yes
#help-27
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eternal adder
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upper schooner
Have you heard of the Lambert W function 
opaque folio
eternal adder
yes but is there another way to do it?
yes this is a way
is there another way?
bcz calculators cant compute the function
warm breach
you can apply taylor series expansion for e^x
warm breach
(at last step)
eternal adder
interesting
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viral rapids
how to do 13
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how to do 13
viral rapids
viral rapids
ye
drifting hearth
ur equations were written with the assumption that you’d start at x=-2
ur line doesn’t have to go from left to right
it can go right to left
viral rapids
ye idk how to flip it
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main relic
Whats up guys
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Whats up guys
main relic
I need someone to verify my solution sketch on:
USA TST 2018/2
It’s not rigorous, it’s just the sketch of the solution but here it is:
think about the numbers on a grid, i’m taking the average of the cell below and left to me.
Then thing of f(x-1,y) and f(x,y-1) like dots on the number line. F(x-1,y-1) reflected about f(x-1,y) and f(x,y-1) gives f(x-2,y) and f(x,y-2) respectively. If f(x-1,y-1) is not the midpoint of f(x-1,y) and f(x,y-1), then by pick the one it is further away from. Wlog is f(x-1,y). Then, f(x-1,y-1) the distance between f(x-1,y-1) and f(x-2,y) is greater than f(x-1,y) and f(x,y-1). If f(x-1,y-1) is the midpoint of f(x-1,y) and f(x,y-1), then reflecting blah blah gives same distance. So we can keep repeating this problem and find these pairs of diagonal numbers who’s distance are nondecreasing.
Now, we prove that if the distance is nonzero, then the distance cannot stay constant indefinitely. Just look at the fucking image i am lazy to type more. Ok so now we’ve proven that there are no diagonal thingies that are different. So the entire diagonal is same. So the entire board is same. Therefore, f = c where c is a constant in [0,1]
Actually
It’s better conveyed on a picture
Let me draw it out
With equality iff the point in the middle is the midpoint
main relic
But then here we prove that it cannot be all midpoints, because someone will go out of bounds as well
So there cannot be a “diagonal pair like that” that has distance nonzero
Which is just another of saying “the entire thing is fucking constant”
Aka f = c where c is a constant [0,1]
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wet orbit
What does this sentence mean?
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What does this sentence mean?
hollow ice
So if its 1,234 you dont call it one thousand and two hundred and thirty four
just callit one thousand two hundred thirty four
still carbon
Topic : numerical methods - fixed point iteration
I just can't understand how they take g(x) without considering the interval in which the root lies. They also didn't check for the condition if |g'(x)|<1.
rustic pagoda
yes ideally you should check for that
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still carbon
Thats what I don't understand
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still carbon
. reopen
meager elk
- If the equation x ^ 2 - 4x - (3k - 1)|x - 2| - 2k + 8 = 0, k \in R has exactly three distinct solutions, then k is equal to
devout snowBOT
8. If the equation x ^ 2 - 4x - (3k - 1)|x - 2| - 2k + 8 = 0, k \in R has exactl...
meager elk
Anyone gonna try this ?
Please solve and explain all the steps 🙏
?
<@&286206848099549185>
tepid fulcrum
first we need to solve the equation, just ignore the k variable for now
how would we do that?
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@meager elk Has your question been resolved?
meager elk
first we need to solve the equation, just ignore the k variable for now
Did you try it
tepid fulcrum
yes
meager elk
What’s your answer coming
tepid fulcrum
have you tried it already?
tepid fulcrum
Ik the solution but I can’t understand it
the solution for k or for x
tepid fulcrum
i don't really understand that either but i would do it a different way which is think is more intuitive
what i would do is just solve the equation and then take the discriminant which determines how many solutions the equation has
and because you're dealing with modulus
or absolute value
you have two equations
meager elk
Yeah
tepid fulcrum
for 1 equation discriminant has to be >0, for the other one it has to be =0
or the other way around ofc
meager elk
One hint is that they said
One root is equal to 0
And other 2 roots are positive
Didn’t understand this stamens
Stantmenr
Statement ****
tepid fulcrum
that's what i just said
you're familiar with discriminants right?
the discriminant is the part under the square root
so b²-4ac
meager elk
Yeah
Bro I know everything about equations
This question is just not it
- I’m half asleeep so brain isn’t braining
Thank you for the help, If you find the solution please write it with explanation please 🙏 I’ll check when I wake up .
