it means sin of a
#help-17
vast shale
ah i see
why can you take the inverse though?
im not familiar with these types of inverse
whole oasis
yeah, sin^-1 is just a way we name it, it's like solving x^2 = 5 then x = sqrt(5) (or minus), we just put a square root sign into place, that's all
obviously it has its own properties and other things which are specific for functions
vast shale
sine wave
whole oasis
im not familiar with these types of inverse
In your level I'd just recommend to memorize that to solve sin(A) = x you can just apply inverse sin
or cos(A) = x inverse cos etc.
vast shale
ah ok
whole oasis
I mean, your question doesn't require any specific knowledge of inverse trig functions
vast shale
yeah its pretty basic
whole oasis
you're just supposed to put it into calculator and read the answer
so don't worry about it
whole oasis
what's the obstacle?
you've already calculated your bounds, you have the functions
aaa, sorry
yeah it would be different
no, formula is basically same, but you would have to do x = f(y) instead of y = f(x)
no, you should do x = f(y)
and then use:
$$V=\pi \int\limits^{b}_{a} x^2 \dd{y}$$
twin meteorBOT
Modus
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humble linden
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dapper lichen
Just double checking to see if this is correct
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Just double checking to see if this is correct
@dapper lichen Has your question been resolved?
dapper lichen
<@&286206848099549185>
full trout
Only $x = -3 + \sqrt{17}$ is the answer because $x = \sqrt{8 - 6x} \geq 0$, whereas $-3 - \sqrt{17} < 0$.
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PowerUp
dapper lichen
Only $x = -3 + \sqrt{17}$ is the answer because $x = \sqrt{8 - 6x} \geq 0$, wher...
So it’s both ? Or
full trout
No only $x = -3 + \sqrt{17}$ is the answer.
twin meteorBOT
PowerUp
dapper lichen
No only $x = -3 + \sqrt{17}$ is the answer.
Interesting okay, here’s what the work looked like for why I put two
full trout
The other solution $x = -3 - \sqrt{17}$ must be rejected because $x \geq 0$.
twin meteorBOT
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dapper lichen
Gotcha thx
full trout
Np
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hasty token
Find the square roots of
vocal sleetBOT
Find the square roots of
hasty token
$9e^{\frac{\pi}{3}i}$
twin meteorBOT
Kap
hasty token
Would you put this into the form a + bi
Then let (x + iy)^2 = that in a + bi form
And solve for X and y?
gaunt sparrow
What's preventing you from using exponents properties here?
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narrow forge
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narrow forge
can someone help me with this question pls
fervent wasp
What’s the question
fervent wasp
I see
elder scaffold
right, ur doing the auxillary angle method?
narrow forge
yes
elder scaffold
next step would be to find alpha
elder scaffold
wait how did u determine that triangle?
narrow forge
from cosa and sina
elder scaffold
which expansion did u use??
vocal sleetBOT
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sudden berry
2+2?
dark kiln
what do you mean
dark kiln
what do you mean
sudden berry
i need help with the problem plz
sly sierra
state your question
sudden berry
2+2
sly sierra
that is an expression, not a question
sudden berry
darn
sly sierra
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sudden berry
Yes
alpine perch
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surreal basin
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covert marten
can anyone do walkthough on the logic from tan3(10) to that complex
urban edge
tan triple angle identity
covert marten
tan triple angle identity
yeah figured that out. the logical explanation requires double angle knowledge so yeah
.close
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graceful echo
Not sure if it was already answered, but Ill give my feedback. Like 60% of the proof is just standard stuff, but in my opinion the way you finish it is confusing and hard to understand(it might be correct!), Im talking about the s’’ part. What I would do here is:
Im on my phone so for the sake of not rewriting stuff lets say () means: for all epsilon>0 exists x in A s.t s-epsilon M-eps<x
• Let M = supA
Suppose that () is not true, so there exists epsilon>0 s.t for all x in A x<=M-epsi. This contradicts the fact that M=supA, because by definition M is the smallest upper bound of A, so if it was true there would exist M’ s.t for all x in A x<M’. So (*) must be true.
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Not sure if it was already answered, but Ill give my feedback. Like 60% of the p...
