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#help-23
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lean otter
help
drifting knot
Yo
drifting knot
Ok
lean otter
is it just because for uniform convergence sup norm should converge to the limit functions sup norm
and this isn't true for pointwise
.close
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dark warren
How do I get to the magnitute of the vector
safe radishBOT
How do I get to the magnitute of the vector
quiet plume
Draw a right triangle, and use Pythagoras theorem
dark warren
like this?
quiet plume
Yes
quiet plume
It will always work.
dark warren
alright
quiet plume
Since the axes are perpendicular, the coordinates will always make a right triangle
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plucky lotus
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plucky lotus
the answer is A but i really do not get it
warm kernel
With this relatively simple image, you can understand what I am trying to say with the figures?
plucky lotus
With this relatively simple image, you can understand what I am trying to say wi...
OKAU THANKS
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frozen pebble
is there a way to solve C1y''+C2(y')|y'|=k?
safe radishBOT
is there a way to solve C1y''+C2(y')|y'|=k?
frozen pebble
without having to integrate twice
wiht Cs and k being constants
sorry mb thats the actual question
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@frozen pebble Has your question been resolved?
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strange plaza
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strange plaza
Quesiton C is wrong in my working out
I was attempting to apply the formula. The only thing different to my answers is the n-1 power was just an n.
Why would this be the case?
knotty pier
Why do u think it is n-1?
eternal carbon
I was attempting to apply the formula. The only thing different to my answers is...
each 0.95 counts as part of one recharge
so 0.95^(n - 1) means the battery is recharged (n - 1) times
knotty pier
Ok so just to be sure
put n=0 when it is not charged at all
U should be getting 32
But u r getting 32/0.95
If it was n rather than n-1
It would be correct
@strange plaza
strange plaza
Why do u think it is n-1?
Thats what ive used from the formula sheet
$T_n=ar^{n-1}$
flat frigateBOT
Jshy
knotty pier
Thats what ive used from the formula sheet
My explanation should be clear?
strange plaza
My explanation should be clear?
I understand that but im more interested in learning why using the formula exactly isnt working out
Does 2 not equal Tn?
Is it because it has already been decharged so its n rather than n-1?
safe radishBOT
@strange plaza Has your question been resolved?
wind laurel
$\frac{(x^2 - x^{-2})^a}{x}$
How would i find the coefficient of $1/x$ in terms of $a$?
flat frigateBOT
woomy
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@wind laurel Has your question been resolved?
lean otter
$\frac{(x^2 - x^{-2})^a}{x}$
How would i find the coefficient of $1/x$ in terms...
what do you mean
twin prawn
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twin prawn
can someone check if my assessment is correct?
wild bough
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@twin prawn Has your question been resolved?
jolly violet
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jolly violet
I just dont get the last part of the solution
or like I forgot what I did
from 2g = 30 + G
or is it just divide both sides by g
mr <@&286206848099549185>
jolly violet
yea I js blanked, cause my notes were messy
stable flint
somber parcel
from 2g = 30 + G
You subtract the g from 2g
safe radishBOT
@jolly violet Has your question been resolved?
summer cliff
why am i wrong
safe radishBOT
why am i wrong
icy lance
(x^2+2)^2 is not x^4+4
also youre doing this in an inefficient way
if dy/dx=g(x)
and youre integrating 3g(x) then its 3 * (y(2)-y(0))
since g(x) integrates to y
bleak osprey
is the answer 60?
safe radishBOT
@summer cliff Has your question been resolved?
bleak osprey
even if you dont hear it, heres a simple way to put it:
you just need to put on relations for equations that you can solve;
say total students is x, total girls are G and boys are B,
if Filipinos are 1/3 of x, x/3, AND 2/3 of girls, 2G/3, it means they both equal each other, then we can find a general equation for x that is: x = 2G
as boys are given, 30, and as x should be the sum of number of girls and boys, x = G + B, that gives us second chance for relating equations, so
as x = 2g and also x = G + B, 2G = G + B, simplifies to G = B, so total students, x, is 2 B, that is 60
we related equations 2 times, first, for getting a equation to relate girls with total students, second to realte boys with girls
bleak osprey
even if you dont hear it, heres a simple way to put it:
you just need to put on...
