if i write sin(x + 2pi)
#help-38
sharp owl
nop
sharp owl
2pi?
sudden mist
What?
sharp owl
4pi?
sudden mist
Are you just guessing?
sharp owl
no i try
sudden mist
Okay, so you said sin is periodic, it repeats for example as you said it
sharp owl
how i can rewerite that?
sudden mist
sin(x+2pi) = sin(x).
sharp owl
yes sin(x+2pi) have a period on 2pi
sudden mist
yup exactly.
So we can rewrite it as sin(x)
Let's go back now to sin(2npi + pi/2)
how can we rewrite this as?
sharp owl
sinx?
sudden mist
and what is x here?
sharp owl
0
sudden mist
What, how?!
sharp owl
x->0
sharp owl
2npi +pi/2 = 0?
sharp owl
then later?
sudden mist
we want to rewrite sin(2npi + pi/2)
sharp owl
how i can rewrite that?
sudden mist
as sin(pi/2)
this was the case when x = 1/(1/2 + 2n)
when n goes to infinity, x goes to 0
it's a subsequence
so if we always get sin(pi/2) for this subsequence
then this converges to sin(pi/2) = 1
but what if we pick say x = 1/(-1/2 + 2n)
then we get that sin(-pi/2) = -1
sharp owl
ooh
sudden mist
so for two different subsequences we find that they convergence to two different limits
thus the limit for sin(pi/x) cannot exist as x goes to 0
and so what you should take away here is to not trust silly programs like the one you showed eariler
sharp owl
Thx i can see
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manic creek
If its X^2/2X^2 y = 1/2 so if x is 3 in that faction overal, y is 6
is this how it works?
but you have to figure out the overal equivelant to plot?
So the ratio between the numerator and denominator is what decides the value of y?
manic creek
So the ratio between the numerator and denominator is what decides the value of ...
But im guessing this is only the case if the Powers are the same on both numerator and denominator so then you check the leading coefficient for the ratio
if numerator power is bigger then y = x always, no matter what. if denominator is bigger, y = 0 is always, thats a rule?
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vital nova
I'm trying to do the chicken mcnugget theorem for 8 9 and 10, And I saw in the original that the original 6 9 20 was used to formulate from 20*9 - 9 - 20 = 151 which disregards the 6, would this work too for 8,9,10? Such that the answer would be 90 - 19 = 71?
sudden mist
Chicken mcnugget theorem?
Are u referring to that one numberphile video?
vital nova
Yuh, it's frobenius coin problem, mn-m-n
sudden mist
Hm sorry can’t help with that, hopefully someone else knowledgeable about the chicken McNugget theorem can chime in
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chilly galleon
Someone help plis,this is making me crazy
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Someone help plis,this is making me crazy
chilly galleon
Just exagerating,but I’ve calculating for like 40 minutes without finishing it
wary basin
Out of curiosity you seen to have division as your largest on the bottom left?
chilly galleon
Yes
wary basin
Wouldn't division have the smallest value?
amber python
you should realise that the logs are irrelevant
chilly galleon
Wouldn't division have the smallest value?
Yea but that how the puzzle is given to me
wary basin
Yea but that how the puzzle is given to me
You can't rearrange?
chilly galleon
Nah and it’s part of my summer assignment so I can’t contact the teacher either
I’m still confused about it
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livid dune
this is a p series right>
earnest niche
Is problem 1, 2, and 4 correct? Also how would you do problem 3?
earnest niche
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earnest niche
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minor geode
a
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merry scaffold
anyway here
minor geode
Please only use the <@&286206848099549185> ping **once** if your question has no...
srry
!15min
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merry scaffold
bcuz the 2 lines are parrallel-> u can conclude that the big tri is similar to teh small one
ye?
merry scaffold
lets call the 3 sizes of the big one x1 y1 z1, respectively similar to the small one x2 y2 z2
minor geode
ok
minor geode
lets call the 3 sizes of the big one x1 y1 z1, respectively similar to the small...
