@chrome plume
#help-42
glad plover
chrome plume
Okey but why is it true since we don't have one factor for logarythm
glad plover
idk what you mean
glad plover
what?
chrome plume
c is 1/x
so then how do i know what b is?
isn't changing exponential function into logharythimc function what i have to do?
glad plover
if a^c = b, then log(b) = log(a^c) = c log(a) always
this is a rule
this is because e^(c log(a)) = (e^log(a))^c = a^c = b
chrome plume
chrome plume
what do you mean by nice world?
glad plover
$$\lim_{x \to 0} e^{f(x)} = e^{\lim_{x_\to 0} f(x)}$$
potent lotusBOT
Kaisheng21
glad plover
in a nice world, this is true
it isn't always true
probably there are some weird cases
but for a nice problem or a nice function or whatever it should be fine usually
chrome plume
if a^c = b, then log(b) = log(a^c) = c log(a) always
what you wrote here is exactly the same as what i wrote above i guess
glad plover
i don't think i understand what you don't get
chrome plume
about which part?
chrome plume
this exercise
chrome plume
so i managed to go to this, and i understand the steps
glad plover
so do you understand my general approach here
.
chrome plume
but then
chrome plume
so do you understand my general approach here
to the point where we have e yes
chrome plume
what?
i am a little bit counfused about this what as what i wrote down is true right?
potent lotusBOT
Kaisheng21
glad plover
right?
chrome plume
right
chrome plume
here i wrote how i see it
but this solution doesn't meet the answer from the book so i guess it may not be right
chrome plume
sin(0) is 0
chrome plume
ln 1
glad plover
which is
chrome plume
0
glad plover
right
so you have 0 times infinity
so you need to work it out more
that's still a limit
find $$\lim_{x \to 0} \frac{1}{x} \ln(1 + \sin(x))$$
potent lotusBOT
Kaisheng21
glad plover
this should be reasonably standard
chrome plume
this should be reasonably standard
glad plover
**Kaisheng21**
find this
chrome plume
will this two together do the trick?
glad plover
no
your algebra is incorrect
i think?
wait
i mean ok no that works
ln(1+sin(x))/x = ln(1+sin(x))/sin(x) * sin(x)/x, sure
chrome plume
ln(1+sin(x))/x = ln(1+sin(x))/sin(x) * sin(x)/x, sure
So it is right then and the answer is e^1?
normal wasp
find ABCD paralelograms A corners coordinates if B (-1.10) C(7.2) and D(1.-4)
normal wasp
<@&286206848099549185>
quick drum
what do you know about parallelograms?
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golden forge
calm coralBOT
calm coralBOT
@golden forge Has your question been resolved?
idle marten
!status
calm coralBOT
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
Do you know soh cah toa
idle marten
Damn you right uhh
golden forge
so i was thinking i might need to find another angle for sine/cosine rule
but i cant find any useful angles lol
idle marten
We can find the angles of the vertical triangles
golden forge
Ok
idle marten
Hmm I am trying to look for another spot
OH
I know
Wait actually i don’t one moment
Ok so
Can you create an equation for each side of the blue triangle
golden forge
uhhh how
golden forge
oh is it like tan40 = x/OB
idle marten
OB = x/tan40
golden forge
and tan25 = x/OC
idle marten
Wait no
yes you’re right
x = tan40/OB
x=tan25/OC
do you see where I’m getting at
idle marten
I have two different expressions for x
golden forge
oh is this simultaneous equations
idle marten
What is the relationship between tan40/OB and tan25/OC
golden forge
they r equal?
idle marten
Ye
golden forge
OHHH is that an isosceles traingle
idle marten
Wait actually idk where I’m going lmao
wanton wave
x = tan40/OB
don't you mean tan40=x/OB?
idle marten
no it’s not an isosceles
idle marten
don't you mean tan40=x/OB?
do you want to help I can only see like 1 foot ahead
idle marten
don't you mean tan40=x/OB?
they’re equal
wanton wave
I think you're on the right track, but your trig equations are a bit off
golden forge
x = OB * tan40 right
wanton wave
so you have trig equations relating x and OB, and x and OC, and then the pythag relating OB and OC
so you can solve simultaneously to find all 3
golden forge
Oh yeah tysm
wanton wave
OCtan25=OBtan40
yes, this, then use OB^2+70^2=OC^2
wanton wave
np
calm coralBOT
idle marten
OCtan25=OBtan40
@wanton wave would you square this then replace OC^2
idle marten
ok
wanton wave
trig gets a little ugly so I'd assign a symbol for tan40/tan25
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arctic grove
A floor plan has a 40: 1 scale. In the drawing, one of the rooms measures 3 8 inches by 1 1 inches. I need to show my answers to the nearest hundredth, even if it means I need to type zeros. I need to answer the actual dimensions would be # feet by # feet.