@jolly violet
summer cliff
if dy/dx=g(x)
and youre integrating 3g(x) then its 3 * (y(2)-y(0))
i dont understand this
bleak osprey
why am i wrong
interesting
icy lance
$\frac{dy}{dx}=g(x)$ so
$$\int_{a}^{b} g(x) dx=y(b)-y(a)$$
flat frigateBOT
AℤØ
summer cliff
@icy lance i just dont understand why answer integrate y when the question ask for integrate g(x) which is deriavatives of y
summer cliff
the answer integrate y
icy lance
which answer?
summer cliff
answer sheet for this paper
icy lance
may i see
summer cliff
is not wt me
icy lance
sure youre remembering that right, not confusing evaluating y with integrating y
icy lance
thats just what i said
it doesnt integrate y anywhere on that paper
it evaluates it
between 0 and 2
summer cliff
so y = g(x)?
summer cliff
ok let me try understand it
bleak osprey
is 8 − 6 ln(3) the answer?
oh nah wait, it might not be
bleak osprey
stop answering that one here
its the answer to @summer cliff 's question
icy lance
most certainly isnt
summer cliff
even i didnt get ln
icy lance
also no
bleak osprey
yeah
icy lance
you do not need to differentiate anything for this question
bleak osprey
for the derivative
bleak osprey
oh wait, lol, yeah he is right
summer cliff
can you explain cause my brain is not functioning
bleak osprey
can you explain cause my brain is not functioning
what I did was in a sense right but it was more complex, this approach is more simpler
just substitute g(x) with dy/dx, then integrate the integral
for simpler sense, imagine it like this, cause explaining integration is hard for me:
put the 3 out for a sec
dy/dx cancels out with dx, leaving y, which is then integrated with the limits
which in fact makes it: 3 [y(2) - y(0)] if you have studied limits
summer cliff
ok let me try and understand it (pls brain)
bleak osprey
eval y(2) and y(0), and as I see it, the answer should be 4
but why doesnt my answer also match, let me analyse wait
summer cliff
basically if i integrate g(x) i get y
ohh
i get it
basically the integration of g(x) is just y
bleak osprey
basically if i integrate g(x) i get y
you are really getting confused on calculus terms
revise it and you are good to go
summer cliff
8/100 additional mathematics
bleak osprey
damn
summer cliff
the only question i got right is triangle
function and calculus i get nothing
so i am trying to revise rn
bleak osprey
g(x) is actually the derivative, we are actually going the derivative of y, that is g(x)
so we are actually finding g(x) in a sense if we dont use direct integration
because if we do, heres what will happen which will lead to my answer
summer cliff
basically the anti derivative of g(x) is just y so i can just sub in 2,0 into y right?
bleak osprey
yeah
summer cliff
damm
summer cliff
because if we do, heres what will happen which will lead to my answer
explain
bleak osprey
the thing is, in calc at least, different approaches get different answers
bleak osprey
but when you simplify it all, it goes all back to 4, in this case
summer cliff
ya
bleak osprey
so when I did it, I first when for y's derivative, that with quotient rule, it would be
4(2-x2)/(x2 + 2)2
put that in the integral in place of g(x), multiplies with 3
now to integrate this
use subtitution, say u, it would make
u = x2 + 2, x dx = 1/2 du
substitute this with the dx in the integral
further simplification (too much to write so I am skipping for now), makes 2 integrals, each of them when integrated, gives out 2 factors, -4/u and ln u
subtract them respectively with the limits and multiply it with the simplified constant(s), which would come from simplication of the substitued integral
and finally, evaluating this down, gives:
@flat frigate help
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bleak osprey
,latex 8 - 6 ln(3)
flat frigateBOT
Greydawn Dewer
bleak osprey
**Greydawn Dewer**
I barely know latex but it works, @summer cliff
but the answer when evaluated with direct integration makes more sense so understand that first
fundamental theorum is more important
bleak osprey
basically u use integrated the quotient rule?
yup
the rule, substitution, form change of the integral, sepration, redefining inetgrals, simplication, evaluation of limits, final evaluation, and the answer
or the direct method, that is, the fundamental theorum, which gives 4
bleak osprey
icic
I really want to know how much have you really studied calculus
just for context
summer cliff
hm
bleak osprey
is a bit too much for me but thx ya
no worries
summer cliff
i know chain rule product rule and quotient rule
actually i forgot about chain rule 💀
for integration, i just know the basic which is find area/volume under a curve
thats it ya
summer cliff
so i should focus on dy/dx?
