Ok cool
#help-19
mystic swan
You want to connect the end points of the purple line with the blue point(speaker)
See if that helps
wide drift
You want to connect the end points of the purple line with the blue point(speake...
Something with trigonometry?
mystic swan
Yeah
mystic swan
You have a right angle triangle with one side being 14 and another being 19
odd edgeBOT
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weary moon
Question:for which real numbers k does curve y =2kx^{2}+(1-3k)x+2k-1 have 2 intersections with x axis.
I have solved this question using the discriminant (D > 0). However when I solve this equation I get the following range k=<1- 2sqrt(2))/7, 1+ 2sqrt(2))/7 >
there is 0 present in this range even though 0 shouldn't be a part of the answer. How should I eliminate 0 from the answer?
weary moon
hardy panther
I dont know you mean by range in this context
These are real numbers
They are just irrational
weary moon
These are real numbers
what do you mean by that
the question is asking for all real numbers k
so I made a range of all real numbers
hardy panther
Let me check rq
weary moon
ignore /a /b and /c in the second line
hardy panther
a=2k, b=1-3k, c=2k-1
b^2 - 4ac >= 0
(1-3k)^2 - 4(2k)(2k-1) >= 0
1 - 6k + 9k^2 - 16k^2 + 8k >= 0
-7k^2 + 2k + 1 >= 0
k = {-2 +- sqrt[4 - 4(-7)(1)]}/2(-7)
= [-2 +- sqrt(32)]/-7
= [1 +- 2sqrt(2)]/7
Meaning
k <= [1 + 2sqrt(2)]/7 or
k >= [1 - 2sqrt(2)]/7
weary moon
1 - 6k + 9k^2 - 16k**^2** + 8k >= 0
oop
yeah
but what after
you get the same result
and 0 is still included
@hardy panther
weary moon
clearly, when k=0 this equation has only 1 intersection with the x axis
weary moon
I think the issue is with your inequlity use
how should I write it
hardy panther
Check my (updated again) answer
weary moon
a=2k, b=1-3k, c=2k-1
b^2 - 4ac >= 0
(1-3k)^2 - 4(2k)(2k-1) >= 0
1 - 6k + 9k^2 -...
shouldnt k >= [1 + 2sqrt(2)]/7 or
k <= [1 - 2sqrt(2)]/7 be inverted though
since its a negative hyperbole
k <= [1 + 2sqrt(2)]/7 or
k >= [1 - 2sqrt(2)]/7
hardy panther
shouldnt k >= [1 + 2sqrt(2)]/7 or
k <= [1 - 2sqrt(2)]/7 be inverted though
Yes, you are correct
I didnt notice my mistake
Also, when k=0, the discriminant is still >= 0 (it is 1), so its no problem
weary moon
wdym there's no problem
weary moon
here it shows there is only 1 solution
hardy panther
wdym there's no problem
When k=0, the discriminant = 1, which is >=0, so your answer is still a real number
K is allowed to be 0
weary moon
so when k=0 there are 2 intersections with the x axis?
hardy panther
The range of values that give you real number answers are
[(1 - 2sqrt(2))/7, (1 + 2sqrt(2))/7]
hardy panther
so when k=0 there are 2 intersections with the x axis?
Oh I see
Well, just exclude 0 then
hardy panther
[(1 - 2sqrt(2))/7, 0) U (0, 1 + 2sqrt(2))/7]
orchid torrent
K is allowed to be 0
When k=0, the 2kx^2 term vanishes, leaving you with a linear eq (which can only have one soln)
hardy panther
but how would I know to exclude 0 without using desmos
Because when the discriminant is 0, you have one repeated real root
(Multiplicity 2)
weary moon
When k=0, the 2kx^2 term vanishes, leaving you with a linear eq (which can only ...
Is that the only way to see that 0 shouldn't be an answer?
orchid torrent
Because when the discriminant is 0, you have one repeated real root
But if the poly on the left side has a degree of 1 when k=0, then how can the root have a multiplicity of 2?
Plus, the repeated roots occur at the endpoints of the interval (when the discriminant is zero, which does not occur at k=0 here)
hardy panther
Is that the only way to see that 0 shouldn't be an answer?