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real path
Can anyone tell me how can I prove this?
vocal sleetBOT
Can anyone tell me how can I prove this?
graceful echo
Can anyone tell me how can I prove this?
I have a proof but Im not sure you are going to like it, it does not involve any numbers
graceful echo
hmm okay
real path
Thank you very much mate
graceful echo
Suppose you are given n letters „a” and n letters „b”. You want to find the number if distinct „words” of length 2n that you can create with them. There is exactly (2n)!/n!n! of them. This number must be divisible by 2, because for each word there is a „reversed” word, by that i mean:
We have word
aabbaa, the reversed word would be bbaabb.
So basically the total number of words must be even because you can kind of pair them together
graceful echo
However I guess the explanation of why there is 2n!/… words is needed
graceful echo
do you need it to be in notations only?
graceful echo
I think the symbolic solution wont habe much in common with mine
mine is pretty exotic
real path
If it works it works
graceful echo
but if i were trying to prove it i guess id divide numerator and denominator by n!
and start from there
graceful echo
no worries
real path
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stoic citrus
how to factorise 9x^2+6xy+y^2
using identities
vocal sleetBOT
how to factorise 9x^2+6xy+y^2
using identities
candid kettle
this is a stats question but i confuse about the calculus part
vocal sleetBOT
this is a stats question but i confuse about the calculus part
lucid crypt
what is the definition of a pdf?
candid kettle
so in order to prove g(x) is a valid pdf we need to integrate it from -inf to inf. Then we sub u = F(x) and du = f(x) dx then the limit of integration changed because the lim x-> - inf F(x) = 0 and Lim x-> inf F(x) = 1.
lucid crypt
yep
candid kettle
i dont understand why the limit of integration changed
lucid crypt
that is standard procedure when doing u sub
when you go from x to u, you're essentially scaling your axes, so the limits of integration will change with respect to that
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cerulean spear
Solve this guys!
hushed pewter
Solve this guys!
!noans
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Solve this guys!
The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.
hushed pewter
Solve this guys!
Stay in one channel please. Are you done in #help-1?
cerulean spear
Stay in one channel please. Are you done in <#269573202018041856>?
I'm done with that channel
hushed pewter
Solve this guys!
!status
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1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
1
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knotty lynx
Solve this guys!
Let CG be $b^2$ and DC be $a^2$ so that $BC = AB = ka$ and $FG = EF = kb$
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StrangeQuarkAL
knotty lynx
Using the fact that both squares must touch as in the diagram, find an equation relating $b$ , $a$ and $k$
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StrangeQuarkAL
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eager zenith
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eager zenith
can someone explain how to find n
lime basin
it says 10 years
eager zenith
because each time i do these questions their explanations is either because its compounded monthly so n=2 for example
lime basin
as the time
lime basin
yes, because it is compounded monthly
eager zenith
ohhh
lime basin
no problem
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little adder
hi
little adder
An air ambulance is travelling from Barrie to Toronto. Toronto is located 90 km [S5°E] of Barrie. If the wind is blowing from the South with a velocity of 62 km/h, and the plane's air speed is 375 km/h, what direction must the pilot fly to make it to Toronto?
@stone gazelle
Please help
stone gazelle
<@301654480804642816>
I’m a bit busy right now but i’ll be free to help you in about an hour if no one else gets to you first
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<@&286206848099549185>
little adder
I dont have a hour to wait tho
@stone gazelle I know you are busy but I cant wait more and i really need your help since no one else is helping me
stone gazelle
What have you done so far
stone gazelle
Hmm
little adder
I think I did it wrong since the answer is S 5 E
I found the answer online but no steps
stone gazelle
Hang on im thinking
I got S 4.17° E
But the wording has confused me a bit
Specifically the wind direction
little adder
Can you show me how you got S 4.17 E
stone gazelle
It says ‘wind from south’ so I take that to mean the wind direction is going North
little adder
Yes most likely
little adder
Yes
stone gazelle
I honestly really dislike these questions
stone gazelle
Right well hope that helps
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vital wave
#6 wtf is this
vocal sleetBOT
#6 wtf is this
solar barn
probably L'Hopitals rule.
lucid bane
note that f(2)=0 and g(2)=0 and their limits at 2 are also 0
so you have a 0/0 limit, you can use lhopitals rule
vocal sleetBOT
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vital wave
so you have a 0/0 limit, you can use lhopitals rule
Yea but on what equation
Oooo
It’s f’/g’
Wait but it doesn’t have the equations of f and g
vital wave
probably L'Hopitals rule.
