220 divisor
#help-10
robust moon
woeful edge
mhm
robust moon
okay
woeful edge
now do the euclidean division of the divisor by the remainder
woeful edge
not only that
robust moon
Should have done 220 / 35
woeful edge
u did smt else wrong
woeful edge
im gonna confuse u like that
woeful edge
now do the euclidean division of the divisor by the remainder
js follow my lead
woeful edge
yes
robust moon
so I'm supposed to divide those
woeful edge
yes
woeful edge
220 = 35×6 + 10
goodjob
now
do the euclidean division of the divisor by the remainder yet again
robust moon
35/6 = 6*5 +5
woeful edge
is 6 the remainder?
robust moon
5/5 = 1
woeful edge
.
woeful edge
tgen, the gcd is
the last remainder that comes before reaching 0 as the remainder
which is 5, yes, good job
robust moon
okay
woeful edge
so eucludean algorithm
robust moon
well I'm glad we unfucked that lol
woeful edge
is js the succession of eucludean divisionsb
1575 = 220×7 + 35
220 = 35×6 + 10
35 = 10×3 + 5
10 = 5×2 + 0
thats what weve been doing
dividing the divisor by the remainder until u reach remainder 0
woeful edge
well I'm glad we unfucked that lol
fortunately yes
robust moon
okay so what's the linear expression of that then?
jaunty stirrup
okay so what's the linear expression of that then?
Do you have an example of one from your notes or something?
jaunty stirrup
is it the process of combining after the euclidean theorem or forming it into an actual for ex 5 Equivalent to 2 (mod 3)
jaunty stirrup
not a 100% certain but this looks like combining
robust moon
yeah
jaunty stirrup
which then in order to do it, you reformulate all the euclidean theorem logic into what gives you your remainder
so if you have 22 = 7 * 3 +1
make that become 1 = 22 - 7(3)
and do that for all the remainders until the remainder of 1
neglect the remainder of 0 in this case b/c you will never use it
robust moon
okay
jaunty stirrup
then, one at a time, you expand one of the 2 terms,
jaunty stirrup
and reduce them down to primes?
hmm show me
robust moon
not with the answer she posted
jaunty stirrup
might be doing something similar but different lol
robust moon
for her example problem
sighs My professor has a PHD in the stuff
and I get the feeling
that that much math
makes you a little insane
jaunty stirrup
no no fair,
htinkikng about it now
i may have been thinking of relatively prime gcds
which is why this happened
jaunty stirrup
ok ok yeah, not 1 =
the actual gcd
so after you find the gcd, you do as i said earlier with making all the euclidean work, become num = something - something
jaunty stirrup
for which
robust moon
for 1575 and 220
jaunty stirrup
did you work it out with the euclidean theorem?
jaunty stirrup
divisor / remainder right?
not sure what you mean by this, way we do it is different
but since we know the gcd is 5
now we can say that 5 = 35-3(10)
and then looking at all the other remainders, we either expand the left or the right, one at a time and combine , up until there are no remainders to to expand from.
jaunty stirrup
divisor / remainder right?
if this is how you do the euclidean theorem then yeah
For sure
good luck
dry panther
Linear regressions don't seem to mix well with horizontal lines. Is this normal ? I am trying to detect whether points form a line or not. For slanted lines, I seem to get a high rvalue, but for horizontal its extremely low. I'm led to believe that I don't understand rvalue, pvalue and standard deviation.
obtuse pebbleBOT
Linear regressions don't seem to mix well with horizontal lines. Is this normal ...
cold thistle
Think about what a horizontal line implies in the context of a correlation between two variables graphed on the xy plane
dry panther
Well if I view it as f(x) = y and y was a constant then I'd say that the parameter x has no impact
cold thistle
Exactly
And the correlation coefficient (r) in a linear regression is measuring to what extent the correlation between the two variables is linear
So if there's little to no correlation between x and y (intuitively, x has no impact on y), what would you expect the r value to be---where closer to 0 is less correlation and closer to 1 is more
dry panther
Then what kind of "test" could I use to verify if some x,y points can "fit" around a line ?
cold thistle
Somewhere in the calculations for the linear regression, if I recall correctly, changes in x and y coordinates are multiplied within a summation, and if the changes in y are very small or zero, the resulting r value is very low
I guess they fit around a horizontal line but the correlation coefficient in that situation suggests that there's little correlation between the two variables
Said horizontal line could be used to predict unknown values but it seems to be messed up a bit by how little impact x has on y
dry panther
Yes that's somewhat been my observation I've seen with my previous lack of understanding of r
I could easily detect those slanted lines(with the blue marker) with line regression and checking rvalue, but for the horizontal lines I've had no luck
obtuse pebbleBOT
@dry panther Has your question been resolved?
dry panther
Is there a method for me to detect if a segment of data is a line, whether its near horizontal or slanted ?
bump. If not for r^2 in a linear regression, what should I look for ?
dry panther
Bumpx3
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rare terrace
I need help
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I need help
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
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rare terrace
2
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calm kayak
how do i do b) after i use the question before
obtuse pebbleBOT
how do i do b) after i use the question before
red ice
how do i do b) after i use the question before
yes so you just need to show 16 cos^4 t = 2 cos 4t + 8 cos 2t + 6
try writing cos(4t) = cos(2t + 2t) and then trying to simplify
use the double angle identity cos(2t) = 2 cos^2 t - 1 and sin(2t) = 2 sin t cos t
once you make a solid attempt, if you're still stuck from there, show what steps you have done and then we can talk
calm kayak
alr ty ill try that
red ice
np!
