What is the significance of root 2 in these curves? https://mathcurve.com/surfaces.gb/coussin/coussin.shtml
#help-28
warm ravine
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What is the significance of root 2 in these curves? https://mathcurve.com/surfac...
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wanton niche
I am justbreally confused how to start
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I am justbreally confused how to start
wanton niche
I have this so far
I am mostly stuck on bullet 4 idk how am suppose to set it up
Once i do that then i can do the rest
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<@&286206848099549185>
I know im suppose to combine them into tan but idk how am supposed to go about it
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torn jolt
is there anyone who is good using calculator
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is there anyone who is good using calculator
balmy lion
Wdym?
torn jolt
i keep getting this weird thing
1570°0'0''
<@&286206848099549185>
this my calculator
gritty rose
google your calculator brand and model number and problem
torn jolt
i want to have this in my calculator
something like this
gritty rose
google your calculator brand and model number and problem
your calculator's stuck in degree mode
gritty rose
Deg is probably what you're stuck in
Sci is what you want
Actually i have no idea what your mode is called
google is your friend
gritty rose
MthIO Deg Gra Sci LineIO Rad Fix Norm
google the meaning of all your calculator's modes
torn jolt
MthIO: Selects MathO or LineO. MathO displays input and calculation results using the same format as they are written on paper. LineO displays input the same way as MathO, but calculation results are displayed in linear format.
DEG is degree.
RAD is radian.
Scientific notation mode (Sci) displays all decimal numbers in scientific notation using a specified number of significant figures. This mode is entered using (SETUP) (Sci) followed by the number of significant figures required, for example . When your calculator is set in this mode, the display indicator SCI is shown.
Norm displays numbers in the normal notation
btw these ones are shift + mode
gritty rose
Sci is probably the most common so go with that
gritty rose
just try and see if it's right for you
it's not like your calculator will break and you can't change the mode again
steel hemlock
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ivory cairn
what have you tried?
steel hemlock
I tried writing some summation formulas, but nothing was able to get exact values
(1/6)n(n+1)(n+2)
Maybe it would work
ivory cairn
So
1 rows: 1 ball
2 rows: 1+2 balls
3 rows: 1+2+3 balls
4 rows: 1+2+3+4 balls
etc
subtle cobalt
Your nth term would be $\frac{n^{2}}{2} + \frac{n}{2} - does this help?$
steel hemlock
Your nth term would be $\frac{n^{2}}{2} + \frac{n}{2} - does this help?$
Yeah i did exactly that
Is that correct ?
glossy valveBOT
Sam.
steel hemlock
subtle cobalt
Yep
steel hemlock
Oh thanks
subtle cobalt
Plug your number in and you’re good
junior marlin
Hey whoever wants to help me, I have a question regarding force, I’ll post a couple pictures and then I’ll explain my troubles
still spruce
just post the question immediately
junior marlin
Ok so my question is, the formula for work is W = ||F||||s||cos(theta), but the formula to find the angle between 2 vectors is theta = cos^-1((u dot prod v)/||u||||v||)
Oh it erased my magnitude sticks but anyways, is my work correct?
still spruce
it looks good to me
junior marlin
Does anyone know what the question means by minimum magnitude of force? I don’t understand how you could make it any smaller and not change the total amount of work.
junior marlin
Sorry the question got cut off but the rest says “to obtain the same work? Explain@
“
fossil stump
If W is the same, and F decreases, then one of the other factors in the equation must increase to counterbalance the decreasing F
(Small hint) ^^
junior marlin
So the angle should change?
Wait, I’ll go over a couple concepts quickly and come back
I understand that, but how would I solve the expression if I don’t know the minimum F and also what the angle should be in order for me to get that minimum
torn jolt
It's asking what the minimum of |F| is so how can you find |F|?
junior marlin
Setting the angle to 0, but I have to keep work the same, idk if I’m making sense
Or no that would be finding the maximum, setting the angle to 90, but still I don’t think that’s right
still spruce
yeah yeah
junior marlin
Sorry in my original question I cut out a bit and posted it underneath
That’s where much of the confusion must be coming from, the final words were “to obtain the same work”
junior marlin
Wouldn’t that solve for maximum, or do you mean cos(1)
torn jolt
What equation do you get when you solve for |F| while treating work and |s| as constants?