How do I find the equations
knotty lynx
What's the relationship between the gradient of the tangent line and the gradient of the curve at a given point?
vital wave
I forgot
vital wave
What's the relationship between the gradient of the tangent line and the gradien...
What is a gradient again
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keen osprey
Is my answer correct?
vocal sleetBOT
Is my answer correct?
vocal sleetBOT
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twin meteorBOT
drifting scroll
Why did you use 1.09361 and not 1.0936 or 1.094 or 1.09?
blissful sentinel
To convert from meters to yards
blissful sentinel
It looks good!
blissful sentinel
sure
drifting scroll
Looks like way too many digits than needed
blissful sentinel
xD
keen osprey
Looks like **way** too many digits than needed
I hope it’s the answer tho.
drifting scroll
HAHA LOL XDXD 69420
keen osprey
I just round at the end
blissful sentinel
I just round at the end
Yeah that seems reasonable to me
keen osprey
Yippie
I may or may have not got this one wrong.
But it’s ok that’s how u learn, I fix it easy.
blissful sentinel
So, the top of the trough is not covered, right?
Kinda hard to tell from the image, but it looks like the trough only has the two faces and then the bottom two sides
keen osprey
Trough is open at top
it’s basically one of those things you fill up with water.
So one side is just open
.close
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keen osprey
Solved
blissful sentinel
(the formula shouldn't be (a+b+c) * d then)
(that would assume all three sides are present)
keen osprey
(that would assume all three sides are present)
I drew it wrong
This is the one my friend helped me with.
Either it’s wrong or it’s assuming the trough isn’t fully blocked off.
So you aren’t using a b c x d
blissful sentinel
.reopen
vocal sleetBOT
✅
blissful sentinel
you're writing equals signs where it doesn't make sense, but other than that, the method looks good
Like here for example idk why you wrote an equals sign there
keen osprey
I see
vocal sleetBOT
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vast shale
how do I find the next number of squares in the circle? the "quadrant" length is always 2 and the diameter of the squares is increasing by 2
vocal sleetBOT
how do I find the next number of squares in the circle? the "quadrant" length is...
vast shale
the decimal stuff isn't important, it's just how much of the circle is filled
vocal sleetBOT
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vast shale
I probably used the wrong word, like the length of the square starts with 2, then it goes to 6, then 8
I think the radius of the circle is sqrt(n^2+1)
vast shale
I couldn't find it on oeis either lol, it does show up for when the "width" touching the circle is 1 instead of 2
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tawny nacelle
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https://discord.com/channels/268882317391429632/1260424130822541403/126045904571...
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waxen hawk
Q: How many ways of arrangement are there for a six-digit number that consists of a group of numbers 1,2,3,4,5,6, given that number 1 has to be set before 2 and number 3 has to be set before 5 and 6.
vocal sleetBOT
Q: How many ways of arrangement are there for a six-digit number that consists o...
waxen hawk
This is a self-made question
I would like to know the answer.
<@&286206848099549185>
nocturne mantle
Q: How many ways of arrangement are there for a six-digit number that consists o...
Hmmm
I think you may use combinatorics
waxen hawk
I think you may use combinatorics
I got 120
nocturne mantle
Wait
waxen hawk
Wait
NYPD
I almost lose my patience, I got PTSD waiting for your answer
it might be due to my ADHD
glossy tinsel
Q: How many ways of arrangement are there for a six-digit number that consists o...
what do you mean by "consists of a group of numbers 1,2,3,4,5,6"? Is it a permutation of 1,2,3,4,5,6?
