Which theres no prior mention of
#help-38
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amber tulip
how do you deal with the |f(x)| term after distribution |f(x)||g(x) - g(x_0)| + g(x_0)|f(x) - f(x_0)|
green ridge
@austere cedar does it not?
remote trout
how do you deal with the |f(x)| term after distribution |f(x)||g(x) - g(x_0)| + ...
i don't think you want to use product rule here. you just need the limit
put fg(x) into the definition of epsilon-delta limit, then expand it: fg(x) = f(x)g(x)
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wraith hinge
can someone explain how/why we assumed |x-c|<1?
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can someone explain how/why we assumed |x-c|<1?
vagrant marsh
we start by picking an arbitrary c close to x
trim lichen
to make a bound on |x+c| happen
ionic pendant
we are allowed to do that as long as we later define delta < 1
since |x - c| < delta < 1
wraith hinge
we are allowed to do that as long as we later define delta < 1
but then can't i pick any strictly positive no. instead of 1 which can be greater/smaller?
ionic pendant
it didn't have to be 1 specifically
wraith hinge
so there's no reason of picking 1?
ionic pendant
1 was chosen just because it's a nice number
and we did have to make some choice of bound
wraith hinge
and we did have to make *some* choice of bound
i see, okay i got it
thank you!
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lofty raptor
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lofty raptor
Help I don't know anything
Guys
I was watching this video
And I can't understand how we jumped from black bubble to white bubble
<@&286206848099549185> guys can you please help me have a nice day
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signal harness
is someone able to walk me through solving thisproblem i havea general idea of solving basic subspace problems but not things in this type of form ...
ionic pendant
what are the conditions of the subspace test?
signal harness
the zero vector has to exist W is closed under addition and W is closed under scalar multiplication
ionic pendant
yes
signal harness
im just not sure how to apply it to a problem like this
ionic pendant
well let's start with the first one
what is the 0 vector in F(-infinity, infinity)?
signal harness
it would just be 0 ?
ionic pendant
well it has to be a function
signal harness
fo(x) ?
ionic pendant
what is fo?
signal harness
the zero function
ionic pendant
yes, the zero function is our zero vector here
so we need to find out whether the zero function is in W
in other words, is the zero function even?
signal harness
yes
ionic pendant
so then that's the first condition fulfilled
signal harness
ah ok that makes sense
ionic pendant
because W is the set of even functions, a function belongs to W if it is even
so then the next thing is, given two functions are in W (are even), is their sum in W (even)?
ionic pendant
yes
so "the sum of two even functions is even" is exactly equivalent to saying "W (the set of even functions) is closed under addition"
signal harness
okok
and for the third test the closed under scalar multiplication since youre multiplying a scalar to a function thats even for all x's the function times the scalar will always be even as well right ?
so thats why its in W
ionic pendant
a constant multiplied by an even function does produce an even function
your reasoning is a bit unclear
signal harness
what i was thinking was
we have f(x) = f(-x) for all x
and then if i multiply it by a scalar k it would be like k*f(x) right
and since f is even f(x) = f(-x)
modest scarab
never give up you sigmas
signal harness
thank you sir
modest scarab
you are well come mr
signal harness
and since f is even f(x) = f(-x)
if u multiply it by a scalar k
since f(x) = f(-x) and its even
kf(x) = kf(-x)
that was kinda my thought process
ionic pendant
yes, that works
signal harness
would u be able to assist me on this problem as well ?
ionic pendant
sure
signal harness
for this one im not really given like a function though
ionic pendant
your set is the set of vectors lying on the x and y axes
in other words the set of vectors which either have x-coordinate 0 or y-coordinate 0
signal harness
so for starter
the zero vector is (0,0) obviously
and it exists since when its (0,0) it confirms x = 0 and y = 0 righ t?
ionic pendant
i wouldn't say it "exists" because it exists anyway, but it is in W
signal harness
hm okok
for the addition test
would i just like
pick a vector where x=0
and then another vector y = 0
and then just add them togehter ?
ionic pendant
what do you get if you do that?
signal harness
if i chose something like
(1,0) + (0,1)
both coordinates exists in W since it has x=0 and y=0 right ?
but when u add it tgt
it doesnt have a 0 in any of the coordinates
so it fails the addition test ?
ionic pendant
yes, you have found a counterexample
signal harness
so thats enough to show that the subspace doesnt exist
if i was to do the scalar multiplication test
ionic pendant
it's enough to show that the set W is not a subspace of V
signal harness
yeah
signal harness
if i was to do the scalar multiplication test
if i do this test
1,0 and 0,1 exists in W
if i multiply 1,0 and 0,1 by a scalar k
i would get k,0 and 0,k right ?