bleak osprey
yeah mainly that, because integration will be more easy then
summer cliff
ic
bleak osprey
at least the questions
summer cliff
fyi, i am learning standard normal distribution currently
bleak osprey
because you know, integrals are really the 'anti' derivatives
bleak osprey
fyi, i am learning standard normal distribution currently
I see
bleak osprey
ok i ma do some differentiation question
yo, I wanna tell a thing, the approach for the substitution method was fine, but my answer... is actually wrong 😂
4 is the correct one
my calculations went wrong, but the method is fine
but these questions need basic theorums like the fundamental one, so stick to that, yeah
keen thicket
Why does defining T(v) this way implies that there is at most one linear map T with T(vi) = wi, i.e why there cannot exist other linear map where T(vi) = wi?
safe radishBOT
Why does defining T(v) this way implies that there is at most one linear map T w...
peak estuary
T(v) isnt defined that way. its already forced to equal that result just by setting T(vi)=wi and requiring T to be linear
keen thicket
I don't understand why it writes "First we verify there is at most one linear map T with T(vi) = wi"
can't they just skip that and say "First we set T(vi)=wi"
peak estuary
the theorem claims there is a linear map and it claims that map is unique. so there is two things to show. they first show the uniqueness part
keen thicket
Ahhh
peak estuary
its often easier to assume first that something exists and then work with it, discovering some properties
and then afterwards using the properties you just discovered that such an object should have to then define that object
in this case equation 6.3
keen thicket
so by defining T(vi) = wi, T can be written as equation 6.3 and then we proof the existence of this equation 6.3?
peak estuary
we first assume that a linear map satisfying T(vi)=wi exists
then we find out that T(v) for some arbitrary v is given by equation 6.3
and then we use this equation to actually define T
keen thicket
ohhh because at first we aren't even sure that a T s.t T(vi) = wi exist, which means we can't jump and define it
so we first assume T(vi) = wi exist
i'm sorry but i haven't take any proof writing class and jump to linear algebra right away
i mean the book says "Linear Algebra as an introduction to abstract mathematics"
peak estuary
yeah its a good introduction
keen thicket
ok i can see why a linear map with this property exist but why is it unique? i.e why there can't be any other linear map where T(vi) = wi?
peak estuary
because just from T(vi)=wi its already forced what T has to do for every v
so any other function S with S(vi)=wi would need to do the same for every v
so S(v)=T(v) for every v
aka S=T
keen thicket
i see
idk if this is a stupid question or not: this logic only works because S is linear right?
peak estuary
not a stupid question
yes
being linear is very important
good catch, I failed to mention that
keen thicket
alright man, thanks for answering but there are one other theorem that i don't understand yet (it is connected to this one)
but i'm trying to do my best to understand it by myself first
so... maybe we should close this one for now
keen thicket
alright man, thanks for answering but there are one other theorem that i don't u...
but if i don't understand it can i ask you again? lmao
peak estuary
maybe I'll see your help channel
but there are certainly also other good people on here who can help you
keen thicket
Alright, Thankssss!!!
harsh peak
Can someone help me with number 4?
safe radishBOT
Can someone help me with number 4?
hard crest
what have you tried or noticed so far?
hard crest
okay, I don't think that desmos will be necessary here
harsh peak
Idk I thought I could graph it or something and see if there are intersections
hard crest
perhaps you could, but that will not tell you the exact solutions
still though - what do you notice about the equation?
harsh peak
Yea ik but there isn’t a pi symbol when u put in the equation
The left side has a lot of pi going on
hard crest
or what are some techniques and procedures you've learned to manipulate expressions?
good
harsh peak
Wait could I factor the right side like what’s in the log
harsh peak
Okok ima do it and show u
I’m thinking maybe I could have x² rep a different variable
Like x² = y
hard crest
as for the left side, I'm actually not sure what will be the most productive way to manipulate it. One thing you could try is using angle sum formulas to at least get rid of the 5π term, but perhaps that will not be helpful
sure
if that makes it easier for you to factor it
hard crest
i do not understand how you arrived at that expression
hard crest
oh, the discriminant
hard crest
hmm, then perhaps factoring may not be the way to go
harsh peak
Does that mean there are no real solutions since u can’t square root a negative?
