frac{a + \frac{1}{b}}{a + \frac{1}{c}} = \frac{bc}{bc} \times \frac{a + \frac{1}{b}}{a + \frac{1}{c}} = \frac{abc + bc\frac{1}{b}}{abc + bc\frac{1}{c}} = \frac{abc + c}{abc + b} = \frac{c (ab + 1)}{b (ac + 1)}$$
twin meteorBOT
Shuba
quick crag
I've got the same 🙂
sterile swift
do you have the answer key ?
sterile swift
i just simplified it but i didn’t do the rest i’m lazy lol but chatgpt says that answer as well
sterile swift
yeah it's right
that’s good
quick crag
My scrawls, should it help 🙂
onyx night
thanks
sterile swift
My scrawls, should it help 🙂
pretty cool
onyx night
My scrawls, should it help 🙂
mine looks different I just use the calc to factorise the cubic polynomial and cancelled out
After expanding
quick crag
yeah, factorising cubics takes too much brain power for me XD
onyx night
vocal sleetBOT
heady vine
sqrt(a)*sqrt(b)=sqrt(ab)
onyx night
I don't get it
heady vine
like sqrt(a)*sqrt(8a)=sqrt(8a^2)
heady vine
First off correct your mistakes cuz it should be 4a(sqrt2)
heady vine
then yeah just
9a=54
and the value of a use it to find b
heady vine
in equations in form
a+bx=c+dx (where x is an algebraic number)
a=c , b=d
heady vine
but why would 9a = 54?
To be more exact
9a=54
4a=b
onyx night
in equations in form
a+bx=c+dx (where x is an algebraic number)
a=c , b=d
Oh okay
are there any other similar rules to these I should know
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torpid steppe
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torpid steppe
How would I approach this problem? (7)
velvet karma
use the distance formula
torpid steppe
?
torpid steppe
So it’s (-3 - 6)squared + (-4-3) squared?
And then the square root of that answer?
vocal sleetBOT
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idle temple
Guys, I may be kinda slow, but how on earth do I get velocity given position and theta?
vocal sleetBOT
Guys, I may be kinda slow, but how on earth do I get velocity given position and...
idle temple
My struggle is that velocity, by definition, needs time. But all the equations I'm given require velocity to find time.
I know it has something to do with the fact gravity is constant, but idk how to use that to my advantage
(btw, I am in algebra based physics)
vast shale
My struggle is that velocity, by definition, needs time. But all the equations I...
Do you have the question in text format?
dark rune
Guys, I may be kinda slow, but how on earth do I get velocity given position and...
this is not enough information to understand your question
idle temple
Do you have the question in text format?
Number 4
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idle temple
<@&286206848099549185>
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@idle temple Has your question been resolved?
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abstract monolith
can someone help me
vocal sleetBOT
can someone help me
vast shale
calculate slope for each function on that interval
bronze osprey
yes and not the instantaneous slope, so do not draw a tangent
it's (f(5) - f(2))/(5 - 2) and so on
vast shale
yes
abstract monolith
.close
prime breach
How could the video have played for -(6/5) seconds, this might be referring to the time that the timer spent without actually starting to count but it seems like weird phrasing
vocal sleetBOT
How could the video have played for -(6/5) seconds, this might be referring to t...
prime breach
am i reading the fraction wrong?
proven knot
If time zero is when it started
Then the -1 is 1 second before it started
The way they explained it
Although the video first displayed at time zero, it was running for several seconds before that
prime breach
right, so there's implied negative time before the timer actually started
prime breach
thanks, just wanted to see if other people thought the same to make sure, i'll solve the actual problem now
.close
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merry prawn
isn't the gradient T evaluated at (1,1,1) = -(2,4,4) ? it seems they divided by 2. i don't think i can just divide by 2 in this case ...
vocal sleetBOT
isn't the gradient T evaluated at (1,1,1) = -(2,4,4) ? it seems they divided by ...
hard atlas
well the direction ends up being the same but yeah they messed up
tawny hollow
Okay so it’s a bit misleading, since it’s not actually equal to it, but they’re in the same direction which is the more important part
merry prawn
ye
because after this they ask
so, the dt/ds is not -3, is -6 for me.
so this secodn part is also wrong.
but I am correct saying that I shouldn't just "simplify" the magnitude of the gradient vector right? I'm scaling it down that way.
for direction yea doesnt matter cause it's normalized.
remote portal
hello could anyone please help me with this question
vocal sleetBOT
hello could anyone please help me with this question
vocal sleetBOT
@remote portal Has your question been resolved?
fickle dock
hello could anyone please help me with this question
You must know from somewhere how many litres is used in average amount of time
remote portal
idk it doesnt mention anything about litres
fickle dock
Is it somehow connected to previous problems you've solved?