and they would both exist in w so
its closed under scalar multiplication right ?
ionic pendant
yes, although you have to be a bit more general, since your argument has to work for all the vectors in W
signal harness
okok yeah
could i ask 1 more question just interpreting the problem this time
cause i think my trouble is coming from the interpretation of the problems
ionic pendant
sure
signal harness
so for this problem
w is the set of functions y=y(x)
sastifying y'+xy=0
C1(-inf,inf) is the vector space of real valued functions
ionic pendant
C1(-inf,inf) is the vector space of real valued functions with a continuous firsr derivative
signal harness
yeah
and then we use the subspace test to see if W is a subspace of V
when we perform the different tests what exactly do u like test it on if my question makes sense
like the set of functions in this case for this problem ?
signal harness
and u use those vectors in W to test W
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nocturne sky
Find the value of x without giving the value of y.
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Find the value of x without giving the value of y.
nocturne sky
my work so far
trim lichen
hold on a minute
-10x^2y^2 + 9x^2y^2 simplifies to -1x^2y^2
in fact your entire LHS simplifies to zero
@nocturne sky are you 110% sure you did not miscopy or misremember or anything?
frail heron
Looks legit
nocturne sky
aw lemme do it again
trim lichen
the equation becomes 0=100, which obviously has no solutions at all.
trim lichen
aw lemme do it again
we are asking about the original problem.
nocturne sky
oh i missed the b part
it said that if that equation is false, prove why
ok now i know why
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trim lichen
this is always why you always have to post the ENTIRE thing
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green valve
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green valve
good morning, I was wondering on what to do from now on. the 1- infront if making me question stuff
west sleet
Equate to 0 to find stat pts
green valve
oh so im already at the critical numbers step?
west sleet
Use first or 2nd derivative test to find nature of stat pts
west sleet
oh so im already at the critical numbers step?
Ye
green valve
this guy frl
green valve
ya i unfortunatly didnt really get that
i did precalc last semester and the teacher was terrible
green valve
nah this is just me and my alternative school path
i didnt think i would be in university at all
west sleet
Oh
green valve
wasnt really supposed to
west sleet
This is uni?
green valve
its complicated
our school system where i am is different than the rest of canada
basically went to sorta trade school
west sleet
Anyways we have 1-f/g
Where f/g is the fraction which I'm too lazy to type out
So I'll just notate the functions on the numerator and denominator with f and g
So since 1-f/g=0
Then f/g=1
green valve
yes
west sleet
And as such f=g
green valve
ok i can do the rest
i wasnt sure on the rules about the 1-
would i multiply the 1 by the (x=5)^2
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limpid dawn
im still stuck with this basic algebra
then why'd you close your channel, george?
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green valve
cause im at the step where you loose your hair
limpid dawn
which is it
green valve
if i understood from online you can just take the numeroter and multiply t he other side by it
green valve
which is it
testing points
limpid dawn
is it this?
green valve
Heres where im at
Going to erase and test with the interval and my critical points
limpid dawn
pastel wren
Looks fine where’s the issue
limpid dawn
i see
empty orchid
To be honest, the derivative is better taken without quotient rule
You can simplify it to $125+\frac{A}{x+5}$, for some $A\in\mathbb{R}$
solid kilnBOT
;(
empty orchid
what does that do
Restrict it to the other answer
green valve
empty orchid
Yes. Have you heard of the Candidate’s test?
green valve
maybe but my prof never mentionnes the names of the stuff we do
empty orchid
Ok.
For minima and maxima on an interval, you want to test critical points and endpoints.
west sleet
Sorry am back
west sleet
For minima and maxima *on an interval*, you want to test critical points *and* e...
Oh yea mb
green valve
oki yes this is what i was about to do
west sleet
Usually our syllabus doesn't have us test end points
empty orchid
Usually our syllabus doesn't have us test end points
That’s a concern.
empty orchid
oki yes this is what i was about to do
So do it!
west sleet
That’s a concern.
Well you'd have to take it up with big math
In fact there was a question in my textbook that said to find a maximum of a cubic
Which like huh
The answer they gave was the local maxima
But that's not the maximum they specified
My math teacher just said the publisher was tweaking
Also they took out modulus from our syallbus
So our math syallbus is kinda fucked imo
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green valve
im doing another one
limpid dawn
when i reopened they come like mosquitoes, and then leave you when i leave it up to them
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smoky kite
,rotate
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trim lichen
take e^(both sides)
smoky kite
What happens to the exponential on the right though
Doesn’t it remain
I wouldn’t have thought to do that
Oh nvm I’m misreading my own thing
Yeah I’m still not getting it
Ok got it thanks
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vocal cobalt
how do I solve this?