*the
merry scaffold
-> x2 = 7/12 x1; y2 = 7/12 y1; z2 = 7/ 12 z1
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merry scaffold
oh ok :(
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pulsar dust
just prove that they are equal
sun the values of p and q
notice that $p^2+q^2-2pq=(p-q)^2$
solid kilnBOT
convergence
pulsar dust
we know what is p-q
now just sub p,q for it
just do it you just need to prove that eq is equal to 0
nah you just need to prove that its equal to 0
yes
there are many methods to do that but the method of just doing it is the best
the other methods are long and honestly a waste of time
jade jacinth
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mild oxide
@clear cloud
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mild oxide
Yo
unique field
dull temple
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jovial trail
Haiii Help plss
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jovial trail
😭 Everyone is busy someone pls
spiral ocean
Ok
What are the conditions for a function to be differentiable
If such conditions are satisfied, there is a unique derivative
spiral ocean
What are the conditions for a function to be differentiable
.
jovial trail
yes
spiral ocean
The derivative must approach same value from left and right, right?
jovial trail
What are the conditions for a function to be differentiable
Um limits
jovial trail
The derivative must approach same value from left and right, right?
Yes
spiral ocean
So, no sharp turns, no cusps, no vertical line
Because sharp turns result in different limits
jovial trail
So, no sharp turns, no cusps, no vertical line
yes
spiral ocean
So, does the first one have a unique derivative at (0,0)?
jovial trail
No
jovial trail
So, does the first one have a unique derivative at (0,0)?
Right?
jovial trail
Yeah, there’s no derivative
Yes then for second one its no and 3-4 one is yes.Am i correct?
spiral ocean
Yes
jovial trail
Then the answer will be 2 curves
spiral ocean
Yes
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hasty turtle
How??
simple warren
make two axes on your grid
one in the left-right direction and the other in the up-down direction
and draw in the vector sum A+B and B+A
hasty turtle
This???
hasty turtle
do you know vector addition
hardly bro im meant to learn it for physics
simple warren
okay so
scalar addition is just adding the two values
2 and 9 are both scalars, and 2+9 = 11
That is simple
simple warren
But vectors aren't just magnitudes, they also have direction
hasty turtle
Oh okay
simple warren
but before that
vector addition instead sums up the magnitudes in each direction
so the vector A is 4 cm to the right or the vector from (0,0) to (4, 0)
vector B is 3 cm downwards or the vector from (0,0) to (0, -3)
A goes 4 in the positive x-direction and B goes 3 in the negative y-direction
does that make sense
hasty turtle
yeah
simple warren
So algebraically, vector addition is adding up the magnitudes in each direction
A+B = [ 4 + 0 , 0 + (-3) ] = [4, -3]
but geometrically its like attaching the two vectors "tip to tail" where you attach the start of the second vector to the tip of the first one and draw the resulting vector
Like this
C = a + b
simple warren
and its the vector you get from drawing a line from the start of A to the end of B if you attach B to A
Its like
hasty turtle
like that?
simple warren
The sides of the triangle are just B and A
But B+A is actually just the hypotenuse
hasty turtle
how
simple warren
It's okay
Honestly I would really recommend watching a video that explains vector addition because I don't think I am doing it justice
This is a good one
Suited for physics
hasty turtle
alright
thanks
a+b would be 5 right
@simple warren i also have substractig vectors
A-B and B-A
simple warren
a isn't just 4, b isn't just 3, and a+b isn't just 5
they have those magnitudes, but they aren't just their magnitudes
since they are vectors, they also have direction
simple warren
yeah, but watch the video I highly urge you to do that
You will be able to do the subtracting ones with ease too
hasty turtle
alr
simple warren
dm me if you still have questions after watching
turbid mantle
hey can anyone hel me with the highlighted question
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hey can anyone hel me with the highlighted question
turbid mantle
clear cloud
Essaye d'encadrer la fonction f entre deux valeurs
e^-x est bornée entre deux valeurs pour x>0
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swift pewter
Hello. I solved this problem and I think I messed up somewhere. It does not match the correct answer in the answer key. I cannot find where I went wrong.
