I think is called ivt
#help-49
merry pewter
!occupied
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merry pewter
and if this is monotonically decreasing function
shouldn't be monotone, cos^2 decreases sometimes
tidal turret
wat do u suggest then
merry pewter
(0,1) even
tidal turret
?
merry pewter
cos^2 is between (0,1), since cos is between -1 and 1
tidal turret
idk bro this one is a hard one
my life is a disaster and I want to cry and get hugged by a math girl
merry pewter
my life is a disaster and I want to cry and get hugged by a math girl
we all do, so this is no time to give up
so a collision can only be for x in [-1/4, 0] right?
tidal turret
right yeah
merry pewter
alright, so now we can notice that -4x is decreasing, but cos^2 is increasing on this interval
strictly
tidal turret
0 <= -x <= 1/4
0 >= x >= -1/4
tidal turret
alright, so now we can notice that -4x is decreasing, but cos^2 is increasing on...
exactly
merry pewter
exactly
ok so what can we conclude
actually wait i totally missed that we just have that 4x+cos^2x is monotone increasing
ok all of this was completely unnecessary
tidal turret
actually wait i totally missed that we just have that 4x+cos^2x is monotone incr...
what about negative x values, is it still increasing?
merry pewter
what about negative x values, is it still increasing?
yes
tidal turret
positivity is not the same as monotnically increasing I notice
merry pewter
because 4 > 2cos x sin x
merry pewter
positivity is not the same as monotnically increasing I notice
just take a derivative and you will se
grand pondBOT
merry pewter
,, f(x) = 4x+\cos^2 x, f'(x)=4-2\cos x \sin x, 4 > 2 \ge 2\cos x \sin x
grand pondBOT
Bair
merry pewter
cosx, sinx <= 1
tidal turret
cos, sin, [-1,1]
merry pewter
so 4-2cos x sin x > 0
tidal turret
right
merry pewter
so f is increasing
tidal turret
,w simplify 2cos(x)sin(x)
grand pondBOT
tidal turret
f'(x) = 4 - sin(2x)
okay perfect
4 - sin(2x) > 0
monotonically increasing is f(x)
-1 <= sin(2x) <= 1
okay thank u blair
but basically for anyone watching
since is motonically increasing function because f'(x) > 0
tidal turret
that says this function is monomorphism
aka injective
so only one solution there is for f(x)=0
one possible x
anyways, ty I couldnt have done it
without u
.solved
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tidal turret
Evaluate the limit:
[
\lim_{x \to 1} \frac{e^{3x-3} - x^3}{\ln^2(x) + (x-1)^2}
]
Options:
[
\text{(A) } -\frac{3}{4} \quad \text{(B) } \frac{3}{2} \quad \text{(C) } -\frac{3}{2} \quad \text{(D) } \frac{3}{4}
]
midnight plankBOT
Evaluate the limit:
\[
\lim_{x \to 1} \frac{e^{3x-3} - x^3}{\ln^2(x) + (x-1)^2}...
grand pondBOT
Renato Chavez
tidal turret
,, \lim_{x \to 1} \frac{e^{3x-3} - x^3}{\ln^2(x) + (x-1)^2} \overset{\textbf{L'H}}{=} \lim_{x \to 1} \frac{3e^{3x-3} - 3x^2}{\frac{2\ln(x)}{x} + 2(x-1)} \ \lim_{x \to 1} \frac{3e^{3x-3} - 3x^2}{\frac{2\ln(x)}{x} + 2(x-1)} \overset{\textbf{L'H}}{=} \lim_{x \to 1} \frac{9e^{3x-3} -6x}{\frac{2 - 2\ln(x)}{x^2} + 2}
,w differentiate ln^2(x)
mellow sand
chain rule
grand pondBOT
Renato Chavez
tidal turret
3/4
9e^{3-3} = 9
(2-0)/(1) = 2
(9-6)/(2 + 2) = 3/4
,w limit x to 1 of \frac{e^{3x-3} - x^3}{\ln^2(x) + (x-1)^2}
grand pondBOT
tidal turret
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rare oxide
hello, how would i integrate the right side?
midnight plankBOT
hello, how would i integrate the right side?
rare oxide
i have moved the dx to the right, isolating the dy
ive integrated the dy to y, but i havent integrated the right side
worthy wing
Then do it
rare oxide
thats my question
worthy wing
Partial fraction
tribal yew
yeah partial fraction
rare oxide
with what denominators
worthy wing
x^2–1
elder zephyr
(1-x)(1+x)
rare oxide
ah ty
worthy wing
-(x+1)(x-1)
rare oxide
(1-x)(1+x)
if i use this for the partial frac decomp, i think the answer comes out different
elder zephyr
if i use this for the partial frac decomp, i think the answer comes out differen...
you can use (x+1)(x-1) if you are struggling with this
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@rare oxide Has your question been resolved?
rare oxide
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empty tide
help how do i do functions that has exponents? the question is:
the function g(x) = x^2 + 2x - 8 and function h(x) = x^2 - 3(x-4), determine:
a. the formula
b. value of n if g(n) = h(n)
c. value of g(a + 3)
midnight plankBOT
help how do i do functions that has exponents? the question is:
the function g(...