waxen hawk
yes, it is a permutation of these group of numbers under some circumstances
glossy tinsel
If so the answer I got is 120
waxen hawk
If so the answer I got is 120
NYPD
waxen hawk
If so the answer I got is 120
you must be really smart then
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vast shale
vital loom
vocal sleetBOT
vital loom
ahh
xd
so I don't get the shape or the intercept
also why is this x = 3
and not x less than 3
wait no i think i got that
its cause thats where y = 0
but the graph dosen't go below the x axis after that
vital loom
Like
I don't even know what k is
so how am I supposed to know how much the graphs been shifted by in the y coordinate
vital loom
oh right yeah ofc
thanks
but also the way they draw the graph like
how do they know it goes above the x axis
in the left curve
oh wait cause k
has to be greater than 4 right
so it gets shifted up by at least 4
oak magnet
limit calculus
4/x goes to -inf for 3.99999 (you see)
and 4/x goes to +inf for 4.00000001 (you see)
vital loom
so it gets shifted up by at least 4
can i just think of it as this tho xd
think I'll just stick with that
thanks
.close
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oak magnet
wait it's not tottaly about limit
oak magnet
ye
oak magnet
all good for this ?
vital loom
oh yh thanks
I think next time I'll highlight the graph for where the graph is less than or equal to 0
acc idk if im allowed to in exam lol
but yh no think i got it
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somber quarry
help me with this What term is the number 6 in the sequence 84, 78, 72,...?
hardy vector
This is an arithmetic sequence
somber quarry
yep
hardy vector
First you need to know how an arithmetic sequence is defined. a_n = a + (n-1)d
Once you find a, d just sub n = 6
oak magnet
oh nvm its given
what is d so ?
somber quarry
d is 6
oak magnet
no
oak magnet
so -6 ?
somber quarry
oh yeaaa
oak magnet
so what is a6 ?
somber quarry
wait whattt
somber quarry
6-1?
oak magnet
cuz you want the 6th term ?
hardy vector
You seem really confused
somber quarry
xdd
somber quarry
alright man thanks\
oak magnet
np
hardy vector
alright man thanks\
!done
vocal sleetBOT
alright man thanks\
If you are done with this channel, please mark your problem as solved by typing .close
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.close
vast shale
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vast shale
the sin theta in this ain't a function right?
this is confusing
function suppose to give single value
left tendon
function suppose to give single value
It does
Depending on the quadrant
You mean de +- in the sqrt right?
mild flower
try substituting in some angles, like theta = π/6 or 7π/6
vast shale
You mean de +- in the sqrt right?
yes
left tendon
What you are doing is taking the sqrt at both sides. $\sqrt{x^2}=|x|$
twin meteorBOT
Ij37
left tendon
In the case of the polynomial example both signs are valid but in the case of sin, you have to determine the sign by the quadrant
vast shale
In the case of the polynomial example both signs are valid but in the case of si...
so its more of
piece wise
function?
left tendon
piece wise
Yes
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pine temple
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drifting scroll
Why does this work, and how do I extend it to numbers other than six digit numbers?
vocal sleetBOT
Why does [this](https://worldmentalcalculation.com/mental-square-roots-algorithm...
@drifting scroll Has your question been resolved?
drifting scroll
<@&286206848099549185>
drifting scroll
Why does [this](https://worldmentalcalculation.com/mental-square-roots-algorithm...
^^
vocal sleetBOT
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drifting scroll
start a new channel
nobody will answer your question if you don't
<@&286206848099549185>
Why does this work, and how do I extend it to numbers other than six digit numbers?
drifting scroll
<@&286206848099549185>
vocal sleetBOT
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drifting scroll
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drifting scroll
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spiral turtle
@drifting scroll you can use 316^2 = 99856 and 999^2 = 998001 to do largely the same thing with larger numbers.
The method seems to just be the old hand method of calculating a square root
It works somewhat like long division
Let's walk through an example.