hard crest
it means that the expression is not factorable.
harsh peak
Aw man 😔
honest perch
can't you still factor it
faint seal
Can someone help me with number 4?
probably something to do with the range of each side
honest perch
it means what's inside the log is never zero which is good
hard crest
you could factor it over the complex numbers, but I think you may be better off completing the square
faint seal
yeah just complete the square of both sides
that should be enough
you should probably factor out a pi first, from inside the sin()
honest perch
right of course
harsh peak
Doing that rn, factoring out pi
hard crest
in fact it looks like all five of these problems share that theme
harsh peak
okok
hard crest
i don't think you'd be able to factor it
harsh peak
That’s like dividing the b by 2 then squaring it right?
hard crest
well, yes. i would hope you're familiar with this procedure
honest perch
rip
hard crest
I shall arrange a séance
bleak osprey
a lot of havoc here, I sense
harsh peak
Ding dang darn math
I forgot how to complete the square 😭
I remember having to add and subtract something so they cancel out
Was it like this
hard crest
yes that
harsh peak
Oh okay good
hard crest
and now the first three terms form a square trinomial
harsh peak
Yea now I take the last term out
Is it x - 9/2 or x + 9/2
It’s - right?
I took out the -81/16 and added it to 5
Got -1/16
Now it’s this
honest perch
should be (x - 9/4)^2
harsh peak
Why?
-9/2 was the original b value
Then I divided it by 2 and squared it to get 81/16 and so on so forth
harsh peak
Okay
harsh peak
Wdym
honest perch
wdym wdym
harsh peak
Where?
honest perch
Now it’s this
here
honest perch
(x - 9/4)^2 = x^2 - 2(9/4) + 81/16
you have this
harsh peak
Idek anymore 😭
honest perch
Now it’s this
ok what you have in the first line is correct
honest perch
(x - 9/4)^2 = x^2 - 2(9/4) + 81/16
just replace the first 3 terms with this
harsh peak
But why do I put 9/4? Does that replace the b value
harsh peak
This one
honest perch
yea it becomes (x + b/2)^2
because when u expand it it's 2(x)(b/2) = bx which is what you had originally
do you know how to expand something like (y+z)^2
harsh peak
I thought it’s supposed to be like that
honest perch
yes correct
harsh peak
So in 2) instead of 9/2 it’s 9/4?
honest perch
no
harsh peak
So it’s still 9/2
honest perch
mhm
hard crest
so $x²-9x+\f{81}4$
flat frigateBOT
hayley 🥥 🌴
harsh peak
Yea basically
Should I just go cry in a corner?
Maybe guess and check
Not guess and check
There could be multiple solutions
😔
hard crest
$x^2-\f92x+\f{81}{16} = \lp x-\f94\rp^2$
flat frigateBOT
hayley 🥥 🌴
hard crest
it's... just a number
harsh peak
So now it’s 2sin(pi((x-9/2)²-1/16))
hard crest
$2\sin(\pi\blue{(x^2-\f92x+5)})$
flat frigateBOT
hayley 🥥 🌴
hard crest
you may
harsh peak
Lemme pull it up
hard crest
it might be helpful
hard crest
if it makes it easier for you to complete the square, sure
harsh peak
Alright
hard crest
the quadratic formula will not be necessary though
harsh peak
Yea that was from earlier lol
Sorry I had to do something but I’m back now😭
I’ll do it now
dense moon
on this thing how would you do question 3
dense moon
sure cause im lost
harsh peak
R u also doing the summer thing
dense moon
yeah
harsh peak
dense moon
same i got 2 as well but i got lost somewhere
harsh peak
Ok what abt 6?
dense moon
wait for number 3 did you assume a =b at one point or no?
harsh peak
wait for number 3 did you assume a =b at one point or no?
Idk I forgot
If it’s in the pictures then yea if it’s not then no
Sorry I just really wanna get this done 😭
hard crest
hmm there's a step that requires some understanding of logarithms and quadratics in vertex form
i don't want to say it because that's the core of the problem, and this is indeed a problem solving exercise
you should work with cosmos if you are working on the same problem set
harsh peak
I didn’t learn much abt logs yet
Bc I only did up to grade 11 math rn
Are there no real solutions?