What about problems one, 2 and 3?
fickle dock
idk it doesnt mention anything about litres
?
remote portal
Is it somehow connected to previous problems you've solved?
wait ill show u the question before it
this was it
fickle dock
Come on where are number two and one.
fickle dock
wait ill show u the question before it
Where are numbers two and one
remote portal
what numbers two and one
fickle dock
what numbers two and one
?
remote portal
thats 2
thats 1
thats the graph
the answer was 3938 or 3937 but i wanna know how it reached to the answer
fickle dock
Use the ten litres per minute
remote portal
so i multiply 11.15 by 10?
fickle dock
its 11.25
remote portal
why
fickle dock
11 minutes and 15 seconds is 11 minutes. and point 25 One 4th of a minute.
fickle dock
Hint next time actually try reading. I don't wanna sound mean but it's obvious that this question can't be answered because it doesn't have anything about leaders. So the obvious answer is, look for that information somewhere else, most likely in the previous questions
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ivory parrot
need help with this,if i emember correcly you need to multiply 3 with 120
vocal sleetBOT
need help with this,if i emember correcly you need to multiply 3 with 120
@ivory parrot Has your question been resolved?
ivory parrot
<@&286206848099549185>
brazen crest
Is this a proportional expression or something else
fringe smelt
definition of ratio
vocal sleetBOT
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deft flicker
what is the inverted function of this function: f ∶ [−1, +∞) → R ∶ x ↦ 2e(x+1)2
− 3
vocal sleetBOT
what is the inverted function of this function: f ∶ [−1, +∞) → R ∶ x ↦ 2e(x+1)2
...
deft flicker
<@&286206848099549185>
wraith mist
Are you sure that's how the function was written?
I assume it's supposed to be 2e^(2(x+1)) - 3
naive ingot
what is the inverted function of this function: f ∶ [−1, +∞) → R ∶ x ↦ 2e(x+1)2
...
that's weird
wraith mist
Or even $2 e^{(x+1)^2}-3$
deft flicker
lemme sent screenshot its double exponenet
twin meteorBOT
EQUENOS
deft flicker
yeah
wraith mist
okay now it makes sense
deft flicker
its multiple choice and I have four options
wraith mist
Solve $y=2 e^{(x+1)^2}-3$ with respect to x
twin meteorBOT
EQUENOS
wraith mist
You'll get a function of y, which will be the inverse
deft flicker
its dutch a means there is no inverted
the function insnt surjective right so doesnt that mean there is no inverted function ?
wraith mist
There is an inverse, but it's not defined everywhere
It exists because the function is strictly increasing on (-1, +inf)
deft flicker
it the answer then b
wraith mist
yes
deft flicker
k ty
sudden pagoda
How can i get a better understanding of set membership
vocal sleetBOT
How can i get a better understanding of set membership
peak matrix
this is false
sudden pagoda
is there a way i can get to understand that more
also not sure why the tex isnt working
peak matrix
Z is a set of all integers
so if N was in Z, it would mean that N itself is an integer
sudden pagoda
okay great
peak matrix
if everything in A is also in B, then A is a subset of B
if A is in B, then A is a member of B
sudden pagoda
one more thing, the empty set is an element of all sets? or a subset of all sets? or both
peak matrix
one more thing, the empty set is an element of all sets? or a subset of all sets...
is the empty set an integer?
sudden pagoda
no, therefore it is not a member right
peak matrix
no, therefore it is not a member right
yes, so it's not a member of Z
sudden pagoda
but how is it a subset?