nimble copper
"the formula" is about as vague as it gets
torn flint
"the formula" is about as vague as it gets
If I had to speculate, I would say it’s the quadratic formula for each
nimble copper
i'd rather not speculate
torn flint
I did it for you
midnight plankBOT
@empty tide Has your question been resolved?
empty tide
"the formula" is about as vague as it gets
its like
wait the raw translation says
"rumus"
which in english is formula
nimble copper
can you send the original
empty tide
sure
empty tide
diketahui fungsi g(x) = x^2 + 2x - 8 dan fungsi h(x) = x^2 - 3(x-4), tentukan:
a. rumus fungsi g(n) dan h(n)
b. nilai n jika g(n) = h(n)
c. nilai dari g(a+3)
empty tide
into a qudratic too?
i dont know what this means
empty tide
ooh thats it?
lyric owl
yes
for 2 set them equal to each other
u will get a number
the number will be even
empty tide
for 2 set them equal to each other
what does this mean?
empty tide
OOH so i just put in the formula i know from the question?
empty tide
by the way how do i finish the exponents?
lyric owl
wym finish the exponenets?
empty tide
waitt let me write it
lyric owl
known function g(x) = x^2 + 2x - 8 and function h(x) = x^2 - 3(x-4), determine:
a. function formula g(n) and h(n)
b. value of n if g(n) = h(n)
c. value from g(a+3)
empty tide
like g(a+3) = 3a^2 + 2a + 3 - 8?
empty tide
(a+3)^2 +2(a+3) - 8
i kind of wanna know the solution iygwim
empty tide
u need parenthesis
oh why
lyric owl
like g(a+3) = 3a^2 + 2a + 3 - 8?
this would be like g(a)
except u added 3 for no reason
g(a) = 3x^2 + 2a - 8
empty tide
except u added 3 for no reason
oh i thoiught i had to add it since there was a +3
lyric owl
nah whatever is inside the g()
is a quanity that u set the variable in the function of g to
for example
g(x) = 3x + 1
g(x^2) = 3(x^2) + 1
if g(x) = 3x^2 + 1
then g(x^2) = 3(x^2)^2 + 1
g(x) is just a function. a function basically means inputs and outputs
x is the input
y is usually the output
y = g(x)
and g is the formula
empty tide
for example
g(x) = 3x + 1
g(x^2) = 3(x^2) + 1
if g(x) = 3x^2 + 1
then g(x^2) ...
uhhhhhh sorry for this dumbass question but how did g(x) make 3 an exponent
lyric owl
uhhhhhh sorry for this dumbass question but how did g(x) make 3 an exponent
where did i make 3 an exponent?
which one are u talking about
empty tide
if g(x) = 3x^2 + 1
lyric owl
yes
lyric owl
x^2 is an exponent yes
the base is x, the exponent is 2
3 is the factor
sorry i meant coefficent
empty tide
how did x^2 become an exponent
lyric owl
because i made it an exponenet
sorry thats for a different problem i was using as an explanation
i should have used a different function
d(x) = 3x^2 + 1
empty tide
i should have used a different function
u dont have to apologize im just slow
lyric owl
d(x^2) = 3(x^2)^2 + 1
lets go back to your question now
diketahui fungsi g(x) = x^2 + 2x - 8 dan fungsi h(x) = x^2 - 3(x-4), tentukan:
a. rumus fungsi g(n) dan h(n)
**a. since the new variable in the functions f and h are "n" u just replace the x's with "n" **
b. nilai n jika g(n) = h(n)
b. since u wanna know when they would be equal, u set them equal to each other and u solve for n
c. nilai dari g(a+3)
**c. since they wanna know for (a+3), you just replace the x's with (a+3) in the function g **
empty tide
diketahui fungsi g(x) = x^2 + 2x - 8 dan fungsi h(x) = x^2 - 3(x-4), tentukan:
...
okay ill try doing it wit hthe soltuions tysm!
.close
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lyric owl
okay ill try doing it wit hthe soltuions tysm!
no problemo
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subtle torrent
I would like a hint for this 🤔
midnight plankBOT
I would like a hint for this 🤔
mellow sand
y is an increasing function if you haven’t seen that already
west iron
looks like basically a diffeq lol
midnight plankBOT
@subtle torrent Has your question been resolved?
rare oxide
is this best completed by first using partial frac?
midnight plankBOT
is this best completed by first using partial frac?
sharp coral
you can try, but i don't think you would get anything useful out of partial fraction decomposition
rare oxide
so how would you approach it
sharp coral
a good first thing to try for any integral is substitution
rare oxide
the hw is on Separable Differential Equations
sharp coral
yes, so the first step is always to do the separation of variables
rare oxide
yea check
sharp coral
so what do you have at this point?
rare oxide
x=intgrl 1/(5+y)^2 dy
sharp coral
ok
rare oxide
how do u recommend i proceed
sharp coral
a good first thing to try for any integral is substitution
like this
rare oxide
u sub?
sharp coral
yes
rare oxide
so -1/(5+y) + c =x?
sharp coral
yes
rare oxide
do i just isolate the y from here?