Or is there at least one?
hard crest
that is indeed the question
harsh peak
I hate this problem set 🤩
hard crest
it's a good problem set
but it seems like you don't have the mathematical familiarity to quickly work on it
where did you get it?
harsh peak
Waterloo summer thinking problems solving course thingy idk what it’s called
Do u want pictures of the problems sets? I can give u them
If u wanna do them
hard crest
oh, sure
safe radishBOT
dense moon
.reopen
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Available help channel!
uncut juniper
I need help with this question
safe radishBOT
I need help with this question
uncut juniper
I'll try to translate it
a radioactive material decays, and after (a) days, p% of the original radioactive material remains
how much time has passed?
this is my work
I don't seem to be arriving at the correct answer
hard crest
a radioactive material decays, and after (a) days, p% of the original radioactiv...
you need to know the half life
uncut juniper
it's 0.5
safe radishBOT
@uncut juniper Has your question been resolved?
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@uncut juniper Has your question been resolved?
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@uncut juniper Has your question been resolved?
uncut juniper
.close
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daring forge
hi
daring forge
i need some help calculating profit on an investment
sweet mica
Ask
bleak osprey
i need some help calculating profit on an investment
elaborate
daring forge
so basically i risked 15% on a $100 account
i had 3 targets
first at 1.23 times risk
second at 2.35 times risk
third at 3.35 times risk
the whole position was 0.13 lots
i closed 0.03 lots at first target
i closed 0.06 lots at second target
i closed 0.04 lots at third target
i now i want to know how much i would profit compared to my risk of all 3 targets are hit
and im trying to make a formula to use in the future
i have tried like 5 times now but i cant seem to make an accurate one
honest perch
how did you risk the $15
daring forge
wdym
honest perch
so basically i risked 15% on a $100 account
wdym by this
daring forge
that is what i put into the trade
daring forge
let say that yes
honest perch
the whole position was 0.13 lots
wdym by lots
daring forge
basically a lot is just the unit of the size of the position in trading
my trade was 0.13 lots
honest perch
too vague
daring forge
i entered a trade risking 15 dollars
and i had stop loss set at a point
for me to be able to have the stop loss i wanted and risk 15 dollars, i had to enter with 0.13 lots
i can illustrate it if you want
i finally figured it out
daring forge
the first part is the risk
then the risk is multiplied by the take profits
first, i closed 3/13 of my position at 1.23, then 6/13 of my position at 2.35, then 4/13 of my position of 3.35
so basically each of the 3 blocks inside the big parentheses work like this:
(amount of gain in terms of risk)(amount of position taken off at the level)(the risk)
idk why this took me so long
wasnt really that complicated, just looks like it
but anyway ill close it
.close
safe radishBOT
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Available help channel!
dire storm
what is meant by the encircled statement
safe radishBOT
what is meant by the encircled statement
@dire storm Has your question been resolved?
wanton plover
Find fe* 1 (1+x2)3/2 X + √1+x2 dx.
safe radishBOT
Find fe* 1 (1+x2)3/2 X + √1+x2 dx.
rustic goblet
Find fe* 1 (1+x2)3/2 X + √1+x2 dx.
I cannot parse this question at all... 
can you show the original?
safe radishBOT
@wanton plover Has your question been resolved?
hasty wagon
well, that's out of my expectation lol, right? @rustic goblet
hasty wagon
found it
hasty wagon
<@1109359213672661124> Has your question been resolved?
@wanton plover you can press the cross first
so that the channel wont close
Hint: let u=x/sqrt(1+x²)
rustic goblet
clever!
wanton plover
yeah
wanton plover
yeah but whats after diff both side
hasty wagon
note that if we have u=x/sqrt(1+x²)
then du/dx = 1/(1+x²)^(3/2)
then we can rewrite the integral as
int (e^x du/dx) dx + int (e^x u) dx
hasty wagon
then we can rewrite the integral as
int (e^x du/dx) dx + int (e^x u) dx
2nd hint: integration by parts @wanton plover
safe radishBOT
@wanton plover Has your question been resolved?
sinful spire
safe radishBOT
rustic goblet
not sure how to simplify sin^2-sin^4/cos^2 - 1/sin^2
consider looking at the first term, and factoring sin^2 out
sinful spire
sin^2(1-sin^2)?
sinful spire
not sure
devout shale
Ptolemy
sinful spire
use the pythageoren idneity
sinful spire
do you put the sin in terms of cos and then cancel it out with the denominator?