peak matrix
so it certainly cannot be a member of all sets
peak matrix
but how is it a subset?
because every thing in {} is also in Z
and if you disagree, tell me something in {} that's not in Z
sudden pagoda
sets are so confusing
sudden pagoda
and if you disagree, tell me something in {} that's not in Z
reductio ad absurdum!
peak matrix
reductio ad absurdum!
sort of, lol
sudden pagoda
i guess i get it, but it feels very unmathematical and not concrete
is there a more concrete way to describe the empty set being a subset of all sets
brisk moss
because every thing in {} is also in Z
oh yea? name some of those things then
peak matrix
oh yea? name some of those things then
Why?
brisk moss
just laugh at my joke and don’t question it pls
peak matrix
is there a more concrete way to describe the empty set being a subset of all set...
Well, it is a subset of every set, because
"everything in {} is also in every set" is true. Because there are no things in {} that could make it false
sudden pagoda
so nothing is part of every set..
sudden pagoda
Well, it is a subset of every set, because
"everything in {} is also in every s...
thats what this says i think
i guess it's just an axiom?
something you just have to know?
sudden pagoda
that means "for all" right?
peak matrix
You can get an idea of why it works like that by considering that there are no counterexamples to it
peak matrix
that means "for all" right?
yeah
sudden pagoda
You can get an idea of why it works like that by considering that there are no c...
i see
peak matrix
there is nothing in {}, so any statement starting with ∀(x in {}) will be true
{1} is a subset of {1, 2} is a subset of {1, 2, 3} is a subset of {1, 2, 3, 4}...
It would also be quite natural to have {} as a start of this chain
sudden pagoda
∀(x in {}) there exists x
is always true for all x ?
peak matrix
∀(x in {}) there exists x
is always true for all x ?
once you use x in one quantifier, you shouldnt be using it in any other
sudden pagoda
{1} is a subset of {1, 2} is a subset of {1, 2, 3} is a subset of {1, 2, 3, 4}.....
ohhhhhh
sudden pagoda
once you use x in one quantifier, you shouldnt be using it in any other
my bad i mistyped
∀(x in {}) there exists y
is always true for all y ?
peak matrix
∀(x in {}) there exists y
is always true for all y ?
well, this is not really a well-formed sentence
even something like:
∀(x in {}) (1 = 2)
would be true
sudden pagoda
oh..
i need to read more..
i guess the empty set is a just a really weird outlier
is that a good way to describe it?
i think i just need to build intuition for it
sudden pagoda
you're awesome thank you so much!
peak matrix
np :)
sudden pagoda
one final thing
peak matrix
it's just something you will have to convince yourself about
sudden pagoda
is N a subset of {Z}
the set continaing the set of all integers
the answer is no right?
peak matrix
the answer is no right?
correct
peak matrix
is N a subset of {Z}
If N was a subset of {Z}, then everything in N would also have to be in {Z}. But the things in N are numbers like 1 and 2, but 1 isn't in {Z}, nor is 2. The only thing in {Z} is Z itself
sudden pagoda
If N was a subset of {Z}, then everything in N would also have to be in {Z}. But...
yes exactly
that makes a lot of sense
.close
vocal sleetBOT
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sinful falcon
help
tropic stone
Use binomial expansion
sinful falcon
ye
fringe smelt
so what is it asking, the coefficient of x^10?
sinful falcon
ye
fringe smelt
Use binomial expansion
then do this
fringe smelt
ahh then expand it by NCR
sinful falcon
whas NCR
fringe smelt
i use the 10c10
this
sinful falcon
wait leme try
fringe smelt
find the correct input and it will yield the solution of part a, and actually similarly for the remaining
sinful falcon
oh thanks
for the denominator do i times or i can cancle
oh nvm
i think thimes
times
<@&286206848099549185>
this is what i got
but the answer is 3360x^10
fringe smelt
but the answer is 3360x^10
hints, 2 exists in (-2/x^2), so you need to take that into account, also, it is not simply 10C10
so you are correct at the first half, x^3 times 6
what will be the second half?
it is (-2/x^2)^k but k is not 10
median mortar
hints, 2 exists in (-2/x^2), so you need to take that into account, also, it is ...