drifting scroll
sure
spiral turtle
Let's do √12345
So we want to find x such that x^2 = 12345
We break the number up into hundreds: 1 23 45 and consider just the largest place. So √1 is 1, so we put 1 on the top in the hundreds place (because sqrt roughly halves the number of digits in your value)
So we have (100 + y)^2 = 12345 or 200y + y^2 = 2345
We want to find the largest value possible where this isn't exceeded. Mechanically, we double our running root (1 -> 2) then put a blank next to it (2_) and then try to find the largest n such that (20 + n) * n is not bigger than 23. The largest number is 1. So that's the next digit. 23 - 21 = 2, so our next value is 245 we double our root again and write a blank, 11 -> 22_ and find that 221 * 1 is the largest n again. So we get 245 - 221 = 24
The next value we bring down a pair of zeroes 2400 and we double the root and blank 111 -> 222_ finding again that 1 is the largest value and wow, I really should have picked a different number for the example
@drifting scroll
I have √12345 ≈ 111.1
drifting scroll
ok
We want to find the largest value possible where this isn't exceeded. Mechanically, we double our running root (1 -> 2) then put a blank next to it (2_) and then try to find the largest n such that (20 + n) * n is not bigger than 23. The largest number is 1. So that's the next digit. 23 - 21 = 2, so our next value is 245 we double our root again and write a blank, 11 -> 22_ and find that 221 * 1 is the largest n again. So we get 245 - 221 = 24: What blanks
spiral turtle
Now let's look at this from a digits perspective to see why this works:
We have a number written in digits as [ABCD] is equal to (A * 1000 + B * 100 + C * 10 + D * 1)
So if we have ([ABCD])^2 we get A^2 * 10^6 + 2AB * 10^5 + (B^2 + 2AC) * 10^4 + (2AD + 2BC) * 10^3 + (C^2 + 2BD) * 10^2 + (2CD) * 10 + D^2
Notice how each step we take peels off two of these
We find A first by examining the top pair of digits this gives us A^2, which we subtract off of the top: A^2 * 10^6
Next we have the second pair, we double the running root ([A000] * 2) and use a blank to find (2 * [AB00] * B) which turns into (2AB * 10 + B^2) we're left with the 2AC leftover which we take care of next.
2AB * 10^5 + (B^2 + 2AC) * 10^4
I should write numbers in []s to indicate that I'm treating the variables as digits, one second
ocean pendant
Im still having problems with this question because I cannot seem to find how many combinations/ways of stringing together 6 and 7 Cs (in pairs and in solid chains of Cs). Please help by explaining it in a straight and clear way if possible 🙏
vocal sleetBOT
Im still having problems with this question because I cannot seem to find how ma...
ocean pendant
Especially with finding how many ways to pair 6 cs where there are three pairs of "CC"
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left cosmos
Im still having problems with this question because I cannot seem to find how ma...
Bro just imagine C s as one latter
And then creat 8,7,6,5,4,3,2,1 sides strings with A s and B s
Like 1 sized will be all C s
2 sized will be
ACCccc....
Bccccc....
CccccccA
CccccccB
And so on
1-1
2-4
3-3 * (2^2)=12
4-4 * (3^3)
5-5 * (4^4)
6-6 * (5^5)
7-7 * (6^6)
8- 8*(7^7)
In () are A and B permutations
And then sum em up
And that's it
And outside ()-s are C chars positions
And don't forget that U mustnt include only A and B strings
@ocean pendant
next bay
And don't forget that U mustnt include only A and B strings
Why the actuall hell is that under your name
ocean pendant
1-1
2-4
3-3 * (2^2)=12
4-4 * (3^3)
5-5 * (4^4)
6-6 * (5^5)
7-7 * (6^6)
8- 8*(7^7...
how are you getting this reccurence pattern?
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sharp comet
vocal sleetBOT
sharp comet
can someone check
drifting terrace
I think it’s right
drifting terrace
left hand side is missing a pi I think but maybe you know that
drifting terrace
just move everything that isn’t r to the other side
vast shale
first cancel pi on both sides
sharp comet
sharp comet
just move everything that isn’t r to the other side
ok
how
should I
do
10/3 first
and move that over
just leaving the base
drifting terrace
for example you can multiply both sides by 3 to cancel out the 1/3
sharp comet
ok
sharp comet
sharp comet
then dividing by 10 on both sides to cancel out the 10
how do I divided 90pi/10
is it just 90/10
or no
vast shale
it is in multi plication so (90/10)*pi
sharp comet
ok
drifting terrace
yeah what they said
vast shale
yes
sharp comet
vast shale
now divide pi on both sides
sharp comet
vast shale
wrong
vast shale
yes
vast shale
welcome,close the chat
sharp comet
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sudden dirge
im doing system of equations : these are the three equations
vocal sleetBOT
im doing system of equations : these are the three equations
sudden dirge
i solved for x in the first equation and got
then pluged that in the second equation and got
but when i pluged x in the third equation i got
how do i get what y is equal to ?