The area of the room would be # ft². What should I start to solve this problem?
arctic grove
I don't really how to start solving this problem. This is a Proportion assignment problem.
<@&286206848099549185>
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serene holly
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old furnace
So for this problem, I need help with finding the constant K
I have already figured out everything else and I prepared a function in the console for solving question 3 once I get the K value. This is the full problem, also the last one I have for this assignment. If anyone could help, I'd be very grateful.
old furnace
also my brain is currently weaving gold into straw, it had shut down after solving the other questions so I might say dum stuff lol
worldly nexus
ok first what is the initial state of cup
worldly nexus
yeah
so you first try to get the general solution
by splitting your variables and integrating
also plug in the Ts
old furnace
How do I split the variables in $dT/dt = k(T-T_s)$ ?
potent lotusBOT
alani
worldly nexus
$dT/(T-Ts) = kdt$
potent lotusBOT
memeprime.
worldly nexus
plug in Ts
old furnace
would T_s be 20º ?
old furnace
so left side would be ln |T-Ts| and right would be kt+C, right?
worldly nexus
since you know $dT/dt = -2$ at $T = 70$
potent lotusBOT
memeprime.
worldly nexus
you can plug in those values and find k
worldly nexus
oh wait you tried tried that already
or no thats the answer
nvm
i never saw this interface
worldly nexus
that probably won't work
old furnace
perfect 100, I'm suprised lol
thanks bro
it makes sense though, simpler than I expected
aight, appreciate the help I'mma close this channel now
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cedar pasture
How many terms are in this sequence? I found 21 but the answer key says 20.
cedar pasture
potent lotusBOT
memeprime.
worldly nexus
woops
it is 14 and 1/3
and 2 and 3/12 or 1/4
you substitute 59 1/3 and solve for n
in which you would get 20
strange badge
i really need help to understand this and i am completely lost because how im a slow learner 😭
calm coralBOT
i really need help to understand this and i am completely lost because how im a ...
@strange badge Has your question been resolved?
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@strange badge Has your question been resolved?
amber wing
calm coralBOT
amber wing
I'm not sure where to start. Do I have to first find f?
calm coralBOT
@amber wing Has your question been resolved?
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@amber wing Has your question been resolved?
spark stratus
I'm not sure where to start. Do I have to first find f?
no
the info they gave you for f is enough
amber wing
alright
am i right to assume that the range is still [0,infinity)
since the square root in the numerator can't be negative
spark stratus
you can try starting with the zeros
you know f(2) = 0 and f(4) = 0
try plugging in numbers into g(x) which will cause an f(2) or an f(4) to appear
see if you can do anything with that to derive some information
amber wing
ok
g(3),g(5) for the numerator and g(0), g(2) for the denominator
but that doesn't mean all of them are zeros right
spark stratus
you plug them in and see what happens
theres an f() on the numerator and on the denominator
amber wing
after i plugged the values in, I got that 3 and 5 were the zeroes, whereas 0 and 2 made it undefined
is that all the domain excludes?
spark stratus
you did find both zeros of g so that's done
domain also has to consider that f(-2) isnt allowed
so any values of x that cause an f(-2) to appear also cant be in the domain
amber wing
gotchu
spark stratus
the two x-values that cause an f(-2) to appear, along with x=0 and x=2 that divides by 0, are what makes g(x) undefined
those are all the domain excludes
spark stratus
not entirely sure on that
did you learn continuity yet?
spark stratus
i'll think about it a little more, but the domain excludes 2, 0, -1, and -4 righ...
yes
spark stratus
np
amber wing
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calm coralBOT
spark stratus
@amber wing alr I can show you a bit of continuity which will justify the range
you can .reopen to see it
amber wing
.reopen
calm coralBOT
✅
spark stratus
the idea is
amber wing
<@600850471330119680> alr I can show you a bit of continuity which will justify ...
