see
#help-43
compact pewterBOT
@proper swan Has your question been resolved?
proper swan
this step is correct
im back
proper swan
hi
proper swan
you can dm me if you often have doubts
are you Italian by chance
proper swan
me not always online here
its fine
proper swan
you can dm me if you often have doubts
i still didn't understand the thing though
srry
hmmm
ok we left off at like
quartz yoke
are you Italian by chance
wish i could be
quartz yoke
this step is correct
.
what you wrote is correct
you just have to cross multiply to solve for x
x is the answer that you require
proper swan
x is the answer that you require
i dont know how to cross multiply thats why i was so confused
what is cross multiplication
proper swan
ok
proper swan
il write it out
stark marsh
$\frac{d}{d}\cdot\frac{a}{b}=\frac{c}{d}\cdot\frac{b}{b}$
boreal girderBOT
yoboiqimmah
quartz yoke
noooooooo
proper swan
π
quartz yoke
.
quartz yoke
**yoboiqimmah**
.
.............
lets start with basic problems
6x = 12
whats the value of x
proper swan
12:6=2
proper swan
15:7
proper swan
yeah
proper swan
well we gotta do 1:7 first
past finch
proper swan
then when we get that we move 5
past finch
the right side is cross multiplication and the left side shows how multiplying by the denominators on both sides is the same thing as it
proper swan
and you get the x
proper swan
brb
stark marsh
stark marsh
genius
My brain is fighting the thought of just dividing 5 because it wonβt be obvious lol
quartz yoke
My brain is fighting the thought of just dividing 5 because it wonβt be obvious ...
loll
proper swan
so im supposed to make it equal
stark marsh
so im supposed to make it equal
multiply them out and make them equal yea
for some cases it might in the form
ax=b just divide the a and you'll get x=b/a
quartz yoke
yup
quartz yoke
so im supposed to make it equal
there are other ways to solve it too
which makes the calculation easier
compact pewterBOT
@proper swan Has your question been resolved?
compact pewterBOT
compact pewterBOT
Available help channel!
sick kiln
6,66,666,6666, ...
Find the sum of nth term
compact pewterBOT
6,66,666,6666, ...
Find the sum of nth term
sick kiln
i found the sum of the differences in terms but im not sure where to go after that
i thoguht of (the sum of differences in terms) +6n but it didnt work when i plugged it in
stoic dove
you can multiply by 3/2 and add one and subtract one for each term
stoic dove
basically it becomes 2/3(9+99+999+9999...nth term)
now you can write this as
2/3(10+100+1000+10000+... 10^n -n)
does that make sense?
and can you proceed from here?
sick kiln
i found the sum of the differences in terms but im not sure where to go after th...
will this work or is it lost?
gleaming grotto
will this work or is it lost?
It prolly won't as it is in gp (kinda)
sick kiln
what does gp mean
stoic dove
what does gp mean
geometric progression
gleaming grotto
what does gp mean
Geometric progression
eternal pulsar
i found the sum of the differences in terms but im not sure where to go after th...
Have you tried it out for the first few numbers?
sick kiln
wdym?
eternal pulsar
Did you test your conjecture out?
sick kiln
you mean my initial answer? yeah i subbed the number of terms but got it wrong
did n=2 but answer wasnt 6+66 basically
eternal pulsar
Okay.
sick kiln
i did this but ended up in a reepating loop so i realised it was wrong
sick kiln
found another way to represent it but its very impractical
compact pewterBOT
found another way to represent it but its very impractical
sick kiln
is there anyway to make it more cohesive?
cohesive as in how the equation is structured
river tapir
Factor out 60/9?
compact pewterBOT
@sick kiln Has your question been resolved?
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Available help channel!
opal stirrup
how do i calculate this "glass has 250g of water and salinity is 3%, how many grams of salt is in the glass"
compact pewterBOT
how do i calculate this "glass has 250g of water and salinity is 3%, how many gr...
kind viper
do you know how percentages work in general?
opal stirrup
yes
kind viper
ok, so then would you be able to find 3% of 250?
opal stirrup
0.30 x 250
potent berry
thats 30
kind viper
0.30 would be for 30%
kind viper
0.03 * 250
potent berry
asterisk *
tacit geode
compact pewterBOT
tacit geode
I am trying to do this problem and I am a little bit stuck- again
trail cave
y = 2? from the last block
lowkey i can't read that are those 7s or 1s
and what's going on in the first block
lone quartz
What have done in the second step, like multiplied it by (β2+1) or something? Cuz its wrong
tacit geode
tacit geode
I am trying to multiply the first and second equation with the conjugate so that I simplify things so that I get the form of (a+b)(a-b) = a^2 - b^2
lone quartz
(β2+1)^2 is not equal to ((β2)^2+1)
tacit geode
(β2+1)^2 is not equal to ((β2)^2+1)
(β2+1)^2 = 3
lone quartz
$(a+b)^2= a^2 + b^2 +2ab$
boreal girderBOT
Nika
tacit geode
yes but we are not doing (a+b)^2 we are doing (a+b)(a-b)
lone quartz
I am talking about the coefficient of y
tacit geode
first equation we multiply by β2 +1 so the coeficient of y is β2+1 => (β2+1)^2 no?
oh i see my mistake. I didn't multiply β2+1 on the right hand side lol
lone quartz
first equation we multiply by β2 +1 so the coeficient of y is β2+1 => (β2+1)^2 ...