fallow wharf
I think you can just expand the binomial for part b an dnot use part a at all
red ice
I think you can just expand the binomial for part b an dnot use part a at all
oh shit that's a great suggestion
I hate the framing of the question
yes it's like that sorry for misleading you haha
it's just that
calm kayak
oh but i thought i was memant to use the question before
red ice
I remember doing this in HS and now it's clicked
fallow wharf
I guess it doesn't matter which way you go, I like the idea of just using the binomial theorem to prove a trig identity though
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worldly bay
how tf i do this
obtuse pebbleBOT
how tf i do this
worldly bay
arent i not even able to do this cuz i dont have x
tough reef
how tf i do this
Isolate a and use identities
tough reef
arent i not even able to do this cuz i dont have x
It will be in terms of x
worldly bay
on the answer key to this (doesnt show the process just answers) it just says a=1/2
how r they getting an entire number when x or tanx or anything like that isnt given
tough reef
Which means through identities the trigonometric functions will cancel
worldly bay
tough reef
Try isolating a first
red ice
also (2 tan x)/(1 - tan^2 x) is just the double angle identity for tan
oh wait you've already done it I see
yeah then you should sub u = tan x
and then you can isolate a, just makes it easier to keep track of stuff
worldly bay
Try isolating a first
tough reef
Almost
worldly bay
mb
tough reef
Almost
worldly bay
??
tough reef
One sign is wrong
worldly bay
tough reef
Right
worldly bay
void holly
it is $-2\tan x \cdot \frac{2\tan x}{1-\tan ^{2}{x}}$
warm shaleBOT
convergence
tough reef
This is not right
void holly
yeah sorry mb i did not see the first part
void holly
mb
try this $a=\frac{1-\frac{2\tan x}{1-\tan ^{2}{x}}\tan^2{x}-2\tan x\left(1-\frac{1}{1-\tan ^{2}{x}}\right)}{2}$
warm shaleBOT
convergence
worldly bay
try this $a=\frac{1-\frac{2\tan x}{1-\tan ^{2}{x}}\tan^2{x}-2\tan x\left(1-\frac...
why
how did u get that
void holly
$-2\tan x +\frac{2\tan x }{1-\tan ^{2}{x}} =-2\tan x\left(1-\frac{1}{1-\tan ^{2}{x}}\right)$
warm shaleBOT
convergence
worldly bay
how
worldly bay
o
warm shaleBOT
convergence
worldly bay
(-tan^2x) / 1-tan^2x
void holly
yep now multiply that with -2tan x what will you get?
worldly bay
void holly
so we now have $a=\frac{1-\frac{2\tan x}{1-\tan ^{2}{x}}\tan^2{x}+2\tan x\left(\frac{\tan ^2 {x}}{1-\tan ^{2}{x}}\right)}{2}$
warm shaleBOT
convergence
void holly
i think you know what to do next @worldly bay
void holly
do i just subtract 1-(fraction with the tanx's on the left) or smth
ok so you have $-\frac{2\tan x}{1-\tan ^{2}{x}}\tan^2{x}+2\tan x\frac{\tan ^2 {x}}{1-\tan ^{2}{x}}$ what is this equal to
warm shaleBOT
convergence
void holly
so what will a be
worldly bay
if ur putting the 1 then 1/2
void holly
yes
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feral pike
I need some help
hollow condor
I need some help
Seeing the inequality of g(x)
Im sure that you have to use squeeze/sandwich theorem here
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bleak gust
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tardy epoch
i dont understand how to solve these questions. they just twist my brain
You're better off uploading a single question at a time. People aren't gonna want to read 8 different images to help
bleak gust
You're better off uploading a single question at a time. People aren't gonna wan...
i wanted to put one question from each category cause someone may know how to do one of them
but i get what you mean
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swift canyon
Guys can someone explain payoff functions to me please 
obtuse pebbleBOT
Guys can someone explain payoff functions to me please <:catking:812386361297862...
hollow gate
Hii
hollow gate
Going to sleep 😴 maybe tomorrow
swift canyon
sweet dreams
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wintry swift
whats your question?
swift canyon
Can you please explain what is a payoff function and how it works
serene fossil
Never heard of a payoff function do you have a definition?
Maybe there’s another term for it
Oh is it a game theory thing?
I guess a payoff function is just a model of the award granted to a given player at the end of the game if a given set of moves/decisions are made
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wanton dune
for my homework i need to determine verity of these statemens
\begin{enumerate}[1)]
\item From every real sequence $\left(a_j\right){j \in \mathbb{N}}$ satisfying $\sup \left{\left|a_j\right| \mid j \in \mathbb{N}\right}<\infty$, it is possible to select a subsequence that has its own limit.
\item Let $f: \mathbb{R} \rightarrow \mathbb{R}$ and $\left(x_n\right){n \in \mathbb{N}}$ be a sequence such that $\lim _{n \rightarrow \infty} x_n=0$. If $\lim _{n \rightarrow \infty} f\left(x_n\right)=5$, then $\lim _{x \rightarrow 0} f(x)=5$ also holds.
\item If a function $g:[1,4] \rightarrow \mathbb{R}$ attains its maximum and minimum on the interval $[1,4]$, then it is continuous on this interval.