that would be really helpful, thanks!
spark stratus
some functions are drawn continuously
but as far as you know, all of them can be drawn continuously
with only a couple of gaps or asymptotes to disprove that
right
amber wing
ye
spark stratus
now you found that one of the zeros was g(3) = 0, right
amber wing
ye
spark stratus
and you also noticed that g(2) causes g(x) to go undefined, right
amber wing
ye
spark stratus
now heres an idea that continuity promises
if a section is continuous, it wont cut off from one value to another
so lets say that the section of g(x) from x=2 to x=3 is continuous
then that would mean you would have to draw this section in one stroke
presumably, right?
spark stratus
it doesnt have to include x=2
the section of g(x) from x=2 exclusive to x=3 inclusive lets say
amber wing
ye
spark stratus
now heres an idea
say you have values that are close to x=2
we'll call these values 2+ for being only a bit more positive than 2 is
for example 2.00000001 would be the kind of value 2+ is
in a way, g(x) is continuous from 2+ to 3
amber wing
ye
spark stratus
now lets plug this 2+ into g(x) and see what happens:
,,g\left(2^{+}\right)=\frac{\sqrt{f\left(2^{+}-1\right)}}{f\left(2^{+}+2\right)}=\frac{\sqrt{f\left(1^{+}\right)}}{f\left(4^{+}\right)}
potent lotusBOT
mtt07734
spark stratus
Ill just plug it in for you
spark stratus
but it can be very close
specifically it can be as close as we want
2+ in a way is a variable to stand in for numbers that are as close to 2 as we want
1+ and 4+ are defined in the same way to be equally close to their respective numbers
so this could be 1.000001 and 4.00001 or 1.000000001 and 4.000000001
you get that?
amber wing
ye
spark stratus
now for f(4+)
notice that f(4) = 0, but f(4+) cant be 0
this doesnt really say much but we can then make another assumption that f(x) is also continuous near x=4
or at least the nearby area to the right of x=4
by doing so, you can imagine that f(x) needs to get to 0 from 'above' since f(x) is never negative
amber wing
ye
spark stratus
however the closer we get to x=4, the closer f gets to 0
and so f(4+) should be 0+ in some capacity, right
amber wing
ye
spark stratus
now keep in mind this wont be as equally spaced anymore
it could be that f makes the space much closer to 0 or much farther from 0
spark stratus
so this could be 1.000001 and 4.00001 or 1.000000001 and 4.000000001
so the equally spaced close doesnt apply anymore
but that doesnt matter because a 0+ in the denominator leads to a more coherent answer
,,\frac{\sqrt{f\left(1^{+}\right)}}{f\left(4^{+}\right)}\to\sqrt{\frac{f\left(1^{+}\right)}{0^{+}}}
potent lotusBOT
mtt07734
amber wing
wait what do you mean by equally spaced?
spark stratus
this from earlier
1+ and 4+ are defined in the same way to be equally close to their respective numbers
so this could be 1.000001 and 4.00001 or 1.000000001 and 4.000000001
so the space between 1 and 1+ and the space between 4 and 4+ are equal
spark stratus
**mtt07734**
you see the problem with dividing by 0 is that you can divide by a negative or by a positive
if you divide by a small negative number, you get close to -∞
if you divide by a small positive number, you get close to +∞
right
amber wing
ye
spark stratus
so we dont get to define dividing by a 0 in a sensible way since -∞ and +∞ cant be equal
right
amber wing
ye
spark stratus
this time though we're exclusively dividing by 0+
so that would be a really small positive number
,,\sqrt{\frac{f\left(1^{+}\right)}{0^{+}}}\to\infty
potent lotusBOT
mtt07734
spark stratus
so this time we get to say that this should tend to +∞
amber wing
yes
spark stratus
now this is where "g(x) is continuous from 2 exclusive to 3 inclusive" comes in
at x=3, g(x) is 0
at x=2, g(x) is undefined
when x is 2+, g(x) is very positively large
as positively large as we need
since 0+ can be as small as we need
oh also that √ shouldnt over the denominator
amber wing
o
spark stratus
so you cant get from 0 to a very large number in one stroke
without going through every number in between
if you get g(2.0001) = 99999 for instance,
then g(x) has to go through 0 through 99999 to get from (3, 0) to (2.0001, 99999)
after all g(x) is continuous
amber wing
so how does that work
spark stratus
which part
amber wing
how are we supposed to connect the two in one stroke then
spark stratus
we said g(x) is continuous
if a section is continuous, it wont cut off from one value to another
amber wing
ooohhh
spark stratus
so a continuous stroke connecting (3, 0) and (2.0001, 99999) has to go through every number inbetween
and even better,
that 99999 can be as big as we need
spark stratus
since 0+ can be as small as we need
since 0+ can be as small as we need
we still can make 0+ approach 0 as close as we want
so that essentially guarantees that g(x) can reach any value 0 and above
you see how that works?
