it seems useful!
#help-10
worthy musk
yeah, idk, I just see those snippets and think they are veyr useful and I wanna see ALL of them ig
polar fossil
,tex .algebra lesson
warm shaleBOT
hayley!
polar fossil
that one's a bit lengthy haha
polar fossil
yeah, idk, I just see those snippets and think they are veyr useful and I wanna ...
set it up for yourself and then you can test it
worthy musk
alr thx
I just wanted to make sure im not missing out on any lol
they're too useful
I got the question done btw
summer pond
there is a machine that has input and output:
Every even number put in will be divided by 2. Every odd will -1.
Suppose that 5 is a 4 step number -> 5-4-2-1-0
How many 10 step numbers are there?
obtuse pebbleBOT
there is a machine that has input and output:
Every even number put in will be d...
summer pond
how can I work this out without doing manually? Any tips?
compact shadow
10 steps to reach zero you mean?
Can’t think of any smart solutions also not needed. Just for any odd number n, draw an arrow to 2n. For a even number m, draw two arrows one pointing to 2m, one pointing to m+1. Write down all numbers that passed 10 arrows
summer pond
.reopen
obtuse pebbleBOT
✅
near marsh
<@&286206848099549185>
wintry swift
.close
cinder ridge
obtuse pebbleBOT
late stump
its an identity
cinder ridge
its an identity
sin(0)/0 is undefined no?
late stump
well identity loosely speaking
cinder ridge
wdym
late stump
sin(0)/0 is undefined no?
yes, but the limit of sinx/x as x>0 is not undefined.
cinder ridge
yes, but the limit of sinx/x as x>0 is not undefined.
but why... 1
like how do you get the identity
late stump
there are proofs available online you can take a look at
https://www.khanacademy.org/math/ap-calculus-ab/ab-limits-new/ab-1-8/v/sinx-over-x-as-x-approaches-0
it uses squeeze theorem
late stump
yes, the video in khan should cover it
cinder ridge
like is it possible to use the precise definition of a limit, create a table, and test out 0- and 0+ values
and see what it approaches
late stump
precise definition of a limit
as in the epsilon delta definition?
cinder ridge
> precise definition of a limit
as in the epsilon delta definition?
mhm
well i mean
no
well like
nono
it's the theorem that states that lim of f(x) as x approaches A is = L is and only if limt of f(x) as x approaches A from both the negative and positive side is L
according to that, i know some limits can be found using a table, since you test out values on the left or right side of the limit and see what i approaches
late stump
oh, you want to look at the left and right sided limits
cinder ridge
im assuming i CAN use it for this one cuz i graphed it in desmos
cinder ridge
oh, you want to look at the left and right sided limits
well can we?
cuz in cases with no calculators, ya know
or no grpahing calculators at least
late stump
you can create a table and test out numbers around x=0
im assuming thats what you mean?
cinder ridge
you can create a table and test out numbers around x=0
mhm
late stump
yeah, you can try out numbers like 1, and then 0.5, and get smaller and smaller, as in approximating the value of a right sided limit
and then do -1, -0.5, and get larger as the num approaches 0
stoic elm
The top and the bottom end of a wiper blade are 12” and 34” respectively from the pivot point on the windshield. If the wiper sweeps an angle of 140, what is the difference in arc length swept out by the two ends?
obtuse pebbleBOT
The top and the bottom end of a wiper blade are 12” and 34” respectively from th...
obtuse pebbleBOT
@stoic elm Has your question been resolved?
ripe quest
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
brisk arrow
how do we call ln(a)
obtuse pebbleBOT
how do we call ln(a)
royal basin
do you mean how to read it out?
"natural logarithm of a"
you can shorten "logarithm" to "log" if you want
kind hawk
"el en of a"
vocal shell
"Log e of a"
versed stratus
lawn of a is also common where I'm from
frank monolith
is it?
versed stratus
at my school ,it was
obtuse pebbleBOT
@brisk arrow Has your question been resolved?
coral sable
lawn of a is also common where I'm from
Oh like lun
merry moth
if w varies directly as the product of uv^3 and inversely as x^2and w +30, when u=6, v=2, x=8. Find the value of w when x = 3, u = 5, v = 8 and the function of w
obtuse pebbleBOT
if w varies directly as the product of uv^3 and inversely as x^2and w +30, when ...
bitter crater
if w varies directly as the product of uv^3 and inversely as x^2and w +30, when ...