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how do I solve this?
trim lichen
vocal cobalt
im kinda confused on where to start i haven't solved calc problems in ages so...
vocal cobalt
yea
trim lichen
at what values of t would either of these things happen?
vocal cobalt
t=0 and t=-1?
vocal cobalt
as t->0 x approaches inf and -inf?
trim lichen
and y?
vocal cobalt
am i getting y from 1/t or t/t+1?
vocal cobalt
why would you imagine it otherwise
what do i do next?
trim lichen
so, as t goes to 0, what does t/(t+1) approach?
vocal cobalt
0?
vocal cobalt
x approach -1 and y approach 0?
trim lichen
$y = \frac{t}{t+1}$ and $t \to -1$, are you sure $y \to 0$?
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Ann
vocal cobalt
it approaches +-inf
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vocal cobalt
<@&286206848099549185>
vocal cobalt
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toxic sorrel
hi can someone verify my work?
trim lichen
!msgdel
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unkempt dew
i am trying to get better at quadratics but im doing this simul equation and completing the square isnt working
unkempt dew
i done from
y=2x^2 -3x-1 y=3x ,
2x^2 -6x -1 =0,
(x-3)^2-10
x=-3 x=10
y=-9 y=30
but the answer is actually
i dont know how to get to there
quadratic equation?
trim lichen
i done from
y=2x^2 -3x-1 y=3x ,
2x^2 -6x -1 =0,
(x-3)^2-10
x=-3 x=10
y=-9 y=...
think you completed the square incorrectly there
tulip violet
i done from
y=2x^2 -3x-1 y=3x ,
2x^2 -6x -1 =0,
(x-3)^2-10
x=-3 x=10
y=-9 y=...
(x-3)^2 = x^2 -6x + 9 - 10 => x^2 - 6x - 1
You didn't account for the 2 when you completed the square
trim lichen
2x^2 - 6x - 1 = 0 doesn't lead to (x-3)^2 - 10 = 0
unkempt dew
(x-3)^2 = x^2 -6x + 9 - 10 => x^2 - 6x - 1
You didn't account for the 2 when you...
😭
how do i bro, ive been at this for a solid 15min
unkempt dew
(x-3)^2 = x^2 -6x + 9 - 10 => x^2 - 6x - 1
You didn't account for the 2 when you...
2[(x-1.5)^2 -2.75]?
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unkempt dew
this still doesnt work
now i got
y=2x^2 -3x-1 | y=3x ,
2x^2 -6x -1 =0,
2[(x-1.5)^2 -2.75]
x=-1.5 x=2.75
y=-4.5 y=8.25
but
the answer is
coarse reef
y=2x^2 -3x-1 | y=3x ,
2x^2 -6x -1 =0,
2[(x-1.5)^2 -2.75]
x=-1.5 x=2.75
...
from 2x^2-6x-1=0
x^2-3x-1/2=0
x^2-3x+9/4-1/2=9/4
(x-3/2)^2-1/2=9/4
(x-3/2)^2=1/2+9/4
x-3/2=+-sqrt(1/2+9/4)
x=3/2+-sqrt(1/2+9/4)
unkempt dew
from 2x^2-6x-1=0
x^2-3x-1/2=0
x^2-3x+9/4-1/2=9/4
(x-3/2)^2-1/2=9/4
(x-3/2)^2=1/2...
why +9/4?
coarse reef
why +9/4?
but yeah you add (middle term divided by 2)^2 to both sides to complete the square
since that will appear when you expand (x-middle term/2)^2
unkempt dew
but yeah you add (middle term divided by 2)^2 to both sides to complete the squa...
never heard of that but thanks ill try it
coarse reef
never heard of that but thanks ill try it
it always works as long the x^2 coefficient is 1
so you have to force it to be 1
unkempt dew
it always works as long the x^2 coefficient is 1
W
unkempt dew
it always works as long the x^2 coefficient is 1
TYSM IT WORKS
gonna have to pin that on my wall ngl
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old terrace
Hey, This is the problem im trying to solve, im having trouble knowing if i should be using the disc method or shell method. I believe its the washer method but I keep seeing others say disc and im going crazy.
real rose
Hey, This is the problem im trying to solve, im having trouble knowing if i shou...
It is indeed disk
You are not rotating around y=c, rather an axis
old terrace
You are not rotating around y=c, rather an axis
Wouldnt the x-axis be considered y=0? If so and your integrating with respect to Y (since its u(y)), i think it would be shell? Unless im just completley mistaken
real rose
Wouldnt the x-axis be considered y=0? If so and your integrating with respect to...