Yh that's right
But just so you know I don't think that's the easiest way to solve this
tacit geode
But just so you know I don't think that's the easiest way to solve this
I know
but I am trying to see different difficulty methods of solving such a problem
lone quartz
Oh ok
compact pewterBOT
@tacit geode Has your question been resolved?
desert frigate
Can someone show me how to solve this? (functions)
f(x) = 4x + 12
but i need to solve it like x is
f(x) = 0
compact pewterBOT
Can someone show me how to solve this? (functions)
f(x) = 4x + 12
but i need to ...
desert frigate
?
kind viper
imagine the question didn't have anything to do with functions, and you only had an equation to solve: 4x + 12 = 0
would you know what to do? yes or no.
forest token
how do u not get frustrated when people reply with a question mark π
desert frigate
would you know what to do? yes or no.
yes
desert frigate
how do u not get frustrated when people reply with a question mark π
?? i was confused
kind viper
how do u not get frustrated when people reply with a question mark π
i do.
desert frigate
ok, then go ahead and do that.
i dont know what this has to do with my question..
atomic canyon
i dont know what this has to do with my question..
it states f(x) = 0
so u can replace f(x) with 0 for the top equation
now u have 0 = 4x + 12
try rearrange and solve for x
lmk what u get
kind viper
i dont know what this has to do with my question..
your question literally asks you to do just this.
you're given the function f(x) = 4x+12 and asked to solve f(x) = 0.
atomic canyon
try think f(x) as y
desert frigate
lmk what u get
0 = 4 x 0 + 12
0 = 0 + 12
0 = 12?
forest token
i dont know what this has to do with my question..
^^
desert frigate
your question _literally asks you to do just this._
''Can someone show me how to solve this?''
forest token
0 = 4 x 0 + 12
0 = 0 + 12
0 = 12?
kill me
kind viper
''Can someone show me how to solve this?''
ok let me say this again
atomic canyon
0 = 4 x 0 + 12
0 = 0 + 12
0 = 12?
ok wait
kind viper
the question
"Here is a function: f(x) = 4x+12. Solve the equation f(x) = 0."
is the EXACT SAME QUESTION as
"Solve the equation 4x+12 = 0."
do you understand that these two questions are the same
tight badger
''Can someone show me how to solve this?''
No. "x" is a variable. You want to find the value of "x" which satisfies the equation when y = 0.
kind viper
i am telling you those two questions are the same
desert frigate
do you understand that these two questions are the same
yes i do but do you understand that i was confused when you began the convo with that? idk how to solve my question, like i dont know where to begin
kind viper
yes i do but do you understand that i was confused when you began the convo with...
so i am telling you where to begin
tight badger
I see what you did. You mistook "x" as a multiplication operator. It is not.
kind viper
you begin by reframing it as i said.
it is just a "solve this equation" question.
you told me that you know how to do the reframed version. that is why i did not linger on it any more.
desert frigate
so y = 0?
desert frigate
alright
desert frigate
so it would be f(0) ?
desert frigate
oh
kind viper
so it would be f(0) ?
no. f(0) would mean you set x to 0.
atomic canyon
that means 0 = 4x +12
kind viper
but also i think all of this talk of y = f(x) is kind of irrelevant to this question in particular.
desert frigate
but also i think all of this talk of _y = f(x)_ is kind of irrelevant to _this q...
just stop pls, youre too confusing and its not helping
kind viper
ok im out sorry
atomic canyon
lmao
tight badger
but also i think all of this talk of _y = f(x)_ is kind of irrelevant to _this q...
It's pretty irrelevant. But I suppose it makes it easier for those who do not understand what functions are to understand what f(x) means.
atomic canyon
but also i think all of this talk of _y = f(x)_ is kind of irrelevant to _this q...
no ti isnt f(x) literally means y
i said that to make it easier for her
tight badger
No worries. Just focus on the question at hand.
tight badger
just stop pls, youre too confusing and its not helping
If you tell me what exactly you are stuck on, then I will be able to help you. What confuses you about this problem?
desert frigate
If you tell me what exactly you are stuck on, then I will be able to help you. W...
okay so, i would know how to solve the problem if the question was f(5) = 10x - 12
but the problem is with the current problem f(x) = 4x + 12 and decide that x is ** f(x) = 0 **
i dont know what they mean by that, nor how to solve it
potent berry
okay so, i would know how to solve the problem if the question was f(5) = 10x - ...