Thank you.
For your info, the answer to question is k=2
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upbeat anvil
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upbeat anvil
How time is 31 s?
dense jay
have you tried to do it
upbeat anvil
Yes i did. For the motorcycle the initial velocity is zero and the final velocity is 45 and acceleration is 3
dense jay
the final velocity is not 45
if it were it would never catch up at all
how could you describe how far the car has travelled after passing the trooper?
upbeat anvil
It did not mention anything
upbeat anvil
how could you describe how far the car has travelled after passing the trooper?
Sorry idk
dense jay
you know the speed of the car
upbeat anvil
Yeah do i need to fine distance in terms of t?
dense jay
yup
upbeat anvil
Still it gives like t=(45/3) = 15
dense jay
no, the motorcycle is not aiming for 45m/s i said that
upbeat anvil
If i use s = ut + 0.5at^2
upbeat anvil
no, the motorcycle is not aiming for 45m/s i said that
Umm ok
dense jay
If i use s = ut + 0.5at^2
you will need that equation, yeah, just not yet
if the car is travelling at 45m/s
and t is the seconds after it passes the trooper, how far does it travel in t seconds
upbeat anvil
45t?
upbeat anvil
I used this
45t= (0.t) + 3(t)^2
upbeat anvil
how about the motorcycle, noting it only sets off a second later
Yes
dense jay
I used this
45t= (0.t) + 3(t)^2
this is close
upbeat anvil
Then for the motor cycle it will be 45(t-1)?
dense jay
you have the right ideas just in the wrong ways
dense jay
I used this
45t= (0.t) + 3(t)^2
lets go from this
its ut+0.5at^2 right, the general formula
dense jay
I used this
45t= (0.t) + 3(t)^2
here you forgot the 0.5
upbeat anvil
Oh sorry I forgot
dense jay
Then for the motor cycle it will be 45(t-1)?
and then need to apply the t-1 here on the right side, not the 45 though
and you should be good to go
upbeat anvil
Oh thankss
upbeat anvil
and then need to apply the t-1 here on the right side, not the 45 though
Okay i got it now thanks
.close
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dense jay
np
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winter wave
For the potentials in this question my answer was k/2 x^2 + c1 and -gx + c2. Do you think its neccesary to find these constants?
winter wave
If you get back to me please @ me :) thank you
flint roost
i want to learn meth
lusty sapphire
i want to learn meth
flint roost
<#488120190538743810>
you want me to help you to how to get help?
lusty sapphire
For the potentials in this question my answer was k/2 x^2 + c1 and -gx + c2...
I don't think the constants are necessary. They're usually implied zero at some reference frame
carmine gorge
For the potentials in this question my answer was k/2 x^2 + c1 and -gx + c2...
I'm thinking no, the question didn't indicate that
actually it looks more like a general question which always have its results containing such constants
winter wave
I don't think the constants are necessary. They're usually implied zero at some ...
hmmm, so in this question particularly shall i assume the constants are 0?
flint roost
1+1+2=5
4=4
45=55
20 = 25
i thoght that i cooked but i actually burnt
winter wave
what are u yapping about
lusty sapphire
1+1+2=5
4=4
4*5=5*5
20 = 25
i thoght that i cooked but i actually burnt
Please go to #discussion if you want to troll about.
flint roost
Please go to <#268882317391429632> if you want to troll about.
alr
lusty sapphire
hmmm, so in this question particularly shall i assume the constants are 0?
Yeah that's fine. For gravitational and spring energy, that's usually how it goes
winter wave
I'm thinking no, the question didn't indicate that
actually it looks more like a...
hmmm okay, im just making sure there is no way to get a value or something for those constants
flint roost
x3+y3+z3=k
winter wave
Yeah that's fine. For gravitational and spring energy, that's usually how it goe...
ahh i see, thank you :)
lusty sapphire
Potential energy is always relative to some reference frame. For g, it's reference is the ground, and for springs, its reference is the rest position
lusty sapphire
x3+y3+z3=k
If you have legitimate questions, please open your own help channel, as described in #❓how-to-get-help
winter wave
Potential energy is always relative to some reference frame. For g, it's referen...
ohhh okay i shall keep that in mind
im gonna close now if thats okay
.close
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lusty sapphire
<@374795910032523266>
Yes. But it is not an available channel. Ask legitimate questions in any of these
lusty sapphire
<#907022703230345237>
Do not advertise your own channels
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flint roost
Yes. But it is not an available channel. Ask legitimate questions in any of thes...
you know abou moderation how to give people limit access
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you know abou moderation how to give people limit access
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@flint roost Has your question been resolved?
hardy imp
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eager nova
What did u try?
eager nova
What figures u see there?