Its a nifty fact ypu should know already about the discriminant
Thats when the parabola touches and bounces off the x axis
As opposed to passing through it (two points of intersection)
...or not passing through at all (a complex conjugate pair of solutions)
hardy panther
Plus, the repeated roots occur at the endpoints of the interval (when the discri...
Oh right
I am confusing myself here
orchid torrent
You understand what I'm saying right
and can explain it?
cause if so, imma go back to eating
hardy panther
Yes, the endpoints cause that issue, not k=0
Obviously, since discriminant is 1 when k=0
^graph above is for the discriminant quadratic, not the given quadratic
You can see that indeed, the endpoint causes the discriminant to be zero
So the endpoints must be excluded
K=0 is fine
( (1 - 2sqrt(2))/7, (1 + 2sqrt(2))/7)
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scenic lodge
Is this substitution rule??
odd edgeBOT
Is this substitution rule??
scenic lodge
Or do I just distribute t^-1/2
cold sage
id just distribute
odd edgeBOT
scenic lodge
.reopen
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✅
scenic lodge
What do you do for this?
chilly galleon
What do you do for this?
well what is sin 2x
scenic lodge
-2cosx
proven sphinx
What do you do for this?
sin2x = 2sinx cosx
scenic lodge
-2cos 2x
scenic lodge
wait how
chilly galleon
it becomes the integral of 2cos x
scenic lodge
what is that
hold on ur oging too fast
im rly tired
ur asking what is sin 2x... u mean the antiderivative of it?
scenic lodge
well what is sin 2x
what do you mean here?
proven sphinx
ur asking what is sin 2x... u mean the antiderivative of it?
no, he meant the simplified trig formula
scenic lodge
ok y did i never learn that befre
can u teach me that
why does sin2x = 2sinx cosx
scenic lodge
no
can u tryy explaining it
before we do that even, why is it better to simplify it to that in the first place?
proven sphinx
before we do that even, why is it better to simplify it to that in the first pla...
then we can use our existing knowledge of derivatives to compute the integration
proven sphinx
substitute a=b
distant pagoda
x + x is what?
distant pagoda
:/
distant pagoda
whats sin(a+b)
distant pagoda
yes
distant pagoda
https://www.cuemath.com/trigonometry/sin-a-plus-b/
now make the subsitutions in this equation here
scenic lodge
sinxcosx + cosxsinx
distant pagoda
yes
scenic lodge
so 2sinxcosx
distant pagoda
yes
distant pagoda
u dont need to
scenic lodge
well its that oover sinx
distant pagoda
What do you do for this?
substitute the value of sin2x here
scenic lodge
yes i do i need the integral
distant pagoda
make the cancellation
scenic lodge
ok hold on
distant pagoda
u'll have simplified it enough
distant pagoda
no
scenic lodge
damn
distant pagoda
thats an easy integral
scenic lodge
ur not getting rid of the 2 cosx
distant pagoda
u dont need to
scenic lodge
ur just getting rid of 1 sinx
scenic lodge
ok true
distant pagoda
its now
scenic lodge
2cosx
distant pagoda
2∫cosx dx
distant pagoda
no more dx
scenic lodge
yeah
wait i just wana do something rly quick
sinxsinxcosxcosx/sinx
yea i still see 2cosx *sinx lol
wtj
wtf
or is that cos^2x
distant pagoda
sinxsinxcosxcosx/sinx
???
distant pagoda
what y wrote is (sinx*cosx)^2
scenic lodge
and you divide both of those by sin
so its cosx +cosx
so that is -sinx + -sinx
= -2sinx
yeah
distant pagoda
what do u get when u differentiate sin x?
distant pagoda
👍
distant pagoda
thats the integration symbol
scenic lodge
or do i just write S sin2x/sinx = 2sinx
distant pagoda
uve already integrated cos x and written sin x in place of it
scenic lodge
how do i write my final answer
distant pagoda
how do i write my final answer
just 2sinx + C
scenic lodge
okkkk
and that is like the area of something?
of some other function or somthing?
like what is the integral for
like S sin2x/sinx dx
that is the area of 2sinx + C ?
scenic lodge
just 2sinx + C
which is either the distance traveled or the change in velocity righyt?
distant pagoda
like S sin2x/sinx dx
when u graph a functyon of x
such that f(x) = sin2x/sinx
what u did gives u the area u der the graph
*under
scenic lodge
but isnt it the area under sinx + C?