$f(5) = 10x - 12$, you say?
desert frigate
$f(5) = 10x - 12$, you say?
if the question was
tight badger
okay so, i would know how to solve the problem if the question was f(5) = 10x - ...
They essentially want you to find the values of x which make the function equal to zero, i.e., the points on the graph at which the function crosses the x-axis.
When a graph crosses the x-axis, what does that always mean for the y-coordinate at that point?
boreal girderBOT
Percy
desert frigate
When a graph crosses the x-axis, what does that **always** mean for the y-coordi...
i dont know
potent berry
**if the question was**
if the question was $f(5) = 10x - 12$, you say?
boreal girderBOT
Percy
desert frigate
if the question was $f(5) = 10x - 12$, you say?
stop?
tight badger
i dont know
It is equal to 0.
So you want to find the x-coordinates at which y = 0.
You can replace f(x) with "y" in this case, if the parentheses confuse you. In the equation 0 = 4x + 12, they are asking you what value you must multiply by 4, then add to 12 to get 0.
desert frigate
wait so
i think i get it
4 x -3 + 12 = 0?
so answer would be -3?
f(x) = -3?
tight badger
so answer would be -3?
Yes! Very nice!
desert frigate
thank god
tight badger
Not f(x), however. x.
desert frigate
thank you man 
tight badger
You're very welcome!
desert frigate
.close
daring axle
For these two circles constructed so that one passes through the center of the other. How do I show that the AB (chord at their intersection) and the chord made by the tangent line AC have equal magnitude/length?
compact pewterBOT
For these two circles constructed so that one passes through the center of the o...
daring axle
Hi, so i got some hint for this
so i'm now working on first showing <NAB = <NAC
could someone help me w that
potent berry
For these two circles constructed so that one passes through the center of the o...
hmmmmmmmmmmmm
eternal pulsar
What is N?
potent berry
something something inscribed angle maybe
daring axle
N is the center of smaller triangle
daring axle
something something inscribed angle maybe
yes it is indeed inscribed angle
but well i guess not yet?
eternal pulsar
N is the center of smaller triangle
Triangle?
daring axle
so i'm now working on first showing <NAB = <NAC
i think this is first step probably
daring axle
Triangle?
circle my b lol
N is the center of smaller circle and M is the center of bigger circle
eternal pulsar
Okay.
daring axle
I have:
AMB = 180 - 2x
ABM is an isosceles triangle with measures (180 - 2x, x, x)
<BAC = 90 - x from alternate segment theorem
eternal pulsar
And A lies on both the large and small circle?
daring axle
yes
eternal pulsar
I would say that the angle bisector of BAC divides ABC into 2 congruent triangles. Though, you will need to prove such.
daring axle
well yeah that's what it looks like
but uh
the other helper suggested to invoke
inscribed angle tbh
so maybe that's the optimal route
eternal pulsar
So maybe extend a point on BC to A, and prove that. Particularly an altitude would be nice.
eternal pulsar
inscribed angle tbh
That also works.
Because of ||the sum of the two arcs||.
Hmm...well, it wouldnβt work out so well.
Anyways.
daring axle
mmmm
kind crane
mmmm7
upper carbon
For these two circles constructed so that one passes through the center of the o...
this looks really fun
eternal pulsar
mmmm8
pure horizon
mmmm9
eternal pulsar
So maybe extend a point on BC to A, and prove that. Particularly an altitude wou...
I see this as a default, though.
daring axle
this looks really fun
π i'm glad you think that
daring axle
I have:
> AMB = 180 - 2x
> ABM is an isosceles triangle with measures (180 -...
but yeah i have these so far (not much progress ig)
daring axle
so i'm now working on first showing <NAB = <NAC
I think this is the first step to work towards
but yeah i kinda am not sure how to do progress w that
eternal pulsar
||Congruent triangles?||
daring axle
||Congruent triangles?||
but how?
calm trout
it's just alternate segment theorem
eternal pulsar
So maybe extend a point on BC to A, and prove that. Particularly an altitude wou...
^
kind crane
triangle-inside-circle-theorem
daring axle
it's just alternate segment theorem
π but like
didn't i use it
unless i used it wrong ig...
calm trout
daring axle
how are they equal
oh wait
you're right π
you're the genius
okay so we have <NAB = NAC from that cuz isosceles triangle
wait
we're kinda done now right?
calm trout
yes
daring axle
how do you state the conclusion tho? I'm thinking along the lines of
"from the law of cosines" we have that AB = AC
calm trout
NAB and NAC are congruent
daring axle
oh yeah okay
i'm super dumb these days
sorry
yeah SAS congruence
that was pretty simple π in hindsight
tysmm!!! 
calm trout
calm trout
seems about right
calm trout
i don't
calm trout
maybe
daring axle
u remember alternate segment theorem
daring axle
oh
my aops book
didn't teach me that lol
π
maybe i derived it but they didn't name it
calm trout
tragedy
daring axle
okay so i guess it's normal
i'll just do more geo
anyway thanks again π
and bye
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compact pewterBOT
calm trout
quartz yoke
<@&268886789983436800>
compact pewterBOT
quartz yoke
This could be a phising trap
quartz yoke
Thanks
quartz yoke
steamcomNumity or sth like that
Was he banned?