This exercise is solved answering this
hardy imp
a triangle inside of another triangle
eager nova
And the other?
hardy imp
a quadrilateral ?
eager nova
What is the sum of angles on a quadrilateral?
hardy imp
is it 360
eager nova
I think you can already solve this
eager nova
!done
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eager nova
So what is 360 + 113 -360
hardy imp
113
hardy imp
i mean i guess
silver crane
Quick question:
Definition 0.3.19. Given a set 𝐴, a binary relation on 𝐴 is a subset R ⊂ 𝐴 × 𝐴, which are
those pairs where the relation is said to hold. Instead of (𝑎, 𝑏) ∈ R, we write 𝑎 R𝑏.
Take 𝐴 = {1, 2, 3}. Consider the relation ‘<’, does that mean '<' ⊂ 𝐴 × 𝐴 where '<' = {(1,2),(1,3),(2,3)}
stone stump
yes
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restive river
pp
safe fractal
Ah yes, the most difficult problem of them all
safe fractal
Mind sending a screenshot of it instead?
restive river
sure
restive river
its an https but sure
what is happening
where did point D come from and E
whats this shape
this is all i understood from the question
crystal obsidian
huh?
wispy bronze
It is asking to find the volume between the two surfaces, but I dunno how to do it, probably with spherical or cylindrical coordinates. Can anyone help? (The answer of "c" is 7π/6 and the answer of "d" is π/2√2)
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It is asking to find the volume between the two surfaces, but I dunno how to do ...
@wispy bronze Has your question been resolved?
wispy bronze
Ok, c is correct actually, but I have no idea for "d"
wispy bronze
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tame nova
i have no idea how to solve this
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i have no idea how to solve this
tame nova
mild fog
hey guys
i have the amc 12 coming up
from now to then
is it possible to qualify for AIME
tame nova
what?
mild fog
i have done all of the sections on alcmus except for intermediate alg and precalc
i plan to finish intermediate calc by the end of the month
is it possible
and what are tips and tricks
tame nova
i think you'd need to find an unoccupied help channel
tame nova
that's fine
mild fog
just go to <#903486478049488936> or <#907022703230345237> while they are free
alr thanks
velvet rock
what have you tried @tame nova
tame nova
i don't know how 3d vectors work
stark shuttle
Hello
stark shuttle
What about the norm of the dot product of two unit vectors?
upper schooner
"norm of the dot product" 
solar goblet
What about the norm of the dot product of two unit vectors?
?
misty crest
well what if you had the unit vectors i and j
stark shuttle
"norm of the dot product" <:hmmcatfone:849254980812013639>
||v • v||
misty crest
the dot product gives a scalar
solar goblet
dot product produces a scalar
stark shuttle
Yes
upper schooner
As above ^
solar goblet
what you meant is probably absolute value?
stark shuttle
I guess
stark shuttle
I'm trying to solve this question
I know the answer is e)
But I want to know the result
upper schooner
(you should hopefully know what you can do with scalars in norms...)
upper schooner
Hmmm, u.v^2 is very sus notation, and not great 
stark shuttle
How should I change it
upper schooner
It's find that $proj_{\vec{v}} \vec{u} = \frac{ \vec{u}\cdot \vec{v} }{ \norm{\vec{v}}^2 } \vec{v}$, and you can take the norm of that as is
woven radishBOT
@upper schooner
stark shuttle
?
upper schooner
As in, this part isn't correct, so leave that for now
stark shuttle
Oh?
misty crest
the left side produces a scalar which is then multiplied by the vector v
upper schooner
What you can do, noticing that these are scalars, is try to work out the expression
[ \norm{proj_{\vec{v}} \vec{u} } = \norm{ \frac{ \vec{u}\cdot \vec{v} }{ \norm{\vec{v}}^2 } \vec{v}} ]
from there
woven radishBOT
@upper schooner
upper schooner
And there are many things I could say about the notation u.v^2 (that it's slightly ambiguous, that squaring individual vectors, or "multiplying" them, doesn't make sense...)
stark shuttle
And there are many things I could say about the notation u.v^2 (that it's slight...