junior marlin
1/ (F * s)= cos(theta) * Work
I’m sorry I’m really trying to understand
I mean W/s = cos(theta) * F
But I guess you’d then divide both sides by the cosine, but if you have 2 unknown variables it doesn’t help much
torn jolt
Yes so you get $$|F|=\frac{Work}{|s|cos{\theta}}$$
glossy valveBOT
Critzzzy
still spruce
yes but you already know how to maximize cos(theta)
which would minimize Work
you see, having a larger value in the bottom actually makes Work smaller
still spruce
I mean yes. But the values of sin(theta) and cos(theta) are always less than or equal to one. You know the unit circle? r is always 1 so you can just let cos(theta) be 1 to maximize a function like this
also setting cosine to 90 would be 0
junior marlin
Oh true
still spruce
you'd want either 0 or 360 (0 or 2pi)
junior marlin
Yeah, can’t divide by 0 anyways so that’s already a red flag, man it’s 3 am where I live so sorry if I seem a bit foolish, thanks for the help, both of you 🙂
still spruce
it's really okay! :))
junior marlin
So just to be crystal clear cuz I might just cry if I get this wrong after all that, I only need to plug 1 in as the cos(theta) leaving me with essentially W/|s| on the right hand side
junior marlin
Which would just be its magnitude I assume, k great. Well thanks again, much appreciated, and I had just one last question, are you like a math teacher, why is it that you help strangers online, or is it simply to be kind haha
still spruce
I'm a math major in university rn
tbh I just recently starting being active in this discord, but it's fun to help guide people if I can
this is my first day with the Helper tag actually lol
junior marlin
Oh well that’s great, I’ll close this help thread to let someone use it but I just want you to know that it helps a lot : )
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modern zodiac
Theta is 1/4
I don't know how the sine got taken out
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Theta is 1/4
I don't know how the sine got taken out
ember tartan
Theta is 1/4
I don't know how the sine got taken out
what is the full question
ember tartan
is theta given?
meager dew
is that theta or sin(theta)?
ember tartan
Me again 😭 but for this, before i submit anything again 😭, i know the nth term test goes to infinity. Integral test cannot be applied because n is in the exponent right? Therefore it MUST be a divergent series. My question is; how do i tell if its a geometric series or not? Am I even correct?
ember tartan
I know geometric series are in the form of $ar^{n}$
glossy valveBOT
beanbeanjuice
ember tartan
but wouldn't that mean it IS a geometric series?
glossy valveBOT
Bean
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atomic blade
Me again 😭 but for this, before i submit anything again 😭, i know the nth term...
This isn't
This isn't geometric as far as I'm concerned
Because of the +2 at the bottom
ember tartan
For this, using the nth term test, it is inconclusive bc the limit of an is 0. However, we cannot apply the integral test to this right?
ember tartan
So how would we tell if its convergent or divergent
bc its 100% a geometric series
i think at least
so 50%
ivory cairn
why is this not a geometric series?
glossy valveBOT
beanbeanjuice
ember tartan
but if the nth term test is inconclusive
and the integral test cannot be applied
how do we know if its...
convergent or divergent?
ivory cairn
**beanbeanjuice**
and? what is your definition of a geometric series?
ember tartan
and? what is your definition of a geometric series?
$ar^{n}$
glossy valveBOT
beanbeanjuice
ember tartan
ohhhh... but r is the ratio right?
ivory cairn
yeah
ember tartan
but that makes sense then so it is geometric?
ivory cairn
yeah
ember tartan
but how would i know if it converges?
nth term test is inconclusive
you can't use integral test ont his
ivory cairn
when does a geometric series converge or diverge?
ember tartan
if |r| < 1 then they converge
and r is less than 1 in this case
so that means it converges
so its a convergent geometric series
ah i got it right!
tysm
i really appreciate it
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topaz urchin
I need help understanding a solution of a problem
The task is to prove this inequality, where a, b and c are real
topaz urchin
The solution they have is as follows:
- transform the RHS
- and use the Root mean square - arithmetic median inequality
I would like to understand how does one get to the last row (i mean, squaring both sides of the bottom-last row and multiplying by 3 does it), but why is squaring both sides allowed here?