\item If $h: \mathbb{R} \rightarrow \mathbb{R}$ is such that the function $(\arctan \circ \ h)$ has a negative derivative at every point of $\mathbb{R}$, then $h$ is decreasing.
\item No function defined on $\mathbb{R}$ whose range is a two-element set is continuous.
\end{enumerate}
obtuse pebbleBOT
for my homework i need to determine verity of these statemens
\begin{enumerate}[...
warm shaleBOT
Slowaq
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
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gritty raft
whats blue divide by orange?
obtuse pebbleBOT
whats blue divide by orange?
alpine raven
timid silo
Looks like the answer is Green based off the left part
worthy birch
(x+1)(5x- ?
dim burrow
maths teacher was going through this but i dont understand it
this is the division algorithm
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gritty raft
this is the division algorithm
ah thanks
obtuse pebbleBOT
timid silo
cursive tangle
Alors bien vous voulez décomposer la fraction en une différence et puis vous allez appliquer une formule d’angles composés sur la différence. Ici on peut utiliser sin(a-b) = sin(a)*cos(b) - cos(a)*sin(b) et puis on doit utiliser le cercle unité pour trouver les valeurs de sin(a) et sin(b). J’espère que cet indice est suffisant
obtuse pebbleBOT
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tulip fulcrum
Alors bien vous voulez décomposer la fraction en une différence et puis vous all...
Ouii but how do you know it’s a difference
and what angles do I use
cursive tangle
Ouii but how do you know it’s a difference
Well you have to think about which is easiest, for example if I write 13pi/12 = 1 + 1pi/12 then it’s also 1 - (-1pi/12) and sin(1) and cos(1) are things you know, for sin(-1pi/12) you may have to look it up
This seems like the easiest combination to me but maybe you will find one better if you try several things
tulip fulcrum
Okay I see thank you
cursive tangle
Okay I see thank you
pdq :)
cursive tangle
What
frozen zenith
Hi, For these questions I'm quite a bit confused. Shouldn't be the squareroot(f1²+f²) should be the thing to determine if the first two forces are equilibrium to the third? f1+f2=f3 How is the answer C?
obtuse pebbleBOT
Hi, For these questions I'm quite a bit confused. Shouldn't be the squareroot(f1...
frozen zenith
<@718444267168858175>which one
Yeah
The problem is the others have the same idea technically
opal fractal
where did you get 12
frozen zenith
% TeXit only accepts code which belongs inside the document
% Mathematical expression in the document body
[
\sqrt(f1^2+f2^2+2f1f2cosx)
]
warm shaleBOT
harue
frozen zenith
this one
but for equilibrium we usually use only f1 and f2 only
@opal fractal
and how is it 60 when it isnt mentioned
opal fractal
my bad i think its 30
drifting wraith
ok so, 11 is c because 10 and 4 mean it must be a straight line
and 3 is wrong for some other reason
idk
frozen zenith
my bad i think its 30
how
frozen zenith
ok so, 11 is c because 10 and 4 mean it must be a straight line
ive seen yt a diff explanation but i don't get it
"because it's not a straight line we shouldn't get the sum for them and we should treat it as lines of a triangle"
drifting wraith
the two smallest numbers together are larger than the thifrd
that's the rule for whether triangle exists
drifting wraith
so yeah only (c) 5 does that
warm shaleBOT
harue
% TeXit only accepts code which belongs inside the document
% Mathematical expression in the document body
\[
\sqrt(f1²+f2²)
\]
frozen zenith
that's the rule for whether triangle exists
i know but like
why is a triangle associated with equilibrium
drifting wraith
i don't know
frozen zenith
it's confusing
it's not a smooth plane inclined to a horizontal that's why it's not a triangle either
it should be like the drawing epic made
opal fractal
ok so F1 + F2 = F3
all of them are 8 newtons so
for the y direction 8sin + 8sin = 8 sin
for the x direction - 8cos + 8cos = 8 cos
drifting wraith
so we have this
if we focus on the vertical component
the top two forces must be larger than the third, the sums of them.
if they are equal, this is a straight line, so has to be larger
yeah sorry i don't get it
frozen zenith
ok so F1 + F2 = F3
all of them are 8 newtons so
for the y direction 8sin + 8sin...
f1 + f2 isn't inherently equal to f3
% TeXit only accepts code which belongs inside the document
% Mathematical expression in the document body
[
\sqrt(f1^2+f2^2+2f1f2cosx)
]
warm shaleBOT
harue
frozen zenith
this should equal f3
opal fractal
im not sure how to explain how to find the angles but its
8sin30 + 8sin30 = 8sin90
8 = 8 for the y direction
and
-8cos60 + 8cos60 = 8cos90
0 = 0 for the x direciton
opal fractal
this should equal f3
what is that
opal fractal
yeah that equals f3
you can plug in the angles and magnitude and it should give you F3
frozen zenith
you can plug in the angles and magnitude and it should give you F3
there's no angle
squareroot(f1²+f2²) should be the resultant if no angle is specified
it should equal 12
opal fractal
well think of it like there is, but you just dont know that angle
you know theres an angle where two forces are equal to the third force
frozen zenith
well think of it like there is, but you just dont know that angle
you know there...