sharp coral
yes
shadow schooner
Let $f(z) \colon B(0,1) \to \mathbb{C}$ be an holomorphic function for which $\exists M > 0$ such that $\forall z \in B(0,1), |f(z)| \leq M$ and 0 is an order $m$ zero of $f$ i.e. $f(0) = f’(0) = \dots = f^{(m-1)}(0)$ but $f^{(m)}(z) \neq 0$. Show that $g(z) \colon B(0,1) \to \mathbb{C} \colon z \mapsto \frac{f(z)}{z^m}$ is holomorphic if we define $g(0) = \frac{f^{(m)}(0)}{m!}$. Also find $g’(0)$.
midnight plankBOT
Let $f(z) \colon B(0,1) \to \mathbb{C}$ be an holomorphic function for which $\e...
grand pondBOT
pola_touche
shadow schooner
it’ in a homework about taylor series for my complex variables class, for the other parts of the exercise i’m fine, but somehow for this one i’m stuck. if z is not equal to 0, then showing g(z) is holomorphic on B(0,1) is eazy and i have computed the taylor series for g but can’t find a way to compute g’(0) and show that g is holomorphic at 0.
midnight plankBOT
@shadow schooner Has your question been resolved?
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@shadow schooner Has your question been resolved?
twilit field
midnight plankBOT
twilit field
Kind of confused
hard shard
y = f(g(x))
twilit field
so $\frac{dy}{dx} = \frac{\frac{{dy}{du}}{du}{dx}}$ right
grand pondBOT
A dense set(Ping when reply)
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
twilit field
wait
hard shard
chen lu is your friend
grand pondBOT
A dense set(Ping when reply)
twilit field
$\frac{d^2y}{dx^2} = g''(x)f'(g(x)) + (g'(x))^2f''(g(x))$
sharp coral
tex note: use two individual ' rather than the single character "
but yeah that's basically it
twilit field
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A dense set(Ping when reply)
brazen moth
How was the doctor's visit? All good?
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ember sage
How come you reflect the angle to get 2 values
midnight plankBOT
How come you reflect the angle to get 2 values
halcyon vale
It's wherever sin is positive, so in this case, in the quadrants 1 and quadrant 2
For the second question, its where sin is negative, so in this case, we know that sin is negative in quadrants 3 and 4
ember sage
It's wherever sin is positive, so in this case, in the quadrants 1 and quadrant ...
Is there an explanation as to why that’s the case?
halcyon vale
Sintheta is often defined as the y-coordinate on the point of a circle, and we know that the y value is only positive in the first and second quadrant! For sintheta = 1/2, the value of 1/2 is positive, as seen in the question. So we know that the solution MUST lie within the first and second quadrants.
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nimble matrix
First question
midnight plankBOT
First question
nimble matrix
I'm getting no values of alpha and beta, that is for every values of beta, and alpha except alpha = 8 I get a unique set of solution and for alpha = 8 I get no solution, but not infinitely many solution for any values of alpha and beta
Is my answer correct?
My ans: alpha ∈ ∅, Beta ∈ ∅
Question: Verify whether answer is right or not.
sharp coral
you get no solution for alpha = 8 regardless of the value of beta?
sharp coral
can you show your work for this?
sharp coral
so we can see that that is the solution for alpha ≠ 8. but we should look at what equation we would end up with for alpha = 8
nimble matrix
so we can see that that is the solution for alpha ≠ 8. but we should look at wha...
For alpha = 8 we get no solution because equation is undefined there
Denominator = 0
sharp coral
but you arrived at that by dividing by 8 - alpha. so the division was invalid in the first place when alpha = 8
nimble matrix
You're right
I will check for alpha = 8 seperately
I guess it will be infinitely many solution for alpha = 8
Because in equation (8-alpha)x3=36-Beta which means infinitely many x3 at alpha=8
So I feel it will be same for x2 and x1
@sharp coral
sharp coral
well if we have alpha = 8 then we would get
0 x3 = 36 - Beta
for which beta does this have solutions?
sharp coral
but we are interested in when it has infinitely many solutions, not when it has no solutions
nimble matrix
but we are interested in when it has infinitely many solutions, not when it has ...
It feels like there is no scope for infinitely many solution from that equation
Oh that was x3
sharp coral
well if we have
0 x3 = 0
then any value of x3 would work (every value of x3 is a solution)
but if we have
0 x3 = 1
then no value of x3 will work (there is no value of x3 which is a solution)
nimble matrix
X3 does seem to have infinite values for alpha = 8 and beta = 36
nimble matrix
well if we have
0 x3 = 0
then any value of x3 would work (every value of x3 is a...
Yeah
nimble matrix
X3 does seem to have infinite values for alpha = 8 and beta = 36
But is this enough to conclude for x1 and x2 as well?
Ans is Alpha = 8 and beta = 36 then
Right? @sharp coral
sharp coral
But is this enough to conclude for x1 and x2 as well?
x2 and x1 would have values which depend on the value you choose for x3 (but it wouldn't matter even if they didn't, because infinitely many values of x3 means infinitely many values of (x1, x2, x3) )
nimble matrix
x2 and x1 would have values which depend on the value you choose for x3 (but it ...