bro i think something is wrong with that question
fringe smelt
bro i think something is wrong with that question
no, the answer is indeed 3360
vocal sleetBOT
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ruby flicker
Hey guys
Do you know any easy way for factoring?
vocal sleetBOT
Hey guys
Do you know any easy way for factoring?
vast shale
there a lot of of different ways
iron parrot
quadratics?
ruby flicker
I mean totally
arctic mantle
some polynomials are irreducible over certain rings
(fancy words to say you can't factor them)
dire torrent
some polynomials are irreducible over certain rings
Fairly sure we can assume the guy will only be working over the field(which is also a ring) of Reals
arctic mantle
Fairly sure we can assume the guy will only be working over the field(which is a...
yeah ik
dire torrent
And also fairly sure any polynomial can be factored over the complex numbers, due to the fundamental theorem of algebra
ruby flicker
And also fairly sure any polynomial can be factored over the complex numbers, du...
Oh
Tnx
ruby flicker
Yeah
dire torrent
Alright, there you have it then
ruby flicker
f(x)=a(x-r1)(x-r2)...
arctic mantle
well then you must also know that there is no definite solution for quintics and above according to galois theory
dire torrent
f(x)=a(x-r1)(x-r2)...
That's essentially it, yeah
arctic mantle
you can also find roots using winding numbers and contour integrals
but it takes a while
vocal sleetBOT
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dire torrent
you can also find roots using winding numbers and contour integrals
That's most likely quite the Overkill though in almost any case
arctic mantle
ik
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sudden pagoda
whats the cardinality of this set?
sudden pagoda
$$ { (x, y) \in \mathbb{N}^2 , : , x^2 + y^2 \leq 100 } $$
twin meteorBOT
adam
arctic mantle
shouldn't be too hard to count the elements yourself i mean
sudden pagoda
oh sorry typo
$$ { (x, y) \in \mathbb{N}^2 : x^2 + y^2 \leq 100 } $$
i know i can still count them, but is there an easier way?
twin meteorBOT
adam
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sudden pagoda
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cursive turret
well, obviously x and y are < (or <=) 10. counting this caees would need less time than waiting and asking for helpers.
vast shale
back
vocal sleetBOT
@sudden pagoda Has your question been resolved?
cedar burrow
i know i can still count them, but is there an easier way?
Over the reals, x^2 + y^2 <= 10^2 is a filled circle. I suppose this is the set of all whole-number dots in the top right quarter of a circle of radius 10. Idk if that makes counting any quicker for you - but I figured it’s nice enough to highlight
Maybe one can use the formula of the area of the quarter circle cleverly here?
vocal sleetBOT
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formal tusk
Hello
formal tusk
Clueless here lol
If i solve it it just leads to two matrixes which provide no solution
wary mantle
If i solve it it just leads to two matrixes which provide no solution
It will lead to the left hand side matrix being equal to the right hand side matrix
So their entries in the same positions have to be the same
formal tusk
This doesn’t give anything though no
Or am i wrong
@wary mantle forgot to tag sorry
formal tusk
Yh its so confusing
wary mantle
$y + 2 \neq y - 1$ for any $y$
twin meteorBOT
Kepe
wary mantle
transpose
wary mantle
transpose
Atleast that's what anyone would mean by that, maybe your course uses it for something else?
Most likely no, right?
ivory cedar
no idea haha
wary mantle
top left and small t
Yeah my book aswell
formal tusk
WA agrees
Yeah asked claude and chatgpt (even tho they aren’t the best ) and nothing lol. Probably a mistake in the exercise
wary mantle
It doesn't have to be a mistake
It perhaps just wants you to notice there is no matrix A
formal tusk
It perhaps just wants you to notice there is no matrix A
Yeah probably i guess, by the way what was that website
formal tusk
Thank you 🙏
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arctic grotto
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arctic grotto
Can someone help me doing just the 4.1? I did not understand
velvet cove
Can someone help me doing just the 4.1? I did not understand
is [[x]] floor function
what is that
ye
u round down
so basically take the right hand limit and take the left hand limit
and compare
arctic grotto
I have to calculate the limit with the maximum integer
velvet cove
I have to calculate the limit with the maximum integer
yes
so what is the limit as x->0 from the right side
it might be better to break it up into $\frac{[[x]]}{x}-1$
twin meteorBOT
Jash
velvet cove
so what do u get if u plug in like .01 for x
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tired sable
If I have a slope in y =mx + b, where m is not a fraction, what does this tell me?
vocal sleetBOT
If I have a slope in y =mx + b, where m is not a fraction, what does this tell m...
tired sable
Say y = 5x - 7
What is the 5 telling me?