Well y=c where c is not 0
old terrace
Sorry i think im just getting a bit confused since its to respect to y
old terrace
Well y=c where c is not 0
ah okay
real rose
Sorry i think im just getting a bit confused since its to respect to y
Just swap the variables for x if it makes more sense for you
variables are just placeholders
old terrace
Just swap the variables for x if it makes more sense for you
okay so i flipped the signs up everthing
and graphed it out
the slices are parallel to the axis of rotation, I thought his meant it was shell method?
real rose
the slices are parallel to the axis of rotation, I thought his meant it was shel...
You should be having x-slices, not y-slices
old terrace
You should be having x-slices, not y-slices
how come?
sorry if im asking alot im just tryna understand 😭
real rose
how come?
Ah wait
Your picture confused me
If you're rotating around the x-axis, rotate with y-slices, but not around the y-axis lol
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old terrace
Ah wait
Maybe my math website is werid at asking questions, but yeah it was the shell method
regal imp
got not idea what im doing here
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got not idea what im doing here
regal imp
if theres like some type of formula or simple explanation that would help
like- as in steps to complete these questions
real rose
got not idea what im doing here
Similar triangles
regal imp
so all of them are 25?
real rose
I'm not saying that, but there is similar triangles here
Or just use the definition of a midsegment
regal imp
so
UY would be 25 x 2?
I'm still confused, and this has nothing to do with supplementary angles right? only focusing on #5
real rose
UY would be 25 x 2?
Yep
regal imp
got it got it
real rose
I'm still confused, and this has nothing to do with supplementary angles right? ...
Yeah
regal imp
so moving on to 6
real rose
So let's try 6
real rose
Why do you say that
regal imp
for which one?
real rose
For both answers
regal imp
well
i'm not sre
i say the second one because the 57 is right there, and if all triangles are alike, then x would just be 57
my apoligies, and for my first answer i say 360 - 57/2 because they have 57 labeled as an angle
regal imp
sure..
2.7 divided by 2, since the sum of 2 triangles equals 2.7
and it's only asking for 1
real rose
Though I feel it would just be 57
real rose
2.7 divided by 2, since the sum of 2 triangles equals 2.7
Good
regal imp
so that would be 1.35
regal imp
Though I feel it would just be 57
me too honestly, not sure why they would put an angle marking
but when you look at #8
it seems like you would do the 360- 57/2
real rose
Not really
I can explain 8
Basically from similar triangles we have angle WVR= angle WUY and angle VRW=angle WYU
regal imp
right
real rose
SO try to apply that
Then find YZR
And also, YRZ=YWU, I think this is more direct lol
regal imp
im so lost\
real rose
im so lost\
Similar triangle
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trim lichen
also you cannot cancel in the second step bc cos(theta) is not a factor of the numerator
the numerator isn't cos(theta) times something
bright quarry
yes cos^2 - 1 = (cos * cos) - 1 ≠ cos ( cos - 1)
trim lichen
the first step was legal, the second isn't
yes. but those parentheses are implied by order of operations anyway
which is why you don't see them written
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twin yoke
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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
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twin yoke
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bright quarry
anyways
bright quarry
twin yoke
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worthy ether
twin yoke
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bright quarry
no worries jeremy
bright quarry
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did you watch the 3b1b video
twin yoke
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bright quarry
figured
twin yoke
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bright quarry
so first of all is it dy or dx
twin yoke
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bright quarry
mhm
twin yoke
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bright quarry
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now can you draw the radius on this
twin yoke
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bright quarry
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no around a vertical line you mean
x axis is y = 0
twin yoke
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bright quarry
yes
twin yoke
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bright quarry
now what is the red
twin yoke
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twin yoke
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bright quarry
twin yoke
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bright quarry
what is the yellow
twin yoke
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bright quarry
what is that distance in yellow
twin yoke
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bright quarry
i know but what is it
twin yoke
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twin yoke
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bright quarry
the vertical height of the curve at any point is sqrt(x)
twin yoke
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bright quarry
the horizontal distance to the curve at any point is simply x
bright quarry
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no
twin yoke
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bright quarry
sqrt(x) is a y value
twin yoke
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bright quarry
the horizontal distance to the curve at any point is simply x
does this make sense
twin yoke
does this make sense
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bright quarry
ok
now the distance from the y axis to the line x = 4 is what
green line to purple
what’s the distance
twin yoke
now the distance from the y axis to the line x = 4 is what
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twin yoke
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bright quarry
mhm
now
since we’re integrating dy we need to express 4 - x in terms of y
so if y = sqrt(x)
what does x =
twin yoke
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bright quarry
find the volume
twin yoke
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bright quarry
no space
twin yoke
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bright quarry
after the $
solid kilnBOT
Kenzo
twin yoke
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bright quarry
the zero is going to go away obviously
twin yoke
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bright quarry
so just try upper bound
twin yoke
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bright quarry
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sigh
you were doing so well
(a - b)^2 ≠ a - b
twin yoke
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Kenzo
bright quarry
nice
twin yoke
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Kenzo
twin yoke
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bright quarry
which becomes
you don’t even need to simplify btw
ap let’s you leave it
if you put 2 in for y
twin yoke
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bright quarry
yes
twin yoke
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bright quarry
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you’re welcome sir
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willow summit
can someone please tell me where I made mistake here, it's boolean algebra. it's allowed here right?