swift pewter
here is my work:
and this is the answer in the answer key:
I dont know how there is a 8 in the denominator in the answer key answer.
clear cloud
Hum
Let y' = v(x)
y'' = v'(x)
xv' - 7v(x) = 0
v' - 7v(x)/x = 0
(x =! 0)
dv/dx = 7v/x
clear cloud
here is my work:
Antiderivative of x^7 at the end ?
swift pewter
I think so, im working through what you have typed out
swift pewter
how do you end up with x^7 though?
oh I see. It would be x dv/dx - 7v = 0. Then I would move the 7v over and take the integral. Thank you.
.close
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delicate pagoda
How would I show that some given set is a submanifold of $\mathbb{R}^n$ ?\
For instance, that ${(x,y)\in \mathbb{R}^2 \mid \frac{x^3}{y^2+1}=1 }$ is a submanifold of $\mathbb{R}^2$
solid kilnBOT
Bob Goldham
delicate pagoda
not necessarily for that set only, but I figure that an example might be helpful for this
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delicate pagoda
(We defined a submanifold of euclidean space as follows:)
solid kilnBOT
Bob Goldham
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turbid mantle
Essaye d'encadrer la fonction f entre deux valeurs
can you explain further
turbid mantle
Open a new channel
how
clear cloud
Drop the image of the problem in the free help channel above this section
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**Bob Goldham**
<@&286206848099549185>
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sage jacinth
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solemn wagon
Can the angle bisector ever not hit the other side of the triangle at a point?
merry scaffold
no in my opinion
but be aware that there are 2 types of angle bisectors
outter and inner sth i forgor
but ye the outerone doesnt hit
but the inner one (if that is what ur mentioning) does hit
solemn wagon
i have an exercise
Given a triangle 𝐴𝐵𝐶 that is not isosceles. In this triangle, the measure of the angle 𝐴𝐵𝐶 is
twice as large as the measure of angle 𝐵𝐴𝐶.
Show that the lengths of the sides of this triangle satisfy the condition
AC^2=BC^2+AB*BC
this is my sol
and I was told my the examiner that some triangle doesnt exist in some cases?
merry scaffold
,rotate
solid kilnBOT
merry scaffold
and I was told my the examiner that some triangle doesnt exist in some cases?
cant think of one
merry scaffold
Can the angle bisector ever not hit the other side of the triangle at a point?
the quesiton is this ?
yes/mo quese 💀 ?
solemn wagon
omg
solemn wagon
i have an exercise
Given a triangle 𝐴𝐵𝐶 that is not isosceles. In this trian...
this is the exercise
coukd you please also check the screenshot
i mean picture
if its done correctly
merry scaffold
wait still how CD * ac = bc^2
huh ?
solemn wagon
from tangent
merry scaffold
ye how
merry scaffold
imagine I got a 0
💀
merry scaffold
4/10 ?
solemn wagon
whole exam?
merry scaffold
ye
solemn wagon
40/50
solemn wagon
ye
merry scaffold
ooof
solemn wagon
its such a big deal cuz its university admission exam
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merry scaffold
tyy
dang just 1 ques i just researched
uni in polan is 13-15
ppl do this when they are 13 💀 ?
merry scaffold
from 18 and so on is uni ?
solemn wagon
from 19
merry scaffold
oh i got it, sry for ur time :3
solemn wagon
np ty you your time
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ocean latch
bro someone plz help im going crazy
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bro someone plz help im going crazy
ocean latch
tried this shit for a good 30 mins still cant figure out
still rose
try to square on both sides
it will remove the square root
try it for both equations
ocean latch
bro i literally did that
i m stuck after that part
i am getting
4x=(20y/x)+(16x/5y)
i cant proceed firther
ocean latch
yep
ocean latch
did you add both equations?
yes
empty sluice
4x=(20y/x)+(16x/5y)
What if you simplify this?