The RHS doesn't always have to be positive, and that confuses me here, I'd like any help on this
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half scarab
Hey can you please help me with finding HCF it is so hard I’m crying
half scarab
How please explain
quasi plaza
What can b be
half scarab
I am so stressed
quasi plaza
With the first one see if you can get an interger
half scarab
Please what is answer
signal solstice
Hold on
quasi plaza
But what if b is 6 or 5
quasi plaza
But HCF is a function that takes only intergers
quasi plaza
But what about 7(b+1)(2+b) has to be an integer, therefore if b+1 or b+2 is a multiple of 7 then the HCF is not 7 its 49
quasi plaza
Please what is answer
Do have the right answer?
north crest
what is the question
signal solstice
7(1 + 6)^2
and 7(2 + b) (1 + b)
What is hcf of these 2
Posted by @half scarab
7(1 + 6)^2 = 343
signal solstice
Exactly
north crest
second one is
signal solstice
7 (2 + 3B + B^2)
signal solstice
Like @quasi plaza said, can it be 49?
half scarab
I'm confused
I am confused to
north crest
one thing is guarenteed that it is a multiple of 7
half scarab
My teacher tried explaining and I did have no idea
north crest
HOW IS IT 49
north crest
u cant have a number more than 14
signal solstice
Mhmm
half scarab
The hcf is 7(1+b)
half scarab
Idk
signal solstice
Did you write the wrong questions
half scarab
This teacher is confusing
signal solstice
-s
half scarab
No it’s is completely correct
signal solstice
How??
quasi plaza
HOW IS IT 49
but what if (b+1)(b+2)=49
north crest
but what if (b+1)(b+2)=49
u cannot asume the value of B
signal solstice
Exactly
signal solstice
Assuming values when it's an expression is impossible
signal solstice
Yeah
quasi plaza
But if you shouldn't you list what the HCF could be depending on what b is, becuase you do not know what b is?
north crest
But if you shouldn't you list what the HCF could be depending on what b is, becu...
since its a variable it multiplies with its coefficient which means the hcf of the coefficients is the hcf of your 2 numbers
quasi plaza
Wait is it the HCF of the coefficient
north crest
yes
because variables multiply
so they will still be able to be divisible by your hcf
signal solstice
Yeah
quasi plaza
but its the highest common factor not just a common factor
north crest
u have to take the highest common factor -_-
quasi plaza
b+6
signal solstice
Yeah, b+6
half scarab
That’s answer
I thought that to
Yes
Nvm guys
This is w
Nvm guys I need to solve this
This is I don’t know
Wha is hcf
<@&286206848099549185>
Please help
quasi plaza
lol, First Question: if $b=\frac{-3\pm\sqrt{49M\times 4 -1}}2$ then HCF is 343
otherwise if $b=\frac{-3\pm\sqrt{7M\times 4 -1}}2$ then HCF is 49
otherwise HCF is 7
glossy valveBOT
Debeast
quasi plaza
Nvm just ignore it.
signal solstice
React with "old_delete", in case you want to delete the LaTeX equation
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silver flax
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https://imgur.com/a/2PrCsAi
silver flax
Recently had some homework on Stokes theorem - the questions are contained here
J wanted to check whether my approach for 2b and C are correct - my attempt is included as well
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exotic harbor
Hi. I've been stuck on converting a sentence into two equations and then solving for part b. Sentence is:
"There were 96 people in a party. One man leaves and is replaced by a woman, leaving three times as many women as men at the party.
a) Form two equations of the above information given that m represents men and w represents women at the party."
part b is: "Solve the two equations simultaneously to find how many men and women were there originally at the party."
Best I've come to is: m+w=96 and so as there is 3 times as many women as men: 3m=w so 3m+m=96 which gives m=16. Substituting into 3m=w gives w=48 which of course, 48+16 only gives 64, not 96. Have I missed a step somewhere or messed a part up? Originally I thought you don't even need simultaneous equations here as you can divide 96 by 3 to get 32 as the total number of men, then subtract 32 from 96 to get 64 being the total number of women right? And if that were the case, would the two equations be: m=96/3 and w=96-32?
exotic harbor
or rather, the second equation would be: w=96-m (without putting in the value of 32 just yet as that is what you are supposed to do for part b)
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tiny mango
Hi. I've been stuck on converting a sentence into two equations and then solving...
One man left,so count of men in the party is m-1.
New woman enters, new count of women is w+1.
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tribal stratus
Why are some parts open and some parts closed brackets?