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can someone please tell me where I made mistake here, it's boolean algebra. it's...
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spice shuttle
help me here
willow urchin
what did u try
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spice shuttle
what did u try
dont know how to proceed 😭
strong delta
help me here
in what intervals is f(t) not differentiable and why
simple panther
help me here
Didn't they give the solution there?
spice shuttle
i couldnt understood that one
spice shuttle
mains
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willow urchin
dont know how to proceed 😭
i would compute f' then see what values of lambda and mu make f' exist everywhere
spice shuttle
Is this understandable?
isnt f' this?
spice shuttle
18
tidal zenith
Hmmm ok 😌
spice shuttle
i got it now lol
spice shuttle
Is this understandable?
so basically funtion is not differentiable at 0 and f'(0)= mu now?
willow urchin
isnt f' this?
no, u need to be careful about sin(2|t|)
oh you computed f' on t>0, what about t<0?
willow urchin
you need to find lambda and mu such that f'(0) exists
spice shuttle
ok i got that as mu = |lambda| then?
willow urchin
ok i got that as mu = |lambda| then?
i checked with a graph and this seems right
spice shuttle
i checked with a graph and this seems right
yeah i mean to say i got the lambda where it exists but what now?
willow urchin
yeah i mean to say i got the lambda where it exists but what now?
from mu = |lambda| can u see any restrictions on lambda or mu?
spice shuttle
wym by restriction?
willow urchin
does this equation imply anything about lambda?
spice shuttle
does this equation imply anything about lambda?
see what i m getting from here is f(t) has to be differentiable so we calculated the points such that fn is differentiable which is |lamba| = mu but cant find narrow down wht other relation is there
spice shuttle
R? coz it has modulus so basically any number will give out positive value?
spice shuttle
mu can take any as well?
willow urchin
can it?
spice shuttle
if we put negative value or positive in both cases it will not break any rule/ ig
where i m wrong
willow urchin
try out some pairs of values and see when they satisfy the equation...
spice shuttle
ok
willow urchin
lambda=2,mu=5 obviously doesnt
but 2,2 does so try tweaking this pair and checking again
willow urchin
$\lambda\in\bR,~\mu\ge0$
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willow urchin
yes?
spice shuttle
yes
willow urchin
now see what answer matches this
spice shuttle
thanks
willow urchin
ur welcome 🙂
spice shuttle
ur welcome 🙂
i m just confused in theory a bit here tbh like
- I found since LHD isnt equal to RHD so function is not differentiable at x=0
- but since S has to be differentiable
- why cant we remove 0 from domain also how we proceeded ahead with finding lamba = mu
- why we took |lamba| = mu in our focus? and not the actual equation?
vagrant imp
i m just confused in theory a bit here tbh like
- I found since LHD isnt equal ...
t belongs to R is a condition imposed by the question, you cant just remove ti
spice shuttle
t belongs to R is a condition imposed by the question, you cant just remove ti
how we found lambda = mu and why we consider domain of this ??
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vagrant imp
btw for this qs you have to solve by taking log @spice shuttle
vagrant imp
how we found lambda = mu and why we consider domain of this ??
to make the function differentiable at that point thas why
if it wasnt then funcn would not be differentiable
spice shuttle
yeah this one got solved
serene storm
with question 17a, why is the working out 4C2 - 4?