sudden dirge
ueah but for the third equation.
flint idol
solve for z and substitute that in
sudden dirge
ok
flint idol
i meant like substituting the y equation into that
sudden dirge
oh, so for the third equation i substitute y instead of x?
flint idol
but when i pluged x in the third equation i got
okay so like keep what you have up here
flint idol
then pluged that in the second equation and got
but use this equation to make it one variable
sudden dirge
thanks
flint idol
yw!
sudden dirge
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sharp comet
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tranquil trellis
I don't think 2 is correct
drifting terrace
you did 48/3 instead of 48*3
sharp comet
48*3
then
I did
16/4
oops
no
wait how did I get 16
I multiplied
ok
so
it is suppose to be
r=6
tranquil trellis
yes
sharp comet
ok
sharp comet
yes
can I check this problem
I think I did it correctly
this problem I got wrong
last time
because I forgot that triangle pyramid is 1/3 of a triangle prism
so here if triangular pyramid is 237
then 237*#
237*3
is 711
so the volume of the triangular prism is 711 cm^3
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idle nacelle
How would you graph this equation?
vocal sleetBOT
How would you graph this equation?
sage hedge
somewhat cooking. make sure you have the number of x's correct when you expand your 2nd equation
idle nacelle
the number of xs…?
sage hedge
fixed
sage hedge
what’s the next move here
(x-6)^2 = x^2-12x+ 36
wet valve
This is almost right, maybe review completing the square
idle nacelle
How did we get there
sage hedge
you have too many x's. Try completing the square or choosing a number other than -6
idle nacelle
Oh pause I can do that
sage hedge
(x-6)(x-6) -> distribute
sacred plume
How would you graph this equation?
i would group x and y terms and then complete the square
strong kayak
can you solvsolvee for x, yy
sage hedge
can you solvsolvee for x, yy
idle nacelle
(x-6)^2 = x^2-12x+ 36
Ok I see so them do k do the same with the y?
sage hedge
you still want the circle equation you have here
idle nacelle
So what’s a girl to do
sage hedge
so it needs to be of the form (x-something)^2 + (y-something)^2 = something
completing the square
if we're just working with x:
- you have an x^2 - 6x
- (x-something)^2 = x^2 - 2x*something + something^2
idle nacelle
Tears are threatening to fall from my eyes
sage hedge
can you figure out what the "something" is
have you not done completing the square before?
idle nacelle
I might have
A year or two ago
I’m a grind and perform kind of a girl
And then it disappears
Like smoke in the wind
sage hedge
I might have
https://www.mathsisfun.com/algebra/completing-square.html
read this. Just the first section of "completing the square"
sage hedge
I’m a grind and perform kind of a girl
can't really do math like that. Have a weak foundation and the eiffel tower comes crashing down
idle nacelle
I was never the Eiffel Tower
I’m already crumbling
this is my demise
I’ve met my fateful end
sage hedge
ur fine. light work. just read up a bit
idle nacelle
So
idle nacelle
But there’s 3 of them can I just like discard the one
sage hedge
But there’s 3 of them can I just like discard the one
3 of what
you have a x(x-3)-3(x-3). You factor out a (x-3) and you get (x-3)(x-3)
idle nacelle
somewhat cooking. make sure you have the number of x's correct when you expand y...
I was not somewhat cooking why did you lie
sage hedge
yeah that's right. You can probably figure out the rest
idle nacelle
Wait so it’s this one?
sage hedge
look at your circle equation form again
sage hedge
This is your form: (x-a)^2 + (y-b)^2 = c^2
This circle has a center of (a,b) with radius c.
If you have something like this: (x+a)^2 + (y-b)^2 = c^2
This circle has a center of (-a,b) with radius c.