Should I read it as 5/1 so going up 5, going right 1
rocky lake
Say y = 5x - 7
The slope is 5 up and 1 right
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tame river
Not sure if my answers are right
vocal sleetBOT
Not sure if my answers are right
vast shale
Not sure if my answers are right
How'd the + become a - from line 1 to 2?
tame river
How'd the + become a - from line 1 to 2?
?
vast shale
(x+3)ln(3) somehow became xln(3)-3ln(3)
tame river
oh
heavy raft
hey mathcord i need help with simplifying complex numbers
vocal sleetBOT
hey mathcord i need help with simplifying complex numbers
heavy raft
I need to know how do you simplify complex numbers?
I read something that no matter what it is you divide that number by 4 then based on the remainder you get a number
is that right?
Take i^243 = -i since the remainder of 243/4 is 3
prisma rain
yes, $i^n = i^{n \text{ remainder } 4}$
twin meteorBOT
kaue
prisma rain
keep in mind this is a property of $i$ specifically, not complex numbers in general
twin meteorBOT
kaue
heavy raft
oh okay
heavy raft
Take i^243 = -i since the remainder of 243/4 is 3
but is this correct?
prisma rain
but is this correct?
it is
heavy raft
okay how do it do something like 6 - 2i / 2 - 3i
prisma rain
to divide complex numbers, multiply the numerator and denominator by its conjugate (the conjugate of a complex number is itself but with the sign of the imaginary part swapped), so in this case you need to multiply by (2 + 3i)
the conjugate of the denominator*
heavy raft
and 6 + 2i is what you multiply the numerator by
prisma rain
6 + 2i is the numerator and 2 - 3i is the denominator, you need to multiply both by the conjugate of the denominator
heavy raft
oh okay multiply both by the conjugate of the denominator
prisma rain
this is because (a + bi)(a - bi) = a² + b² so the denominator turns into a real number
prisma rain
oh okay multiply both by the conjugate of the denominator
yes
it's kinda like rationalizing the denonimator, if you heard about it
heavy raft
.close
vocal sleetBOT
vocal sleetBOT
Available help channel!
eternal grail
vocal sleetBOT
eternal grail
i accidently deleted my original one
eternal grail
But i think ur reason is correct
What about my answer
sleek swan
Ya
sleek swan
Did u press angle subtraction
sleek swan
cuz it says it dosent have vertical angles
Is the input in box angle subtraction postulate
sleek swan
u have to press
Angle subtraction
I think
Cuz the reason is not correct
Currently
eternal grail
sleek swan
Only other reason i can think is base angle of isoceles
sleek swan
With the base angle of an isoceles triangle
I think thats the answer
Cuz 180=40 +2x
eternal grail
sleek swan
?!
sleek swan
I dont think so
hidden turret
i feel so congruuent rn
eternal grail
i feel so congruuent rn
?
sleek swan
i hate these types of questions where it has proof
But for second question is there a option with similar triangles
or ratio
eternal grail
@sleek swan yo can u help with the other question
sleek swan
Ya the second ine
sleek swan
Hm
hidden turret
similar enough or something
sleek swan
Similar triangles
eternal grail
@sleek swan what option is that
hidden turret
i feel like you would say ae silly equals ac idk tho dont ask me
sleek swan
Write the 2 angles
eternal grail
sleek swan
There the same triangle bur the ratio is different
eternal grail
eternal grail
What grade r u
10
hidden turret
do you guys not know how to write angles correctly
eternal grail
do you guys not know how to write angles correctly
i missed this whole lesson bc i wasn't in
hidden turret
wait can you only do it once
eternal grail
eternal grail
wait can you only do it once
not even sure
eternal grail
?