Okay sir, thank you for your help
.close
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flint axle
Hi guys,
We know centre radius form equation of a circle is
(x-h)² + (y-k)² = r²
Where we know r is radius
And we know (h,k) is the cordinates of the centre
So what does (x,y) represent?
midnight plankBOT
Hi guys,
We know centre radius form equation of a circle is
(x-h)² + (y-k)² = r...
runic hamlet
(x,y) are the points on the circle
a point (x,y) is on the circle if and only if it satisfies the equation
in other words, the circle is the set of all the solutions (x,y) to this equation
runic hamlet
if h=k=0, then the centre is at the origin
flint axle
Yeah
runic hamlet
and thr equation says x^2+y^2=r^2
flint axle
Right
runic hamlet
this might remind you of pythagoras
flint axle
It did ngl
runic hamlet
its all the points (x,y) which have distance r to the origin
flint axle
Right
runic hamlet
which is exactly what a circle is
all points that have the same distance to some other point
flint axle
I see
So could i think of it this way
We took a triangle with constant hypotenuse
And then we changed the angle from 0to 360 degrees and and added all the values and somehow formed an eqn that way?
When i say angle
I mean that one
runic hamlet
in some sense, yes
flint axle
in some sense, yes
I see i get it a bit now
So we must have integrated something
From lower limit 0 to 2pi
runic hamlet
not really
flint axle
Then?
Im sorry i just want to find out how we got the eqn and if i watch a video it wont answer specific doubts of mine
runic hamlet
the distance from a point (x,y) to (0,0) is sqrt(x^2+y^2), yes?
flint axle
Yeah
flint axle
Yeah
runic hamlet
or x^2+y^2=r^2
and thats it
a point satisfies this equation if it has distance r to the origin
which is what we want
flint axle
Vut that is only when the centre is at origin
Right?
What if its not
At the origin
runic hamlet
then the distance to the centre (h,k) is sqrt((x-h)^2+(y-k)^2)
again, pythagoras
and again we want this to be equal to r
giving (x-h)^2+(y-k)^2=r^2
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barren onyx
barren onyx
<@&286206848099549185>
barren onyx
<@&286206848099549185>
feral sedge
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remote spade
How to find value of irrational square root number (for ex: root of 3 value)
remote spade
(Approximate value)
steep falcon
Do you want to know how calculators do it or do you want a method to quickly do it by hand?
midnight plankBOT
@remote spade Has your question been resolved?
remote spade
Do you want to know how calculators do it or do you want a method to quickly do ...
I want to know how to find it by hand
Hmmm
last slate
square root of an integer?
remote spade
search on google
It didnt worked
oak slate
oak slate
this probably first iteration from newton rhapson method
last slate
it gives an approximate
remote spade
it gives an approximate
I didnt asked for exact value
gaunt otter
newton raphson is best
last slate
ok
gaunt otter
but you need to be good in arithmetic
remote spade
but you need to be good in arithmetic
Question is, which square root is nearest to 3?
oak slate
4
remote spade
Oh nvm i am sometimes stupid, i was thinking i need smaller number than 3
gaunt otter
sqrt(9) = 3
remote spade
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remote spade
if you want more precision you can do more iterations
I just wanted to find equilateral triangle area
Which is sqrt(3)/4 x sides^2
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remote spade
Which is sqrt(3)/4 x sides^2
(Area of equilateral triangle)
midnight plankBOT
(Area of equilateral triangle)
oak slate
normally you just leave it written like that, you don't always need to put an approximation
remote spade
normally you just leave it written like that, you don't always need to put an ap...
Cant do that in exam
Cause answer sheet have answer with approximation
oak slate
for equilateral triangles it's always √3, you could just remember an aproximation for √3
remote spade
for equilateral triangles it's always √3, you could just remember an aproximatio...
Welp there is another topic in next class book about finding irrational number value
So i thought it could be cool to know about how i can find its value
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inland patio
Let $f$ be complex-valued. Is it true that $$\left|\mathrm{Re}f\left(x\right)-\mathrm{Re}f\left(y\right)\right|\le \left|f\left(x\right)-f\left(y\right)\right|?$$For some reason, I don't see how to show this.
midnight plankBOT
Let $f$ be complex-valued. Is it true that $$\left|\mathrm{Re}f\left(x\right)-\m...
grand pondBOT
psie
runic hamlet
Re is linear
so on the left is |Real part of f(x)-f(y)|
compared to just |f(x)-f(y)|
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last nebula
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last nebula
can someone explain to me how to do these types of questions?
ripe gulch
Convert the square roots to exponent form and use exponent laws
rugged bay
yeah just remember that multiplication is exponent addition and division is subtraction
power to power is multiplication
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chrome ibex
Can anyone help me with time series ?
midnight plankBOT
Can anyone help me with time series ?
chrome ibex
I have this boxplots which represent the stock price of Microsoft between 2020-2024
the variance seems to be different from time to time right ?
since the lengh of the box changes
my english is not the best sorry for that
so i thought to analyse this time series i need to make it stacionary so first of all lets remove the variance by using a Box-Cox transformation
but i got a lambda of 1 (almost)
which menas variance is constant right ?