distant pagoda
no
distant pagoda
2sinx + C gives u the area
scenic lodge
oh wtf
distant pagoda
ofc u only get the area when u put it as a definite integral
scenic lodge
so if i graph those 2 line it willl show me the area or nah
scenic lodge
ofc u only get the area when u put it as a definite integral
put what as the definite integral
distant pagoda
so if i graph those 2 line it willl show me the area or nah
yes but simply subtituting for x in 2sinx + C wont do it
distant pagoda
put what as the definite integral
what u solved was an indefinite integral
intead it couldnt been a definite integral
with numbers on top and bottom of big S thing
scenic lodge
yea h;ha
im doing a definite integral now
$\int_{0}^{pi/3} \frac{sin(\theta) + sin(\theta)tan^2(\theta)}{sec^2(\theta)} d\theta$
clever fjordBOT
wakamole
scenic lodge
so for thiis it is F(b) - F(a)
and F is the antiderivative of f(x)
so i need the antiderivative...........
what the hell is the antiderivative of sin(x)tan^2(x)? ?? @distant pagoda
chilly galleon
what the hell is the antiderivative of sin(x)tan^2(x)? ?? <@731360367283798056>
first multiply by cos ^2 theta on top
scenic lodge
first multiply by cos ^2 theta on top
why
scenic lodge
I NEED TO KNOW HOW TO DO IT
chilly galleon
1/sec^2=cos^2
scenic lodge
how do you know hwo to do that
like how do you recognize that is the first step?
i rly need help i suck at integrals
damn i suck so bad at trig idintities
im never taking a summer math class ever again
ok i did the first step
odd edgeBOT
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Available help channel!
polar hazel
im not sure how to do this
odd edgeBOT
@polar hazel Has your question been resolved?
stuck raven
I don’t know how to do part(a), I don’t know how can I utilise the hint
latent scaffold
What do you get when you integrate every term in the sum?
odd edgeBOT
@stuck raven Has your question been resolved?
woeful rivet
how do i do this without converting to degrees
odd edgeBOT
how do i do this without converting to degrees
woeful rivet
first
nimble blaze
familiarise yourself with radians
woeful rivet
familiarise yourself with radians
howwwww
this is what they did but i dont ge thow they got that
nimble blaze
practice
even properites,
supplementary identities
the applicable identities are essentially the same
woeful rivet
even properites,
supplementary identities
is it just memorising
nimble blaze
better to understand the unit circle
woeful rivet
better to understand the unit circle
i dont get this one
what if theta is greater
then 270
and its in the sin quadrant
uneven osprey
i dont get this one
angles in radians are defined from unit circle
woeful rivet
what?!?!?!
but doesnt it go all the way into the sin quadrant again
and become positive
nimble blaze
wdym
woeful rivet
bc they still go into sin and all quadrant
nimble blaze
try drawing it out
uneven osprey
see, sin(-181) = -sin(181)
here you are thinking that it will be in second quadrant so it will be positive, right?
woeful rivet
yes
nimble blaze
terminal arms for 181°
and -181°
uneven osprey
okay so see actually the sin(181) itself will be negative
which cancels out the negative sign
got it?
uneven osprey
okay so see actually the sin(181) itself will be negative
beacause that will be in third quadrant where sine function is negative
odd edgeBOT
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Available help channel!
robust pollen
Does |R| = |N| where R is the set of real numbers and N is the set of natural numbers. And how to proof?
ember oak
Does |R| = |N| where R is the set of real numbers and N is the set of natural nu...
No
Non surjective maps to power sets
odd edgeBOT
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tranquil hatch
tranquil hatch
<@&286206848099549185>
tranquil hatch
<@&286206848099549185>
exotic comet
@tranquil hatch notice that $SS'=TT'=\frac{1}{2}(AB+BC+AC)$:
clever fjordBOT
Cooper Wang
tranquil hatch
Indeed
exotic comet
$S_{\triangleABC}=2S_{OSS'O'}-2S_{\triangleAOB}-2S_{\triangleAO'C}\=(a+b)\frac{AB+BC+AC}{2}-aAB-bAC\=\frac{(b-a)AB+(a-b)AC+(a+b)BC}{2}$
clever fjordBOT
Cooper Wang
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
exotic comet
sorry, typing mistake
tranquil hatch
i would like to understand the process if possible
i didn't read your answer yet because i would like to make some of the process by myself to practice a little bit
heady plover
Why here Γ (1+1)=1 ?