How about ||v||^2
upper schooner
That is fine as it is, you're squaring a scalar
As would something like (u.v)^2, that's squaring a scalar, but u.v^2 could imply multiple things...
stark shuttle
So u||v||^2 is the answer?
upper schooner
Erm, no 
stark shuttle
I don't understand
u • v is a scalar
||v||^2 is just one
So that means ||u • v • v||
But since it's a scalar
We don't need the abs
misty crest
how are you taking a dot product with three vectors?
stark shuttle
What does that emoji mean
upper schooner
You can't take the dot product of three vectors like that 
stark shuttle
Oh wait
misty crest
dot product is between two vectors
stark shuttle
I see what you guys mean
misty crest
producing a scalar
upper schooner
Anyways, a new question, do you know how to deal with $\norm{\alpha \vec{v}}$, where $\alpha$ is a scalar?
woven radishBOT
@upper schooner
stark shuttle
\||(u • v )• v\||
So then this is answer, no?
upper schooner
How would you move it out?
stark shuttle
allvll
upper schooner
So then this is answer, no?
And be careful, that could be taken to mean the dot product of three vectors, as per our previous complaint
stark shuttle
Can't I distribute them
I thought dot products were associative
Or was that for matrices
upper schooner
Probably matrices you're thinking of 
woven radishBOT
@upper schooner
stark shuttle
Okay
upper schooner
An absolute value gets introduced when you take the scalars out
stark shuttle
Ohhh
upper schooner
What you can do, noticing that these are scalars, is try to work out the express...
Anyways, remember how I said that this is a scalar, right?
upper schooner
Almost that, $\frac{ \abs{ \vec{u} \cdot \vec{v} } }{ \norm{ \vec{v} }^2 } \norm{ \vec{v} }$
Urgh can't be bothered 
stark shuttle
Doing Latex in Thursdays be like
woven radishBOT
@upper schooner
upper schooner
There we go 
stark shuttle
Why not just consider the denom as 1?
upper schooner
Anyways, you can simplify that, I'm sure 
stark shuttle
Or are we trying to do something else
stark shuttle
|u • v|\||v\||?
Because what you did in Latex equals this, no?
upper schooner
Oh, they do tell you that it's a unit vector, don't they
misty crest
mhm
upper schooner
Didn't notice that
upper schooner
|u • v|\||v\||?
In which case, also notice that you have another norm{v} there too, and what v being a unit vector means again
upper schooner
In absolute value, |u.v|
misty crest
Or is it just u
no
upper schooner
That works out at most to be u, but needn't be equal to it
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serene rampart
anyone help
devout snowBOT
anyone help
solid osprey
since AEB is simmilar to CFB, can you conclude AB=BC?
serene rampart
i mean thta's given?
also it's not similar, it's congruent
oh my lord nvm i'm a fucking dumbass
.close
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solid osprey
whoops :p
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empty mountain
guys is CE just 18
devout snowBOT
guys is CE just 18
empty mountain
my brain is absolutely not braining
potent venture
guys is CE just 18
have you tried to make a diagram of this
if you want a starting point, then make a triangle ABC, and the point A is out of the circle, you are correct that CE is 18
empty mountain
yes
empty mountain
if you want a starting point, then make a triangle ABC, and the point A is out o...
yes to the above
thanks bro
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inner ibex
excuse me
lost laurel
Hint:-Multiply and divide by 2
stark shuttle
What about x when it's 5π/6
inner ibex
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rugged jewel
Where does this n come from?
devout snowBOT
Where does this n come from?
rugged jewel
Basically they are expanding the formula for the variance
visual hazel
Basically they are expanding the formula for the variance
you're summing up n xbars
xbar + xbar + xbar + ... n times, which is equal to n times xbar
rugged jewel
Okay but why is 2*x_bar not 2n x_bar then?
visual hazel
why would it be
visual hazel
yep
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serene sorrel
i would assume this is a relatively common problem, but i cannot find anything about it online. If i have an N-pendulum, and i choose a point within its range, how would i go about solving the required angles for each joint for the tip of the pendulum to be at that point? Would this extend into 3D for say, a robot arm? If not, how could i solve this in 3D?
devout snowBOT
i would assume this is a relatively common problem, but i cannot find anything a...
serene sorrel
if this is a named problem, just getting a name/terms to research would be great
devout snowBOT
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serene sorrel
.reopen
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@serene sorrel Has your question been resolved?
serene sorrel
Turns out for 2D what i was looking for is convex polygon equations and for 3D what i was looking for is Inverse Kinematics
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cold bone
How to do this problem?