still rose
is it a integer based question?
ocean latch
What if you simplify this?
bro how
delicate pagoda
make a system of equations and solve for x,y?
then calculate x²+y² based off of that
still rose
ok I got the asnwer
first square the first equation
and then you would get [(x+y)^1/2 + (x-y)^1/2]^2
and use the (a+b)^2 formula
ocean latch
yo i tried trial error, i put x as 5 and y as 1, and both sides are equating but answer is coming 26
howw
ocean latch
and use the (a+b)^2 formula
?
ocean latch
and then you would get [(x+y)^1/2 + (x-y)^1/2]^2
uhh thats what i did, howd you get the answer
still rose
I don't really know how to use the texit
still rose
uhh thats what i did, howd you get the answer
do it for both equations
ocean latch
do it for both equations
yes i squared both sides
empty sluice
I don't really know how to use the texit
Send the pic of your soln
still rose
Send the pic of your soln
alrigth
ocean latch
4x=(20y/x)+(16x/5y)
i got
solid kilnBOT
Alaska
ocean latch
can't send files here idk why
u can tho
still rose
it says 'use apps'
empty sluice
Just tell us the process
still rose
ok so in the first equation
ocean latch
yes bro fr just tell how u did it
still rose
square both sides
still rose
[root(x+y) + root(x-y) ]^2 after squaring
then simplify
do it for the second equation
ocean latch
and then add?
still rose
just simplify you would get it
ocean latch
bro what simplify
still rose
solve for x^2 in first and y^2 in second
ocean latch
solve for x^2 in first and y^2 in second
are u supposed to add? tell yes or no
still rose
no
ocean latch
then what
ocean latch
solve for x^2 in first and y^2 in second
how?
empty sluice
[root(x+y) + root(x-y) ]^2 after squaring
how did you simplify this?
still rose
use (a+b)^2
empty sluice
then how did you get x^2 from this?
still rose
square again
ocean latch
bro if u simplify it, youd get 20y/x= x+y+x-y +2root(x^2-y^2)
ocean latch
square again
youd still get smth in roots
still rose
how
my step is lengthy bc I squared💀 but yea you can just solve for root x^2 -y^2
forgive me for not telling this before
then equate
you can leave the root and equate or just square and equate(lenghty)
empty sluice
Did you get anything like this?
still rose
no
ocean latch
wait ill send mine
empty sluice
ugghhhhh
ocean latch
then tell whats worng
empty sluice
Next step?
still rose
solve for (x^2-y^2) and equate both equations (square it)
empty sluice
solve for (x^2-y^2) and equate both equations (square it)
nah bro doesn't work
Just get the damn app😭
ocean latch
solve for (x^2-y^2) and equate both equations (square it)
nahh bro u capping
still rose
are you sure the equations are correct?
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ocean latch
<@994574861886308473> did you get it?
how plz send pic
empty sluice
I hope you’ll understand the writing 🥹
ocean latch
I hope you’ll understand the writing 🥹
Ohhhh, finally understood, thx so much bro
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radiant portal
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radiant portal
(y+2)^2 + (x+1)^2 = 25
(ax + by + c)/sqrt(a^2 + b^2) = 5
y = mx + c
-mx + y - c
((-m)(-2) + (1)(-2) + c)/sqrt((-m)^2 + (1)^2) = 5
(2m - 2 + c)/sqrt(m^2 + 1) = 5
I still have 2 unknowns, not sure what to do next
<@&286206848099549185>
clear cloud
Hum
tulip sapphire
have you used the fact that m(-1) + b = - 17?
radiant portal
have you used the fact that m(-1) + b = - 17?
But then I have a different 2 unknowns, right?
tulip sapphire
yes
you could do a different method though
use these 2 facts:
f(-1) = m*-1 + b = -17
f(x) = c in one point only
radiant portal
f(x) = c in one point only
Wym by this sry?
tulip sapphire
f(x) is a tangent line of the circle c, so c and f(x) intersect in one point only (by the definition of a tagent line)
tulip sapphire
use these 2 facts:
f(-1) = m*-1 + b = -17
f(x) = c in one point only
b = -17 + m
we can now rewrite f(x) as m*x -17 - m
and now
mx - 17 - m - c = 0. You will when putting back in c, you will end up with some quadratic equation.