Or altleast the change in variance from time to time its not statistically relevant
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main owl
Or altleast the change in variance from time to time its not statistically relev...
i believe everything u said is correct
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true thicket
What is the fourmala of pentagon
midnight plankBOT
What is the fourmala of pentagon
main owl
What is the fourmala of pentagon
what are you solving for
drifting birch
In no exam do you need to know the formula
main owl
In no exam do you need to know the formula
bro you dont even know what the dude is solving for 😭
true thicket
What is the foulmala of pentagon
main owl
What is the foulmala of pentagon
what does that mean
drifting birch
bro you dont even know what the dude is solving for 😭
No but like I've never seen one
drifting birch
He's asking for area I believe
drifting birch
What's the question
brazen moth
Regular pentagon?
main owl
from using google
brazen moth
Idk why you asking this here
true thicket
Thanks diamond
main owl
Thanks diamond
Your welcome
brazen moth
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viral dagger
if BD^2=109.75, and AD:DC=3:1, find AD
midnight plankBOT
if BD^2=109.75, and AD:DC=3:1, find AD
viral dagger
i have actually no idea how to do this
main owl
i have actually no idea how to do this
solving for AC first would def help
viral dagger
no
viral dagger
solving for AC first would def help
how?
brazen moth
pythragous
How do you know that?
main owl
How do you know that?
can u not just
brazen moth
Pythagoras would work
main owl
use
viral dagger
there isnt any right angles (thats known yet atleast)
brazen moth
can u not just
Can't just assume
small jasper
if BD^2=109.75, and AD:DC=3:1, find AD
Did you make typo
brazen moth
Is BD an altitude?
That's why I asked this
small jasper
if BD^2=109.75, and AD:DC=3:1, find AD
Just do law of cosines on angle A twice (aka Stewart’s)
brazen moth
I don't think so
small jasper
isnt stewarts for angle bisectors or am i stupid
Yeah I was gonna say “you might be high” lol
brazen moth
Lol
Used in case when angles are split up due to a side in between
Not necessarily for angle bisectors
small jasper
Btw you should get a positive integer whose digits sum to 9 as your answer @viral dagger
brazen moth
How do you know that?
small jasper
How do you know that?
Because I did the question
brazen moth
Oh
viral dagger
uhh 18?
brazen moth
I thought you used an estimation tactic or something lol
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viral dagger
funnily none of the other questions were using trig
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blissful drum
can someone help me with this?
midnight plankBOT
can someone help me with this?
blissful drum
i keep on getting B
and the answer is A
my workings are:
p(final)
px = -mvcosθ
py = -mvsinθ
p(initial)
px = mvcosθ
py = -mvsinθ
last slate
I agree with your math there, but this phrase here is making me think it's actually D
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wild eagle
$P(X = k) = \binom{n}{k} \cdot p^k \cdot (1 - p)^{n-k}$
wild eagle
Why can (nk) here be used to calculate the paths of k? I understood from where the other calculations are coming from, just not this one
grand pondBOT
Raphaelll
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grim vector
The number of way to choose this event to happen
wild eagle
The number of way to choose this event to happen
I know that
I just wanna understand the reason why n! / k! (n - k)! calculates that
grim vector
Why nCk is this formula ? Or what it is doing in prob ?
wild eagle
Why nCk is this formula ? Or what it is doing in prob ?
I dont understand what u mean
Alright I understood it on my own
.close
chilly cobalt
in olympiad problems, if the question ask "Prove...." would it be different than if it were asking "Show that..."
midnight plankBOT
in olympiad problems, if the question ask "Prove...." would it be different than...
chilly cobalt
for example like if it asks "Show that X is true" then we could say "Assume X is false ...." but with proofs would we need to start and find some relation to show X is true
or am i high
obtuse basin
in olympiad problems, if the question ask "Prove...." would it be different than...
Not really
obtuse basin
for example like if it asks "Show that X is true" then we could say "Assume X is...
A proof by contradiction is also a proof
chilly cobalt
oh
chilly cobalt
for example like if it asks "Show that X is true" then we could say "Assume X is...
usually in solutions i only see them use it like this
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thorn mirage
2)a je sais vrmt pas ou demarrer
midnight plankBOT
2)a je sais vrmt pas ou demarrer
drifting birch
2)a je sais vrmt pas ou demarrer
Can you translate
thorn mirage
Can you translate
Yes
Wait
A. Determine the natural integers n which, in the Euclidean division of n by 4, have
quotient equal to twice the remainder.