Could someone give me the method to answer it?
urban horizon
$\sum_{r=1}\infty\frac{4r^2 - 2}{4r^4 + 1}
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soft umbra
soft umbra
How to do this problem?
Could someone give me the method to answer it?
Do you have any idea in the first place?
cold bone
Do you have any idea in the first place?
zero idea
cold bone
How about transforming C into 180-(A+B)
okay, I'll try
late sail
I would just use the method guess and hope for the best
You could notice the formula cosx^2 + sinx^2 = 1
Which would be satisfied if A is equal to B and C would be a 90 degree angle
Which would then give you your answer
cold bone
I would just use the method guess and hope for the best
You could notice the fo...
My teacher solved it that way
but it seems really strange
cold bone
So A
it is also C but the problem is that, it doesn't make much sense to me(the whole method of solution)
late sail
Its just about comparing it to trig identities you do know in this case sin^2 + cos^2 = 1
cold bone
It’s kinda technical
you have the same way ig?
cold bone
My process requires more observation
like what type?
cold bone
Its just about comparing it to trig identities you do know in this case sin^2 + ...
thank you Sir too
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cold bone
is bro back with trick ques
such a strange question
cold bone
that's what she said
she?
warm breach
it's a meme
cold bone
it's a meme
ah okok
I am kinda socially inactive
warm breach
yup np
gentle crow
How to do this problem?
Could someone give me the method to answer it?
Put random values of angles,then u can solve this in seconds
cold bone
Put random values of angles,then u can solve this in seconds
random values?
like
?
.reopen
devout snowBOT
✅
gentle crow
random values?
Suppose the answer is right angle triangle either A or B else C equals 90 degree and sum of others =90
soft umbra
Me interested too
gentle crow
For equilateral put all angles 60 ,if the equation satisfy then ____
For isoscales put one 30, another 45 etc
Hope u understood
cold bone
For equilateral put all angles 60 ,if the equation satisfy then ____
like more of a hit-n-trial method
cold bone
Hope u understood
yeah I got it
gentle crow
Yaaaaaa bro
cold bone
thank you bro
cold bone
That’s what I said
that's also thijs said😂
everyone has same method
just different way to convey
gentle crow
everyone has same method
There are a lot of methods bro to solve a trigonometric equation
But this was small
cold bone
either way thanks y'all
polar chasm
Suppose the answer is right angle triangle either A or B else C equals 90 degree...
hmm, what if D was the right answer?
gentle crow
👍
gentle crow
hmm, what if D was the right answer?
If equation is not satisfied by those 3 options,then D
cold bone
!done
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polar chasm
If equation is not satisfied by those 3 options,then D
So you checked that if a triangle is right, then it satisfies the equation
polar chasm
but what if the equation implied that the triangle is right, or has 45° angle
then A wouldnt be the right answer
and you wouldnt've known that
by your approach
gentle crow
but what if the equation implied that the triangle is right, or has 45° angle
Are u joking
If triangle is satisfied by any value like c=90,a=30&b=60
Then for all values,it will be right angle triangle
That's why we use a equation
I think you need to work on fundamentals
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polar chasm
I think you need to work on fundamentals
Eh
polar chasm
You proved this
gentle crow
Lol help channel opened
polar chasm
if the triangle is right, then the equation holds
but the question is asking you to prove this:
if the equation holds, then the triangle is right
I'll propose another question
gentle crow
I mean to say that ,there is only one fundamental equation of parabola, y=4ac ,but it satisfies all parabola
gentle crow
I mean to say that ,there is only one fundamental equation of parabola, y=4ac ,b...
Same logic works here
polar chasm
If in a triangle ABC, cos^2(A) + sin^2(A) = 1, then the triangle is
A) Right
B) Equilateral
C) Isosceles
D) None of these
now by your approach
we would check whether A works
and it actually does
but the statement
"If in a triangle ABC, cos^2(A) + sin^2(A) = 1, then the triangle is right" is false
gentle crow
If in a triangle ABC, cos^2(A) + sin^2(A) = 1, then the triangle is
A) Right
B)...