not equal? shouldn't they be different
opal fractal
no i mean the two forces summed up
for equilibrium
just picture this
just that the magnitudes or angles might differ
opal fractal
theres 3 forces on an object, they are all 120 degrees relative to each other like a triangle. if they are all the same magnitude can you see that they cancel each other out
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full elm
is there a domain for n?
obtuse sage
is there a domain for n?
so do u know how ?
full elm
one second
obtuse sage
ok
full elm
I think induction wont work because the function is not constantly decreasing so P(n+1)<P(n) will not be true always
obtuse sage
its not a sequence ?
full elm
One idea that I got could be to replace h with 1-h as they have the same domain
full elm
You can think of it like every y = 1-h will correspond to a value of h
basically if you plot a graph with h as the variable then itll just get flipped but the values from 0 to 1 stay that place only
like this
obtuse sage
this sounds weird i can't think about it actually
like we can't do this with induction ?
full elm
maybe we can with some manipulation
obtuse sage
how
full elm
Ok I did it
Is this correct?
@obtuse sage
basically when n < h/1-h, I proved using inequalities and then took it as base cases for induction, then when n > h/1-h, proved using induction
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vagrant breach
Hello, I am working on a research project, and once I have reached the result, I have to calculate the uncertainties, there comes the problem, I would like someone who knows how to find the uncertainty of the slope of a line. I'm desperate and all help is welcome.
obtuse pebbleBOT
Hello, I am working on a research project, and once I have reached the result, I...
vagrant breach
I would like to calculate the uncertainty of the first number, that is, the slope of the line.
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vast tree
I need help too
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velvet spoke
What's the problem
spare sorrel
What's the problem
i need help finding sin X
velvet spoke
sin(x) = opposite/hypotenuse
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verbal musk
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verbal musk
how do I use the system of equations on the left to describe the solution set in terms of z
worn yoke
use the equations you are given from gauss-jordan to solve for x and y in terms of z
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mellow skiff
Note that
A= 28%
B= 8%
C= 13%
D= 18%
E=13%
obtuse pebbleBOT
Note that
A= 28%
B= 8%
C= 13%
D= 18%
E=13%
mellow skiff
I solved it but i just want someone to double check it for me
Assumptions:
• Q1 sales start at RO 2,500.
• Sales double every quarter:
• Q2: 2,500 \times 2 = 5,000
• Q3: 5,000 \times 2 = 10,000
• Q4: 10,000 \times 2 = 20,000
a) Total Sales (Quarterly and Yearly)
• Q1: RO 2,500
• Q2: RO 5,000
• Q3: RO 10,000
• Q4: RO 20,000
• Yearly Total: 2,500 + 5,000 + 10,000 + 20,000 = RO 37,500
b) Cash Sales (Yearly and Quarterly)
• Cash sales = A\% of total sales (A = 28%).
• Q1: 2,500 \times 0.28 = RO 700
• Q2: 5,000 \times 0.28 = RO 1,400
• Q3: 10,000 \times 0.28 = RO 2,800
• Q4: 20,000 \times 0.28 = RO 5,600
• Yearly Total: 700 + 1,400 + 2,800 + 5,600 = RO 10,500
c) Credit Sales (Yearly and Quarterly)
• Credit sales = B\% of total sales (B = 8%).
• Q1: 2,500 \times 0.08 = RO 200
• Q2: 5,000 \times 0.08 = RO 400
• Q3: 10,000 \times 0.08 = RO 800
• Q4: 20,000 \times 0.08 = RO 1,600
• Yearly Total: 200 + 400 + 800 + 1,600 = RO 3,000
- Cost of Sales (Quarterly and Yearly)
a) Material Cost
• Material cost = C\% of total sales (C = 13%).
• Q1: 2,500 \times 0.13 = RO 325
• Q2: 5,000 \times 0.13 = RO 650
• Q3: 10,000 \times 0.13 = RO 1,300
• Q4: 20,000 \times 0.13 = RO 2,600
• Yearly Total: 325 + 650 + 1,300 + 2,600 = RO 4,875
b) Labor Cost
• Labor cost = D\% of total sales (D = 18%).
• Q1: 2,500 \times 0.18 = RO 450
• Q2: 5,000 \times 0.18 = RO 900
• Q3: 10,000 \times 0.18 = RO 1,800
• Q4: 20,000 \times 0.18 = RO 3,600
• Yearly Total: 450 + 900 + 1,800 + 3,600 = RO 6,750
chilly plover
Is RO a currency?
mellow skiff
Overheads
• Overheads = E\% of total sales (E = 13%).
• Q1: 2,500 \times 0.13 = RO 325
• Q2: 5,000 \times 0.13 = RO 650
• Q3: 10,000 \times 0.13 = RO 1,300
• Q4: 20,000 \times 0.13 = RO 2,600
• Yearly Total: 325 + 650 + 1,300 + 2,600 = RO 4,875
-
Depreciation
• Depreciation = 8% of the machine cost (RO 4,000).
• Depreciation = 4,000 \times 0.08 = RO 320 . -
Gross Profit and Net Profit
a) Gross Profit (Quarterly and Yearly)
• Gross Profit = Total Sales - (Material Cost + Labor Cost + Overheads)
• Q1: 2,500 - (325 + 450 + 325) = RO 1,400
• Q2: 5,000 - (650 + 900 + 650) = RO 2,800
• Q3: 10,000 - (1,300 + 1,800 + 1,300) = RO 5,600
• Q4: 20,000 - (2,600 + 3,600 + 2,600) = RO 11,200
• Yearly Total: 1,400 + 2,800 + 5,600 + 11,200 = RO 21,000
b) Net Profit (Quarterly and Yearly)
• Net Profit = Gross Profit - Depreciation (depreciation distributed equally over quarters).