odd edgeBOT
Why here Γ (1+1)=1 ?
odd edgeBOT
jade cairn
since Gamma(n) = (n-1)! for intergrs n >= 1
oh, I forgot about this
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Available help channel!
obtuse pasture
odd edgeBOT
static totem
interesting
late dust
What have you tried?
odd edgeBOT
@obtuse pasture Has your question been resolved?
obtuse pasture
What have you tried?
ok so i tried dividing fifty with
uh
3
but then i realised thats not possible
it'd have to be a sequence or probability
and then i looked at the number of possibilities for the product of three numbers
thatd be
like
-1^3
or 1^3
or
-1^2x1
or 1^2x1
which would both be 1
late dust
If instead of 50 you only have 6 numbers, what would be the answer?
obtuse pasture
3 hints?
late dust
Why?
obtuse pasture
or 4?
because
you can make 4 pairs of 3 in 6
because i think each number would have a minimum of inclusion in 2 sets of 3, and a maximum of 3 sets of 3
late dust
Not sure what you mean
obtuse pasture
uhh lemme try explaining again
you have 6 numbers in 6: 1,2,3,4,5,6
now your first set of 3 would be 1,2,3
stark heart
Wait first can you use the hint to choose the 3 consecutive numbers or just gives you a random product of 3 consecutive numbers
obtuse pasture
your next would be 2,3,4
third would be
3,4,5
fourth would be
4.5.6
so you'd have 4 sets of 3 numbers
obtuse pasture
Wait first can you use the hint to choose the 3 consecutive numbers or just give...
wdym
late dust
Wait first can you use the hint to choose the 3 consecutive numbers or just give...
Having randomness would make it a stupid question, there would be no minimum number of hints
stark heart
Having randomness would make it a stupid question, there would be no minimum num...
Yeah that what I think
late dust
so you'd have 4 sets of 3 numbers
I think you're forgetting that the numbers are written along a circle
obtuse pasture
how does a circle make a difference though?
late dust
In other words the first and last ones are consecutive
obtuse pasture
oh yes
so it'd be +1
so then the last set would be 5,6,1
so actually 5 sets huh?
late dust
... why not include 6,1,2 in that case
late dust
Wat
obtuse pasture
nothing thats just another way of saying im so cooked
stark heart
But if they are 6, isn't the solution 2 because we would get the product of the first 3 number and the product of the last three numbers then multiply the 2 of them
obtuse pasture
please continue
obtuse pasture
But if they are 6, isn't the solution 2 because we would get the product of the ...
why would you multiply the two of them
late dust
Reframe the problem
You have a1, a2, a3, a4, a5, a6
You don't know the individual values
You want the value of a1*a2*a3*a4*a5*a6
A hint can give you:
a1*a2*a3a2*a3*a4- ...
a6*a1*a2
obtuse pasture
yea
late dust
So what hints do you need to get a1*a2*a3*a4*a5*a6?
late dust
If you meant you need 6 hints, no you're not really onto something
obtuse pasture
If you meant you need 6 hints, no you're not really onto something
damn it ok
late dust
Let me rephrase that last part
A hint can give you:
- A:
a1*a2*a3 - B:
a2*a3*a4 - C:
a3*a4*a5 - D:
a4*a5*a6 - E:
a5*a6*a1 - F:
a6*a1*a2
odd edgeBOT
obtuse pasture
.reopen
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✅
late dust
Which hints, among A,B,C,D,E,F, do you need in order to be able to calculate a1*a2*a3*a4*a5*a6?
late dust
You're only interested in the final result a1*a2*a3*a4*a5*a6
It doesn't matter if you calculate it as [a1*a2*a3]*[a4*a5*a6] or [a2*a3*a4]*[a5*a6*a1]
stark heart
Yeah
But the problem becomes a bit complicated though when the number of numbers becomes not divisable by 3
obtuse pasture
Yeah
But the problem becomes a bit complicated though when the number of numbers...
make a range ig
obtuse pasture
It doesn't matter if you calculate it as `[a1*a2*a3]*[a4*a5*a6]` or `[a2*a3*a4]*...
because you get the total product of the numbers in the range?
and all we're trying to find is the product of all the numbers, not all the numbers individually
stark heart
I think if the question is 4
We gonna need 4 hints
Multiply all of them together then take the square root of the result
late dust
I think if the question is 4
We gonna need 4 hints
Multiply all of them together...