Is that supposed to be w=30?
merry moth
yes
bitter crater
Well from your question
W ∝ uv^3/x^2
Now in order to remove the proportionality you can add a constant k such that
W = k(uv^3/x^2)
And you can calculate the constant from the values given in the question
obtuse pebbleBOT
@merry moth Has your question been resolved?
obtuse pebbleBOT
@merry moth Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
gaunt walrus
.
lime mural
Where did I go wrong here?
obtuse pebbleBOT
Where did I go wrong here?
lime mural
what about the ^2?
frank monolith
you did that right
lime mural
isn't 2sin(u)(pi) already y'?
gentle atlas
you do sin(πx)^2 ==> 2sin(πx) ==> 2sin(πx)cos(πx) ==> 2πsin(πx)cos(πx)
warm shaleBOT
ren
gentle atlas
you forgot to differentiate sin(πx)
lime mural
you do sin(πx)^2 ==> 2sin(πx) ==> 2sin(πx)cos(πx) ==> 2πsin(πx)cos(πx)
i thought pi x was the inner function?
gentle atlas
the outermost function is ^2 and then there is sin() function inside then inside that is the πx
gentle atlas
you also have to multiply with π
lime mural
it's like chain rule inside a chain rule?
gentle atlas
it's like chain rule inside a chain rule?
yes
the chain can be as long as many steps
lime mural
What do you call that? i wanna try to practice solving them
frank monolith
lime mural
or their just really chain rule?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
last reef
can someone tell me why this is wrong?
obtuse pebbleBOT
can someone tell me why this is wrong?
last reef
the answer is supposed to be (7 +- √33)/4
royal basin
what happened from line 3 to line 4?
last reef
the answer is supposed to be (7 +- √33)/4
last reef
ohhhh is that cuz the base is different here?
last reef
ohh ye ye i get it now
thanks!
royal basin
my question went unanswered.
tacit scarab
I think they multiplied by 2a
last reef
yea
frank monolith
np
strong sun
How do you do part A of this question?
obtuse pebbleBOT
How do you do part A of this question?
tardy epoch
How do you do part A of this question?
Find the radius as a function of height
strong sun
How would you do that?
strong sun
Do you mind sending a worked solution potentially? This geometry stuff is always the weakest but the second part which is the related rate of change is a breeze
strong sun
Problem is I was never taught it was removed because of COVID
obtuse pebbleBOT
harsh remnant
I tried to solve using ratios of the area and one length of the side
In which I set up a ratio like this
21:7 = 56:x
21x = 392
It gives x as 56/3
And that's impossible
Not sure what to do now
crude coral
Isnt that pretty simple?
harsh remnant
Isnt that pretty simple?
Tell me what to do next then
crude coral
Area of walkway is 56m sq
And the area of garden is 21m sq
So the total area of the shape becomes 77 m sq
harsh remnant
Ohhh
crude coral
Oh wait no
crude coral
Im being confused but if that helped you , ur welcome
harsh remnant
Yeah that helped
crude coral
Yeah prob take ratios of that area so
21 : 3 = 77 : x
harsh remnant
I just realized the walkway was just only a stroke of the area of the garden
Thanks
.close
humble umbra
obtuse pebbleBOT
humble umbra
So, isn't the integral:
def integral from 3 to 0 (2y-y^2) - (y^2-4y^6) dy ?
teal turret
It’s not 4y^6
spice citrus
The 6 is part of the number line
plucky rivet
So i tried to prove this by contrapositive, assuming that 4 does NOT divide (x²-5) and tried to show that 2 does NOT divide (x²-5) as well, so since 4 cant divide that expression,
I considered the cases where
i) x²-5 =4p+1 (for integer p)
ii) x²-5 = 4p+2 (where p is an integer)
iii) x²-5= 4p+3 ( for some integer p)
Then when i came to ii) case i realized that 2 in fact would divide it if x²-5 = 4p+2= 2(2p+1)
Then i noticed, 2 and 4 can only divide x²-5 when x is odd, so i just gave up on this proof and started a new one:
Making a lemma which proved that x is odd if 2 divides (x²-5) (by contrapositive). Then i succesfully continued the proof using that.