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Why are some parts open and some parts closed brackets?
spark valve
closed brackets include a and b
tribal stratus
right
spark valve
open brackets dont
spark valve
well it just means that the interval that is continuous includes a and b
fossil stump
If a function is differentiable at a point a, that means it has to be continuous around that point
tribal stratus
right but why isn't it including a and b
when it states that it must be differentiable on (a, b)
if that makes sense
stray abyss
right but why isn't it including a and b
ig it means that the function need not be differentiable at a and b
stray abyss
for example |x| in the interval [0,1]
tribal stratus
so it says that because
not all the functions
that are increasing
will be differentiable at it's end point
if there are holes in the end points
it's still increasing
tribal stratus
for example |x| in the interval [0,1]
oh I see
that's a good example
because it's technically still continous
stray abyss
yeah
tribal stratus
ohhh
stray abyss
but not differentiable at 0
stray abyss
still it's increasing
tribal stratus
It is
stray abyss
yeah so makes sense now?
tribal stratus
yea yea
it has to be continous
or else it won't follow
but differentiable depends
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torn jolt
I’m stuck at the start of a problem, it’s one of those “reality problems”, here goes:
“in a mixing vat there are 10000L of water with 50kg of salt mixed in. at t=0, pure water starts being poured into the vat at a rate of 120L/minute, at the same time, the liquid in the vat starts to get drained from the bottom at the rate of 120L/minute. call d(t) the concentration of salt in the vat, expressed in Kg/L.
torn jolt
the first question that I am stuck on is: what is the relation between the velocity v(t) at which the quantity of salt in the vat changes and the concentration d(t)
the book says it’s v(t)=120d(t) but it doesn’t make sense to me
every minute 120L flows into the vat, and 120L flows out, so the volume remains 10000L
so the vat is losing an amount of salt equal to the current concentration times 120L
do I just have to say that?
it should be -120d(t)
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fast sleet
i mean the quantity still changes with 120 d(t) right ?
the amount of salt changes with 120d(t) regardless of it flowing in or out of the vat
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torn jolt
Hi, pls could somebody check if this is right?
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Hi, pls could somebody check if this is right?
ivory veldt
torn jolt
Sorry, you can't ask a question in a channel that's being used 😅
sonic marlin
Hi, pls could somebody check if this is right?
both correct
torn jolt
how is this inequality derived?
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how is this inequality derived?
torn jolt
Context:
last image is where I’m stuck
o yea forgot to mention this complex analysis btw
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torn jolt
<@&286206848099549185>
quiet stirrup
|f(z) - f(w)| < eps_1, |f(z)| > |f(w)|/2.
torn jolt
Hi, can anyone help me with this?
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Hi, can anyone help me with this?
rancid arrow
Are you familiar with logarithms?
dusk inlet
Take ln of both side.
torn jolt
Okay, is the formula ln(a^b)=bln(a)?
rancid arrow
yes
echo lance
Okay, is the formula ln(a^b)=bln(a)?
you don't need that here though
fast sleet
you don't need that here though
it's convenient though
torn jolt
hmm I'm not sure what to do then 😅
echo lance
it's convenient though
I don't see where you use that formula here
ln is already inverse of e^x
fast sleet
I don't see where you use that formula here
ln(e^{x-2}) = (x-2) ln(e) = x-2
fast sleet
ln is already inverse of e^x
yes but they aren't familiar with that
torn jolt
I'm not sure what to do without that formula haha
echo lance
I'm not sure what to do without that formula haha
you can use the formula it works
but you don't really need to
dusk inlet
e^x = m iff ln(m) = x.
e^1 = e so ln(e) = 1.
echo lance
just ignore what I said though if it confuses you
dusk inlet
My bad iff means if and only if
torn jolt
The formula is the only way I would think of doing it, whats the other way
dusk inlet
Another way to do this will be more complicated.
echo lance
The formula is the only way I would think of doing it, whats the other way
ln is the inverse of e^x, so when we ln both sides we just have f^-1(f(x - 2)) on LHS which is x - 2
fast sleet
The formula is the only way I would think of doing it, whats the other way
the formula is derived from a different identity, jsut a quicker way of doing it
rancid arrow
yes
torn jolt
okay! let me try that
light sonnet
but you don't really need to
It's a log identity. It's used
torn jolt
wait, I'm being dumb, how would i type it into a calculator?
light sonnet
Type what exactly?
Ln(10)? Because there should be a button for that, depending on the calculator you have
torn jolt
okay ill try that
dusk inlet
wait, I'm being dumb, how would i type it into a calculator?
You need to find x.