short ferry
apparently
compact pewterBOT
Available help channel!
unkempt lion
compact pewterBOT
unkempt lion
for b) idk why im inccorect
this should be the answer
thanks for any help
idk why im incorrect
because if we orient our head in the direction of the normal, the circles are always on our right
which means its got negative stokes orientation
<@&286206848099549185>
copper sierra
@unkempt lion the orientation instead depends on whether the surface is to our left as we travel the curve
as we travel A and B we see P on the left so they have + orientation. along C we see P on the right so it has - orientation
unkempt lion
the head need to be point in the same directs as the normal of P right?
I pointed the head in the direction of the normal of the circles which is why I got the answer wrong
is this right?
copper sierra
the orientation instead depends on whether the surface is to our left as we travel the curve
that seems equivalent to this
hmm i dont think the head thing works very well in this problem
unkempt lion
then how would we orient our "guy" travelling along the curve. He could then be upside down or head pointing left/right...
copper sierra
you know what it works
u just have to locally reshape the surface to look like this
then u can talk about matching heads or seeing the surface on the left
but in any case u do have to match the P normal
unkempt lion
yea because in our textbook the teacher just said point the head in the direction of the normal and I though it to be the normal of the circle or smt
anyways thank you alot for this. I hope you have a great day
copper sierra
np
unkempt lion
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compact pewterBOT
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thorny leaf
Idn't know how to solve it
compact pewterBOT
Idn't know how to solve it
lone pasture
Idn't know how to solve it
u know that AB is 7
and since u can see 2 radii of the circle, OA and OB
would u agree that AOB form an isoceles triangle
even better here
a tangent of a circle to a radius should always be 90 degrees
thorny leaf
would u agree that AOB form an isoceles triangle
my answer was a perimeter of 49cm.
no
27cm*
lone pasture
my answer was a perimeter of 49cm.
before i continue yapping what made u get to 27cm
i'd like to know ur thinking process
before i completely obliterate ur way of thinking 
thorny leaf
(using translator)
found the angles of the triangle AOB, I thought that at the point where the radius touches the circle it does so perpendicularly, so I used that to find the missing angles in ACB, and determined that it was isocels with sides of 7 cm.
lone pasture
(using translator)
found the angles of the triangle AOB, I thought that at the p...
and ur angle in ACB was 60 correct?
thorny leaf
yes
thorny leaf
yes
lone pasture
but now hold on a second
thorny leaf
wait
lone pasture
if all angles are the same, 60
all sides should be the same as well
so if AB is a given side, 7cm
thorny leaf
sorry i donΒ΄t now the types of triangles
lone pasture
u were right the other sides were also 7cm
thorny leaf
it is equilateral
lone pasture
sorry i donΒ΄t now the types of triangles
if all the angles of a triangle are the same, all sides are the same
thorny leaf
...
thorny leaf
was unfocused
thorny leaf
at least now I know my thinking was good, thank you.
itΒ΄s my first math olympic
river shuttle
Show that there does not exist a holomorphic branch of the logarithm in Ο= the unit circle minus 0
compact pewterBOT
Show that there does not exist a holomorphic branch of the logarithm in Ο= the u...
@river shuttle Has your question been resolved?
compact pewterBOT
@river shuttle Has your question been resolved?
slate gulch
Hi I was trying to solve this, but I dont know what values the red and yelllow rope should take, I know theres other way that is just count the ropes and then divide the mass with that number, but ,how is solving it the analitycal way?
compact pewterBOT
Hi I was trying to solve this, but I dont know what values the red and yelllow r...
timber cipher
You solve these systems by noting the wire lengths are constant
Blue wire = constant
A + (A - B) = constant
Then the second derivative:
2accel(A) - accel(B) = 0
eternal holly
i joined a math server expecting this to help high school and middle school students but what is this π
@everyone
slate gulch
Then the second derivative:
2accel(A) - accel(B) = 0
Is static
timber cipher
Sorry I didn't quite get that
slate gulch
I know the lengths are not important in this case, I just write T for tension
slate gulch
Sorry I didn't quite get that
Dw
compact pewterBOT
@slate gulch Has your question been resolved?
bright bobcat
how can i prove that $\lim_{n\to\infty}\sin(\frac 1n)=0$ without using that $\sin(x)$ is a \continuous function
compact pewterBOT
how can i prove that $\lim_{n\to\infty}\sin(\frac 1n)=0$ without using that $\si...
boreal girderBOT
pirateking0723
bright bobcat
I am not sure if i can use sin(1/n)=<1/n but i dont think that i can
bright bobcat
well i know how to do this if i am allowed some more tools
but i am not sure what i am allowed to use lol
boreal girderBOT
knief
native shard
so just use comparison with 1/n
bright bobcat
I am not sure if i can use sin(1/n)=<1/n but i dont think that i can
but this holds like this too
bright bobcat
so just use comparison with 1/n
well the thing is that i dont know if i am allowed to do such a comparison or no
thats why i am asking for something else
native shard
why not?