How about not giving answers?
stark heart
Okey sorry but that was a thought though I don't know if it is possible to be less
late dust
@obtuse pasture You have a1, a2, a3, a4, a5, you want their product
obtuse pasture
Ok now let's try with 5 numbers
2 sets?
royal crag
I think if the question is 4
We gonna need 4 hints
Multiply all of them together...
This doesn't seem right?
late dust
Can you list the possible hints and then try to combine them?
obtuse pasture
Can you list the possible hints and then try to combine them?
A: a1*a2*a3
B: a2*a3*a4
C: a3*a4*a5
D: a4*a5*a1
E:a5*a1*a2
stark heart
This doesn't seem right?
Yeah, it is not right || it is cubic root ||
late dust
Use `<text>` to write stuff like this without * and _ having an effect because markdown
obtuse pasture
yea sorry about that
late dust
A: `a1*a2*a3`
B: `a2*a3*a4`
C: `a3*a4*a5`
D: `a4*a5*a1`
E:`a5*a1*a2`
Right so if you took A and D for example, you end up with a1*a2*a3*a4*a5*a1, which is no good, right?
obtuse pasture
yes
late dust
What does a1*a1 equal?
obtuse pasture
yes
late dust
What happens if you add hint C to this?
late dust
Do you mean that's what you get from A and C?
late dust
Yes
late dust
Right
obtuse pasture
yususus
late dust
Can you see a way to get what we want, a1*a2*a3*a4*a5, even if it's not using the minimum number of hints?
obtuse pasture
i think
late dust
Elaborate
obtuse pasture
a * c * e
wait no
just multiply everything together
which would give you the cube ov every digit
and root it?
late dust
Why that last step?
obtuse pasture
ok yea you probably dont have too
late dust
(-1)^3 = -1, 1^3 = 1
late dust
So yes you're correct
static totem
i think 50 is a boring answer
royal crag
the max answer has to be 50
late dust
You can only have 50 hints
royal crag
There are only 50 hints possible
obtuse pasture
You can only have 50 hints
but the question doesnt say
late dust
What's hint number 1 and hint number 52?
late dust
No that's hint number 50
royal crag
Then what's hint 50
late dust
Hint number n starts with a_n
obtuse pasture
ah ok
royal crag
Hint number n starts with a_n
This indexing isn't given directly by the question but it works
late dust
Assuming hint number 1 starts with a1 and you continue the natural pattern
Anyway you now know that using all possible hints gives you the answer, but you don't really know if it's the minimum
obtuse pasture
yea
late dust
After all for 3k numbers, you only need k hints
obtuse pasture
where k<n?
late dust
Where k is a natural number
obtuse pasture
k hints
late dust
1 <= n <= 50
late dust
If n = 43, my question is which hints include a_43
late dust
The a's are the numbers, if you want a letter to refer to the hints, use h
obtuse pasture
ok sorry
obtuse pasture
1 <= n <= 50
is this still our range
late dust
Yes
late dust
I think you're confused
obtuse pasture
no i
my brain stopped working
it'd be h= 41, 42
and 43 if we're considering that as well
late dust
$h_n = a_n \cdot a_{n+1} \cdot a_{n+2} \
h_1 = a_1 \cdot a_2 \cdot a_3$
clever fjordBOT
Nel
late dust
Does that definition work for you?
obtuse pasture
yea
late dust
Also we're working mod 50 so a_51 = a_1 and h_51 = h_1
obtuse pasture
ok makes sense
late dust
Ok so I believe you understand that three hints include a_n, namely h_{n-2}, h_{n-1}, and h_n
obtuse pasture
yes
late dust
If you use only one of these hints, you get to keep a_n in the final product, right?
obtuse pasture
yes
late dust
If you use two of them, what happens?