R Show gue nour any relative integern (2n+ 1)nn -5) is an even integer and also a multiple of 3
devout gull
Hello
thorn mirage
Hello
thorn mirage
A. Determine the natural integers n which, in the Euclidean division of n by 4, ...
I don't know how to start
elder zephyr
2)a je sais vrmt pas ou demarrer
n = 4q + r
q le quotient, r le reste
q = 2r
thorn mirage
n = 4q + r
q le quotient, r le reste
q = 2r
Oe c est ce que j ai fais
Genre ça j ai compris
Mais c est apres le probleme
Genre apres ça jsp ou partir
elder zephyr
bah n = 9r quoi
thorn mirage
Oui?
elder zephyr
cest tout
thorn mirage
Mais je doit pas trouver des nombre ?
elder zephyr
les nombres sont egal a 9 fois leur reste
cest tt
je vois pas ce quon peut fair de plus
elder zephyr
vasy
elder zephyr
5 x 13^{3n} + 7^{5n} est congru à 0 modulo 6
thorn mirage
Oui ça je l ai
elder zephyr
ce qui veut dire que tout ce truc est égal à 6k, k un entier
hmm att
non cest ce quon veut montrer mdr
elder zephyr
ah ?
thorn mirage
Mais tu peux me dire si c est juste
elder zephyr
oui vas y je regarde
elder zephyr
,w 5 divided by 6
thorn mirage
Je suis con
grand pondBOT
thorn mirage
Oui ta raison
Mais je pars d ou
On part de 7
On marque 7 est congru dans 1 modulo 6
A ouiii
C est ça
elder zephyr
7 = 1 [6]
elder zephyr
cest aussi congru à 1
elder zephyr
tu refais la meme pour lautre terme
elder zephyr
13 = 1 [6]
13^{3n} = 1 [6}
5 x 13^{3n} = 5 [6]
tu fais la somme tu tombe sur du 6 modulo 6
elder zephyr
np
thorn mirage
??
elder zephyr
mdr
thorn mirage
Vasy merci bonne journé l ami
elder zephyr
bonne journée 🫡
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last slate
How to solve ABC = 30
A+B+C=10
AB+BC+CA = 31
midnight plankBOT
How to solve ABC = 30
A+B+C=10
AB+BC+CA = 31
zealous schooner
think of a cubic equation which has A, B and C as its roots
quaint trail
Help meeeeeeeeeeeeeeee
tribal heron
Help meeeeeeeeeeeeeeee
Uhm it would be better if you tried to post that in a channel which is not already occupied.
quaint trail
Oke
obtuse basin
Alternatively there is a trivial solution that's easy to find since 30 doesn't have many divisors
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foggy tartan
The distance between the Sun and Earth is 𝑟𝐸=1.5×10^11 m. The distance between the Sun and Jupiter is 𝑟𝐽=5.2𝑟_𝐸. Jupiter completes one orbit around the Sun in 𝑇_𝐽=11.86 Earth years. At a certain moment, the angle between the Sun and Jupiter, as observed from Earth, is 20∘ . Determine the instantaneous angular velocity of Jupiter as observed from Earth at that moment.
plain osprey
The distance between the Sun and Earth is 𝑟𝐸=1.5×10^11 m. The distance between...
make another help channel
this ones closed
foggy tartan
.close
thorn mirage
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lethal path
you've posted 6 questions at once
also thanks for showing the original question but we also need the English translation
thorn mirage
Yeah but i have only 1 question
thorn mirage
also thanks for showing the original question but we also need the English trans...
Yeah
Actually I don't know how to do the 2)B)
B. Show that, for any relative integer n, (2n+ 1)n(n - 5) is an even integer and also a multiple of 3.
modern bolt
B. Show that, for any relative integer n, (2n+ 1)n(n - 5) is an even integer and...
Product them
Tf
thorn mirage
???
lethal path
<@&268886789983436800> spam
lethal path
B. Show that, for any relative integer n, (2n+ 1)n(n - 5) is an even integer and...
ah, so if n is even for example, we are done
but if n is odd, then n - 5 must be even
similarly, you can assume that n = 3k + 1 for some integer k
see what 2n + 1 and n - 5 become in terms of k
then try again with n = 3k + 2
lethal path
Yeah i do n=3k+0
well n = 3k isn't needed since this will automatically mean that you have a multiple of 3
but yes split into those three cases
thorn mirage
But i find for n=3k: 54k^3-90k^2+9k^2-15k
thorn mirage
but yes split into those three cases
Yes
thorn mirage
But i find for n=3k: 54k^3-90k^2+9k^2-15k
But how does this show that is a multiple of 3
modern bolt
Instead of cases pain old muplication will be easier tho
thorn mirage
????
modern bolt
But i find for n=3k: 54k^3-90k^2+9k^2-15k
Take 3 common?
thorn mirage
A yesss
lethal path
But i find for n=3k: 54k^3-90k^2+9k^2-15k
don't expand
thorn mirage
don't expand
Why
lethal path
if you have $3k (k + 1234567910)^3 (2k - 23892130)^7$
grand pondBOT
southlander!
lethal path
that's automatically a multiple of 3
thorn mirage
A yeah
lethal path
cause $k(k + 1234567910)^3 (2k - 23892130)^7$ will be an integer if $k$ is an integer
grand pondBOT
southlander!
lethal path
you just have to spot the multiple of 3 when you do n = 3k + 1, 3k + 2
lethal path
I must expand
no
and then it's very similar, write the expression as 3m where m is an integer
modern bolt
B. Show that, for any relative integer n, (2n+ 1)n(n - 5) is an even integer and...
Actually it's not multiple of 3 tho the n3 will always be 2n^3 so it can't be multiple of 3
lethal path
alright I'll do n = 3k + 1 then
2n + 1 = 6k + 2 + 1 = 6k + 3, which is a multiple of 3 as 6k + 3 = 3(2k + 1)
so (2n + 1)n(n - 5) = 3m where m = (2k + 1)n(n - 5), where k, n are integers
thorn mirage
Actually it's not multiple of 3 tho the n3 will always be 2n^3 so it can't be m...