hidden turret
wait a second
the angles are the same
in that corner
EAD and CAB are the exact same
hidden turret
they all correspond to each other
set the reasoning to cptpc
and say <ACB = <AEC
with the funny equals sign tho
eternal grail
what for the reason
hidden turret
what are the possible reasons ?
hidden turret
Corresponding parts of congruent triangles are congruent
CPCTC
wait this is due to similarity
not congruence
hidden turret
ohh
eternal grail
@hidden turret
hidden turret
its reflecive property i think
hidden turret
oh yay it worked
if those two angles are the same
that means the last one has to be the same
hidden turret
<x = <y
hidden turret
i think its maybe just try saying triangleXYZ = triangleTUV
it should work because of two angles already
then triangle ABC = ADE
which should just solve it
eternal grail
hidden turret
XYZ TUV was just a reference to the triangle you needed to use ABC and ADE
in the solution
hidden turret
what does the classify a triangle do?
eternal grail
what does the classify a triangle do?
?
eternal grail
not sure
hidden turret
check what it does
eternal grail
hidden turret
Since DE is parallel to BC, angles ADE and ABC are congruent.
Angles DEA and CBA are also congruent due to corresponding angles formed by parallel lines.
Angle A is common to both triangles.
ok im going to sleep now
vocal sleetBOT
@eternal grail Has your question been resolved?
vocal sleetBOT
@eternal grail Has your question been resolved?
grand frigate
$\lim_{x \to 0} \frac{\sin^2(x) + x \sin(x)}{1 - \cos(x)}$
vocal sleetBOT
$\lim_{x \to 0} \frac{\sin^2(x) + x \sin(x)}{1 - \cos(x)}$
twin meteorBOT
Fω 2.718ℓ
grand frigate
I don't know how to proceed
wait ima send the original question as well
This is the original question
I multiplied by conjugates and used the half angle rule for the denominator
vast shale
l'opital is not allowed?
grand frigate
it's allowed
vast shale
well?
vast shale
leave it as sinxcosx
grand frigate
[
\lim_{x \to 0} \frac{2\sin(x)\cos(x)+ \sin(x) + x \cos(x)}{\sin(x)}
]
twin meteorBOT
Fω 2.718ℓ
vast shale
and since you have a sinx in the denominator also you can cancel it out
grand frigate
but that would leave me with an xcos(x)/sin(x)
vast shale
you know that sinx / x is 1
vast shale
either you could do l'optial again
since its a 0/0 form
or
you could get x to the denominator giving you cosx / (sinx/x)
grand frigate
ah... okay i get it
thanks alott
t!rep @vast shale
welp
it doesnt work anymore?
vast shale
whats that?
vocal sleetBOT
vocal sleetBOT
Available help channel!
vast shale
Can I ask a math question but the subject is Chemistry?
vocal sleetBOT
Can I ask a math question but the subject is Chemistry?
pine hull
Can I ask a math question but the subject is Chemistry?
You can, if someone knows they will respond
vast shale
Okay
I don't know how to identify equations regarding Gas Laws.
Boyle's Law
Charles' Law
Gay-Lussac's Law
Ideal Gas Law
Dalton's Law of Partial Pressure <- Idk if this is a gas law
Can someone help me?
brazen crest
What exactly don't u know
tawny nacelle
what do you mean by "identify equations"?
vast shale
what do you mean by "identify equations"?
Like there are questions like it could mix up and I have to find out which law is being used???
fringe smelt
I don't know how to identify equations regarding Gas Laws.
Boyle's Law
Charles'...
Ideal Gas law is combination of all three laws above, dalton law should be different from of those you have mentioned but more oftenly seen in chem
tawny nacelle
ideal gas is a generalization of the first three yes
but uhh, the first three are usually easier for students to use
tawny nacelle
Like there are questions like it could mix up and I have to find out which law i...
you always always always look at your givens
which variables are you given values for? which variables do you need to solve for?
vast shale
Can't we just go by order?