By this we cannot tell type of triangle
polar chasm
By this we cannot tell type of triangle
correct
and how can you be sure that by this we can?
gentle crow
If in a triangle ABC, cos^2(A) + sin^2(A) = 1, then the triangle is
A) Right
B)...
That's why this question is never asked on books
polar chasm
and how can you be sure that by this we can?
What if this equation was right only for triangles which either have 90° angle or 45°angle
gentle crow
and how can you be sure that by this we can?
Ohh bro, we can say here because 3 angles are given
polar chasm
uh
If in a triangle ABC, cos^2(A) + sin^2(A) + cos^2(B) + sin^2(B) + cos^2(C) + sin^2(C) = 3, then the triangle is
A) Right
B) Equilateral
C) Isosceles
D) None of these
Better?
gentle crow
What if this equation was right only for triangles which either have 90° angle o...
Lol ,bro u are wrong ,cos(180)=(-1)
Hense 90 degree not possible
polar chasm
okay
gentle crow
If in a triangle ABC, cos^2(A) + sin^2(A) + cos^2(B) + sin^2(B) + cos^2(C) + sin...
This will not make a triangle
polar chasm
If in a triangle ABC for at least one angle called p, cos(8p) = 1, then the triangle is
A) Right
B) Equilateral
C) Isosceles
D) None of these
soft umbra
Lol ,bro u are wrong ,cos(180)=(-1)
it's actually possible
polar chasm
If in a triangle ABC for at least one angle called p, cos(8p) = 1, then the tria...
What about this?
soft umbra
I mean meth's condition
polar chasm
it works for A, it doesnt work for B and C, but A is not the right answer
gentle crow
it's actually possible
Not possible, tell this to him
polar chasm
you don't get my point. Your approach doesn't prove anything
gentle crow
I mean meth's condition
His all equations are not possible to make a triangle
polar chasm
its more like an educated guess
polar chasm
His all equations are not possible to make a triangle
which one?
point out a single one
gentle crow
you don't get my point. Your approach doesn't prove anything
Ya I know, but this approach proves that the fundamental is clear, we use it because it is fast
gentle crow
point out a single one
Both
polar chasm
Ya I know, but this approach proves that the fundamental is clear, we use it bec...
it doesnt rule out D
D could be the right answer, and by your approach you wouldnt eliminate it
gentle crow
point out a single one
First one can make but u have to give an condition that A<90degree
polar chasm
As an example, take this
If in a triangle ABC for at least one angle called p, cos(8p) = 1, then the triangle is
A) Right
B) Equilateral
C) Isosceles
D) None of these
polar chasm
First one can make but u have to give an condition that A<90degree
cos^2(A) + sin^2(A) = 1 this one?
gentle crow
As an example, take this
If in a triangle ABC for at least one angle called p, c...
This will not make a triangle,
Because we get p=0 here
polar chasm
cos^2(A) + sin^2(A) = 1 this one?
this equation is true for any A.
,w cos^2(69) + sin^2(69)
woven radishBOT
woven radishBOT
polar chasm
,w cos(pi/2 * 8)
woven radishBOT
boreal helm
Lol
polar chasm
,w cos(3pi/4 * 8)
woven radishBOT
polar chasm
to sum up
polar chasm
that equation is true iff one of the angles is 45 or 90 or 135
polar chasm
that equation is true iff one of the angles is 45 or 90 or 135
so by your approach, you would find out that A works
polar chasm
but if I have a following triangle: 45 - 35 - 100, then the equation is working too
devout snowBOT
polar chasm
damn, that's it?
probably
I only needed to point out that the approach used worked only bc of luck
(and also argue about it for a while)
gentle crow
It was entertaining
Bro he was really testing my patience @cold bone
That's why I left
soft umbra
nah
cold bone
i don't think so
gentle crow
I believe he just wanted a debate
Yaaaa
cold bone
because he has done it b4
fr
gentle crow
😂
cold bone
bro's a 🐐 after all
gentle crow
bro's a 🐐 after all
Ne need a he-goat😂
devout snowBOT
Available help channel!
sour spire
hey guys how to do this
devout snowBOT
hey guys how to do this
winter patrol
what are you being asked to do
restive river
make the 2nd term 0
sour spire
Oohh
devout snowBOT
@sour spire Has your question been resolved?