sinful spire
wait so its 1-cos^2(1-sin^2)/cos^2
rustic goblet
I think you've applied it incorrectly
can you state the Pythagorean identity for me?
sinful spire
cos^2+sin^2 =1
flat frigateBOT
higher!
rustic goblet
also $1 - \sin^{2}(x) = \cos^{2}(x)$
flat frigateBOT
higher!
rustic goblet
**higher!**
this is the one you probably want to use
sinful spire
oh mb i meant 1-cos^2(1-sin^2)/cos^2
rustic goblet
that is true, but it doesn't help you as much 
void crag
rustic goblet
**higher!**
@sinful spire I suggest changing the (1-sin^2) term in the numerator to cos^2
desert pasture
,rotate
flat frigateBOT
sinful spire
so its not an idenitty then
sinful spire
.close
safe radishBOT
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Available help channel!
loud cedar
help about quadratic equations
safe radishBOT
help about quadratic equations
timber karma
help about quadratic equations
what about them?
loud cedar
how do I use factoring method
timber karma
like x^2 - (a + b)x + ab?
loud cedar
Yep
craggy sedge
what about them?
loud cedar
How will I know if which solving technique will I use? Since there are 4
lapis shadow
Do u have a specific problem?
lapis shadow
Completing the square will always work
timber karma
How will I know if which solving technique will I use? Since there are 4
it relies mostly on experience and pattern recognition
but quadratic formula will always work
but for some questions factoring is easier
loud cedar
Completing the square will always work
Does it work for every form
craggy sedge
Yes for every quadratic equations
loud cedar
.close
safe radishBOT
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grizzled hound
Is it safe to assume that A - B = 0 here since there’s no x^2 in the numerator to compare it to?
safe radishBOT
Is it safe to assume that A - B = 0 here since there’s no x^2 in the numerator t...
fresh sun
Is it safe to assume that A - B = 0 here since there’s no x^2 in the numerator t...
yupp
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hardy tapir
e
jolly ledge
What will be the formula if we are required to find the number of combinations of r objects out of n with q identicals? Also, can someone explain why nPr = nCr * r! without deriving the formula?
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What will be the formula if we are required to find the number of combinations o...
craggy sedge
nPr =nCr*r! factorial is esy to explain if you remember the definitions of them
unreal ice
What will be the formula if we are required to find the number of combinations o...
nPr is just permutations
jolly ledge
nPr is from n arrange r objects
So we will have n!/(n-r)!
nCr is from n choose r objects
craggy sedge
yes
unreal ice
we divide the number of ways to arrange n elements by the number of ways to arrange n-r after we take r to arrange, to avoid overcounting
so it makes sure every permutation is counted once
unreal ice
when we multiply nCr by r!, we are getting rid of the number of arrangements of the r!
unreal ice
After simplification, I get r!/(n-r)!
recall that nCr = n!/r!(n-r)!
so when you multiply by r!, it cancels with the denominator
to get n!/(n-r)!
nPr
jolly ledge
Yeah but
jolly ledge
when we multiply nCr by r!, we are getting rid of the number of arrangements of ...
I don't get this
jolly ledge
so it makes sure every permutation is counted once
Nor this and the one before
Say, if we arrange 3 objects out of 5, we divide it with the ways to arrange 2 out of 5
What does that even mean...?
unreal ice
Say, if we arrange 3 objects out of 5, we divide it with the ways to arrange 2 o...
we divide the number of ways to arrange 5 elements (5!) by the number of ways to arrange 2 elements (5-3)!
craggy sedge
for the combination we dont care abt the arrangements of those we choose
unreal ice
in combinations, order is not important
jolly ledge
Then...?
How do we actually choose r objects out of n, assuming all n objects are distinct?
Is it like, after arranging r objects out of n objects, we divide it by r to neglect the order of arrangement?
Well that explains it
Thanks guys
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white needle
Just need some help confirming whether i have the right approach or not
white needle
here is the problem if you cant see it properly
thin bridge
river field
but you put those arrows lol
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next inlet
can someone explain to me why this is wrong
safe radishBOT
can someone explain to me why this is wrong
craggy sedge
what is (2m)^2?
next inlet
well we dont know what m is
im guessing its 4m? but like
my mind is telling me no because we dont know the value of m
next inlet
confusin
cant we just keep scaling it then
if 2m^2 is 4m^2 then isnt it just keep going
oh wait the brackets
oh because its a
a = 2m
so a^2 = (2m)^2
craggy sedge
yes
next inlet
alright
cheers
2*(2m^2 + 2n^2)
need to do more practice problems
keep forgetting my algebra
well basic bedmas i guess
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halcyon light
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halcyon light
Why can't I use y = x in this question?