Then type the answer to the calculator.
torn jolt
how would i find x?
echo lance
would it be ln(e^x-2)=ln(10)?
this was the first step
torn jolt
ohhhh
light sonnet
And you should know what ln(e) is
torn jolt
1
hoary summit
I 100% agree with the logic of just inverting e^(x-2)
It’s by far the most intuitive way to understand logarithms imo
echo lance
are there other ways of defining log 
hoary summit
Standard education basically doesn’t define them
light sonnet
I 100% agree with the logic of just inverting e^(x-2)
Ln(a^b) = bln(a), I'm pretty sure it how the logic was defined
hoary summit
People just memorise log_a(n) = x => a^x = n
I know but learning it based on the idea we can just remove exponentiation with logs is more useful imo
Makes manipulation way easier
torn jolt
ahh I am confused, could someone pls walk me through the steps?
hoary summit
Because people just memorise rules when it’s not necessarily here
torn jolt
I am not good at this haha
hoary summit
ln(x) is the inverse of e^x
In the same way dividing is the inverse of multiplying
Subtracting the inverse of adding
torn jolt
right!
hoary summit
If you take the natural log of e raised to the something you remove the e
torn jolt
okay
hoary summit
And in the same way if you raise ln something to the e it removes the ln
So you can look at that equation and transform it like that immediately
hoary summit
Taking the ln of the left-hand side removes the e from it
So it’s just x - 2 that’s why it’s so useful to think of it that way
Then the right-hand side is ln10
torn jolt
oh okay
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faint dock
That is so many questions. What have you done and where are you stuck
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crimson stag
@faint dock I'm sorry i guess that was too many questions. I'm stuck a,b and e
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earnest frigate
What have you tried?
Do you remember the theorem?
…
Do you remember the theorem correctly?
Open ur notes
_Given: In ΔABC, AD is the external bisector of ∠BAC and intersects BC produced at D.
To prove : BD/DC = AB/AC_
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gray magnet
The above screenshot lists the entire question.
Specifically, I was able to graph the original Supply and Demand function as well as find the market equilibrium. Using one of the formulas from my course (which I wrote below), I was also able to find the new equilibrium after tax but I am not sure how to graph the new Supply function. The only formula I was given is : Qr^s refers to Qs with ad valorem tax, Qr^s(p) = Qs(p-rp) where r is an unknown variable that refers to the rate of taxation. 0 <= r <= 1.
gray magnet
more specifically, I am looking for a solution to the last parts of the question, which are: How much of the tax has been passed on to the consumers? and What is the maximum tax, r, that can be imposed if this market is to continue functioning?
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velvet dove
You can just depict the graph with r.
When you have tax is imposed, the price raise is spited by consumers and firms. It is described from the original equilibrium.
To continue this market, the products must be positive then.....
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wet zinc
help i-
tight glen
does m_1 stand for measure of angle 1??
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tight glen
if yes, then do you know the exterior angle property?
by that, you can say that angle 3+angle 4=angle 1
angle 3=angle 2 since they are vertically opposite
so, angle2+angle4=angle 1
angle 1 must be greater than angle 2 then
you can follow the same line of logic in the next one also
do you understand now @wet zinc
?
light reef
can someone plz explain how i do all parts of these questions
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can someone plz explain how i do all parts of these questions
@light reef Has your question been resolved?
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dull orbit
Impulse is change in momentum
Conservation of momentum states that the momentum of one object +another before collision = momentum of object1+2 after collision
And e =Vb-Va/Ua-Ub
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potent galleon
is there a formula for circumcenter?
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is there a formula for circumcenter?
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potent galleon
.reopen
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potent galleon
is there a formula for circumcenter?
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wet zinc
do you understand now <@903518272413114380>
sorry i was sleeping on that time
wet zinc
Thanks anyways
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wet zinc
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calm kayak
need help with this question
fathom saddle
Do you know how to integrate functions?
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orchid whale
A train has 30 first class seats and 70 economy seats. What percentage are first class seats?
So I used part/whole and then x 100.
100/30 =3.3 so 33%
That’s correct right?
onyx glen
no
100/30 is not equal to 3.30 like you wrote, and 3.30 * 100 would be 330%, not 33%
and even disregarding all that, you confused the part with the whole.
100 is the whole.
orchid whale
So what’s the proper way to do it?
I thought you had to add the total amount 30+70=100 and then divide by the 30 seats
orchid whale
Part would be 30 and whole is 100?
vapid barn
Yep
torn jolt
i just need someone to check my work because im not really confident with my answer and im probably off
ivory cairn
that's right
brazen tundra
I need help finding the perimeter on this one.