restive river
devout snowBOT
sand dove
oh not necessarily
restive river
oh not necessarily
you have to
then how else woud you find the min
differentiate f(x)
innit
sand dove
you can do that of course
sand dove
no
restive river
i dont know any other method
sand dove
just notice that xtan^-1(x) >=0
and for t >=0, the function you're integrating is positive
so it's about minimizing xtan^-1(x)
restive river
THATS SO FUCKING SMART
cold bough
THATS SO FUCKING SMART
you are so smart!
sand dove
your method works fine too don't worry xd
devout snowBOT
@restive river Has your question been resolved?
cyan needle
Simplify:
(3^4+3^5)/(3^6)
So far I've gotten it down to 4/9 but the answer key is saying that it's actually 3^3 and/or 27 simplified down? I'm confused how to get to that point, maybe I messed up somewhere?
dense lynx
it's 4/9
cyan needle
Right?? I feel like I'm going crazy
dense lynx
3^(4 + 5) / 3^6 is what's 27
cyan needle
Did I just read the equation incorrectly then?
I'm gonna post the screenshot for it rq
dense lynx
that's definitely 4/9 yes
cyan needle
warm karma
3^4 + 3^5 < 3^5 + 3^5 + 3^5 = 3^6 => solution < 1
sand dove
wrong exercise or bad notebook
warm karma
maybe it was meant to be $\times$
woven radishBOT
CyclicTree
sand dove
maybe it was meant to be $\times$
yeah I bet they did that
cyan needle
wrong exercise or bad notebook
I think it's just a bad notebook, I triple checked to be sure that I wasn't looking at the wrong one 
Okay cool, I appreciate all of you
.close
latent sundial
Is this a place I can ask a calculus question?
devout snowBOT
Is this a place I can ask a calculus question?
mystic scarab
faint zinc
Are you simply asking if your work is correct?
latent sundial
I'm getting this problem wrong and I can't figure out why
I followed the process from my example problem exactly
faint zinc
do you know what the answer ought to be?
latent sundial
I don't. The answer I got was dH/dt = 0.609 m/min
I took thorough notes from my tutorial example problem in Cengage Learning. Should I upload photos?
faint zinc
It's fine, let me read through your solution rq
latent sundial
awesome, thank you
faint zinc
I don't see a mistake. Can you show the original problem?
latent sundial
yes, I'll send a screenshot
faint zinc
just in case your mistake is transferring it from the source to your page
latent sundial
latent sundial
ohh thank you so much!!
faint zinc
yw
latent sundial
wow, sometimes another set of eyes does wonders
can I send you another one?
I have two more problems...one that I got wrong, another I'm unsure how proceed. These related rates problems are very challenging for me
faint zinc
You are doing really well on the related rates problems, if your approach to the one above is any indication
it's very clean and structured.
which is important in related rates.
latent sundial
I've worked really hard, but maybe you can find my error in this next one...
faint zinc
sure thing
faint zinc
you forgot the pi
faint zinc
that's why I thought you definitely seemed to have the ideas down
just getting tripped up on the algebra
latent sundial
I have one more that I'm having a hard time figuring out how to go about
latent sundial
faint zinc
and I need to go do errands 🙂
latent sundial
lol ok, sorry, if you need to go that's ok
faint zinc
volume of a triangle prism is area of triangle times depth
faint zinc
1/2(bh)*10
latent sundial
ohh I see
faint zinc
where the b is proportional to 4 and the height is proportional to 7
latent sundial
thank you so much
faint zinc
this is just geometry, not calculus
latent sundial
I should be good for a bit
faint zinc
so again, you seem to have related rates down pat
latent sundial
good, whew!
faint zinc
you're just rusty on the more basic concepts.
latent sundial
Yes, it's been awhile since pre-calc
urban moat
guys
torn bane
close this one or the other one first, you have two channels open
devout snowBOT
@urban moat Has your question been resolved?
dense thorn
I'm confused about how to analyze this graph. The right answer is C can somebody explain that to me? Also, does F have a relative max at x = 2?
devout snowBOT
I'm confused about how to analyze this graph. The right answer is C can somebody...
gray mirage
Ive been staring at this and honestly think this is a misprint.
Like, here’s an example of what the graph might look like for C to be the only false statement:
gray mirage
Like, here’s an example of what the graph might look like for C to be the only f...