My question here is:
Why did contrapositive fail me on my first attempt, and how can i catch it instantly next time?
obtuse pebbleBOT
So i tried to prove this by contrapositive, assuming that 4 does NOT divide (x²-...
compact shadow
2|x^2-5 gives you 2|x^2-5+2(2)=x^2-1
So 2|(x+1)(x-1)
So 4|(x+1)(x-1)
4| x^2-1
So 4| x^2-1-4=x^2-5
Done
obtuse pebbleBOT
@plucky rivet Has your question been resolved?
plucky rivet
I dont know modular arithmetic so not sure if i can use that, but it makes sense since if a|b and a|c then a|(b+c)
I didnt ask for another solution though, i asked why contrapositive fails on divisibility but i kinda saw that n was restricted to be odd after making up the lemma, hence why my first proof hard failed
plucky rivet
4| x^2-1
I dont get the 4|(x+1)(x-1) step, how do we achieve that
Is it like a lemma or something
slender nest
It's quite hard to use contrapositive here, and why would you?
4 is a multiple of 2, that's solves everything
obtuse pebbleBOT
@plucky rivet Has your question been resolved?
compact shadow
2|(x-1)(x+1)
Meaning at least one of x-1 x+1 is even, then they both are even
Because their difference is 2
Therefore 4|(x-1)(x+1)
Then rest is clear in my answer
@plucky rivet
obtuse pebbleBOT
plucky rivet
i see
obtuse pebbleBOT
Available help channel!
tepid urchin
obtuse pebbleBOT
errant lark
What did you even do for v-substitution?
If you applied integration by parts, you haven't done it correctly at all.
tepid urchin
noice
viral blade
You did w*dv instead of w*v right
tepid urchin
for where
viral blade
w*dv - ...
viral blade
that seems to be the mistake
viral blade
ye np
tepid urchin
.close
obtuse pebbleBOT
viral blade
idk what the other guy was talking about
obtuse pebbleBOT
Available help channel!
fast dome
When you integrate questions like 1/(3x+5), the answer is ln(3x+5)/3 but when I integrate questions like 1/(3x^2 +5), why are answers in arctan correct instead of ln(3x^2+5)/6x
obtuse pebbleBOT
When you integrate questions like 1/(3x+5), the answer is ln(3x+5)/3 but when I ...
vast willow
because $\frac{d(arctanx)}{dx}=\frac{1}{x^2+1}$
warm shaleBOT
calculus is fun
vast willow
and $\frac{d}{dx}{lnx}=\frac{1}{x}$
warm shaleBOT
calculus is fun
fast dome
Yes I know that but why can’t I use the natural log answer? Is it coz the denominator is a higher power and ln only applies to linear equations?
vast willow
now try differentiating $ln(3x^2+5)$ wrt $x$
warm shaleBOT
calculus is fun
fast dome
6x/3x^2+5
vast willow
ok this doesnt seem like a correct answer
pulsar quarry
will x be there in the numerator?
vast willow
and if you want $\frac{ln(3x^2+5)}{6x}$ then try differentiating this wrt $x$
warm shaleBOT
calculus is fun
vast willow
this will also not give you $\frac{1}{3x^2+5}$
warm shaleBOT
calculus is fun
fast dome
Ohh
vast willow
,w differentiate \frac{ln(3x^2+5}{6x}
warm shaleBOT
vast willow
this is the result of differentiating
fast dome
Oh
vast willow
it is because you will always have to use chain rule and so on
so ln wont give you the desired answer
fast dome
So the natural log thing only works correctly for denominator with linear eq?