Hopefully that helps
idle nacelle
So the center is at 3,-1
sage hedge
So the center is at 3,-1
yeah
idle nacelle
SO ITS C
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distant echo
hello, i need help with this question. i don’t know where to start, and just struggling in general.
vocal sleetBOT
hello, i need help with this question. i don’t know where to start, and just str...
urban edge
are you familiar with SOHCAHTOA?
distant echo
no i have never heard of that
urban edge
what do you know about sine cosine and tangent?
distant echo
i know that each one uses ratios like sine could be the opposite side of the hypotenuse something like that.
urban edge
ok, so SOHCAHTOA is a memory trick
sine = opposite/hypotenuse
cosine = adjacent/hypotenuse
tangent = opposite/adjacent
distant echo
oh yes yes i do remember that
urban edge
do you know which ones are opposite and hypotenuse to find sin(O)?
distant echo
would the hypotenuse be square root of 41 and the opposite 5?
urban edge
hypotenuse is correct
remember that opposite is literally on the opposite side of the angle
adjacent means next to
ycan you see how the side with 5 is touching O?
distant echo
oh yes
urban edge
by touching i mean next to
urban edge
so you want to other leg
distant echo
okay square root of 41 over 4? Do i divide
urban edge
what is opp?
distant echo
4
urban edge
what is hyp?
urban edge
hyp is sqrt41
distant echo
yes
urban edge
so what is opp/hyp?
distant echo
sine
urban edge
yes, but what is the value of it?
distant echo
25
distant echo
41 i can’t simplify it cs it can’t
opp/hyp how do i figure out the value? i got the numbers now what do i do from opp/hyp
urban edge
opp/hyp just equals 4/sqrt41
if you look back at how you jeed to answer the problem, it is in the right form
distant echo
so the answer would have been 4/sqrt41
urban edge
yes
urban edge
hello, i need help with this question. i don’t know where to start, and just str...
you would put 4 / sqrt 41
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tight heath
been wondering how to find the shaded area. there are two semicircles and one rectangle
vocal sleetBOT
been wondering how to find the shaded area. there are two semicircles and one re...
covert python
semicircles?
urban edge
you need integration to find the area on the left
tight heath
im trying to find a youtube video on this particular question
yeah nah im confronting my dad why he gave me this
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vast shale
Let f: R -> R be defined by f(x) = sin (x^3). Then f is continuous but not uniformly continuous. ** [True/False]**
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Let f: R -> R be defined by f(x) = sin (x^3). Then f is continuous but not unifo...
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@vast shale Has your question been resolved?
gaunt sparrow
I think you can check whether the derivative is bounded
There are a few theorems that involve that at least
You might want to check into it
vocal sleetBOT
@vast shale Has your question been resolved?
brisk moss
let n be a positive integer. how many n length strings from the dictionary {a,b} (e.g. aaababa is a 7 length string) are there with all of these properties:
- doesn't start with ba
- doesn't end with ab
- doesn't contain aba
vocal sleetBOT
let n be a positive integer. how many n length strings from the dictionary {a,b}...
brisk moss
my first thought was recursion which might work but i'd rather not if there is something better
oh oh maybe stars and bars
river kettle
fmtb
brisk moss
this is a serious channel
only people who have contributed significant math to it are allowed to meme
which is currently nobody
peak arrow
Use PIE
Condition an and b are trivial, so it remains to simply solve for codntion 3.
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vast shale
Hey
vast shale
Can anyone help me in studying calculus?
brisk moss
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@vast shale Has your question been resolved?
fervent wasp
Can anyone help me in studying calculus?
I suppose no one here could guide you step by step
However, we can assist you with solving the question 🙂
vast shale
vocal sleetBOT
vast shale
So in the first i found the derivatives separately and then multiply. But the yt guy says find derivate of the first multiply woth other and find derivate of the second and mulitply with the first. Sum is the answear.
normal ridge
yup that’s called the product rule
oak magnet
So in the first i found the derivatives separately and then multiply. But the yt...
it's the formula
oak magnet
So in the first i found the derivatives separately and then multiply. But the yt...
if you want you can develop the expression and then derivate but it will not work in many cases
vast shale
Can somone define better to me what does these really mean : []*[]
oak magnet
it's brackets
oak magnet
no
vast shale
Why than?
oak magnet
Why than?