spark stratus
from this, you can conclude that g(x)'s range is [0, ∞) and so doesnt stop or end at any value
amber wing
i see
spark stratus
now for your class you have a watered down version of this idea
amber wing
so my assumption was right but i just didn't know the reason why it was right
kinda just a lucky guess
spark stratus
yea because its a fundamentally simple assumption
Im already watering down some part of it but theres still a simple part I need to show
amber wing
ok
spark stratus
if you choose to guess a function for f(x) anyway, g(x) has an asymptote at x=2
and touches 0 at x=3
what we really used to show ∞ here is an asymptote
this asymptote gets higher as x gets closer to 2
(f(x) is green, g(x) is orange)
in a way you anticipate that a number that can divide by anything from f ought to be able to reach any number at any height
that division by 0 should get you an ∞ of some sort
so between the ∞ and the 0 has to be every value in between
the asymptote is what we used when we got √f(1+)/f(0+) to be as big as we want
spark stratus
visually thats what youd expcet
but now we have a vaguely more rigorous way of going about it
only slightly more
but its nice to see that you dont really need to ask for much out of f and g for this
it could be that everything else was so jagged that a continuous stroke wasnt possible
or it just skips some values from like 50 to 60
amber wing
i see
it's starting to come together alot more now
o
tysm for teaching me continuity
spark stratus
np
amber wing
im just gonna leave it open for now since i might need help on the last few questions
spark stratus
alr
amber wing
.close
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vague vigil
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vague vigil
Part (iv)
So i transformed the original eqn into lgy= lgbx-A, and got A as 2 and b as 1.2
The graph for lg y against x
Then i transform y^5=10^-x into lgy= -x/2
But then what do i do?
past moon
NEED help with this question asap. Please explain how to get the answer. It is due in a while for coursework.
past moon
I dont know how to work it out
prime arch
I dont know how to work it out
Which part are you struggling with?
past moon
Which part are you struggling with?
Im stuggling with all cause my teacher in school never showed me the correct method of working it
prime arch
Im stuggling with all cause my teacher in school never showed me the correct met...
So uh I'll try to do them 1 by 1 but I rarely use discord and I have no idea how latex works
For 5 a) you need to substitue the given integers into x
For example, to find f(3) you will substitue 3 into where x is
Thus f(3) = 1/3 times 3 (previously x here) - 2
Which will give you -1 for f(3)
The same applies for f(-3)
Any difficulties with that?
past moon
Is the answer for A = -4
prime arch
Is the answer for A = -4
Yes
past moon
Okay
prime arch
Do you have the gist of b?
past moon
Nope B and C are very difficult for me
prime arch
Nope B and C are very difficult for me
Alright so
For b you need to sub in 5 as the result of f(x)
Basically so that 1/3x-2 =5
Because you are looking for a value of x that when subbed into f(x) will give you 5
prime arch
Basically so that 1/3x-2 =5
And you can try solving this
past moon
Is the answer -1/3
prime arch
Is the answer -1/3
No
First, i'd reccomend moving the constants to one side
In this case you would transfer -2 over to the LHS
However, you have to remember that moving constants to the other side will flip their sign
past moon
Whats constants? And LHS?
prime arch
Meaning that the LHS becomes 5+2 which = 7
prime arch
Whats constants? And LHS?
Constant is a fixed value
E.g. just a normal number like 4 or 5, without a variable like x or y attached
LHS is short for left hand side, you'll use it a lot later on for proof questions as it's just easier to write 
But back to the question, now you'll have 7 = (1/3)x
And uh multiplying both sides by 3 to remove the denominator
We get x = 21 for b)
past moon
Wait
prime arch
?
past moon
Oh u moved the 1/3 on the otherside making it 3/1 and making it 21 for the answer?