• Quarterly Depreciation: 320 / 4 = RO 80
• Q1: 1,400 - 80 = RO 1,320
• Q2: 2,800 - 80 = RO 2,720
• Q3: 5,600 - 80 = RO 5,520
• Q4: 11,200 - 80 = RO 11,120
• Yearly Total: 1,320 + 2,720 + 5,520 + 11,120 = RO 20,680
Yeah
mellow skiff
Oh cool,btw which standard question is that?
What does it mean?
chilly plover
What does it mean?
I mean, from which grade this question is from
mellow skiff
College
chilly plover
Overheads
• Overheads = E\% of total sales (E = 13%).
• Q1: 2,...
All these calculations seems correct to me
mellow skiff
What about the methods that have been used to calculate each question
@chilly plover
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proven mirage
hi can somoene explain me this
obtuse pebbleBOT
hi can somoene explain me this
proven mirage
if u need more context, h is the hypotunese, L is the base
so how do we take that error in l is estimated by delta l / delta h
shouldnt we calculate it from the ratios of L/h, then using that ratio to calcualtion delta L
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proven mirage
<@&286206848099549185>
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<@&286206848099549185>
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@proven mirage Has your question been resolved?
desert light
shouldnt we calculate it from the ratios of L/h, then using that ratio to calcua...
no, that would assume the ratio is constant
use a^2 + l^2 +- 2ldl = h^2 +- 2hdh
so 2hdh = 2ldl
so in this case you would be right
obtuse pebbleBOT
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inland hill
Does the fundamental theorem of algebra only apply over C and it's isomorphic sets? Not to it's supersets?
obtuse pebbleBOT
Does the fundamental theorem of algebra only apply over C and it's isomorphic se...
kind hawk
the fundamental theorem of algebra is specifically about C
inland hill
Thanks
wild swallow
isomorphic sets?
wild swallow
but as fields you mean
inland hill
For a counterexample consider the roots of x^2 + 1 in quaternions btw
Them not a field are they
wild swallow
not a field 
sage geode
Whoops
wild swallow
For a counterexample consider the roots of x^2 + 1 in quaternions btw
you stole this from my mg question didn't you 
sage geode
What question
inland hill
So
wild swallow
inland hill
The theorem is only over C
sage geode
Yeah
obtuse pebbleBOT
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heavy sedge
This is a tiny semantic thing for set theory for analysis. For x = y does {{x},{x,y}} simplify to {x} or {{x}}. Or does it not matter?
obtuse pebbleBOT
This is a tiny semantic thing for set theory for analysis. For x = y does {{x},{...
brazen gorge
This is a tiny semantic thing for set theory for analysis. For x = y does {{x},{...
{{x}}
it does matter
x ≠ {x} ≠ {{x}}
heavy sedge
That's what I thought.
Do you know of anywhere that this concept is explained in depth?
I guess it's pretty straightforward
brazen gorge
Do you know of anywhere that this concept is explained in depth?
which concept?
brazen gorge
I guess it's pretty straightforward
yeah
thing and a set that has the thing aren't the same
obtuse pebbleBOT
kind hawk
sets are bags
heavy sedge
.reopen
obtuse pebbleBOT
✅
kind hawk
a bag with a bag with something in it is different than just a bag with something in it
heavy sedge
a bag with a bag with something in it is different than just a bag with somethin...
This is a very useful explanation
.close
obtuse pebbleBOT
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median carbon
$\lim_{n\rightarrow \infty} (\frac{3^n+2^n}{3^n-2^n})^{3^{n}} = \lim_{n\rightarrow \infty} (1+\frac{1}{\frac{3^n-2^n}{22^n}})^{3^{n}}=\lim_{n\rightarrow \infty} ((1+\frac{1}{\frac{3^n-2^n}{22^n}})^{\frac{3^n-2^n}{22^n}})^{x_n}=\lim_{n \rightarrow \infty} e^{x_n}$
where $x_n = 3^n \frac{22^n}{3^n-2^n}}=2 \frac{6^n}{3^n-2^n}$
so $\lim_{n \rightarrow \infty} x_n = +\infty$, so $\lim_{n \rightarrow \infty} e^{x_n} = \lim_{n \rightarrow \infty} e^{+\infty} = +\infty$
obtuse pebbleBOT
$\lim_{n\rightarrow \infty} (\frac{3^n+2^n}{3^n-2^n})^{3^{n}} = \lim_{n\rightarr...
warm shaleBOT
Lambda
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)
median carbon
Ok, my question is if I made any mistake
Cuz desmos shows me that the limit is 1
median carbon
But it looks like it's having problems graphing this function, so maybe it's desmos' fault
<@&286206848099549185>
sullen spruce
**Lambda**
Compile Error! Click the <:errors:504266556054962196> reaction for mo...
💀
what is this
median carbon
.close
twilit meteor
can someone help with the 5th question
obtuse pebbleBOT
can someone help with the 5th question
radiant patrol
x^3+3x+2=0 can help to solve it
obtuse pebbleBOT
@twilit meteor Has your question been resolved?
obtuse pebbleBOT
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clever tundra
i'm going insane are the final two options not the same answer?
obtuse pebbleBOT
i'm going insane are the final two options not the same answer?