Use the quadratic formula and whatever is under the square root (also known as the discriminant) will be some function of m. Remember that the quadratic formula will give you 1 result if and only if whatever under the square root is 0
and since f(x) intersects c in one point (cause its tangent to c) you are looking for what "m" will make whatever is under the square root equal to 0
radiant portal
b = -17 + m
Im still not following completely sry
tulip sapphire
Heres what i did to get that step:
f(-1) = -17; so
-m + b = -17
b = -17 + m
oof i just realised i made a mistake
radiant portal
Wait why does f(-1)=17?
tulip sapphire
because the tangent line goes through the point P(-1,-17)
so at that point the function mx + b needs to satisfy m*-1 + b = -17
tulip sapphire
f(x) = y = mx + b is the function of the tangent line
we also know that this line passes through the point (x=-1;y=-17)
this means that f(-1) = -17
by defintion f(-1) = m(-1) + b
so -m + b = -17
radiant portal
Ok yes
I get you now
so b = -17 + m
What do we do with this? We still have 2 unknowns
tulip sapphire
cause now we can change the function f(x) = mx + b with the fact that we know that b = -17 + m
f(x) = mx + b
b = - 17 + m
=> f(x) = mx -17 + m
tulip sapphire
whats the other unknown?
radiant portal
the x?
tulip sapphire
x isnt an unknown, its just a variable, cause its a function not an expression.
tulip sapphire
you will just recieve -17 = -17
tulip sapphire
the reason as to changing b into that so that we have a function with only one unknown: m
now you need to see when f(x) and the circle intersect
from there try to get a quadratic equation. Solve with the quadratic formula, treat "m" as just some number thats part of the equation.
After solving with the quadratic formula you will reach a point where you have something with m under the square root. Since we want the functions to intersect in one point only. this will happen when whatever is under the square root is equal to 0. So you will need to find m such that whatever is under the square root is 0. From their you will get your value of m (there might be 2) and then the value of b cause b = -17 + m
radiant portal
the reason as to changing b into that so that we have a function with only one u...
I dont understand, what about the x and y?
Theyre just variables yes but we still need to get rid of them,
tulip sapphire
you can get rid of the y by changing the circle into a function. This will cut half of the circle off, but we can treat each half seperately
cause we will have
y = mx -17 + m
y = (the circle but as a function)
now since they're both equal to y:
mx - 17 + m = (the circle as a function)
radiant portal
I'm sorry but my brain is exhausted from this question 😭
I need a quick break
Thank you for helping me this far
tulip sapphire
No problem hahaha, math is exhausting lol
tulip sapphire
Thank you for helping me this far
Np! If you have any issue changing the circle into a function, check out this link ||https://www.symbolab.com/solver/solve-for-equation-calculator/solve for y%2C y^{2} %2B 4y %2B x^{2} %2B 2x - 20 %3D 0?or=input||
radiant portal
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tulip sapphire
You are awesome
thankss :]
radiant portal
Np! If you have any issue changing the circle into a function, check out this li...
Ahh ye I will
Thanks again!!
tulip sapphire
yw!