youβve just said you canβt use continuity of sin x and donβt want to bound it by a convergent sequence..
bright bobcat
no problem if i bound it with a convergent sequence
native shard
brother youβre tying your hands behind your back and legs together
native shard
no problem if i bound it with a convergent sequence
1/n
bright bobcat
then everything is fine
native shard
take N = 1/eps
native shard
take N = 1/eps
ceiling if youβre being extra precise
then just use a chain of inequalities n > N β>β¦
bright bobcat
this means that for all n>=N, 1/n<Ξ΅
but then what
how do i relate it to sin(1/n)
bright bobcat
well what i am trying to do rn is prove that |sin(1/n)|<1/n
i can bound it by a convergent sequence to use squeeze theorem
but i think that i am not allowed to write this inequality directly
(i am not sure tbh)
but since i am not sure then i just have to prove this inequality
native shard
i can bound it by a convergent sequence to use squeeze theorem
well you donβt even need to cite squeeze theorem here
native shard
|sin(1/n)| < 1/n < eps
this is sufficient
bright bobcat
yea it is
bright bobcat
but since i am not sure then i just have to prove this inequality
but how do i do this
bright bobcat
no
native shard
so no mean value theorem..
you donβt need taylor series here
bright bobcat
just convergence of sequences and series
bright bobcat
so no mean value theorem..
no
native shard
ππ
bright bobcat
well if there is no way to prove it with these tools then ig i am allowed to use it after all
otherwise it wont be logical to have such a question lol
native shard
ask your professor
this is clear from mvt
yo aeooeoeo has been cooking for a minute
bright bobcat
this is clear from mvt
well i am sure that i cant use this
bright bobcat
yo aeooeoeo has been cooking for a minute
yea let him cook
native shard
well i am sure that i cant use this
you learned it in calculus
bright bobcat
ask your professor
i will ask him tomorrow
bright bobcat
you learned it in calculus
yea but that doesnt mean that i can use it in analysis rn 
native shard
yea but that doesnt mean that i can use it in analysis rn <:hmmcat:8315088016467...
π€·πΌββοΈπ€·πΌββοΈ
but you havenβt even defined sin(x) either
ππ
native shard
did you ask him
bright bobcat
i cant ask him rn it is 11:40 pm
native shard
he probably is letting you use the 1/n bound tbf
bright bobcat
well i have him tomorrow so i am not rushing, i prefer not to disturb him rn ngl
bright bobcat
he probably is letting you use the 1/n bound tbf
but yea i think he is allowing this
given what i can use
quartz yoke
Thought I was cooking only to cook myself in the end
uneven birch
Why would you not use that sin is a continuous function ?
quartz yoke
I'm still curious if a geometrical proof with triangles is possible...
bright bobcat
ah..
native shard
Why would you not use that sin is a continuous function ?
probably had to use epsilon N definition
uneven birch
Why not use the fact that it's decreasing and bouded ?
bright bobcat
so i show that it decrasing and its inf is 0
sounds good
how to show that it is decreasing though
native shard
so i show that it decrasing and its inf is 0
yea but have you proved this part of monotone convergence
bright bobcat
yea
quartz yoke
I have a feeling it might be circular though I don't remember the proof
bright bobcat
how to show that it is decreasing though
do i use sum to product trig formula to transform sin(1/n)-sin(1/m) into a product ?
uneven birch
do i use sum to product trig formula to transform sin(1/n)-sin(1/m) into a produ...
No you can just say that 1/n+1 < 1/n
for n > 2/pi . 0 <1/n < Pi/2 . Meaning sin(1/n) is decreasing
bright bobcat
ohh i see
as for the infimum , i need to look at inf |sin(1/n)| right ?
because well idk if i am tripping or no but i dont think that inf sin(1/n)=0
for example if you take 1/(2Ο)<n<1/Ο then Ο<1/n<2Ο which means that sin(1/n)< 0
well i gtg sleep now tysm everyone for your help
have a great day/night
.close
compact pewterBOT
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uneven wolf
can someone explain the solutions first step?
compact pewterBOT
can someone explain the solutions first step?
rotund sphinx
,w characteristic polynomial {(8,2,-2),(2,5,4),(-2,4,5)}
boreal girderBOT
rotund sphinx
but the matrix is symmetric (and hence diagonalizable), so the minimal polynomial always factors into distinct linear factors
and then the stated result follows upon some rearranging
@uneven wolf ^
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quick jewel
proof of sigma n^4 with the use of x^5 - (x-1)^5
compact pewterBOT
proof of sigma n^4 with the use of x^5 - (x-1)^5
quick jewel
some1 pls help with this
like i have reached nearly the last step
but i cant take out common
acoustic yarrow
show your work
compact pewterBOT
@quick jewel Has your question been resolved?