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with question 17a, why is the working out 4C2 - 4?
serene storm
what’s the reason behind subtracting 4?
i know they’re picking 2 points out of 4 vertices
trim lichen
what’s the reason behind subtracting 4?
the 4 sides
they are not diagonals
yet 4C2 counts all possible pairs of points incl adjacent ones
serene storm
wdym by adjacent ones?
there’s only 4 points on the quadrilateral u can pick from tho
like the 4 vertices
oh wait 4C2 means 4 pairs of points choose 2 pairs of points??
is that what you and the solutions are saying?
trim lichen
you are picking 2 points (a pair) from the 4 vertices of the quad.
serene storm
ahhh
trim lichen
when you count the number of ways to do that with 4C2,
your count includes all the diagonals, BUT it also includes the pairs consisting of two adjacent vertices.
serene storm
yeaaaa
trim lichen
you don't want to count those, but you know exactly how many there are. so you subtract them away.
trim lichen
you can work out nC2 as n(n-1)/2 if you want, and go from there
serene storm
isn’t nC2 = n!/(n-2)!x2!?
trim lichen
n! = (n-2)! * (n-1) * n
trim lichen
don't use the letter x as a multiplication symbol
trim lichen
but why tho
very easy to confuse for actual letter x. not worth remembering when confusion can and can't happen, easier to just not use it at all
if you must, use an asterisk.
in TeX, \cdot or \times.
trim lichen
is TeX latex
yes
serene storm
is it hard to learn?
trim lichen
depends
the basics are not terrible but you can do some really out there wack shit with it
serene storm
do you think it’s worth learning?
trim lichen
depends. are you going to major in math?
or some kind of sciencey field like physics?
serene storm
or some kind of sciencey field like physics?
so far my choices for careers are neurosurgery or nuclear medicine/chemistry
trim lichen
then i would say yes it is worth familiarizing yourself with latex just in case.
serene storm
then i would say yes it is worth familiarizing yourself with latex just in case.
in which situations would you have to use latex?
like if i’m doing nuclear chemistry, when will I use latex?
trim lichen
LaTeX is for when you need to publish articles to journals
in principle not even necessarily scientific ones
but since LaTeX is purpose built for typesetting math shit all pretty like, it's popular
serene storm
LaTeX is for when you need to publish articles to journals
ohhh right right
ok thanks again
.close
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hardy socket
how do i prove this?
my approach was
V is a euclidean vector space with the inner product ⟨⋅,⋅⟩
so the inner product ⟨⋅,⋅⟩ is positive definite
meaning the determinant of the fundamental matrix is not 0 so its non-degenerate
so if we look at the isomorphism Φ ⟨⋅,⋅⟩^: V --> V* (V* being the dual space), where a v gets projected onto〈·,v〉then we know its injective and even bijective because of dim V being finite
we got now β_θ which goes from V x V to R which can be transformed to a linear function
β_θ^ which is V --> V* and concatenate it with the inverse of the isomorphism Φ-1 and we get an endomorphism from V to V
Φ-1 o β_θ^: V --> V
meaning we can assign the bilinear form an endomorphism
hardy socket
wrote it down (sorry for the german) 😭
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hardy socket
<@&286206848099549185> 🥹
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@hardy socket Has your question been resolved?
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@hardy socket Has your question been resolved?
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dapper mesa
Ay man I saw your doubt and i didn't really understand any of it because I'm too dumb but I felt bad cuz no one was helping you 😭 so I'm just here for moral support
You got this gang
hardy socket
Ay man I saw your doubt and i didn't really understand any of it because I'm too...
i appreciate you gang fr 😭
i dont know what im doing myself im cooked
exam is on Wednesday
💀
dapper mesa
It looks like vectors and stuff. And I only know how to add them 💔
hardy socket
my man 🧎♂️
lime sphinx
maybe try #linear-algebra
high cipher
how do i prove this?
my approach was
V is a euclidean vector space with the inne...
i don't really understand your proof
but the problem looks quite easy
$ \beta_{\theta} = (\theta x)^T A y = x^T \theta^T A y $
texit pls
okay whatever here it's written in paint
sacred jackal
$ \beta_{\theta} = (\theta x)^T A y = x^T \theta^T A y $
,,\beta_{\theta} = (\theta x)^T A y = x^T \theta^T A y
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vin100
high cipher
,,\beta_{\theta} = (\theta x)^T A y = x^T \theta^T A y
that's how it's done now?
high cipher
okay, i'll keep that in mind thanks
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nimble girder
Help
nimble girder
draw a sketch
How can i do it algebrically
I did this but i didnt get the correct ans
dull island
How can i do it algebrically
solve it piecewise
although that's not very nice and you want a sketch anyways
dull island
I did this but i didnt get the correct ans
this doesn't work because $(1-|x|)^2 = 1-2|x|+|x|^2$
which leaves you with a modulus anyways
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Xetrov
nimble girder
which leaves you with a modulus anyways
So then how do i solve it
dull island
draw a sketch first
it'll end up being algebraic dw
but just draw y=2x+1 then reflect off x axis
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dire dagger
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dire dagger
idk what to do
split chasm
apply tangents to a circle from a point theorem
dire dagger
apply tangents to a circle from a point theorem
yea ik they r tangent
what i do after?