I know Boyle's law is when pressure is up temp goes down and temp goes up pressure goes down
tawny nacelle
answering these two questions will help you identify which equation to use
vast shale
What I understand during an quation is
Boyle's Law is looking for anything new like new pressure, new temp
Charles' Law is looking for any increase or decrease
and aiueghfundfikjcfffubxkcvj ,mmaihbudvhkcx
I DON'T GET IT
tawny nacelle
nono
Boyle's law tells you how the pressure changes if the volume changes, and vice versa
vast shale
Charlies' Law?
tawny nacelle
Charles' law tells you how the volume changes if the temperature changes, and vice versa
Gay-Lussac's law tells you how the pressure changes if the temperature changes, and vice versa
fringe smelt
In other words, it actually depends on which variable is fixed. All three laws have a corresponding fix variable.
fringe smelt
Charlies' Law?
also i think it is charles law lol
vast shale
Charlies' Law?
tawny nacelle
why Charles' law?
vast shale
They have the same pressure and temperature?
tawny nacelle
Charles' law concerns the relationship between volume and temperature as one of them changes
in this problem, the temperature is always 25C
it's not changing
vast shale
but..?
fringe smelt
tawny nacelle
take a close look at what is changing in the problem
the pressure goes from 1atm to 2.5atm
and the problem wants you to find how the volume changes
for a fixed temperature of 25C 
vast shale
I don't get it
tawny nacelle
Boyle's law says that if you have fixed temperature, the product of a gas' pressure and volume is constant (P_1 * V_1 = P_2 * V_2)
we have a changing pressure in this problem, and one of the known volumes
vast shale
What about Charlie's law?
vast shale
Why is Charlie's law an incorrect answer?
tawny nacelle
What about Charlie's law?
this one says that if you have a fixed pressure, then the quotient of the volume by the temperature is constant (i.e. V_1/T_1 = V_2/T_2)
tawny nacelle
Why is Charlie's law an incorrect answer?
it's incorrect because the pressure is not fixed in this problem, so Charles' law doesn't apply
there's always three variables that can change (volume, temperature, pressure); any single one of these laws is concerned by how two of them change when the last one is held fixed
vast shale
stolen from the internet
So..
If a gas at 25.0*C occupies 3.60 liters at a pressure of 25.0 atm. <question>?
vast shale
So..
If a gas at 25.0*C occupies 3.60 liters at a pressure of 25.0 atm. <questi...
This is how Charlies' Law represent in an equation?
tawny nacelle
This is how Charlies' Law represent in an equation?
I don't understand what you mean 
tawny nacelle
write down our givens!!!!!
just do this, I promise it'll make your life so much easier
vast shale
I don't get the difference of Boyle's Law and Charlie's Law in an equation
vast shale
stolen from the internet
P1V1 = P2V2
(25.0*C) (1 atm) = P2 (2.50 atm)?
wet solstice
2.50 atm is pressure
tawny nacelle
25.0C is temperature, and 2.50atm is a pressure
but yes that is the correct equation
you just plugged in the numbers strangely
vast shale
But it says volune not temp....?
wet solstice
2.5 atm is not a volume
vast shale
Then.. what is volume? the liters?
tawny nacelle
yes, but you plugged in the temp for V_1, and then the pressure for V_2
tawny nacelle
Then.. what is volume? the liters?
yes
volume is in litres
V_2 is unknown; it is what you want to solve for
V_1 is known
vast shale
P1V1 = P2V2
(1 atm) (3.60 liters) = (2.50 atm) V2?
vast shale
1 atm x 3.60 liters / 2.50 atm = V2
1.44 liters = V2
vast shale
Okay now I understand Boyle's law a bit how about another one just to make sure?
tawny nacelle
tawny nacelle
<:FS_Acry:805128160881803294>
no crying! >.<
you are capable of doing this, I promise
vast shale
Charles' Law?
vast shale
The givens are Volumes and Temperatures
tawny nacelle
that's correct!
vast shale
AHHH I GOT ITTT
tawny nacelle
vast shale
V1/T1 = V2/T2
900 ml/27*||.||C = V2/132C
900ml x 132*||.||C/27C = V2
4400 ml = V2
vast shale
Why?