But if 1/3 was multiplying. Why didnt it divide when you moved it
prime arch
Oh u moved the 1/3 on the otherside making it 3/1 and making it 21 for the answe...
? I didn't 'move' it per se
I multiplied both sides by 3
To turn the 1/3 coefficient of x into 1
And 1x is just x
You can also divide both sides by 1/3 which does the exact same thing
prime arch
What do i have to do
So for C, first you have to replace f(x) with y
At this level they are basically the exact same thing
So you now get y= (1/3)x -2
Next, you swap the locations of the x and y
So you will get x = (1/3)y - 2
And you can re arrange that to make y the subject
x+2 = (1/3) y
3x+6 = y
And that is your inverse
past moon
So for C, first you have to replace f(x) with y
Thanks for helping me solve it. I have to practise more
prime arch
Thanks for helping me solve it. I have to practise more
No problem, good luck
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quartz estuary
hi can someone see if my work is correct here, i had this equation and i tried to convert it to y = mx + b form. 4 (x+5) - (y - 1) = 16, i ended up with y = 4x + 5
quartz estuary
i expanded first so it was 4x + 20 - 1y + 1 = 16
then moved the numbers with no variable toward the 16
4x -y = -5
moved the 4x to the right and multipled everything by -1
is this correct
grizzled mist
yes it is correct
calm coralBOT
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dusty crater
in a mathematics paper, should I \cdot or \times when denoting multiplication?
proud bronze
in a mathematics paper, should I \cdot or \times when denoting multiplication?
Usually, you’d use \cdot
I find it that it’s fairly rare that you need to explicitly denote multiplication though
$\mathbb{R}^2 = \mathbb{R} \times \mathbb{R}$
potent lotusBOT
Intrer
proud bronze
\times is mainly for Cartesian products like this
dusty crater
\times is mainly for Cartesian products like this
in a situation such as this, how would u denote multiplication?
proud bronze
in a situation such as this, how would u denote multiplication?
I’d use \cdot instead of \times there. The notation might depend on where you’re from though
\cdot is the most common tho
calm coralBOT
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austere surge
Help
austere surge
calm coralBOT
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
I just wanted to verify my answer
I use the sub z=ix to get -i × int (e^ix+e^-ix)/2x^4 dx
Now e^ix + e^-ix / 2 is cos x. So this is int cos x/x^4 dx
Now here if it were over a circle containing 0, then I could just say this is 2pi × a_3, where a_3 is the third coefficient in power series of cos x.
But since cos z is an entire function, maybe I can show that the integral over gamma is same as integral over a circle centered at 0 whose interior contains gamma
austere surge
If it's a closed curve then you just need residue theorem.
We haven't studied that yet
What do you get using residue theorem?
austere surge
Hmm, I'm doing something wrong then
Oh, wait
a_3 is zero in power series expansion of cos z
So I do get the integral zero
So if it is zero, then the answer I get is correct. Can someone verify my method though?
potent igloo
I got zero from residue theorem, for what that's worth
Your work is basically residue theorem but explicitly stated
It looks like your class is prepping you to learn it very soon
austere surge
But since cos z is an entire function, maybe I can show that the integral over g...
I guess this is the only thing I need to figure out how to prove now.
I'll try to prove this.
Thanks for help
.close
calm coralBOT
median oyster
I think that follows from deformation of contours?
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remote mural
i need help with what this symbol besides L means
calm coralBOT
i need help with what this symbol besides L means
pallid halo
probably "divides", but what's the context
remote mural
what is it called
pallid halo
in english it's usually read as "p-1 divides L" which means "p-1 is a factor of L" or "L is divisible by p-1"
pallid halo
that's the "not" version
remote mural
ok
pallid halo
q-1 does not divide L
remote mural
how do i find that
pallid halo
L is not divisible by q-1
find as in how do you typeset it in latex?
$\not |$ maybe?
remote mural
google docs
potent lotusBOT
Bungo
pallid halo
oh not sure about google docs
remote mural
oh ok
calm coralBOT
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serene basin
How can I find P(C = H) given P(C = H | D) and P(D)?
calm coralBOT
How can I find P(C = H) given P(C = H | D) and P(D)?