💀
dense breach
after you know they are tangents
then you apply tangents to a circle from a point theorem
dire dagger
then you apply tangents to a circle from a point theorem
what do it mean
dire dagger
which ones r equal
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dire dagger
and RP and SP
x=13 and y=5?
boreal geode
x=13 and y=5?
Yes
dire dagger
sui
boreal geode
Oh
boreal geode
this one porfavor?
dusty sleet
,rccw
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boreal geode
225 is from 15 square btw
dire dagger
do u get what I am doing thou
why you did 1.5?
dire dagger
why u squared a?
boreal geode
Pythagoras theorem the 100 is from 10^2
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As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.
boreal geode
As a helper, please do not give out answers that could be copied as a homework s...
Sorry
dire dagger
So I find the VZ and scale it to VY
you use the whole traingle vxy?
this part i dont understand the most
dire dagger
o
boreal geode
As a helper, please do not give out answers that could be copied as a homework s...
(Btw I am just like a friend rn discussing yk)
inner sand
Plz can someone teach me Venn diagram step by step
boreal geode
Plz can someone teach me Venn diagram step by step
Hi I think u can make a channel
inner sand
Kk
dire dagger
did you didvide 3 by 2 to get 1.5 or sum
boreal geode
Ya
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inner sand
Plzzz who can teach me to solve these questions 🥺🥺
boreal geode
Plzzz who can teach me to solve these questions 🥺🥺
i am bad at vẹn diagram lol so I can’t
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Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).
dire dagger
why 1.5a = a+25
boreal geode
why 1.5a = a+25
a represent the whole thing
(But I am pretty sure there might be an easier way but I just decide to solve it with the step in my mind)
dire dagger
oh
boreal geode
why 1.5a = a+25
15+10 =25
dire dagger
need helpp
hybrid field
hint: QST is the same as QRS + ST
boreal geode
i thought its same as qrs
Does ST = SPT (I am just confused about how it is written
hybrid field
i thought its same as qrs
i assumed it went above and around the circle, Q-R-S-T
it's not written the best way it's kinda hard to understand what they're trying to say
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tribal tapir
If t=tanh x/2 prove that sinhx= 2t/1-t² and coshx= 1+e²/1-e²
simple haven
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radiant portal
Part (c)
radiant portal
I got a negative for the area 🤔
First sub in x = 0 to get the y intercept ln(2)
So our limits are ln(2) and 0
ln(2 + x) = y
2 + x = e^y
x = e^y - 2
x^2 = (e^y - 2)^2
x^2 = (e^2y - 4e^y + 4)
so we integrate (e^2y - 4e^y + 4) with limits ln(2) and 0
(e^3y)/3 - 4e^y + 4y
((e^3[ln(2)])/3 - 4e^[ln(2)] + 4[ln(2)]) - ((e^3[0])/3 - 4e^[0] + 4[0])
dull pilot
why are you integrating x^2-?
radiant portal
(8/3 - 4(2) + 4ln(2)) - (1/3 - 4)
(-16/3 + 4ln(2)) - (-11/3)
-16/3 + 4ln(2) + 11/3
dull pilot
why is it not just $\int^0_{-1} \ln(2+x) dx$ lol
solid kilnBOT
Percy
radiant portal
-5pi/3 + 4ln(2)pi
radiant portal
why is it not just $\int^0_{-1} \ln(2+x) dx$ lol
Its around the y axis
dull pilot
well why are you integrating x^2 dy not x dy
also is there a reason not to integrate the y values or just preference /gen
i might have misunderstood the question
radiant portal
well why are you integrating x^2 dy not x dy
For a volume of revolution youre supposed to square it before you integrate if im not mistaken (maybe another helper can confirm 😅 )
Yeye its x^2
Big image wtf
Anyways, I got -5pi/3 + 4ln(2)pi and they wanted this vv I got close but what did I do wrong?
dull pilot
For a volume of revolution youre supposed to square it before you integrate if i...
oh i thought you were asking about the area lol
radiant portal
Ohhh I think I see my mistake
(e^2y)/2 - 4e^y + 4y (instead of (e^3y)/3 - 4e^y + 4y)
Gives us:
((e^2[ln(2)])/2 - 4e^[ln(2)] + 4[ln(2)]) - ((e^2[0])/2 - 4e^[0] + 4[0])
(4/2 - 4(2) + 4ln(2)) - (1/2 - 4)
(4/2 - 16/2 + 4ln(2)) - (-7/2)
-12/2 + 4ln(2) + 7/2
-5/2 + 4ln(2)
pi(-5/2 + 4ln(2))
Which is what they wanted 😄
Alright awesome!