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woeful egret
hi
wind cloak
!status
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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
can you show the work?
woeful egret
well i kind of just did it
dull temple
i got my answer as 3x^(2)cos3x^2 * 5^sinx^(3) * ln5
almost right
order it by the chain rule to clearly see
woeful egret
almost right
order it by the chain rule to clearly see
like this?
woeful egret
how do i do chain rule here
dull temple
well it's $\ln(\bsq)$
solid kilnBOT
hayley 🥥 🌴
woeful egret
yea ik that the derivative is d/dx of inside / the inside
but i dont get how u do the chain rule here
woeful egret
1/x
dull temple
and u in this case is that fraction right?
woeful egret
yea
dull temple
ok so write down 1 over that fraction
then a dot
then find the derivative of that fraction
using whatever method you want
dull temple
that would be one way or if you know the quotient rule you could do that
woeful egret
i tried doing the quotient rule but i just got 0
dull temple
doesn't seem right
woeful egret
what do i do
tribal sonnet
i tried doing the quotient rule but i just got 0
Could you show your calculations?
woeful egret
Could you show your calculations?
ik i should use the chain rule then quotent rule but idk how to do chain rule first
tribal sonnet
How did you get 0?
Did you work out the brackets?
I don’t see what you’ve done here…
woeful egret
I don’t see what you’ve done here…
oh wait i forgot to distribute the e^x to both the 1 and the -e^x in the parenthesis
would e^x * e^x just be e^2x
tribal sonnet
yes
woeful egret
tribal sonnet
small error here
woeful egret
oh it would be plus
tribal sonnet
and I don’t think you can simplify it anymore
tribal sonnet
,w is the derivative of ((1+e^x)/(1-e^x)) equal to (2e^x/(1-2e^x+e^(2x)))?
solid kilnBOT
tribal sonnet
i have to put that derivative over the original
yes, we still need to do a bit.
tribal sonnet
It looks right, I’ll verify with wolframalpha
woeful egret
dont we need to simplify?
tribal sonnet
,w is the derivative of ln((1+e^x)/(1-e^x)) equal to (2e^x/(1-2e^x+e^(2x)))/((1+e^x)/(1-e^x))?
solid kilnBOT
tribal sonnet
dont we need to simplify?
I don’t know how it works in your country, for mine there is a rule that states that every version of the answer must be counted correctly. (Except when they explicitly state otherwise in the question)
woeful egret
what do you mean by counted
tribal sonnet
that you get full marks for it
woeful egret
ok so no need to simplify that any further?
tribal sonnet
,w simplify (2e^x/(1-2e^x+e^(2x)))/((1+e^x)/(1-e^x))
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obtuse ledge
how to solve thijs
fickle ledge
how to solve thijs
what was the original question
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trim locust
Hello
trim locust
Why did they use the distance formula as their comparsion for Lagrange Multiplier?
maiden hare
f gives you the distance (squared) from the origin at every point in space, that's what you want to minimize
g is the constraint (the plane itself)
trim locust
Does that mean I can use Lagrange Multiplier for this question too?
maiden hare
Of course
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wraith hinge
Problem 15
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Problem 15
wraith hinge
Idk where to start or what to do
burnt mulch
Idk where to start or what to do
Hint: complete the square (you'll have to expand everything out first)
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wraith hinge
Hint: complete the square (you'll have to expand everything out first)
Like 14((a + b + c)^2 - 2ac - 2bc - 2ab))?
wraith hinge
Oh
Ok I try
How do I do that
I expanded it but idk how to complete the square with three variables
burnt mulch
split it up
Spoiler alert: You should have something resembling (...)^2 + (...)^2 + (...)^2 = 0
wraith hinge
split it up
I’m stuck on that
wraith hinge
13a^2 + 10b^2 + 5c^2 = 4ab + 12bc + 6ac
burnt mulch
$13a^2+10b^2+5c^2-4ab-12bc-6ac=0$
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Civil Service Pigeon
burnt mulch
I'll start with the -4ab term as an example
can you think of any binomials that have a -4ab in their expansion when squared?
wraith hinge
where's this from btw
Maths club
wraith hinge
can you think of any binomials that have a -4ab in their expansion when squared?
(a - 2b)^2?
burnt mulch
(a - 2b)^2?
any others?
wraith hinge
any others?