It's a multiple of 3 otherwise the question is no sense
lethal path
so m is also an integer
lethal path
Actually it's not multiple of 3 tho the n3 will always be 2n^3 so it can't be m...
jesus that's the wrong reasoning
take n = 3 for example lmao
also you haven't expanded all the terms
modern bolt
take n = 3 for example lmao
Oh
lethal path
ah, so if n is even for example, we are done
but if n is odd, then n - 5 must b...
it's just this
lethal path
And how n-5 is even??
well, if you let n = 2k + 1 as usual.............
thorn mirage
But I don't understand why we use n=3k to show us that is a multiple of 3
lethal path
But I don't understand why we use n=3k to show us that is a multiple of 3
3 * any integer = multiple of 3
thorn mirage
3 * any integer = multiple of 3
Yeah but 3k+1 is not a multiple
lethal path
Yeah but 3k+1 is not a multiple
but some other term, either the 2n + 1 or the n - 5
will become a multiple of 3
dim anchor
pls help
dim anchor
So i made assumption that A is infinite set
And i have to show that for every n in N |{1,.....,n}| =< |A|
And i know that |{1,.....,n}| =< |A| is true only if there is injective function
And also i know from a theory 7.15 (its in my lecture outline) that for every infinite set there is a countable subset
But i dont know how to begin with the proof
Also i defined f as injective function such as f: {1,.....,n} - A
visual tiger
did you try induction?
visual tiger
well can you find an injection {1} -> A?
dim anchor
I can find injection for that yeah if n = 1
Oh, so if i use induction then n=1
and then i expect that it will work also if n=k
visual tiger
n=1 is true
so we just proved this
visual tiger
if n=k is true then n=k+1 is true
now suppose n=k works, meaning there is an injection f:{1,...,k} -> A
can you make an injection {1,...,k+1} -> A?
dim anchor
Yes because of cantor theory
Um so
i have to show that k_1,k_2 in {1,...,k+1} : k_1 != k_2 so f(k_1) != f(k_2) ?
dim anchor
{1,...,k} is subset of {1,...,k+1}, so k+1 is an new element
or something like that..?
dim anchor
oh f(k+1) must be in A
visual tiger
I don't expect every g(z) to be defined
visual tiger
oh f(k+1) must be in A
f(k+1) makes no sense
f:{1,...,k} -> A
k+1 is not an input that works with f
dim anchor
Oh um so can i write it something like that
visual tiger
ok
so?
f(k+1) is still not defined
we have to define a new function
from {1,...,k+1} to A
that is injective
that's our goal
we may use the fact that f is defined on {1,...,k} to build our new function
start by this: is f surjective?
visual tiger
why/why not?
visual tiger
Because set A is infinite
yes, mostly because an infinite set cannot be in bijection with a finite set
if f is surjective, f is bijective
and thus {1,...,k} in bijection with A
impossible
dim anchor
But wait, if we move back to defining f(k+1) = a, so a isnt in {f(1),....,f(k)}
visual tiger
But wait, if we move back to defining f(k+1) = a, so a isnt in {f(1),....,f(k)}
ah hah, but this is only possible now
that we know f is not surjective
so a exists
we still have to give it a new name since it's not the same function anymore
call g(j) = f(j) when 1<= j <= k
and g(k+1) = a
g:{1,...,k+1} -> A
what can you say about g?
visual tiger
yes
last slate
pp
last slate
main owl
i could be wrong but are you not just making the point -2 positive 2
since its absolute value
last slate
what about point q?
last slate
so point q will be 2,5 ?
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rugged bay
,rotate
grand pondBOT
rugged bay
Can someone explain why 14 is incorrect
Why is it not diverging
Nevermind im fucking stupid it’s 0
.close
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twin ridge
Does my logic make any sense? Or did I do this wrong
midnight plankBOT
Does my logic make any sense? Or did I do this wrong
graceful drum
Its correct
twin ridge
Ok cool.
Is this one slightly different? Each sum has a corresponding probability, so do I need to add or multiply the probabilities together?
Like if I got a 7 on the first roll, the second roll could be 1 6, 2 5, or 3 4.
But if I got a 2, there's only 1 1.
graceful drum
Wait do they mean u roll once for the sum
then u roll twice for to get the sum to compare with
?
twin ridge
then u roll twice for to get the sum to compare with
Right.
Slightly different than the usual, as there's a red and a white dice.
So for 7, it's really 1+6, 2+5, 3+4, 4+3, 5+2, 6+1, if the first number is red and second is white.
graceful drum
Ok, if u get x on the first roll , there are x-1 ways the sum of the next two will be same out of the 36 possibilities
so total number of ways you can roll the three dice are 6.6.6, and number of favourable outcomes is 1-1 + 2-1 + 3-1 + 4-1 + 5-1 + 6-1
graceful drum
Ohhhh
sorry for the misundestanding
then u need to calculate the probability of getting each sum for two rolls of one of the dice
and then u multiply with itself to get the probability the sum is same for the other dice
and then add them ig
like probability of getting 2 = 1/36
''' 3 = 2/36
...