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
1
I don't know what formula to use. I know marginal probability is the sum of the rows of that outcome, but that's for a standard multivariate graph, not one based on a condition
calm coralBOT
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serene basin
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remote mural
So i'm doing homework 
and i'm kinda not sure on how many rows i will need to answer question c
remote mural
I assume that it'll take 16 rows but that can't be true right?
Question c
oh wait wtf
am i doing
.close
west stratus
compute the scalar-surface integral f Ds:
double integral g x^2zdS where G is the cylinder (including the top and bottom) x^2 + y^2 = 4, 0 <= z <= 3
calm coralBOT
compute the scalar-surface integral f Ds:
double integral g x^2zdS where G is th...
west stratus
can anyone lp me set this up
<@&286206848099549185>
<@&286206848099549185>
<@&286206848099549185>
untold drum
do not occupy multiply channels with the same question.
west stratus
soz i forgot to close
i closed old
calculate the double integral
integral from 0 to 2 pi integal from 0 to 2 (rcos(theta))^2z(1/2(rcos(theta),rsintheta,0)rdr*dtheta
compute the scalar-surface integral f Ds:
double integral g x^2zdS where G is the cylinder (including the top and bottom) x^2 + y^2 = 4, 0 <= z <= 3
@untold drum
compute the scalar-surface integral f Ds:
double integral g x^2zdS where G is the cylinder (including the top and bottom) x^2 + y^2 = 4, 0 <= z <= 3
<@&286206848099549185>
calm coralBOT
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west stratus
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calm ivy
does anyone have an idea on how to go about solving this? i think the base case was pretty straight forward (sqrt 2 < 1.5) but i am pretty lost on what to do in the inductive step
random adder
Well generally $\sqrt[n + 1]{n + 1} < \sqrt[n]{n}$
potent lotusBOT
casework
random adder
Try proving that
mortal orbit
only for n > 2 though
random adder
More like only for n >= 4
mortal orbit
works for n >= e
calm coralBOT
@calm ivy Has your question been resolved?
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@calm ivy Has your question been resolved?
calm ivy
<@&286206848099549185>
blazing coyote
try proving that the RHS is more than the LHS at 2
and increases faster thereafter
maybe that will work
calm coralBOT
@calm ivy Has your question been resolved?
calm ivy
ill try that, thanks 🙏
hearty peak
calm coralBOT
hearty peak
Ok so I have no idea from where to start
mortal orbit
so first of all, "is an equivalence relation", not "the"
many equivalence relations can exist
hearty peak
so first of all, "is ***an*** equivalence relation", not "the"
I used google translate because the original exercise is not on english
mortal orbit
what's the original language?
mortal orbit
alr
hearty peak
anyway
hearty peak
can you understand the problem?
mortal orbit
yes
hearty peak
great
mortal orbit
do you know what 3 properties an equivalence relation verifies?
hearty peak
so the relations has to be reflexive, symmetric and transitive?
mortal orbit
yes
hearty peak
ok so after I prove those 3 points I can say its equivalent?
mortal orbit
yes it would then be an equivalence relation
question two is about finding all x such that xR3
and question 3 is about finding all the equivalence classes
hearty peak
I am having problems with understanding the second and third question
mortal orbit
well 2nd question is about finding [3]_R
and third question is about finding all the possible [x]_R
hearty peak
also had problems with understanding this example
someone told me that there is mistake in the second example
mortal orbit
also had problems with understanding this example
example number 2 is wrong
hearty peak
it should be 3 and 4
mortal orbit
yes
hearty peak
can you explain how and why?
mortal orbit
well for each number you find its equivalence class
In example 2 :
[1] = [2] = {1,2}
[3] = [4] = {3,4}
so there are only 2 different equivalence classes
{1,2} and {3,4}
hearty peak
it cant be [2] = [4] ?
hearty peak
oooooooooh
mortal orbit
the equivalence class regroups all numbers that are related to each other
2 and 4 are not related so they belong to different classes
mortal orbit
it only asks about 3
calm coralBOT
@hearty peak Has your question been resolved?
mortal orbit
except 4
we're not asking about 4
asking about 3
which x verify 4|x-3
And no x = 3 is not the only solution
hearty peak
no idea
hearty peak
I dont know if a/b or b/a
mortal orbit
?
hearty peak
nvm
mortal orbit
so what's the definition of "a|b"?