Is it just a coincidence
it looks like y = x
icy lance
you shouldnt assume
cedar void
Is it just a coincidence
these diagrams are not drawn to scale so you can't claim that by just observation
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halcyon light
I differentiated this
and subbed in x = 2
and then used that gradient to find the equation of the tangent
Is that the right method?
I feel like its wrong
cedar void
and then used that gradient to find the equation of the tangent
it is correct
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halcyon light
because its in the form
safe radishBOT
because its in the form
desert pasture
what do you mean?
cedar void
.
halcyon light
Like I got y = 25x - 43
it doesnt say y is a constant
oh
right
to get the gradient
fakkkk
ok kl thanks
cedar void
nw
halcyon light
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fathom jewel
been waiting since 1964
kindred fjord
been waiting since 1964
mb I went to sleep cuz it was 2 am for me 😭
fathom jewel
yea no worries
flat frigateBOT
𝔸dωn𝓲²s
fathom jewel
for y
kindred fjord
idek what I did it was 2am i need to recheck this 💀
fathom jewel
Otherwise I can't tell what you did
fathom jewel
yea you did a minor mistake
it should be division by -2 not -3
If you bring 3y on the other side you get -2y = 6x²-54
then divide by -2
y = (6x²-54)/(-2) = -3x²+27
kindred fjord
damn do i see weed 💀
Nah thats eraser shavings 😭
fathom jewel
you should work on your drawing skill, also the parabola is smoothly curved, not edgy at its max
but other than that it's okay
kindred fjord
okay thanks
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winter whale
Whats the logic behind it
wet wigeon
I dont think its anything special, you can achieve any number by manipulating the equation
x/c + y/d = non zero constant in general
You can divide both sides by that non zero constant to get that in form of x/a + y/b = 1 again
For example consider the line 2x + 3y = 2, dividing both sides by 2 you get
x/1 + 3y/2 = 1
@winter whale Did you understand the proof
Given in the book
winter whale
I did
Thought there was something to more to visualising it being equal to 1
Well no matter, thx for the help
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hasty cairn
How does the graph compress by b^-1 when f(x) becomes f(bx) with b > 1?
compresses means a 1/4 of it was compressed by a factor of 2
Like it’s now like 3/4 of what it was before
safe radishBOT
Why is this true? https://media.discordapp.net/attachments/268882317391429632/12...
lapis shadow
so think f(x) vs f(2x)
when x = 10, say f(10) = 1
so u must go all the way till u reach 10 on the x axis to output 1
but with f(2x)
with x = 5, u get f(2*5) = f(10) = 1
so u dont have to go that far out
u see the inputs sooner
without having to go very far out
so it compresses it horizontally
hasty cairn
That compresses horizontally by 2 not 1/2 right?
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@hasty cairn Has your question been resolved?
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misty agate
Let ${B_i}_{i \in I}$ be a family of pair-wise disjoint
nonempty sets. Using and stating the axioms used, prove that exists a
set $B$ which shares exactly a single element with each set $B_i$.
flat frigateBOT
yehelip
misty agate
So I suppose the solution is either based on the recursion theorem, or the AoC with some manipulations
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@misty agate Has your question been resolved?
leaden parcel
I need help with this question, I'm not exactly sure how to solve, although I think I know it. You have to multiply the denominator by 10, but I don't know if you have to do it with the numerator too. Well, how do I do it anyways?
safe radishBOT
I need help with this question, I'm not exactly sure how to solve, although I th...
leaden parcel
The triple dots indicate it's endless
paper flume
I need help with this question, I'm not exactly sure how to solve, although I th...
do you know the decimal expansions for the ninths?
paper flume
Yeah
then you dont need to do it for the numerator
numerator sorry
write each of them as mixed numbers
leaden parcel
So, I multiply 1,0333... By 10 and leave the other alone
1,222... - 0,111... ÷ 10,333...