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I need help finding the perimeter on this one.
nova flume
alright, look up the 45 45 90 triangle and see if you can figure it out
brazen tundra
I tried that, I got 71.7 if you round to nearest tenth
nova flume
is it incorrect?
brazen tundra
and 71.7 didnt work as an answer
dim wolf
My first thought was pythagorean theorem and add up
nova flume
it'll give the same answer i believe
brazen tundra
yes
strange sand
round up the 71.7 to 72 maybe?
nova flume
area was right tho?
brazen tundra
i assumed that the area was right, because since i have multiple attempts on this homework, i tried different answers for perimeter, but kept the area the same, it remained 1 / 2 score so I know the area is right
nova flume
interesting. area should be right. i have no idea what could be wrong with the perimeter. does the website malfunction often?
brazen tundra
It could be that my teacher just put in the wrong thing as an answer
its alright, its the only question i got wrong on it ill talk to her tomorrow
ty for your help tho
nova flume
yeah👍
brazen tundra
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white charm
Help me with this question pls
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Help me with this question pls
tidal citrus
@white charm You need to use Similar Triangles and you would know that if you were taking notes or paying attention to the name of the assignment you are working on.
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brisk lake
hihi! could i please have help with this question?? I have substitution of u = 2x +7
glossy valveBOT
waler
oak basin
check your derivative again
oh excuse me, you did the substitution u=2x+7
it's not a bad substitution, but u=sqrt(2x+7) is a better one
brisk lake
oh excuse me, you did the substitution u=2x+7
aa the question asks for u = 2x+7 and then afterwards its sqrt(2x+7)
brisk lake
i have 1/2 x sqrt(u). du
brisk lake
x= (u-7)/2
brisk badge
anyone can help ?
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anyone can help ?
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sweet ingot
With?
brisk badge
what with?
brisk badge
Surely you have seen/done finding maximum/minimum before?
not yet, coz I dont understand
sweet ingot
You have never seen it before? You are supposed to derive the method on your own?
I doubt that
brisk badge
the derivative is 3/4 x^3 - 3??
sweet ingot
Almost
sweet ingot
si
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brazen portal
Hey
winter isle
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light reef
plz can someone explain how to do this im so stuck
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plz can someone explain how to do this im so stuck
@light reef Has your question been resolved?
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gritty rose
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torn jolt
Help
meager dew
you're just pluggin in numbers
kind jay
nothing is hard
torn jolt
Man y’all always up in this server
I’m at school rn
And my teacher tellin everyone to do this
kind jay
yeah
torn jolt
It’s hard man
kind jay
what u no undrstand about it
atomic blade
Bro this chat breakin
torn jolt
Like f(x)
torn jolt
What’s that mean?
atomic blade
Well
kind jay
it makes a sexy graph
atomic blade
Basically f(x) is dependent on x
atomic blade
it makes a sexy graph
Ayo you good?
kind jay
yes
atomic blade
Bet
torn jolt
So how do I plug or get the numbers?
atomic blade
What’s that mean?
So whenever x = a, where "a" is any value, you subsitute x with "a"
atomic blade
So how do I plug or get the numbers?
Plug in the numbers
Like
Replace x with the values given
torn jolt
I gotchu
Hold up
So the first box I would put 0?
Assuming
Nah then they would all be 0
glossy valveBOT
Umbraleviathan
torn jolt
Next one is 2
atomic blade
Yup
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teal prism
Prove that there are no natural number n such that 0<n<1
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Prove that there are no natural number n such that 0<n<1
teal prism
I mean no idea how to start
solemn kestrel
ithink you can start by the definition of natural numbers
goes from 0,1,2,3...
take 0 and 1 by cases
you can easily show that neither n=0 or n=1 is between 0 and 1
the question seems a little too straightforward so im not sure how rigorous of a proof there needs to be but thats my approach
teal prism
Well
The original question was
Prove that there is no natural number such that m<n<m+1
And I said because addition is moniton that then n=m+b
So m<m+b<m+1
And then I substract m
solemn kestrel
right, i think for a question like this, the definition of natural numbers may be the easiest
you know m+1 - m = 1
so then as u said before
0 < n < 1
which is not possible by definition of natural numbers
spice orchid
A way to see this is assume there is a natural number ,n, between 0 and 1, thus it must be the successor of some natural number n' >= 0
But following this we will arrive at n=1 which contradicts our assumption
torn jolt
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torn jolt
also is there any procedural way of doing these problems?
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torn jolt
<@&286206848099549185>
unborn solstice
cant you just prove that log(x) < sqrt(x) for all x>0
or is that not how you do this
sweet ingot
log(x)=2*log(sqrt(x)) from log properties
Hmm maybe not this either but you just need to know log(x)<x and result follows
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edgy cloud
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quiet stirrup
u = t dv = sin(at)
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tacit pewter
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tacit pewter
anyone would like to help me out with this one right here
west sail
@tacit pewter note that angle TUS + angle TUA = 180 degrees
you can start from there
once you get 2 inner angles of the triangle, you can easily guess the leftover angle
tacit pewter
so the answer is 65
light sonnet
No
Apply the concept of supplementary angles to find TUS
Wait.... Sorry
I thought you were saying what x was
light sonnet
so the answer is 65
Yes
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earnest coral
Hello I have this shape and need to prove that EC and OB when they cut each other’s to do 90 degree xd hope u understand
earnest coral
Like this
It’s given that EOC = 90
So what I did is BEO = BCO = 90
And BCOE all angles should be 360 so EBC = 90 also
So this shape is a dalton (or idk what it’s called in English xd)
earnest coral
Like this
And dalton prove that EC and BO do this
Is that right what I did here ??