vast willow
or if you can perform a substitution
fast dome
I kind of get what ur saying, basically I can try integrating q and get ln answer but when I differentiate that I won’t get the original q
In that case even though it seems correct it’s not correct math
Thanks
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
hexed nest
how would I solve this
obtuse pebbleBOT
how would I solve this
frank monolith
just expand ()^2
burnt vale
(1+cotx)(1+cotx)
compact shadow
Just factor (1/sin^2) out
hexed nest
Just factor (1/sin^2) out
wait how did it turn into this
compact shadow
1+a/b=b/b+a/b=(a+b)/b
hexed nest
I’m even more confused
compact shadow
a=cos,b=sin here
hexed nest
do I expand first and factor it ?
compact shadow
Anyway I better leave. Because simplifying is not a specific requirement having a specific answer, no idea the result should be in which form
frank monolith
do I expand first and factor it ?
you can do anything you want (as long as its correct)
there is no specific method here.
hexed nest
I’m still confused
obtuse pebbleBOT
@hexed nest Has your question been resolved?
timid silo
I’m still confused
confused with?
hexed nest
how to solve the question I wrote out
timid silo
i guess you can solve that with multiple approaches
hexed nest
Which one is the easiest?
or which one would you do?
I don’t understand what I’m supposed to be doing
timid silo
erm cotx = cosx/sinx?
hexed nest
yea
timid silo
proceed then
timid silo
well
nocturne minnow
I have no idea what to do
Did you try, (1+cotx)(1+cotx)?
timid silo
Did you try, (1+cotx)(1+cotx)?
better one
nocturne minnow
do I factor it?
No because then you end up where you started
hexed nest
Oh ok
nocturne minnow
But what exactly is the goal with (1 + cot x)^2? All you can do is just expand and there's nothing much you can do
timid silo
yeah
hexed nest
it says I have to multiply it and simplify
nocturne minnow
All you can do is just expand and there's nothing much you can do
timid silo
cosec²x + 2cotx
how can you further simplify this?
nocturne minnow
Did you expand (1+cotx)(1+cotx)?
hexed nest
yea
nocturne minnow
And you get?
timid silo
just expand this
hexed nest
how?
nocturne minnow
What did you get when you expanded (1+cotx)(1+cotx)?
hexed nest
I haven’t done it yet, don’t know how
nocturne minnow
Can you expand (x + 2)^2?
timid silo
use identity (a + b) ² instead
hexed nest
….what
nocturne minnow
So you don't know the concept of FOIL?
hexed nest
I just started back uni again
nocturne minnow
First, Inner, Outer, Last?
hexed nest
I don’t remember anything
hexed nest
First, Inner, Outer, Last?
no but I’ll try to remember it
hexed nest
thank you
hexed nest
So after doing FOIL is that the end?
nocturne minnow
Were you able to expand (x + 2)^2?
hexed nest
I think so?
nocturne minnow
What did you get?
nocturne minnow
Write that as one expression now
nocturne minnow
Combine like terms
hexed nest
x^2+4x+4?
nocturne minnow
What about First?
hexed nest
I’m on the last one
nocturne minnow
so far I have 1 + cot x + cot x + ?
So far so good
nocturne minnow
so would multiplying cot x by cot x be cot^2x or 2cotx?
First one
nocturne minnow
Yes
nocturne minnow
so far I have 1 + cot x + cot x + ?
You had a 1 + here
hexed nest
yea what do I do with that ?
nocturne minnow
What is the current expression you have?
nocturne minnow
Yes, apply one of those identities to
1+ 2cot x + cot^2x
nocturne minnow
Use one of those identities to simplify 1+ 2cot x + cot^2x
hexed nest
so rearranging it?
nocturne minnow
Yes
hexed nest
ok so
wait
if it’s 1 + 2cot
do I move it
So that it starts as 1 + cot ^2x + 2cotx
hexed nest
and since 1+cot^2x equals cot^2x it becomes cot ^2x + 2cot x
nocturne minnow
Not just csc
nocturne minnow
So 1+ 2cot x + cot^2x equals what?
hexed nest
no wonder I got confused reading it
so
oh gosh I almost had it but I just confused myself
nocturne minnow
You have 1+ 2cot x + cot^2x, then got 1+ cot^2x+ 2cot x, then used the identities
To get 1+ cot^2x = csc^2x
I'm now asking what is your final answer
hexed nest
csc^2x + 2cotx
nocturne minnow
Yes exactly
nocturne minnow
I have 1 last question
What's that last question?