paper flume
well not quite
leaden parcel
What is it then
paper flume
if you multiply the denominator by 10 youre changing the value
leaden parcel
Yes
paper flume
so you need to multiply the numerator by 10 as well
leaden parcel
12,222... - 1,111... ÷ 10,333...
paper flume
12,222... - 1,111... ÷ 10,333...
yep
can you see why its equivalent to the original expression
paper flume
so your original was $\frac{1.2\dots - 0.1\dots}{1.03\dots}$
flat frigateBOT
esca
leaden parcel
Yes
But it looks like I'm getting a huge number with it
Sorry for the angle
I'm in the bus
paper flume
now if you multiply both the numerator and denominator by 10 you get $\frac{(10)(1.2\dots - 0.1\dots)}{(10)(1.03\dots)} = \frac{10}{10}\times\frac{1.2\dots - 0.1\dots}{1.03\dots}$
flat frigateBOT
esca
leaden parcel
But it looks like I'm getting a huge number with it
That's for the 12,2...
paper flume
why are you multiplying by 10 at the end?
you already multiplied it by 10
110/9 is correct
leaden parcel
Isn't it multiplication of a fraction?
Like, when you multiply 1/1 by 10 it becomes 10/10
paper flume
yes
leaden parcel
So technically it is 12,222/10 now
paper flume
1.222 yes
paper flume
well you multiply by 10/10 first because it makes it easier to solve
leaden parcel
12,222... - 1,111... ÷ 10,333...
Thiu
paper flume
1,222... - 0,111... ÷ 10,333...
convert this to an expression in terms of fractions
leaden parcel
This
paper flume
sorry woops
leaden parcel
But it looks like I'm getting a huge number with it
So i get that
leaden parcel
Yep
paper flume
do the rest
leaden parcel
it's 110/9 x 1/10?
paper flume
which one
leaden parcel
110/90
paper flume
12.222 = 110/9
you dont have to divide by 10 again
because youre already multiplying the denominator by 10
leaden parcel
Oooh
Okay wait
110/9 - 10/9 ÷ 93/9 x 1/10
Let me that that at the paper
I can divide 93 and 90 by 3
So
leaden parcel
because youre already multiplying the denominator by 10
You said it
paper flume
You said it
yeah the denominator multiplied by 10 is 93/9
so uh
$\frac{\frac{110}{9}-\frac{10}{9}}{\frac{93}{9}}$ should be correct
leaden parcel
100/93?
flat frigateBOT
esca
leaden parcel
Like, when you multiply 1/1 by 10 it becomes 10/10
.
leaden parcel
Hmmm
Okay
I think I understand
Aight
I think we're done here
Thank you seriously 🙌
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lean otter
hello! what is the method to solve questions like this? i know the answer is 3 but i got there in a stupid way
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hello! what is the method to solve questions like this? i know the answer is 3 b...
main mural
hello! what is the method to solve questions like this? i know the answer is 3 b...
brute force lol
main mural
brute force lol
just trying out the possible solutions
fathom adder
:D
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fathom adder
thank you!
(Let n be the thing you search for)
And apply the question to it setting up an equality
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west hedge
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leaden harness
Its about ellipses
The coefficient isn’t one, I’m not sure how to convert it into standard form
hard crest
complete the square with the x terms
then complete the square with the y terms
it sounds like you're already on your way to doing that
leaden harness
Yeah, but the y’s coefficient isn’t 1, how’d I do that
twilit moat
The coefficient isn’t one, I’m not sure how to convert it into standard form
do you know the standard form of an ellipse?
leaden harness
Yea
hard crest
didn't i tell you this earlier? $\f{(x-h)^2}{a^2} + \f{(y-k)^2}{b^2} = 1$
twilit moat
all that indicates is your shift like in a circle
flat frigateBOT
hayley 🥥 🌴
twilit moat
^
leaden harness
didn't i tell you this earlier? $\f{(x-h)^2}{a^2} + \f{(y-k)^2}{b^2} = 1$
Yeah thats what I’m trying to do
twilit moat
so you would complete the square for x and y separately
leaden harness
Yeah for x its (x+4)^2
twilit moat
remember that you just need to complete the square with your x^2 and x + y^2 and y terms
twilit moat
Yeah for x its (x+4)^2
yeah so you do this for x and y
and then subtract the left constants
leaden harness
Yeah
twilit moat
so (x^2 +8x) can be thought of as (x+4)^2-16