@clever tundra Has your question been resolved?
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clever tundra
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obtuse pebbleBOT
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left needle
for which values of x is the sixth term of (sqrt(2^(log(10-3^x)))+5throot(2^((x-2)log3)))^n equal to 21 if the double binomial coefficient of the 3rd term is equal to the sum of binomial coefficients of the second and fourth term.
i got that n=8
but then i get this and i dont know how to solve that
obtuse pebbleBOT
for which values of x is the sixth term of (sqrt(2^(log(10-3^x)))+5throot(2^((x-...
left needle
obtuse pebbleBOT
@left needle Has your question been resolved?
left needle
<@&286206848099549185>
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@left needle Has your question been resolved?
carmine mulch
carmine mulch
<@&286206848099549185>
obtuse pebbleBOT
@carmine mulch Has your question been resolved?
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@carmine mulch Has your question been resolved?
surreal arch
Ok, I have come to a question I cannot do myself. I do not know what a slope field is. Could I get some help?
obtuse pebbleBOT
Ok, I have come to a question I cannot do myself. I do not know what a slope fie...
surreal arch
https://www.khanacademy.org/math/ap-calculus-ab/ab-differential-equations-new/ab...
Right, I’ll look through this. Thanks :)
surreal arch
https://www.khanacademy.org/math/ap-calculus-ab/ab-differential-equations-new/ab...
That helped greatly. I should be able to do the rest myself
Thank you very much, I never would have thought to use khan academy
.close
obtuse pebbleBOT
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sudden sage
i'm supposed to find the radius of convergence for this power series
obtuse pebbleBOT
i'm supposed to find the radius of convergence for this power series
sudden sage
i got |x|<1/3 but when i subbed it into wolfram i got this
obtuse pebbleBOT
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sudden sage
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visual onyx
increasing just means that as you go further right, does the function go up, or down?
parabolas go in one direction until they reach their vertex, at which point the switch, and go on for infinity
so on that parabola, when you're to the right of the vertex, is the function going up or down?
verbal musk
it keeps going up
visual onyx
and to the left of the vertex it's going down
verbal musk
right
visual onyx
so if the vertex is at x=3, and after that it increases forever, what interval would "starting at 3, and going forever" correspond to?
visual onyx
because an interval is made of 2 parts, where it starts, and where it ends, respectively
both A and D have infinity as their second component, which is correct
but A has -2 as its first
which would mean that the function starts increasing after x=-2
but if you look at the graph, from x=-2, until x=3, it's still decreasing
which isn't increasing
visual onyx
yes
visual onyx
you could do that
verbal musk
add 6y to both sides
visual onyx
yes, as you want it in the form of y alone equalling something
visual onyx
you can simplify the y and constant terms, but since on the x term you'll be dividing 3 by 6, you'll end up with 1/2
visual onyx
wdym move left?
verbal musk
left of 0,0
visual onyx
the constant term provides the y intercept, so since the constant term is -3 here, it will hit the y-axis at y=-3
and the slope is 1/2, and from the concept of rise over run, that means that for every 2 units you "run" to the right, you will rise 1 unit
so usually it's easy to build a linear equation from its y intercept and its slope
verbal musk
so start at -3
visual onyx
just whatever scale the graph is in
"unit" just being a vague term for distance when you don't have actual units given like meters or feet
visual onyx
when you moved the 6y over to the other side, you were adding 6y to both sides
that cancels out the -6y on the left
but then on the right you have just 6y
so you only need to divide by 6 to get it in terms of y=mx+b
verbal musk
oh yeah
I wrote it as 3x+6y on my paper
would that make 12 a straight line
going through 4
yeah ok
what about 13?
visual onyx
12 would be a perfectly vertical line, at x=4, yes
verbal musk
and 13?
visual onyx
i'm not really sure what that one's asking
verbal musk
I guess use the coordinates to write the equation in point slope form lol
which is y - y1 = m(x-x1)
visual onyx
sorry but i never did that, and i can't really understand what the question is asking
verbal musk
yeah
I kinda get it after searching it up
thanks for clarifying the first 3
.close
obtuse pebbleBOT
ember crescent
Need help with this question
obtuse pebbleBOT
Need help with this question
ember crescent
13a is 54°
13b is 41°
13c is 26°
13d is 9°
But I don’t know what to do next to determine the triangle with the greatest area
obtuse pebbleBOT
@ember crescent Has your question been resolved?
obtuse pebbleBOT
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wide oracle
what does dx and du really mean here?
obtuse pebbleBOT
what does dx and du really mean here?
lost zenith
what does dx and du really mean here?
dx is the infinitesimal unit you’re adding up
Du is the same
The thing is, the function you’re integrating isn’t straight forward so you want to simplify using u-substitution
When you do that you need all variables to be to respect to u
Let me walk you through your example problem
wide oracle
Let me walk you through your example problem
ok
lost zenith
x*e^x^2, you chose u to be x^2
Now you need to change the integration from being with respect to dx to being with respect to du, to do that you need differentiate both sides of u = x^2 with respect to x
It will equal du/dx = 2x
You need dx alone in one side to know how much du is it equal to.
du/dx = 2x, multiply by dx then divided by 2x
You reach du/2x = dx
Now replace dx in the integral with du/2x and replace x^2 with u, to finish what we started.