obtuse pasture
you use a_n in 2 seperate hints
late dust
Yes and the point of using hints is to multiply them together, so what happens when you do that?
obtuse pasture
Yes and the point of using hints is to multiply them together, so what happens w...
you get a product of only 2 numbers not 3
late dust
(I assume we agree that there is no way to use hints other than to combine them as a product)
obtuse pasture
(I assume we agree that there is no way to use hints other than to combine them ...
yeaeghuiegh
late dust
you get a product of only 2 numbers not 3
Rephrase please?
obtuse pasture
the product
that you get
when you multiply 2 hints together, is the product of only 2 numbers, one of those 3 numbers will get squared and therefore nulled
cus its jsut 1
after squaring
not null idek
late dust
Ok but it results in a product of 4 number, not 2
obtuse pasture
oh yea
late dust
Or 3, depending on which hints you use, but whatever
late dust
If you use h_30 and h_31 you get a_28 * a_33
Huh actually I got confused
So it's 2 or 3
obtuse pasture
lol
late dust
Ok if you use h_30 and h_32, what do you get?
obtuse pasture
h_30 = a_30 * a_31 * a_32
h_32 = a_32 * a_33* a_34
which gives you
a_30 * a_31 * a_32 * a_33
and
wait
i need a_31 in there
late dust
Yes, so a product of 4 numbers
Anyway that's not the point
The point is that you lose all information about a_n because a_n*a_n = 1
obtuse pasture
yes
late dust
Now if you use all three hints, you get that information back
obtuse pasture
yea
late dust
Ok so with 50 numbers total, do you agree that you cannot use a set of hints such that all numbers are covered once and only once?
Like you could with just 6 numbers
obtuse pasture
Ok so with 50 numbers total, do you agree that you cannot use a set of hints suc...
yea
late dust
That simply comes from the fact that 50 is not divisible by 3
obtuse pasture
That simply comes from the fact that 50 is not divisible by 3
yea
late dust
Alright and if you don't cover a number, you can't get to the answer
late dust
So you necessarily have to cover at least one number twice (or thrice)
obtuse pasture
yes
late dust
But if you cover any number only twice, you still can't get to the answer since that number is lost
obtuse pasture
yes
late dust
So at least one number is covered thrice
obtuse pasture
yes
late dust
That means the next number is already covered twice
late dust
?
late dust
If a_n is covered thrice, which hints have you used?
late dust
a_n-1, a_n and a_n+1
Again those are numbers, not hints, and you seem to have changed the indexing
obtuse pasture
oh yea
late dust
(btw I haven't defined "being covered" but it's fairly obviously "being included in a hint that is being used")
obtuse pasture
(btw I haven't defined "being covered" but it's fairly obviously "being included...
yea i got that afterwards but it clicked
late dust
h_n-1, h_n and h_n+1
If $h_n = a_{n-1}a_na_{n+1}$ then fine
clever fjordBOT
Nel
obtuse pasture
yea thats what i mean
but like
in hints
basically you have hint n
and you use the the hint previous and the hint next in line
late dust
You define that however you want, it really doesn't matter as long as you're consistent
obtuse pasture
okeokriekie
late dust
h_n-1, h_n and h_n+1
So how many times is a_{n+1} covered?
obtuse pasture
add?
late dust
Which additional hint do you need to use
obtuse pasture
wouldnt it be a continuous loop
late dust
a_{n+1} is covered by both h_n and h_{n+1}. There's only one other hint that you haven't used that still covers a_{n+1}
late dust
No
late dust
Yes
late dust
Now a_{n+2} is covered twice but needs to be covered thrice instead
obtuse pasture
yes
late dust
And so on until you use every hint
obtuse pasture
add a(n+3)
obtuse pasture
And so on until you use every hint
yea
late dust
Well that's the proof
Not exactly rigorous but one can make it rigorous, though you seem to lack quite a bit of rigor
Or maybe you're just "cooked"
obtuse pasture
no i think im just sleepy
because i onto something at 2
but now my brain is completely not functioning
late dust
So take a break then come back to this and try writing a proof from it
obtuse pasture
or idk maybe i am cooked
obtuse pasture
because i onto something at 2
was*
obtuse pasture
So take a break then come back to this and try writing a proof from it
alright
btw the question has a part two
but i believe we've covered most of it's proof as well
late dust
Do tell?