mortal orbit
alr no prob
mortal orbit
but remember that a|b if b = ka for some k
hearty peak
so its basically a / b = k?
calm coralBOT
@hearty peak Has your question been resolved?
blazing coyote
The locus of the midpoint of teh chord of contact of tangents drawn from points lying on 4x-5y=20 to x^2+y^2=9 is?
blazing coyote
!status
calm coralBOT
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
Why am. I here
blazing coyote
but how do I use that here
I've seen solutions online
but they make no sense to me
here's a diagarm
<@&286206848099549185>
Nvm
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shut halo
someone help me solve this limit pls
calm coralBOT
someone help me solve this limit pls
vernal crest
someone help me solve this limit pls
Is the answer 1
shut halo
and it's def right
desmos confirms it as well and if I get √e I'll finally get the right ans to a question I've done like like 8-9 times now 💀
final problem now
I thought of using l'hopitals rule but it got too complicated
JessicaK been typing for a while I'm getting scared now 
spare beacon
You're either going to use L'Hopital's or apply a maclaurin expansion to log(1+1/x). You don't have a huge number of options that doesn't get much more advanced.
shut halo
You're either going to use L'Hopital's or apply a maclaurin expansion to log(1+1...
I see, I haven't actually studied maclaurin expansion unfortunately
And idk it feels like L'hopitals rule won't help much
but I'll give it a shot then
past zinc
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empty tartan
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empty tartan
The question was to prove n^2-1 is divisible by 3 if n is not a multiple of 3 for integer n
why do they choose n=3k+-1
remote mural
if n is a multiple of 3, then n + 1 is not a multiple of 3
you can prove the above via contradiction
swift laurel
we know that 3k is a multiple of 3, 3k + 1 can't be a multiple of 3, 3k + 2 can't be a multiple of 3, 3k + 3 is a multiple of 3. so that gives 3 possibilities. but 3k + 2 = 3n - 1 for some different choice of integer n
empty tartan
so is this saying that n^2 is a multiple of 3 so n^2-1=3k-1 which is not a multiple of 3?
oh wait i see
i see they're just showing that for non multiple of 3 n, this is divisble by 3. thanks
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spiral dagger
calm coralBOT
spiral dagger
I have question concerning the solution to this problem
In the diagram they use variable x and y for the variables we are trying to minimise area with respect to
But then they use the same variables x, y in the point slope equation for the line
It is not clear if they are the same
swift laurel
they are the same variables. the 3 vertices of the triangle are (0,0), (0,y) and (x,0)
spiral dagger
How do you go from that to the point slope equation
swift laurel
the point-slope equation corresponds to the hypotenuse of the triangle
spiral dagger
the point-slope equation corresponds to the hypotenuse of the triangle
If i substitute x=0 into $y-4=m(x-8)$ do i get $(0,y)$
potent lotusBOT
shrödinger
swift laurel
x and y in that point slope equation are normal variables that can have any value. it may have been less confusing to call the side lengths x1, y1 by contrast
spiral dagger
Like this?
calm coralBOT
@spiral dagger Has your question been resolved?
spiral dagger
No
hot creek
But then they use the same variables x, y in the point slope equation for the li...
the point they used is represented as $ (x↓1 , y↓1)$
spiral dagger
the point they used is represented as $ (x↓1 , y↓1)$
x1, y1 is (8,4)
calm coralBOT
hot creek
x1, y1 is (8,4)
yes.
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dark ridge
it is conjectured that a number is divbisible by 4 if the sum of twice the tens digit and the ones digit is a multiple of 4. Prove that this conjecture is true for a 4 digit number
dark ridge
can someone help me with this
Nvm I got that one
Please lmk if it is incorrect
Can someone help me with part b
untold drum
its not exactly the hint, but i would start with 0 <(a-b)^2=(a+b)^2-4ab. with some transformations you will get M>=H.
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quick stump
I have to deal with the social surplus the problem is Prices and quantities demanded at dates t = 0, 1 are as follows:
P0 = 8, P1 = 10 and Q0 = 30, Q1 = 20.
What is the arc elasticity of demand?
I found 3.37
calm coralBOT
I have to deal with the social surplus the problem is Prices and quantities dema...