Thanks
❤️
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karmic kernel
"Is there a 2x3 matrix A and a 3x2 matrix B such that the product AB is invertible?
Provide an example or show that such matrices do not exist."
karmic kernel
I dont know how to approach this problem
the solutions just says "Yes, for example"
But they dont say how they got it
vernal briar
It's easier if you think of the matrices as linear transformations
See what happens to the standard basis
That's probably how you'd come up with this
B maps R^2 to R^3
A maps R^3 back to R^2
If we want our product to be the identity (so obviously invertible)
We could map the standard basis in the way you see in your picture
marble wharf
you dont need to do that. you can just imagine that A and B were 2x2 matrices in disguise
aka, block matrices consisting of 2x2 matrices and then a zero row or column
vernal briar
That's considered a block matrix?
marble wharf
sure
vernal briar
Yeah ok that's easier
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karmic kernel
We could map the standard basis in the way you see in your picture
ok i guess i get that, i understood it as it is (obvoiusly) possible to map two 3D vectors in 2D space and them being linearly independent
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kindred current
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kindred current
Given a and b we must show that the marked condition is true
rn do I just replace a,b with their values? or..?
trim lichen
work out ab separately and also work out 1/a + 1/b
as intermediate steps towards finding the value of x
kindred current
work out ab separately and also work out 1/a + 1/b
So separate x into 2
kindred current
don't like that phrasing
why did we place + if we have minus since we are not mulitplying
trim lichen
-1/a - 1/b = -(1/a + 1/b)
kindred current
-1/a - 1/b = -(1/a + 1/b)
I think I found the value of x
tho i did a mistake somewhere bec it is supposed to be positive
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umbral lily
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tawdry oasis
u speak indonesian ?
lyric musk
<@&286206848099549185>
You can you this website to help you: https://www.symbolab.com/solver/y-equals-mx-plus-b-calculator
rancid carbon
Use desmos
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edgy kindle
$(1/-x^2)-(2/x^2)+(1/x^2)=0$
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$(1/-x^2)-(2/x^2)+(1/x^2)=0$
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ninjew
main sigil
$\frac{1}{-x^{2}}+\frac{2}{x^{2}}+\frac{1}{x^{2}}$
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MathIsAlwaysRight
main sigil
notice that 1 / (-x^2) is same as - 1/x^2
after that, all the fractions will have the same denominator. So you can just add them standardly
edgy kindle
its a quadratic formula thing, wait lemme send the starting point so u can see if and where i went wrong
ex70
text translate to: unique equations
in the next equations connect each sides alone, factor and solve
<@&286206848099549185>
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worldly wing
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worldly wing
I assume this is only true for real matrices Q
how would I prove this?
$Q+Q^T=0\implies v^T(Q+Q^T)v=0\implies v^T Qv+v^T Q^Tv=0$
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kheerii
worldly wing
if $v$ is an eigenvector of $Q$ with eigenvalue $\lambda$ then $v^T\lambda v+(\lambda v)^T v=0\implies 2\lambda v^Tv=0\implies\lambda=0$
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kheerii
worldly wing
I assume the issue here is that I need to use the adjoint, not the transpose
so I'd get lambda + lambda* = 0
but I don't know how the adjoint works
I think I got it
$Av=\lambda v\implies v^Av=v^\lambda v\implies \lambda v^*v=v^*Av=-v^*A^*v=-(Av)^*v=-(\lambda v)^*v=-\bar{\lambda}v^*v\implies\lambda+\bar{\lambda}=0\implies\Re(\lambda)=0$
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kheerii
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tardy ledge
can i get some help with this
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can i get some help with this
tardy ledge
I have to solve using calculus
so initially what I did was integrate a(t) to find velocity which was 10t + C
and then integrate velocity to get displacement
which was 5t^2 + cT + C
but then i am lost
viscid flower
it could be helpful to give more meaningful names to the constants and your results
viscid flower
so initially what I did was integrate a(t) to find velocity which was 10t + C
lets say that this is $v(t)$. Then you'd say since $v(0)=C$, we'd name it $v(t) = 10t + v_0$
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jan Niku
viscid flower
depends, but yea
tardy ledge
well for the 15 floor one isn't it 0?
viscid flower
then youd likewise get $y(t) = 5t^2 + v_0 t + C$ so maybe we say $$y(t) = 5t^2 + v_0 t + y_0$$
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jan Niku
viscid flower
where y0 is the initial height (in meters)
tardy ledge
oh