late dust
Ok well it all depends on the divisibility of n by k
late dust
Yes though it's not as straightforward as either n/k or n
Probably it's just going to be gcd(n, k) but I'm too lazy to prove that
late dust
I'm not a student
late dust
Are college goers not students? 
late dust
Well yeah I'm not old or rich enough yet to be retired so you could say I'm a professional in the first sense of the word
obtuse pasture
so like phd or smth
late dust
Who knows 
obtuse pasture
Probably it's just going to be gcd(n, k) but I'm too lazy to prove that
cud you help me with this later 
late dust
odd edgeBOT
@obtuse pasture Has your question been resolved?
mystic saffron
odd edgeBOT
mystic saffron
i dont understand the problem
i understand it but idk where to look for it
!stat
!status
odd edgeBOT
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
dawn tiger
well they give you the dimensions, right? the side lengths are x, x, and 2x
mystic saffron
it didn't teach me
mystic saffron
well they give you the dimensions, right? the side lengths are x, x, and 2x
yes
dawn tiger
volume of a rectangular prism is length * width * height
dawn tiger
how do you get a hint for a volume formula? that's just something you're expected to memorize in middle/high school
there wasn't really a way for me to give you a hint for what the volume formula is
mystic saffron
well i mean you can just guide me
like umm
not really a guide tho but just a bunch
Anyway thanks
now i fucking know the formula again..
,close
.close
quartz pier
odd edgeBOT
quartz pier
I dont understand how they knew it was complete until level log_(1/(1-alpha))n
n(1-alpha)^d = 1
and I solve for d right?
but then Im getting
(log n)/(log(1/(1-alpha))
im so dumb its the same 🤦
.close
odd edgeBOT
quartz pier
.reopen
odd edgeBOT
✅
quartz pier
why did they pick log_(1/1-alpa)n instead of log_(1/alpha)n
we could have picked either one right?
quartz pier
wanton bison
idk what's happening
quartz pier
do yk whats happening here doe 🙏
wanton bison
unfortunately not, i just got on the channel cause i see you often here 😄
quartz pier
zealous mango
idk what's happening
sorry, dealt with now
odd edgeBOT
@quartz pier Has your question been resolved?
exotic bobcat
why did they pick log_(1/1-alpa)n instead of log_(1/alpha)n
should be equivalent given that all we know about alpha is it's "some number between 0 and 1"
odd edgeBOT
odd edgeBOT
Available help channel!
proven sand
odd edgeBOT
proven sand
hi, in the solution on the right im unsure on the fourth line
the angular motion doesnt match anywhere on the eqn sheet given, so how is it derived?
oops nvm
.close
odd edgeBOT
odd edgeBOT
Available help channel!
ripe turret
hi
ripe turret
can this be derivated at x=2 and x=-2 ?
i know it cant be at 1 and -1
but i feel like the ends should not be able to...
sand horizon
can this be derivated at x=2 and x=-2 ?
Thoses are endpoints, actually i couldnt be able to say if the function is define according to graphics, and its like, they are infinite tangent possible so differentiation here is not possible
sterile blaze
the derivative doesnt exist at the end points
ripe turret
okay
i have one more question
the books says the answer is were "x² + 3x + 2" = 0
why is this?
it makes sense when graphing the function, but how can i know this otherwise?
sterile blaze
a polynomial is differentiable
however with the absolute value function, when the function is zero, the derivative might not exist
so u have to check the points where the function=0
odd edgeBOT
sterile blaze
welcome
odd edgeBOT
Available help channel!
urban garden
odd edgeBOT
urban garden
Can someone do step by step tutorial
silk quail
$\sin^2(x)=\frac{1-\cos(2x)}{2}$
clever fjordBOT
fish
urban garden
Half angle?
silk quail
yeah
but essentially, just use that.