quick jewel
proof of sigma n^4 with the use of x^5 - (x-1)^5
compact pewterBOT
proof of sigma n^4 with the use of x^5 - (x-1)^5
quick jewel
I am sending my work
potent berry
deja vu
potent berry
have you not posted this same thing before
potent berry
also uh... factorisation?
quick jewel
*also uh... factorisation?*
Yes
quick jewel
have you not posted this same thing before
Nope never
quick jewel
*also uh... factorisation?*
How did we reach to 2nd step from 1st step??
kind viper
some kind of factorization trickery. rational root theorem to pluck out those linear factors ig
potent berry
Yeah you can just kinda see that 0 and -1 are roots
then do some poly long divides with factor theorem
quick jewel
Can u pls write the steps
Idk these terms
In my country , I have never heard rational root theorem
compact pewterBOT
@quick jewel Has your question been resolved?
ember hollow
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ember hollow
A girl is holding a ball with a diameter of 3.90 cm and average density of 0.0835 g/cm3 under water. Determine the force (in N) needed to hold it completely submerged.
thats how I thought I would do it
though its not right according to the system of homework
compact pewterBOT
@ember hollow Has your question been resolved?
gloomy narwhal
A girl is holding a ball with a diameter of 3.90 cm and average density of 0.083...
buoyant force is not the only force
gravity is also there
make a free body diagram
and assume equilibrium
ionic heron
compact pewterBOT
pseudo rapids
I got a different c and i can explain how
well then explain how
ionic heron
first i got to e^2x(dy)=6xy^1/3)(dx)
which i eventually got down to 1/6(y^-1/3)dy=x(e^-2x)dx
so far so good?
so basically the first the first line except i had 1/6 on the LHS instead of 6 RHS
ionic heron
well then explain how
i then integrated left side to get 1/4y^2/3, and integrated RHS (integration by parts) to get -1/2xe^-2x-1/4e^-2x
and then once i add my + c on the RHS and subbed in the cords i got 1/2 for c
pseudo rapids
It's still correct
ionic heron
but why does mark scheme show c=3 and no recognitinon for 1/2
ionic heron
It's still correct
And also how would I do this q
?
barren horizon
and then once i add my + c on the RHS and subbed in the cords i got 1/2 for c
if you sub back in the c, what do you get?
ionic heron
if you sub back in the c, what do you get?
sub back in the c into where?
barren horizon
sub back in the c into where?
after the integration
you have 1/4 y^2/3 = ... + c right?
sub the c there, then solve for y^2 like they did
ionic heron
yep
ah i see
okay
lemme try
got it
thanks
@barren horizon
Do you mind helping me out with another q?
barren horizon
you should get the same thing as they did right?
barren horizon
nice
barren horizon
How do i find the horizontal asymptote
you could rewrite it as $y=\pm \sqrt{g(x)}$
then take the limit
boreal girderBOT
Sepdron
ionic heron
i don't really understand
barren horizon
is it still that question?
ionic heron
Yeah
quartz yoke
i tried this question but idk why i still don't understand how to do this. can someone help me out?
barren horizon
Yeah
then you have y^2 = (...)^3
take the sqrt on both sides, and you get
y = Β±sqrt((...)^3)
ionic heron
yeah and what can i do with this after?
barren horizon
yeah and what can i do with this after?
take $\lim_{x \to \infty} y$ then also as $x \to -\infty$
boreal girderBOT
Sepdron
ionic heron
And also how would I do this q
?
all parts for this question
barren horizon
idk how to explain that one, sorry
compact pewterBOT
@ionic heron Has your question been resolved?
faint birch
Three workersβA, B, and Cβare assigned a job. They work in pairs at different rates:
When A and B work together, they complete the job in 6 hours.
When A and C work together, they complete the job in 8 hours.
When B and C work together, they complete the job in 12 hours.
Assuming each worker's work rate is constant, determine the time it would take for each worker to complete the job individually.
compact pewterBOT
Three workersβA, B, and Cβare assigned a job. They work in pairs at different ra...
faint birch
Delete your message also
timber cipher
The trick to these questions is to recognise:
If a is the hours A will take to complete a job, then 1/a is the rate at which A works, in jobs/hour.