<@&286206848099549185> sry but I’m in urgent situation 😅
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haughty solar
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haughty solar
My work
So my question is does it matter where I choose my starting point to be?
zenith kernel
No
zenith kernel
It doesn’t matter
wary nest
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wary nest
for this double integral it doesnt matter where our bounds end up at right?
kind jay
wdym ends up
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zenith forge
3log(a) 8 - 1 , how do I express this as a single log? base is (a)
zenith forge
I got log(a) 8 - 1 = log(a)8 - log(a) a = log (a) 8/a
Is that the simplest form log (a) 8/a
little helm
what about the 3?
zenith forge
sorry that was a typo, no 3
little helm
ohk
little helm
I got log(a) 8 - 1 = log(a)8 - log(a) a = log (a) 8/a
then yeah this seems right
spare nacelle
hello, can someone help me on this?
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hello, can someone help me on this?
tulip beacon
hello, can someone help me on this?
Bro ion know what isomorphism is but i know that a xenomorph is a predator in the movie predators
candid ice
is there a hidden tip in that message i cant tell
I don't think there is a hidden hint in Mortta's message. It helps to identify that the kernel and image are, and then it may be simpler to find the isomorphism
Here's a hint maybe to get you started: what are i^0, i^1, i^2, i^3, i^4, i^5?
spare nacelle
Okay thats what i did actually
candid ice
Okay thats what i did actually
Ok. Should be okay then
spare nacelle
yes but i dont know how to continue
candid ice
yes but i dont know how to continue
What did you get for the kernel and image?
spare nacelle
I got
Ker(φ) = { 4k | k∈Z }
Im(φ) = { i^z | z∈Z }
The Im is just the function itself so i thought i'd just write i^z although im not sure there
oh wait im stupid i didnt give enough information
candid ice
I got
Ker(φ) = { 4k | k∈Z }
Im(φ) = { i^z | z∈Z }
Okay. For the image, you can write $\textrm{im } \phi = {0, i, i^2 = -1, i^3 = -i}$
spare nacelle
brave blaze
i^3 = -i
spare nacelle
that was the previous number
candid ice
Also note that Z/Ker(phi) is Z_4. You should be able to come up with the mapping
glossy valveBOT
1345631
candid ice
that was the previous number
That's fine. The fact that it's a homomorphism means we can compute its kernel and image
spare nacelle
wait so my kernel is wrong?
candid ice
wait so my kernel is wrong?
It's not. Also, you can also do it faster just by using the same construction in the proof of the 1st isomorphism theorem
spare nacelle
It's not. Also, you can also do it faster just by using the same construction in...
i dont think we've learnt any theorems
candid ice
then my image is wrong
No it's not. It's just not simplfiied enough to make it obvious. But if you want to can use the same construction in the proof of the 1st isomorphism theorem to get the answer directly without going through having to find the kernel and image
candid ice
i dont think we've learnt any theorems
Okay, then just write the isomorphism from Z/ker(phi) to im(phi).
spare nacelle
Okay so i have to write a function like the first phi?
ashen crater
Isn't Z/Ker(phi) an infinite set?
spice orchid
Isn't Z/Ker(phi) an infinite set?
no its Z_4
ashen crater
If Z is the integers and you remove those 0 mod 4
candid ice
Isn't Z/Ker(phi) an infinite set?
Ker(phi) is just 4Z, so Z/ker(phi) is Z/4Z, which is Z_4
candid ice
Okay so i have to write a function like the first phi?
Yeah. It shouldn't be too hard. Note that the integer powers of i are periodic with period 4
spice orchid
If Z is the integers and you remove those 0 mod 4
its a quotient ring not a set difference
ashen crater
Ok😂 bit advanced
spare nacelle
Okay. For the image, you can write $\textrm{im } \phi = \{0, i, i^2 = -1, i^3 = ...
i dont quite get that
candid ice
i dont quite get that
Try writing i^z for some integers z
brave blaze
z + ker(φ) ?
spare nacelle
thats the definition of Z/Ker(φ) right?
brave blaze
you said Z/ker(φ) = Z/4Z
its the set of the equivalent class {0, 1, 2, 3} (there is a bar on the top of them, thats the notation)
z is from Z and ker(phi) is a set I dont think that makes sense
candid ice
f: Z/Ker(φ) -> Im(φ), z + Ker(φ) |-> φ(z) like this?