See if any thing cancels with 2x, sure enough 2x before “e” cancels with it, now you’re left with the integration e^u with respect to du, which is straightforward
Any confusion?
Of course you can change u to its value 2x after the integration is done if you wish to, or if the question asks you to
obtuse pebbleBOT
@wide oracle Has your question been resolved?
full moss
obtuse pebbleBOT
full moss
anyone know how to do 9
warm shaleBOT
timid silo
anyone know how to do 9
is that ukmt?
full moss
What
obtuse pebbleBOT
@full moss Has your question been resolved?
obtuse pebbleBOT
@full moss Has your question been resolved?
modern sentinel
Hi please help
obtuse pebbleBOT
Hi please help
wooden slate
not 90
modern sentinel
Is it x
wooden slate
what angle is a straight line
modern sentinel
Omfg,, idk 😭💋
ember frost
they are supplementary angles
ember frost
can you draw a 90deg angle for me
modern sentinel
I_
modern sentinel
thorny idol
obtuse pebbleBOT
<@&286206848099549185> xx
Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
subtle sinew
Do you know what f(6) means?
modern sentinel
Omg sory
modern sentinel
Do you know what f(6) means?
No its a whole seperate question
modern sentinel
Oh yess
subtle sinew
What does it mean?
modern sentinel
5.5
subtle sinew
What
modern sentinel
Im just as confused 😭💋
subtle sinew
I'm just asking what f(6) means
modern sentinel
Ohh
subtle sinew
From what it looks like in the previous problem, you knew what f(1) and f(2) meant
So I'm asking you what f(6) means
subtle sinew
You won't make it far into honors if you just guess and not understand the concept
modern sentinel
You won't make it far into honors if you just guess and not understand the conc...
Wtf omg,, 😭
U ruining my confidence
💔
subtle sinew
For you to achieve far, you should understand the concept, not just randomly guess
subtle sinew
I honeastly dont even know what f means omfg,,,, x
If you don't know what f(x) means, how did you do the previous problem? Where it asks f(1) and f(2)
modern sentinel
I asked chat gbt
subtle sinew
That's probably still not going to really help you get far
Since you're not understanding what to do
modern sentinel
I was accepted into honors anyway- 💋
Chat gpt will save me x
Omfgggg im gonna get into yale 💋😍 xx
University of Talia Queen
Lasrt word omfg-- 💋
ember frost
quick question, how old are you?
subtle sinew
I was accepted into honors anyway- 💋
Chat gpt will save me x
Well, if you don't want to put any effort in actually learning, and just want to chatgpt everything, good luck then
obtuse pebbleBOT
@modern sentinel Has your question been resolved?
daring zodiac
f(x)={x^2)+2x x>0
{x^3)-x x<=0
obtuse pebbleBOT
f(x)={x^2)+2x x>0
{x^3)-x x<=0
daring zodiac
is it just 0
obtuse pebbleBOT
@daring zodiac Has your question been resolved?
daring zodiac
lim x->0 sin3x/5x^3)-4x
obtuse pebbleBOT
lim x->0 sin3x/5x^3)-4x
daring zodiac
how do i go on about solving it
obtuse pebbleBOT
@daring zodiac Has your question been resolved?
obtuse pebbleBOT
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rancid fjord
How do I find the minimum
obtuse pebbleBOT
How do I find the minimum
zenith raft
oh hi @surreal forge
rancid fjord
wsg
this is the 3rd time this is happening
and I ain't actually Mqnic :c
- I got since roots are imaginary and the equation will be imaginary only when x^2+2x+3 is imaginary which is not possible for real roots
but now how do I find the min
worthy birch
Lol
surreal forge
oh hi @zenith raft
surreal forge
but now how do I find the min
x^2 + 2x + 3 = u
f(x) = u^2 + 2u + 3 = (u + 1)^2 + 2
zenith raft
oh hi mark
void ember
x^2 + 2x + 3 = u
f(x) = u^2 + 2u + 3 = (u + 1)^2 + 2
Yeah
void ember
How do I find the minimum
It'll come out to be 11
obtuse pebbleBOT
@rancid fjord Has your question been resolved?
fathom basin
This is a determinant 3x3
obtuse pebbleBOT
This is a determinant 3x3
fathom basin
How i can solve this
pallid basin
Do you know how to do cofactor expansion?
frigid burrow
nah we got chill guy
fathom basin
How we can solve this
pallid basin
How we can solve this
Cofactor expansion: https://www.youtube.com/watch?v=Tvibn_2p83Q
fathom basin
I want use this method
https://youtu.be/ajvwN6FogKI?si=GhGPEgyCEXuI5ncM
For gauss
Is more easy
I need be 0
Thid is true?
obtuse pebbleBOT
@fathom basin Has your question been resolved?
timid silo
obtuse pebbleBOT
timid silo
Pls help with this!