And the rates can just be added together. 1/a + 1/b is the rate at which A and B work together
potent berry
<@&268886789983436800>
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potent berry
lmfao
glacial mortar
oops
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Available help channel!
granite forge
bot
compact pewterBOT
potent berry
IN EVERY HELP CHANNEL
eternal pulsar
Lmfao
granite forge
hacked account
glacial mortar
EVERY CHANNEL
granite forge
crazy
glacial mortar
lol
visual dawn
I just came can anyone give an idea of what goes in this server
eternal pulsar
Also, how many dumb people click these fuckinng steam links?!
granite forge
Discussion and help
Is there an all-subjects version of this server?
granite forge
<#406129911992942593>
thanks
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obtuse sphinx
What went wrong in my solution?
compact pewterBOT
What went wrong in my solution?
obtuse sphinx
never mind. silly mistake on my part π€ͺ
4sqrt(10) instead of 6sqrt(10) as stated in Q
.close
somber shale
How do i factor this?
compact pewterBOT
How do i factor this?
trail cave
How do i factor this?
sum of cubes/ difference of cubes
somber shale
That's a^2 +2ab +b^2 right?
pine osprey
That's a^2 +2ab +b^2 right?
aΒ² - bΒ² = (a+b)(a-b)
pine osprey
You have to simplify ?
somber shale
eh ?
pine osprey
Im asking what you have to do
pine osprey
Yes
pine osprey
Yw
pine osprey
Maybe there is some kind of rule idk
trail cave
sin x tan x = sin^2 x / cos x
somber shale
is that a rule?
pine osprey
What do you mean by rule?
pine osprey
Ah
somber shale
like the pythagorean identities
trail cave
i dont know what rules you have i'm just turning tan into sin/cos...
somber shale
oh ok
somber shale
sin x tan x = sin^2 x / cos x
im just confused on how you got to this
So the numerator tanx gets converted to sinx/cosx
quartz yoke
distribute the denominator maybe it will help
numerator*
1/sinx +1/tanx
Cosec x +cot x
@somber shale that's easy
trail cave
yeah idk what theyre tryna do
somber shale
ok...
quartz yoke
yeah idk what theyre tryna do
they're complicating it further
somber shale
Sorry
quartz yoke
Sorry
dont worry I didn't say that for you
do you need explanation ?or you understood?
somber shale
please explain !! tysm
quartz yoke
okay
we have tanx+sinx/(sinx tanx)
now distribute the numerator
like a+c/bd is a/bd+c/bd
okay?
tanx/tanxβ’sinx +sinx/tanxβ’sinx
tanx will be cancelled in 1st and sinx in 2nd as they're same in numerator and denominator
you will get 1/sinx +1/tanx
1/sinx =cosec x
1/tanx= cot x
cosec x+cotx
any doubt?
quartz yoke
yhhh
Your que is solved now
so close the channel if you don't need any more help π
compact pewterBOT
@somber shale Has your question been resolved?
potent berry
.close
glossy isle
I need help with these types of problems. The only part I know is f(1) the other derivatives I do not understand.
compact pewterBOT
I need help with these types of problems. The only part I know is f(1) the other...
glossy isle
How do I determine whether f'(1) and f''(1) are Positive, negative or Zero?
like i know this is sloping up towards the right and would be positive but I am not sure
gleaming latch
if its sloping upwards, its positive
if you were to write it as an equation mx+b, the tangent line to the function at that point, then m would be the slope (f'(x))
glossy isle
ok, thank you I get f'(x) now but what about f''(1)
gleaming latch
f''(1) is the derivative of the derivative
would you be able to sketch the graph of f'(x)?
glossy isle
for this would it be
gleaming latch
thats not quite right
notice how at these 3 points
are 3 different slopes
first one is steep, second one is not as steep, third one is steep again
compact pewterBOT
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flat jewel
is my solution correct? i just wanted to double check
compact pewterBOT
is my solution correct? i just wanted to double check
@flat jewel Has your question been resolved?
flat jewel
<@&286206848099549185>
flat jewel
<@&286206848099549185>
flat jewel
<@&286206848099549185>
compact pewterBOT
@flat jewel Has your question been resolved?
carmine garden
Prove or give a counter example.
Let $(a_n) \to a$
If every $a_n$ is an upper bound for a set $B$, then $a$ is also an upper bound for $B$
compact pewterBOT
Prove or give a counter example.
Let $(a_n) \to a$
If every $a_n$ is an upper b...
boreal girderBOT
What a wonderful world !
carmine garden
I suspect this is false
molten coral
how
carmine garden
I thought I could consider the set ( 0, \sqrt{2}) and come up with a decreasing seqeunce converging to \sqrt{2}
rigid perch
that's still an upper bound though
molten coral
but then a would be an upper bound?
carmine garden
yeah, just realised
molten coral
I suspect this is false
my analysis brain is sounding alarms at this
i cant vocalize it because bad at math
carmine garden
Hmm, I could try proving it in that case
molten coral
i swear theres some theorem
i mean this is a fundamental idea that you cant suddenly have jumps
i just cant have a word to it
cant remember
carmine garden
Let $a$ not be an upper bound for $B$, it thus follows there exists an element in $B$, such that $bβ₯a$.
\
As $a_n$ is convergent, $\forall \varepsilon >0$there's an $N$, such if $nβ₯N$, $\abs{a_n-a}β€ \varepsilon$
\
We thus have that $\forall nβ₯$, $a_n - a β₯ a_n -bβ₯ \varepsilon$.
\
It thus follows that $a_n. \to b$ and $a_n \to a$
\
Thus $b=a$.