(2a - b)^2?
burnt mulch
yeah
now I'll give this to you
(a-2b)^2 = a^2 + 4b^2 - 4ab
(2a-b)^2 = 4a^2 + b^2 - 4ab
if we go for the first option, (a-2b)^2
we're left with a 6b^2 we still need to group into another perfect square
which is ... not ideal.
so it makes sense to go for (2a-b)^2$
And doing that, we get $$(2a-b)^2+9a^2+9b^2+5c^2-12bc-6ac=0$$
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Civil Service Pigeon
burnt mulch
see if you can continue the process
wraith hinge
$(2a - b)^2 + (3a - c)^2 + (4c - 3b)^2$?
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Yuki
burnt mulch
$(2a - b)^2 + (3a - c)^2 + (4c - 3b)^2$?
recheck this one
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Yuki
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Civil Service Pigeon
wraith hinge
Yep
burnt mulch
can you finish it now?
wraith hinge
I’ll try
burnt mulch
burnt mulch
So it’s 6?
✅
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wraith hinge
.close
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quiet rose
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hallow kite
also i know b i onyl need help with a
if t is the time, and they want to know what "eventually" happens, they're basically asking what the limit of your population is as time approaches infinity
@quiet rose
quiet rose
if t is the time, and they want to know what "eventually" happens, they're basic...
ik that but how to
like
answer
hallow kite
how to take the limit as t approaches infinity of 1000 / (1 + 60e^(-t))?
quiet rose
like i used desmos and put in randomnumbers and it maxes at 1000
hallow kite
are you in calculus?
quiet rose
pre calc
hallow kite
ohh
well from a oversimplified standpoint, think about what your function "approaches" as t gets really big
60e^(-t) is the same as 60 / e^t
e^t gets really big as t gets really big
quiet rose
yes
hallow kite
that means 60 / e^t gets really small
tends to 0
so 1000 / (1 + 60e^(-t)) tends to 1000 / (1 + 0)
quiet rose
so 1000 / (1 + 60e^(-t)) tends to 1000 / (1 + 0)
so basically since e^t just goes on infinitely it will basically go to 0 at one point so than it maxes out at 1000 because it becomes 1+0 on teh bottom?
hallow kite
so basically since e^t just goes on infinitely it will basically go to 0 at one ...
yes
60e^(-t) goes to 0 as t goes to infinity
1 + 60e^(-t) goes to 1
and 1000 / (1 + 60e^(-t)) goes to 1000 / 1 = 1000
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atomic seal
can we use summation as integration for non convergent summation
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kindred pier
like if i have lim(n->inf)Sum(sqrt n)
Not sure what you are trying to do here
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compact dawn
how do i determine what x is from here?
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how do i determine what x is from here?
compact dawn
sorry for messy ms paint
earnest nymph
cause these are to the power of 3, you can start by changing the base to 3 and just simplifying them individually
or you can just write sqrt27 as a power of 3 straight and then write 81 as a power of 3 and divide the powers
compact dawn
so.. sqrt 27 = 3^3/2
81 = 3^4
3^4 / 3^3/2 ?
earnest nymph
so.. sqrt 27 = 3^3/2
81 = 3^4
3^4 / 3^3/2 ?
divide the powers
cause now they have the same base
earnest nymph
4/(3/2)
earnest nymph
👍
compact dawn
is there a term for what this is called?
earnest nymph
if its hard to get your head around, change the base to 3 and then youll be able to see it easier
earnest nymph
is there a term for what this is called?
nah its just simplifying logs
tepid fractal
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tepid fractal
What is going on with this problem?
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<@&286206848099549185>
hexed token
what type of math is this?
tepid fractal
competition math or competitive math. I'm not competing, I'm just curious
tepid fractal
just waiting
hexed token
@tepid fractal sorry
strange stag
What is going on with this problem?