nocturne minnow
Number 3 is the same logic as number 1 except you have a few more terms
nocturne minnow
Try it and post what you have done
nocturne minnow
Yes
hexed nest
and then simplify it
nocturne minnow
Yes
hexed nest
is there any of the identities I can apply to this?
nocturne minnow
Expand it, what do you get?
hexed nest
I’m kind of stuck on the expanding part ;-;
nocturne minnow
If you have sinx(ab + c + d), could you multiply that out?
nocturne minnow
Yes exactly
hexed nest
really?
nocturne minnow
Yes
hexed nest
so (sin x • (sec x • tan x))
nocturne minnow
Do you notice how in sin x(sec x tan x + csc x + cot x), I replaced the stuff inside the parentheses with a, b, c, d?
nocturne minnow
so (sin x • (sec x • tan x))
Yes
hexed nest
Do you notice how in sin x(sec x tan x + csc x + cot x), I replaced the stuff in...
Yea it made it easier to visualize
but do i simplify sec and csc?
nocturne minnow
Not yet
hexed nest
ok give me a sec then to write it out
nocturne minnow
Expand all this first
sin x(sec x tan x + csc x + cot x)
hexed nest
Ok
btw can I add you as a friend ? or is that not allowed? I like how you explain things
nocturne minnow
Sure I guess
hexed nest
If you rather not it’s fine
I know I need a lot of help
and I’m slow
it’s frustrating most of the time
this is what I have now
nocturne minnow
Good, can you rewrite, the sec, tan, csc, and cot in terms of sin and cos and see if things can cancel out?
nocturne minnow
Do you see how some things can cancel out?
hexed nest
I do
for the sin x(sec c • tan x)
The sin x outside the bracket cancels out the sin x inside right ?
nocturne minnow
for the sin x(sec c • tan x)
The sin x outside the bracket cancels out the sin...
Nope
nocturne minnow
Use this line here
hexed nest
yea
nocturne minnow
Do you see how sin (1/sin) how something can cancel?
hexed nest
so I rewrite it ?
oh for the last one also
the sin x cancels out the sin x on the bottom of cos x/ sin x right ?
nocturne minnow
the sin x cancels out the sin x on the bottom of cos x/ sin x right ?
Yes
So you have what left?
nocturne minnow
So far so good, you can simplify the first term a bit more
If you got x(1/y * x/y) what would that be?
nocturne minnow
Nope
nocturne minnow
What if it looked like $\frac{x}{1} \cdot \frac{1}{y} \cdot \frac{x}{y}$
warm shaleBOT
dldh06
nocturne minnow
Not quite what I'm looking for, but do you recall how to multiply fractions?
Where you multiply across the numerator and across the denominator?
nocturne minnow
Yes
hexed nest
so it’s x • 1 • x?
nocturne minnow
That's the numerator
nocturne minnow
So it’s 1 • y • y ?
That's the denominator
hexed nest
I’m confused
nocturne minnow
$\frac{x}{1} \cdot \frac{1}{y} \cdot \frac{x}{y}$
warm shaleBOT
dldh06
nocturne minnow
That's the expression
hexed nest
Yeah
nocturne minnow
When you multiply fractions, you multiply across the numerator and the denominator
nocturne minnow
Then the denominator is 1 * y * y
nocturne minnow
Not quite
nocturne minnow
$\frac{x}{1} \cdot \frac{1}{y} \cdot \frac{x}{y} = \frac{x \cdot 1 \cdot x}{1 \cdot y \cdot y}$
warm shaleBOT
dldh06
nocturne minnow
Do you agree?
hexed nest
yes
nocturne minnow
What is x * x equal to?
hexed nest
I see
nocturne minnow
Can you do the same for the denominator?
hexed nest
Yep
nocturne minnow
You need to multiply this, sin x / 1 (1 cos x • sin x/cos x)
Which was why I did $\frac{x}{1} \cdot \frac{1}{y} \cdot \frac{x}{y} = \frac{x \cdot 1 \cdot x}{1 \cdot y \cdot y}$
warm shaleBOT
dldh06
nocturne minnow
If you noticed, I replaced sin with x and cos with y
hexed nest
yeah I notice it now
so then
sin x • 1 • sin x would be sin^2x?