It's fine
brave blaze
z + ker(phi) is fine ?
candid ice
Check that it is well-defined, that it is bijective, and that it is a homomorphism
candid ice
z + ker(phi) is fine ?
Normally the cosets are represented by xKer(phi), but since the group is additive, we write it additively rather than multiplicatively, so it's x + Ker(phi) in this case.
In other words, the isomorphism is psi: G/Ker(phi) -> Im(phi), which maps the left coset z + Ker(phi) to phi(z).
spare nacelle
Check that it is well-defined, that it is bijective, and that it is a homomorphi...
ok thanks but what is Z_4?
candid ice
ok thanks but what is Z_4?
integers mod 4
spare nacelle
Ker(phi) is just 4Z, so Z/ker(phi) is Z/4Z, which is Z_4
okay but why is Z/4Z, Z_4 then? i thought Z/4Z is Z + 4Z
shouldnt it be then integers * 4 or something like that?
candid ice
okay but why is Z/4Z, Z_4 then? i thought Z/4Z is Z + 4Z
Z/4Z is integers mod 4. Z/4Z is the quotient group, which is the set of left cosets, which are { [0], [1], [2], [3]} where [0] = 0 + 4Z, [1] = 1 + 4Z, [2] = 2 + 4Z. The quotient group is not Z + 4Z
spare nacelle
Z/4Z is integers mod 4. Z/4Z is the quotient group, which is the set of left cos...
@candid ice hey, sorry for pinging but i have another question and you explained it really well. if the subspace U is for example R^3 then. how would R^3/U if U is threedimensional. is it (0,0,0) because the set of left cosets is 0?
spice orchid
if $U \leq \mathbb{R}^3$ and dim$U=3$, what does that tell you about $U$?
glossy valveBOT
iCaird
spare nacelle
so if U is R^0 its infinite dots
U is R^1 its infinite lines
U is R^2 its infinite planes
U is R^3 its 0
thats what i thought
spice orchid
the point is if $U \leq V$ and dim$U$ = dim$V$, then $U = V$
glossy valveBOT
iCaird
spice orchid
and $V/V = {0}$
glossy valveBOT
iCaird
candid ice
and is the rest correct from R^0 to R^2?
Remember that the $0$ in the above is the identity coset, which is $V$.
Note that for a group $G$, we have that $G/G = {gG: g \in G} = {G}$, since $gG = G$ for all $g \in G$.
glossy valveBOT
1345631
spice orchid
Remember that the $0$ in the above is the identity coset, which is $V$.
Note th...
False, the quotient of a group by itself is the trivial group
candid ice
False, the quotient of a group by itself is the trivial group
False, it is isomorphic to the trivial group
candid ice
False, the quotient of a group by itself is the trivial group
{G} is the set containing just G. It is not the same as the set G.
spare nacelle
ok but how does that help me
replace G with R^0?
I thought R^0 for example would just be parallel dots
candid ice
I thought R^0 for example would just be parallel dots
What's the task?
spare nacelle
so if U is R^0 its infinite dots
U is R^1 its infinite lines
U is R^2 its infini...
this
like just explain geometrically how
R^3/R^0, R^3/R^1, R^3/R^2, R^3/R^3
would look like
well now i know that R^3/R^3 = {0}
plain marsh
May I know how he gets this part? Thank you
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May I know how he gets this part? Thank you
gritty rose
$\frac{1}{n3^n} \le \frac{1}{3^n}$ for $n\ge 1$. and $\sum_{n=1}^\infty \frac{1}{3^n} = \frac{1}{1-\tfrac13} - 1$
glossy valveBOT
riemann
plain marsh
ya i get how the equation work
rancid arrow
Series normally beings at n = 0
plain marsh
but how does it goes to -1
glossy valveBOT
Chris24
rancid arrow
Obviously, this case is not included in your sum since the series in question is not defined for n = 0
plain marsh
**Chris24**
oh so i am minusing the first term?
plain marsh
oh so i am minusing the first term?
and I only do that because I want it to use geometric series to sole it?
ahh i see thanks
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modest pulsar
how are decimals and fractions ratios and percents related