vast shale
Oh
tawny nacelle
whereas for Kelvin, 0K means that all molecules stop moving, so the gas isn't really a gas anymore
0K is not possible to reach
0C is haha
vast shale
Oh okay
tawny nacelle
and if we were dividing by 0, we'd be in trouble!
vast shale
Formula for Kelvin *C + 273 right?
vast shale
V1/T1 = V2/T2
900 ml/300 K = V2/405 K
900ml x 405 K/300 K = V2
1215 ml = V2
twin meteorBOT
The current time for ahigherdesire is 03:18 AM (EDT) on Sun, 27/10/2024.
tawny nacelle
vast shale
Okeh
vast shale
Ideal Gas Law?
tawny nacelle
mm, you probably could solve it with IGL, but there's a better choice
IGL is probably too general to solve this quickly
vast shale
Charles' Law?
tawny nacelle
take a look at your givens
you have two pressures, and a temperature
you want to find a second temperature
vast shale
Gay-Lussac's Law
tawny nacelle
take a look at your givens
this is sooooo important to do for problems like these, btw
the givens and required variable always tell you what equation to you
vast shale
15 atm
16 atm
25 C - > 298 K
P1/T1 = P2/T2
(15 atm) (298 K) = (16 atm) T2
(15 atm) (298 K)/(16 atm) T2
279.375 K = T2
THIS IS SO EASYYY I JUST NEED TO UNDERSTAND AND MEMORIZE THE PROBLEM YAHOOOO
tawny nacelle
P1/T1 = P2/T2
(15 atm) (298 K) = (16 atm) T2
(15 atm) (298 K)/(16 atm) T2
279.375 K = T2
where did the division sign go? 
vast shale
I forgot eheh
15 atm
16 atm
25 C - > 298 K
P1/T1 = P2/T2
(15 atm) (298 K) = (16 atm)/T2
(15 atm) (298 K)/(16 atm) = T2
279.375 K = T2
tawny nacelle
uwah
vast shale
But what I did is correct
tawny nacelle
no 
vast shale
WHAAA
tawny nacelle
P1/T1 = P2/T2
(15 atm) (298 K) = (16 atm)/T2
(15 atm) (298 K)/(16 atm) = T2
279.375 K = T2
this is not the correct algebra 
tawny nacelle
you treated it as if it was 16atm * T_2, and divided both sides by 16atm
but it's 16atm/T_2
tawny nacelle
no!!!
you are not dumb
give it one more go 
you're capable
everyone struggles with learning things for the first time
don't feel like you're bad because you're struggling
it's very normal to struggle
vast shale
15 atm
16 atm
25 C - > 298 K
P1/T1 = P2/T2
(15 atm) (298 K) = (16 atm)/T2
(15 atm)/(298 K) x (16 atm) = T2
0.80536912751 K = T2
tawny nacelle
vast shale
WHATTTTT
tawny nacelle
P1/T1 = P2/T2
(15 atm) (298 K) = (16 atm)/T2 (missing division symbol)
(15 atm)/(298 K) x (16 atm) = T2 (algebra is not right
0.80536912751 K = T2
,, \frac{15\text{atm}}{298K} = \frac{16\text{atm}}{T_2}
twin meteorBOT
higher!
tawny nacelle
**higher!**
you have T_2 in the denominator
tawny nacelle
I need to remove atm
yes, but you can remove it in the final step
there's no rush
in the final step, the atm's will cancel out
tawny nacelle
**higher!**
just try rearranging this for T_2, as you normally would
I've seen you do these kinds of rearrangements before, so I know you can do it!
vast shale
I don't get it
tawny nacelle
tawny nacelle
**higher!**
do you mind if I show you where to go?
vast shale
yes
tawny nacelle
,, \frac{15\text{atm}}{298K} = \frac{16\text{atm}}{T_2} \ \frac{T_2 \cdot 15\text{atm}}{298K} = 16\text{atm}
twin meteorBOT
higher!
vast shale
I don't get it
tawny nacelle
we're just multiplying both sides by T_2 to get it out of the denominator
vast shale
why?
tawny nacelle
because when the variable we want to solve for is in the denominator, it's hard to solve for. so we need to get it out of there, and only way to do that is by multiplying both sides by it
vast shale
then we put it at the other side?