and
1 • cos x • cos x = cos^2x ?
nocturne minnow
Yes
nocturne minnow
There's one more step
hexed nest
yea?
nocturne minnow
Do you see what sin/cos equals to?
nocturne minnow
Exactly
hexed nest
I don’t see any identity for tan^2x, so it stays that way ?
oh wait
Ah I see
do we use
1 + tan^2x = sec^2x?
nocturne minnow
Yep
nocturne minnow
So your final answer is?
hexed nest
uh
gimme a sec to write previous steps
wait so
Right now I have
tan^2x + 1 + cos x
nocturne minnow
1 + tan^2x = sec^2x?
Then you applied this here
hexed nest
oh wait
so then
when you say apply
You mean I can write 1 + tan^2 x as sec^2x so it’s sec^2x + cos x?
nocturne minnow
Yes
nocturne minnow
thanks again
So btw I did dm you, if you don't mind
hexed nest
there’s still 4-11
hexed nest
So btw I did dm you, if you don't mind
sure
nocturne minnow
there’s still 4-11
Sounds like a good break time now lmao
hexed nest
Yeah I have to go soon for an eye test
but thanks again for real
I had forgotten so much fundamental concepts
.close
tiny saddle
i need help
obtuse pebbleBOT
i need help
tiny saddle
just a reminder on this
rq
on working out mean from frequency table
and there is a class width
do u times frequency by the mean of the class width
OH NVM I GOT IT
.CLOSE
.close
fathom pawn
i just have a question if this is chain rule and product rule
obtuse pebbleBOT
i just have a question if this is chain rule and product rule
fathom pawn
i have k(x)=(-3x^2+2x)g(x)h(x)
wouldnt i use product rule on g and h then chain rule with the other side?
tardy epoch
that's a product of 3 functions
fathom pawn
so would i just use chain rule then? im confused
haughty coyote
f g h = (f g) h is a product of 2 functions, where one of these functions is a product
obtuse pebbleBOT
@fathom pawn Has your question been resolved?
twin swallow
I need help guys
obtuse pebbleBOT
twin swallow
.close
sly kindle
the question said that the answer is not equal to -2 but the answer on the board is -2
is it because it said "perform the indicated operations?" Then what is the point of saying y is not equal to 2, -2
obtuse pebbleBOT
Available help channel!
misty geyser
can’t see where i went wrong
obtuse pebbleBOT
can’t see where i went wrong
misty geyser
can anyone troubleshoot this (ignore the scratched out part in the middle)
compact shadow
it should be simply by cot^3dx=((1-sin^2(x))/sin^3(x))d(sin(x)), rational. Your first term on last line is wrong , I got -(1/2)csc^2 not -(1/2)csc
Can’t understand how you obtained the last two rows actually
Last three rows actually, you crossed something in the middle and somehow last three lines appear
nocturne minnow
can anyone troubleshoot this (ignore the scratched out part in the middle)
You lost the $^2$ when you did the $-\frac{1}{2} u^2$ part
warm shaleBOT
dldh06
compact shadow
Oh his u is csc and he forgot ^2? I see
nocturne minnow
Oh his u is csc and he forgot ^2? I see
She* btw
misty geyser
oh youre so right
ty
oh thats still nto right though
black is my answer green is the textbook's
nocturne minnow
I'm pretty sure it's the same, it's the + C that makes a difference
violet narwhal
The answers seem like visual intuition to me. But that really just makes me feel lost on what steps I can take make my answers.
obtuse pebbleBOT
The answers seem like visual intuition to me. But that really just makes me feel...
@violet narwhal Has your question been resolved?
latent walrus
id look at the second and maybe the last one
violet narwhal
id look at the second and maybe the last one
second and last what?
Questions you mean?
latent walrus
yeah
latent walrus
at 58?
you can see the velocity is decreasing between those two straight line sections (gradient decreases) around t=58 so acceleration there must be negative
t=58 lies in the curved section between the straight lines
violet narwhal
wait OH
If velocity changes constant even if aiming up, the fact it remains constant makes it 0?
latent walrus
if velocity is constant in any scenario then a=0 in that same direction
violet narwhal
I corrected my answers based on what you told me.