\
This would mean $a$ is an in upper bound
past ginkgo
my analysis brain is sounding alarms at this
its true
its less a thing about jumps and more like
boreal girderBOT
What a wonderful world !
past ginkgo
squeeze theorem
rigid perch
sort of a general principle that limits preserve inequalities (nonstrictly)
past ginkgo
yes
carmine garden
Let $a$ not be an upper bound for $B$, it thus follows there exists an element i...
does this work
past ginkgo
oh yeah, do you have the squeeze theorem
past ginkgo
does this work
its sloppy but sure
instead of "not an upper bound and b\geq a"
do b>a
and get that a_n is eventually b > a_n
OR
carmine garden
oh yeah, do you have the squeeze theorem
yea
past ginkgo
directly show that sup B \leq a
copper sierra
if we can use this fact
limits preserve nonstrict inequalities
then the proof is very fast
past ginkgo
do you have that a_n \leq b_n implies lim a \leq lim b
carmine garden
do you have that a_n \leq b_n implies lim a \leq lim b
yes
carmine garden
oh right
copper sierra
so lim a_n \geq lim b_n = sup B
lim a_n
copper sierra
big pun
copper sierra
u cant keep getting away with this
carmine garden
This is kind of easy to disprove
\
If every $(a_n)$ is rational, so is $a$
\
$a_n= \left( 1+ \frac{1}{n} \right)^{n}$ works, but haven't defined $e$ so a bad example
boreal girderBOT
What a wonderful world !
copper sierra
a_n=nth truncation of pi
past ginkgo
This is kind of easy to disprove
\\
If every $(a_n)$ is rational, so is $a$
\\
...
very easy to disprove yes
past ginkgo
a_n=nth truncation of pi
or: any irrational
carmine garden
a_n=nth truncation of pi
for that I would have to define $Ο$ and prove stuff about it, right
boreal girderBOT
What a wonderful world !
copper sierra
limits were invented to fill in irrational gaps
carmine garden
yea, but Ο is a different beast
past ginkgo
for that I would have to define $Ο$ and prove stuff about it, right
no just take anything irrational
literally any of them
copper sierra
sqrt2 is also famous
carmine garden
okay, $\sqrt{2}$'s digits, I suppose then
boreal girderBOT
What a wonderful world !
carmine garden
okie, thanks
past ginkgo
truly
carmine garden
.close
compact pewterBOT
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chilly basalt
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chilly basalt
Is my work correct? For integrating cos^3
kind viper
assuming no arithmetic fuckups yes
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tacit geode
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tacit geode
i do not understand this problem at all am I even doing this right?
To find x and y I added and substracted the initial set of equations with the hope I can form a new set of equations
i just don't get these problems or how to solve them
kind viper
i do not understand this problem at all am I even doing this right?
not really
in this problem though you can notice two things: that the only two denominators involved are 2x-3y+2 and and 3x-2y+3
which lets you do a certain trick that im about to show on paper
tacit geode
oh ok
tacit geode
and when we find u and v those are howevere not the values of x and y
right?
u and v is just 1/...
kind viper
and when we find u and v those are howevere not the values of x and y
of course they aren't.
but once you find u and v, you can reduce easily to a linear system in x and y
tacit geode
but once you find u and v, you can reduce easily to a linear system in x and y
like this? but if we first said u and v is = to something now we say it's equal to something else? and how does it help me find x and y now
kind viper
ok hold on let me reproduce
tacit geode
alr
kind viper
so i know you got the arithmetic right
ok you did
now
1/(2x-3y+2) = 1/3
1/(3x-2y+3) = 1/2
thus
2x - 3y + 2 = 3
3x - 2y + 3 = 2
and so you have another linear system
tacit geode
1/(2x-3y+2) = 1/3
1/(3x-2y+3) = 1/2
this part i understood very well. the next part not so much. Where did we get those new values from
kind viper
wym
i took the reciprocal of both sides
in each one
you understand that if 1/a = 1/8 then a=8, yes?
kind viper
yea it's the general rule of proportions
if you want, i guess...
kind viper
is this what we do
yes, it's literally what i wrote
tacit geode
yes, it's literally what i wrote
i understand better now i think
ok so 2x-3y = 1
3x-2y = -1
@kind viper i did it!!!
Thank you so so so so much for teaching me this method i had no idea you can even do that it was so much easier
and i actually understood it
kind viper
substitution is a powerful tool
tacit geode
substitution is a powerful tool
I know I just got used using the reduction method like adding ... the equations method
tacit geode
substitution is a powerful tool
i just had no idea you can literally introduce new variables yourself
because doing that helped me alot
This is however factorizing no?
kind viper
no, there's no factorization involved here
deft tangle
Prriod of |sin4x|+|cos4x|
compact pewterBOT
Prriod of |sin4x|+|cos4x|
compact pewterBOT
@deft tangle Has your question been resolved?
deft tangle
No idea
lone quartz
Prriod of |sin4x|+|cos4x|
Do you know what period of |sinx| is?