you can check demos online
but the formula is uv = u'v + uv'
with u and v both derivable fonctions
oak magnet
Most of them doesent tell why..
ima found this for ya
what do you prefer : hardcore algebra or visual ?
vast shale
Idk what are these?
oak magnet
oak magnet
Startong new at derivates
actually the difinition of derivation is based on limit
so every proof are based on those
vast shale
So tell me the order of university calculus
normal ridge
you start with Precalculus, where limits are covered
it’s a prerequisite course to calculus
vast shale
So limits--derivates--antiderivates--integrals?
normal ridge
antiderivatives = integrals
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sick venture
hey in the quadratic formula if our b is a negative number should i put him in the formula as a negative or positive? like X*X - 2X+1=0 , is b = 2 or b = -2
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hey in the quadratic formula if our b is a negative number should i put him in t...
worthy citrus
It's -2
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vocal niche
I haven't encountered a similar question / similar form before. How do I go about solving it?
vocal sleetBOT
I haven't encountered a similar question / similar form before. How do I go abou...
bold hound
you are given a point
points are given in the form (x, y)
so in our case, the point has x=-3
to find y, we can just substitute that x value into the parabola equation
note that the result will still depend on h and k, nothing we can do about that
and since y=n, the alue for y will be the value for n
sour ermine
and (2,0) is the vertex in the form of (h,k)
bold hound
oh i forgot about that
yes, forget what i said
first find h and k
then do what i said before
vocal niche
and (2,0) is the vertex in the form of (h,k)
Is this some sort of rule?
I've honestly never encountered that before
bold hound
we see the vertex in the graph
and if we start with a parabola x^2
shift to the right by h: (x-h)^2
shift up by k: (x-h)^2+k
vocal niche
and if we start with a parabola x^2
shift to the right by h: (x-h)^2
shift up by...
What if you wanan shift left and down?
You change signs up?
bold hound
shift up: +k
shift down by k: -k
vocal niche
and for left?
bold hound
+h instead of -
vocal niche
Ah thank you. This feels like something I vageuly studied in year 7 or something lol
never encountered it since
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vast shale
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vast shale
x1 element of (0,1) be real number between 0 and 1. For n> 1, define x(n+1) = xn -( xn )^ n+1. Then limit xn exist.
hybrid flicker
!status
vocal sleetBOT
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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@vast shale Has your question been resolved?
tawny hollow
maybe a start here would be to try and show it's a decreasing sequence
and positive
tawny hollow
write up the goal and definition
if you can show its positive, the decreasing part almost falls out for free
vast shale
Okay I am trying
vast shale
if you can show its positive, the decreasing part almost falls out for free
Thanks
tawny hollow
did you manage to do it?
tawny hollow
good! now the convergence follows from the monotone convergence theorem
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vast shale
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vast shale
[True/ False]
vocal sleetBOT
@vast shale Has your question been resolved?
lone linden
Can’t you just let $x_i=0$ or am I high
twin meteorBOT
Civil Service Pigeon
vocal sleetBOT
@vast shale Has your question been resolved?
vast shale
Can’t you just let $x_i=0$ or am I high
It is for all possible xi with this condition
tawny hollow
It is for all possible xi with this condition
I think they mean it’s a counter example, if every x_i is just zero
And the sequence (a_i) is unbounded
Then the conditions still hold
So the statement must be false
vast shale
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wise oriole
Where is my mistake?
10=0.0048(x-50)^2+6
4=0.0048(x^2+2500)
4=(0.0048x^2+12)
-8=0.0048x^2
1666.67=x^2
40.8=x
vocal sleetBOT
Where is my mistake?
10=0.0048(x-50)^2+6
4=0.0048(x^2+2500)
4=(0.0048x^2+12)
-8=...
outer warren
first step, you didn't square properly
wise oriole
Can you elaborate?
outer warren
$(a-b)^2 \redneq a^2 + b^2 \
(a+b)^2 \redneq a^2 + b^2$
twin meteorBOT
ℝαμΩℕωⅤ
wise oriole
so its supposed to be x^2+2500?
wise oriole
my fault Im getting confused here
outer warren
when squaring a sum/difference, you don't square each term in that sum individually
ornate cobalt
wise oriole
Whats this for^