According to me geometric image should be (-5π/6,-2π/3) in complex plane
<@&286206848099549185>
!15min
obtuse pebbleBOT
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obtuse pebbleBOT
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obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
umbral moth
need help with this question.
obtuse pebbleBOT
need help with this question.
umbral moth
<@&286206848099549185>
obtuse pebbleBOT
@umbral moth Has your question been resolved?
umbral moth
ohhh
rain forge
and for the second you have the convergence with special critera (dunno the name in english)
umbral moth
u german?
rain forge
french
rain forge
ye
umbral moth
@rain forge i think I actually tried applying the cauchy product to the first one here
but I think I made a mistake
can you take a look?
rain forge
what is your (a_k) and (b_k) here ?
umbral moth
i set my b_k as 2^k/(k+1)(k+2) and my a_k as 1/2^n
rain forge
a_k depending of n
umbral moth
i didn't do my selections based on anything
umbral moth
i just bunched the ones that have k as index as b_k and the ones that have n as index as 2^n
rain forge
don't you see something similar
rain forge
$2^{k}/2^{n} = ..$
warm shaleBOT
phoestaclies
rain forge
ye
wide oracle
@umbral moth what does your name mean?
umbral moth
<@427593293593968654> what does your name mean?
it's my actual name backwards
umbral moth
yuhh
umbral moth
yeah+#
wide oracle
im smart 
umbral moth
@rain forge this look good?
umbral moth
ye
tysm for the tip
@rain forge and for the second one, just use leibniz-crit
can I dm you I run into any other problems?
obtuse pebbleBOT
@umbral moth Has your question been resolved?
split drum
can someone please explain this point to me?
obtuse pebbleBOT
can someone please explain this point to me?
tardy epoch
can someone please explain this point to me?
left f(x) is continuous at a, middle and right are not continuous at a
split drum
what's the dot thing in the first one?
tardy epoch
dots are just values of the function but highlighted for emphasis
just like how the italics don't mean anything in the previous sentece, just used for emphasis
little pelican
hi can i get help here? im just in 9th grade though
tardy epoch
hi can i get help here? im just in 9th grade though
!help
obtuse pebbleBOT
hi can i get help here? im just in 9th grade though
To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.
little pelican
ty
split drum
dots are just values of the function but highlighted for _emphasis_
got it, thank you!
but wait
how do we tell if a function is continuous or not just by looking at it?
if that makes sense
tardy epoch
some teachers let you assume most functions are continuous
also depends what you were taught
obtuse pebbleBOT
obtuse pebbleBOT
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crystal hamlet
Knowing that a+b+c=6p ,how do I prove that a^2+b^2+c^2 is greater or equal to 12p^2 <@&286206848099549185>
obtuse pebbleBOT
Knowing that a+b+c=6p ,how do I prove that a^2+b^2+c^2 is greater or equal to 12...
alpine bison
$a^2+b^2+c^2=(a+b+c)^2-2(ab+bc+ac)=36p^2-2(ab+bc+ca)\ge 12p^2 \iff (ab+bc+ca)\le 24p^2$
warm shaleBOT
everg
obtuse pebbleBOT
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Available help channel!
lime garnet
obtuse pebbleBOT
cedar mantle
ok im not looking through your integration, but have you realized the surface you are given isn't "closed"??
i.e. it doesn't encapsulate the whole sphere
instead, we take the hemisphere
however, this isn't clsoed
so what we do, is we take the integral of the upper half of the sphere
and the integration upon the volume will be equivalent through the flux out of the top sphere, and also the unit sphere lying on the xy-plane
so we need to then subtract the flux of the unit sphere on the xy-plane
lime garnet
im confused what integral did i calculate in my working out ?
chilly lichen
can someone help
obtuse pebbleBOT
can someone help
fallen pine
I'm guessing turning points refers to critical points here
as in where the graph changes from increasing to decreasing or vice versa
chilly lichen
i do think so yes
chilly lichen
it is
fallen pine
Do you remember how to find critical points then
fallen pine
Solve $f^{\prime}(x) = 0$
warm shaleBOT
Ari
gloomy brook
basically means, do the derivitive of the function and set the value to 0
chilly lichen
wym that doesnt make sences can you explain
fallen pine
buddy you said you were in calculus.. you should know what a derivative is
chilly lichen
listen im not the brightest i skipped most of school and just jumped in to gcse
gloomy brook
otherwise take a step back and learn about derivatives, you wont progress further without knowing how they work
obtuse pebbleBOT
@chilly lichen Has your question been resolved?
flat rune
wym that doesnt make sences can you explain
sense*
obtuse pebbleBOT
@chilly lichen Has your question been resolved?
nova iron
How would you find an explicit formula for the local inverse of the manifold $F(x,y,z) = x^2 + y^4 - 2z^2 - 2 = 0$ near the point $(3,1,2)$? I've tried things with the implicit function theorem but I keep getting lost.
obtuse pebbleBOT
How would you find an explicit formula for the local inverse of the manifold $F(...
warm shaleBOT
klausliker421
obtuse pebbleBOT
@nova iron Has your question been resolved?
obtuse pebbleBOT
@nova iron Has your question been resolved?
nova iron
<@&286206848099549185>
nova iron
besties
obtuse pebbleBOT
@nova iron Has your question been resolved?
obtuse pebbleBOT
@nova iron Has your question been resolved?
misty dagger
How would you find an explicit formula for the local inverse of the manifold $F(...
what does local inverse of the manifold mean?
if you wanna write F(x,y,z)=0, as z=f(x,y), then yea you can do it
obtuse pebbleBOT
@nova iron Has your question been resolved?
stoic smelt
2 vertical poles have heights of 7ft and 12ft. A rope is stretched from the top of each pole to the bottom of the other. How far above the ground do the ropes cross
obtuse pebbleBOT
2 vertical poles have heights of 7ft and 12ft. A rope is stretched from the top ...
stoic smelt
Can anyone help me solve this?