Can we assume the shape of L? To make everything easy and actually comprehensive
Like a hexagon
tepid fractal
idk, idk what is the problem talking about
this is just question 2/5 on the competition
tepid fractal
Can we assume the shape of L? To make everything easy and actually comprehensive
supposedly, it's an easy problem💀
strange stag
Probably assuming is the thing they thought makes it easy
Cause hell nah, I'm not talking a n sided polygon for this
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sterile loom
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sterile loom
How do I do - Have no answers
nimble stone
S_n=n/2[2a+(n-1)d]=3n^2-17n
try make the right look like the left, you can then get a and d from that
sterile loom
Ok thanks
But I tried the terms and they got nothing to do with a arithmetic sequence
@nimble stone
Do I don’t know what d is
So
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vale abyss
I'm not really sure how to approach this question
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I'm not really sure how to approach this question
vale abyss
I know how to take do curlF but I'm not sure what to do after that
I would need to make a vector function of t right?
limpid dawn
It says to use Stokes so you dont need curl F
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dense breach
well it seems like what's wanted is to use stokes to relate this to an integral through a simpler surface
otherwise you have to do 4 path integrals
you can just integrate w.r.t x and y right? i have no idea what "make a vector function of t" means
vale abyss
So we wouldn't need curl F?
limpid dawn
vale abyss
I think I'm struggling on figuring out what the normal vector would be
limpid dawn
Try to parametrize the 4 line segments
vale abyss
oh ok
dense breach
it says to use stokes to reformulate the integral in terms of a simple area
convert it to a curve integral, then back to a surface integral
right here
limpid dawn
the bottom is not included
in S
since it's bottomless we would integrate over the boundary which is the 4 line segments
dense breach
bruh
vale abyss
would I need the eqution of the bottom plane?
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slim pawn
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slim pawn
idk if it is ok to read, but it is saying
A can measuring 20 cm x 10 cm x 10 cm, without a lid, is supported by a support, so that one of its shorter edges rests on the horizontal plane and the longer edges form an angle of 45" with the horizontal plane, as shown in the figure. Suppose a liquid is placed in the can, up to height hin relation to the horizontal plane, also as indicated in the figure.
Explain why the maximum height the liquid will reach is 10√2 cm and calculate the volume of liquid in the can when that height is reached.
granite light
notice how there is the direction in which every slice of the volume of liquid has exactly the same area
so this is really a planar geometry problem
slim pawn
so this is really a planar geometry problem
so i don't need to use things related to 3d forms
granite light
i suppose "maximum height" is up to the brim
slim pawn
i suppose "maximum height" is up to the brim
probably
granite light
you can split area nto a triangle and a parallelogram, triangle has sides 10cm, 10cm, sqrt(2) 10cm, and parallelogram has base sqrt(2)10cm and height h - (1/2)sqrt(2)10cm
you can get areas and get volume
oh you also have 20cm/sqrt(2) = h
slim pawn
you can split area nto a triangle and a parallelogram, triangle has sides 10cm, ...
you mean something like it
slim pawn
idk the h of parallellogram
granite light
but you do know side of the triangle right?
granite light
idk the h of parallellogram
also what are the angles in this parallelogram?
slim pawn
slim pawn
also what are the angles in this parallelogram?
90
granite light
so it's just a rectangle then
slim pawn
yeah
granite light
what about the triangle, what are the angles there?
slim pawn
what about the triangle, what are the angles there?
90 and 45 i think
granite light
90, 45, and 45?
slim pawn
90, 45, and 45?
yes
granite light
then it is isoceles
which means sides near the equal angles are also equal
granite light
yes
slim pawn
great
granite light
still need to find the height of the rectangle tho
for that consider the triangle they have drawn in the diagram
slim pawn
maybe it's 5 because the entire side is 20 and we know the triangle is 10
but we are not sure about that
granite light
it actually depends on how full the vessel is
so that's the piece of information you haven't used yet, h
hint: the trick is to find the hypotenuse of the triangle that is drawn next to the can
slim pawn
hint: the trick is to find the hypotenuse of the triangle that is drawn next to ...
i am thinking about
actually
arent we supposed to find the 10√2 cm thing
wait
so it is that
the purple side
is 10√2 cm
granite light
it is also right
if a triangle is right angled you can use pythagoras theorem
slim pawn
alright
granite light
the height of the rectangle, as well as the side of the triangle you have marked in yellow