''' 12 = 1/36
then u square these
and add them for final probability\
(this is the addition principle cus the events are mutually exclusive for different sums)
(and multiplication principle for comparing the sums of two dice)
jolly roost
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jolly roost
can someone help me prove this
tribal temple
Noticing that sin(b) - 1 + cos(b) is really sin(b) - (1 - cos(b)) might help a bit 
edgy chasm
Its prob something with tg
glass gust
can someone help me prove this
My personal method would be starting with LHS, and multiplying with the conjugate
that way you would get squared values, which are then equivilent to some other things
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deft bough
i'm having a very difficult time figuring out how the book got the answer that it got:
midnight plankBOT
i'm having a very difficult time figuring out how the book got the answer that i...
deft bough
it seems to me that the following would work:
midnight plankBOT
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@deft bough Has your question been resolved?
deft bough
<@&286206848099549185>
deft bough
<@&286206848099549185>
fallow scarab
i'm having a very difficult time figuring out how the book got the answer that i...
Show more context. What's v(x, t) supposed to be?
deft bough
v(x,t) is used to reconfigure the problem as a homogeneous PDE
using initial conditions
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@deft bough Has your question been resolved?
graceful ferry
midnight plankBOT
graceful ferry
$Let A be a set and let S, T \superseteq A x A be equivalence relations on A.
Let's define the three-place relation:
S▷◁T={(a,b,c)\mid(a,b)\inS \wedge(b,c)\inT}
Let a,c \in A
1.Prove/disprove: if exists b\inA such that (a,b,c), (c,b,a) \in S▷◁T then c \in [a]_S$
grand pondBOT
prograce
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)
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bold thunder
Determining convergence/divergence for number 15, but im stuck. This section is on alternating series tests
midnight plankBOT
Determining convergence/divergence for number 15, but im stuck. This section is ...
@bold thunder Has your question been resolved?
junior flower
bold thunder
<:eeveethink:601029006418116608>
?
junior flower
idk, this seems a little hard for something in the alternating series test section of a calculus book
bold thunder
Well, its there lol
junior flower
did it mention dirichlet’s test at all?
junior flower
well i dunno then. maybe i’m missing something
bold thunder
lol
tribal temple
Is that supposed to be sin((n + 1/2)pi) they’re representing there 
If so that’s very disgusting notation 
bold thunder
i genuinely
have no idea dude
wait werent u the person who basically taught me direct and limit comparison
tribal temple
Context clues suggest that’s what they meant (as that would be the “alternating” part)
tribal temple
wait werent u the person who basically taught me direct and limit comparison
Yep you remembered me 
bold thunder
Context clues suggest that’s what they meant (as that would be the “alternating”...
makes sense
Thats how i solved that
tribal temple
There’s a similar idea here you can do, you can show that it converges by alternating series but not absolutely (taking that expression to be what I think it is )
bold thunder
im confused
take in mind ive had a sinus headache for like 2 days now, so im barely functioning to do these problems
but i gotta get em done
tribal temple
Alright, do you at least know what $\sin( \qty( n + \frac12) \pi)$ turns into?
grand pondBOT
@tribal temple
tribal temple
my guess is 1 or -1
Well, “yes” 
(It’s (-1)^n, sin(pi/2) is 1, sin(3pi/2) is -1, and periodicity from there)
bold thunder
cool
so taking the lim of 1/(1+n^(1/2)) we get 0, so it converges by AST
then we have to find whether or not the abs val of the original series converges or diverges
to determine abs convergence or conditional
right?
@tribal temple didja disappear?
languid latch
If eveyone need my help with math, pls send me DM>
tribal temple
<@788085606483361802> didja disappear?
I did yep sorry 
i have to go out now 
tribal temple
then we have to find whether or not the abs val of the original series converges...
But yep, basically 
bold thunder
I realized for that problem i dont need abs convergence or conditional
Its just determinin if it converges lol
Thank you again
tribal temple
Awwww 
bold thunder
.close
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last slate
What can the equation of this graph be?
midnight plankBOT
What can the equation of this graph be?
drifting birch
What can the equation of this graph be?
Off of one quick peek just e^x
runic hamlet
more like 2.5^x
worthy wing
Was this a contest?
last slate
Unlike a^x
runic hamlet
just write down random symbols and you have something
last slate
Was this a contest?
nope
drifting birch
more like 2.5^x
Such a strange choice of equation 😂
e^x is a thousand times cleaner
But I guess it does kinda look like it intersects x=1 at 2.5 ish
strong jay
3Blue1Brown has a video on e and it might help make the graph more intuitive if you want.
midnight plankBOT
feral sedge
I am asking for other unique equations
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fleet terrace
midnight plankBOT
fleet terrace
I've taken the conjugate
now what
sterile crypt
do you want the solution?
torn compass
I've taken the conjugate
now what
dont need , try factorizing the numerator