@quick stump Has your question been resolved?
remote mural
calm coralBOT
remote mural
can someone tell me what this notation means
calm coralBOT
can someone tell me what this notation means
calm coralBOT
minor island
why is it when you do cross product of two vectors it is -j?
remote mural
why is it when you do cross product of two vectors it is -j?
open a new help channel. This one is already closing
minor island
oh i thought it was a glitch mb, there are non currently available
remote mural
go to #1021175428326633542 then perhaps
minor island
id rather wait,as i feel my question will be lost in there
marsh agate
the weird circles, and partial differential <:hmmCat:876852574844751872>
interior and boundary
But how do you find yourself in the middle of a topology book without knowing those ?
remote mural
interior and boundary
But how do you find yourself in the middle of a topology b...
this is an analysis book 
i just got into this problem sheet and the notation was unusual so
marsh agate
well, know these are standard/common
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remote mural
calm coralBOT
remote mural
trying to do this question
with the first formula here
already did it with both 2nd and 3rd
calm coralBOT
@remote mural Has your question been resolved?
calm coralBOT
@remote mural Has your question been resolved?
remote mural
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calm coralBOT
final bay
hello
can you help me to find a lower bound of the integral of x exp(-xt)/(t+1) dt
from 0 to 1
when x goes to +infinite
I want to find a lower bound which tends to 1 when x goes to +infinite
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brittle siren
calm coralBOT
brittle siren
CD is a diameter in the circle O1. AB is a diameter in the circle O2. DC is tangent. AB is parallel to CD.
prove that the continues lines of AD and BC meet in pint E
i was thinking
if AB || DC
then ABCD is a trapezoid
that means that DA isnt prallel to BC
so they end up meeting?
or maybe
because AB and CD are both diameters
AEB and DEC are 90 and are angels on the cicrle
so we can then prove similar triangles
spare abyss
Yeah
brittle siren
is proving similar triangles gonna solve this?
spare abyss
Yes
brittle siren
ok
thanks
another question is
that the radius of the small circle is "r"
also angle ADC = 60
express the area of ABCD using "r".
AB = 2r
maybe we can work similarites
why did they give me the value of ADC tho
oh
spare abyss
Use trigo to find the rest of the sides
brittle siren
maybe equalateral?
brittle siren
Use trigo to find the rest of the sides
on which triangle
spare abyss
Oops I read the angles wrong sry
brittle siren
i wills say tho
AEB = DEC = 90
AE^2 * EB ^2 = 4r^2
still dont get why they gave me ADC
oh
damn
its a 90 60 30
maybe
so DE = 1/2 DC
and EA = 1/2 AB
so EA = r
random adder
Ig just get R in terms of r and thats it
random adder
You are basically saying r/R = 2r/2R
random adder
That is true
random adder
$\frac{\cancel{2}r}{\cancel{2}R} = \frac{r}{R}$
potent lotusBOT
casework
brittle siren
yeah that doesnt help me lol
random adder
random adder
Analyze that triangle
random adder
Basically get R in terms of r
random adder
You can do it from that triangle
random adder
This one
random adder
random adder
You can get something out of that
brittle siren
yeah thanks for the heads up
we can see a 90 angle in O2O1 something
maybe pythagoras there
bc DC is a tangent
wait did u mark r or v
brittle siren
You can get something out of that
i dont understand
while it seems better to understand i still dont get it
AO2/DO1 = EA / AD
random adder
Look at the height of the triangle
brittle siren
thats r
random adder
No its $\frac{R\sqrt{3}}{2}$
potent lotusBOT
casework
brittle siren
?
random adder
You also need to prove O2 O1 and E are collinear
But with similarity its pretty trivial
random adder
?
R , R , R triangle
Thats its height
Its height can also be written like $r + \frac{r\sqrt{3}}{2}$
potent lotusBOT
casework
random adder
Look at the triangle
brittle siren
ok
random adder
Write height in 2 different ways
random adder
random adder
brittle siren
i feel dumb
what
are u using a caluclator
somehow
we are working with sides
and "r"
how did we get sqrt 3/2
random adder
brittle siren
damn
i get it
so
AE = r
AB = 2r
EB^2 = 4r^2-r^2
EB^2 = 3r^2
EB = sqrt (3r^2)
random adder
You can see here
brittle siren
which side is r sqrt 3 /2?
random adder
The one which i showed with a line
brittle siren