@dense thorn
dense thorn
well
wait
so i'm a bit confused on what u mean
is the right answer actually C?
as in (C) is the only false statement
can we conclude that based on the graph given?
devout snowBOT
@dense thorn Has your question been resolved?
lofty lintel
I'm confused about how to analyze this graph. The right answer is C can somebody...
what graph??? there is no graph
lofty lintel
no
that’s just x and y axes with some weird empty jump discontinuity thingy in the middle
are you supposed to draw your own graph?
dense thorn
isn't there a point at (2, 1) and (2, -1)
lofty lintel
no
gray mirage
Like, here’s an example of what the graph might look like for C to be the only f...
Like I said, I think that they misprinted and meant to have a graph that looked, for example, like this.
lofty lintel
they would have to be filled-in circles for them to be points
lofty lintel
Like I said, I think that they misprinted and meant to have a graph that looked,...
i think you’re right
dense thorn
Like I said, I think that they misprinted and meant to have a graph that looked,...
OHHHH
dense thorn
Like, here’s an example of what the graph might look like for C to be the only f...
I misinterpreted what you originally meant
gray mirage
I misinterpreted what you originally meant
No worries 🙂
dense thorn
tysm
dense thorn
they would have to be filled-in circles for them to be points
so
would i not be able to say there's a point at (2, 0.9999...)
gray mirage
Generally an un-filled circle in a graph refers to a point 94 jump discontinuity.
lofty lintel
correct, you can not say that
gray mirage
Like this for example
The point is defined at (1,1.5ish), but not at (1,0.5ish)
That’s a depiction of a jump discontinuity
errant hinge
is this correct
devout snowBOT
is this correct
lunar harbor
is this correct
Yeah
devout snowBOT
devout snowBOT
Available help channel!
errant hinge
aren't i supposed to multiply by $\frac{\sqrt[3]{81}}{\sqrt[3]{81}}$
woven radishBOT
SLURPZZZ
lunar harbor
aren't i supposed to multiply by $\frac{\sqrt[3]{81}}{\sqrt[3]{81}}$
You could, but $\sqrt[3]{3}$ is easier
woven radishBOT
Civil Service Pigeon
devout snowBOT
@errant hinge Has your question been resolved?
maiden nexus
I need help
devout snowBOT
I need help
maiden nexus
I don’t understand 5
I see that there are 3 intervals
But I don’t really get what an inflection point is
winter patrol
they're points where the graph changes in concavity
maiden nexus
And that means if it’s going up of down
winter patrol
wdym by "it"
winter patrol
then no
winter patrol
still no
winter patrol
concavity deals with which way the curve is facing
whether the slope is increasing/decreasing
,W graph x^2
woven radishBOT
winter patrol
,W graph -x^2
woven radishBOT
maiden nexus
The first one is concave up and the second is concave down
winter patrol
yes
maiden nexus
winter patrol
and then look at where the curve is changing concavity
maiden nexus
winter patrol
no
winter patrol
there are only two,
maiden nexus
Are both of them wrong
winter patrol
yes
you're not really after intervals
you want points
you seem to be circling when slope is positive which isn't what the question is asking
as implied earlier,
the whole graphs of y=x^2, y = -x^2
are concave up/down respectively
and individually don't have inflection points
so it seems you have some idea of concavity
try identify the location where it changes
maiden nexus
Well I see that it starts changing after the function reaches 0
But that’s the interval
winter patrol
no
winter patrol
yes, those are the x-coord of the inflection points
errant hinge
You could, but $\sqrt[3]{3}$ is easier
Yes but none of those are an option either
lunar harbor
Yes but none of those are an option either
They probably meant inside the radicand -> 3
Bad question ik
winter patrol
good
maiden nexus
And 7 I picked A
winter patrol
is incorrect
maiden nexus
Dang
winter patrol
the function is concave down there, but not full increasing
winter patrol
how are you getting D
winter patrol
yes
maiden nexus
Oh
maiden nexus
winter patrol
yes
maiden nexus
And for 10
maiden nexus
winter patrol
no
maiden nexus
winter patrol
sort of, you should be circling the entire relevant part, not just part of it
maiden nexus
Like
maiden nexus
winter patrol
yeh
woven radishBOT
mighty galleon
Yep, an input can only have one output, it's not a function
woven radishBOT
granite bough
i’m so confused
the highlighted area