$\int_0^{2\pi}\sin^2(x),{dx}=\int_0^{2\pi}\frac{1-\cos(2x)}{2},{dx}=\int_0^{2\pi}\frac{1}{2},{dx}-\int_0^{2\pi}\frac{\cos(2x)}{2},{dx}$
clever fjordBOT
fish
urban garden
1/2 will be x/2
silk quail
yes.
urban garden
What about cos2x
silk quail
you know that $\frac{d}{dx}\sin(2x)=2\cos(2x)$?
clever fjordBOT
fish
silk quail
so just reverse that
urban garden
Sin2x/4??
silk quail
correct
silk quail
what do you mean?
urban garden
Like how am I supposed to know
silk quail
you get it from chain rule and derivative of sine rule
urban garden
Is it an identity?
silk quail
so $\frac{d}{dx}f(g(x))=g'(x)\cdot f'(g(x))$
clever fjordBOT
fish
silk quail
and $\frac{d}{dx}\sin(x)=\cos(x)$ and $\frac{d}{dx}\cos(x)=-\sin(x)$
clever fjordBOT
fish
clever fjordBOT
Twiizly
silk quail
yeah
silk quail
yes
odd edgeBOT
odd edgeBOT
Available help channel!
loud grotto
odd edgeBOT
loud grotto
i need help with a few questions regarding this problem
here is what i know,
the angle of elevation is 53 deg
the length of wire will Marcus need to attach the top of the latticework to the ground is 15 feet
here are the things that have stumped me
i think that 3 and 4 are correct
i dont believe it is possible with the given info
can someone confirm? after that I have more questions about 5 and 6 depending on wether or not I am correct
odd edgeBOT
@loud grotto Has your question been resolved?
loud grotto
<@&286206848099549185> i know its a lot of writing but its a simple problem (i think)
loud grotto
<@&286206848099549185>
odd edgeBOT
@loud grotto Has your question been resolved?
loud grotto
<@&286206848099549185>
mystic saffron
Hello
waxen sierra
geometry?
mystic saffron
I am here
loud grotto
same question as up here still
waxen sierra
i lost hope and went for a bathroom break hope i didnt lose you
so real
i’m not good with word problems
regal apex
i lost hope and went for a bathroom break hope i didnt lose you
are you sure you can't?
loud grotto
are you sure you can't?
no but im pretty sure
sudden hollow
so the angle of elevation at the top of the base is arctan 3/4
loud grotto
yeah 53 deg
loud grotto
so the angle of elevation at the top of the base is arctan 3/4
are 3 and 4 right?
sudden hollow
yeah 53 deg
nah def less than that
loud grotto
no its 4/3
sudden hollow
roughly about 36 degrees
loud grotto
roughly about 36 degrees
isnt it 4/3
odd edgeBOT
@loud grotto Has your question been resolved?
fair canopy
Anyone
fair canopy
Provide me with notes of trigonometry with lots of problems and solutions.
mint mirage
Khan academy
fair canopy
Link for jee?
mint mirage
You didn't say that
uneven osprey
Link for jee?
bruh, they don't teach for JEE
fair canopy
Jee notes
uneven osprey
aren't you enrolled in any coaching or something?
uneven osprey
Or any very good book recommendation
I am assuming you're not a dropper right?
fair canopy
Hmm
uneven osprey
ever heard of cengage?
uneven osprey
That is for advanced
so you're just focused on mains?
fair canopy
Which contains a lot of solved examples
Which has this?
uneven osprey
Which has this?
uh actually I can't think of any purely mains oriented books
but Cengage also have Mains oriented books
or you could view Arihant as well
considering what you need
fair canopy
I just need lot of solved examples
Can u recommend one book
Because then it would be easy
uneven osprey
Can u recommend one book
Actually I am preparing for JEE too
I am an dropper btw
so far what my seniors recommended me is Cengage Advanced series
I have didn't prepared competitively in 11th and 12th so I am not sure about that
uneven osprey
Which is gud?
both pretty good in their own way, Arihant takes level a bit higher sometimes and sometimes easier
Cengage on the other hand stays consistent in higher difficulty
I am myself using Cengage and it has many illustrations, examples and pretty good level of practice problems
uneven osprey
What about sl loney trigonometry?
it is good for practising questions ig
there's not much theory and example in it
crude hollow
odd edgeBOT
crude hollow
A,B,C are angles in a triangle and a,b,c are sides
<@&286206848099549185>
hello?
anyone?
crude hollow
yeH
crude hollow
OHHHHH
prisma moat
odd edgeBOT
odd edgeBOT
Available help channel!
mystic saffron
Why does this compound not have a centre of symmetry