Still off though. Can you ask me something to point me in the right direction?
obtuse pebbleBOT
@violet narwhal Has your question been resolved?
rich moon
I'm looking for the name of a distribution
obtuse pebbleBOT
I'm looking for the name of a distribution
rich moon
I'm looking for the distribution of the number of attempts required to achieve a result N times given each trial is independant and has probability lambda
so for example
distribution of number of coins that must be flipped before getting 3 heads
rich moon
number of success before the rth failure for negative binomial?
i guess that works
i want the opposite
Number of trials expected before attaining N successes
warm canopy
rich moon
so I just need to add the number of success to the x axis to get what I want?
warm canopy
i have no clue what you're doing
rich moon
total number of coins flipped before getting 3 heads (trials), not number of tails flipped (failures)
warm canopy
sure
obtuse pebbleBOT
@rich moon Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
gloomy knoll
hello! I need help on finding the length of a slope of anwedge/isoceles triangle with one angle being 45 and the base is .25 in :D
obtuse pebbleBOT
hello! I need help on finding the length of a slope of anwedge/isoceles triangle...
gloomy knoll
what would the formula be
gloomy knoll
i assume its the non-congruent
high lily
assume? does it not say in the question?
gloomy knoll
bc it says a 45 degree angle between the two sides of the blade
high lily
which sides are the blades
gloomy knoll
well its a wedge of a hydraulic shear
gloomy knoll
Hydraulic shears are used in manufacturing to cut large sheets of metal. Using hydraulic pressure, the machine pushes a wedge that is shaped as an inclined plane-bot bifaced like an axe- to cut the metal. A shear has a 1/4 in thick cutting blade with a 45-degree slope between the two side of the blade....
oh the base is .25 in
but no there was no diagram
but YA I DO
that makes sense
okk tysm ill get back to u
wait so the angles or 90 67.5 and 22.5 right? and then what do i do after that 😅
so whats the formula?
ya trigonometry?
i havent learned it in school but ive seen it multiple times before
yaaa...
is there a formula?
im in geometry rn
obtuse pebbleBOT
@gloomy knoll Has your question been resolved?
late stump
obtuse pebbleBOT
slim cove
So the first step would be to figure out the parameterization
It gives you a hint on how to do it
But you need to figure out appropriate bounds for theta
late stump
i assume the bound is just from 0 to 2pi?
and from my understanding, greens theorem would be
$$\iint_R\curl \vv F\dd A=\oint_C\vv F\cdot\dd \vv r$$
warm shaleBOT
light
late stump
but i dont know what F would be in this scenario
obtuse pebbleBOT
@late stump Has your question been resolved?
slim cove
and from my understanding, greens theorem would be
$$\iint_R\curl \vv F\dd A=\oi...
So the area is just the double integral of 1, so you would want to find some F whose curl is 1
slim cove
i assume the bound is just from 0 to 2pi?
yup!
late stump
So the area is just the double integral of 1, so you would want to find some F w...
oh seriously? i can just pick any arbitrary F here?
okay then
slim cove
oh seriously? i can just pick any arbitrary F here?
yup! pick a convenient one
late stump
So the area is just the double integral of 1, so you would want to find some F w...
right anyways this makes sense so im just gonna run with this for the time being
thanks!
it worked out, cool! thanks!
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
jovial lynx
obtuse pebbleBOT
chrome crypt
apologies renato I was busy with a few things. You seem to be working really hard on this so lets sort it out.
So my first off question is do you understand the epsilon delta proof in general yes or no? Do you understand why it works the way it works?
@jovial lynx
obtuse pebbleBOT
@jovial lynx Has your question been resolved?
jovial lynx
jovial lynx
apologies renato I was busy with a few things. You seem to be working really har...
Hello luffy once again
jovial lynx
So my first off question is do you understand the epsilon delta proof in general...
Mmm I got a rough idealisation of it
obtuse pebbleBOT
@jovial lynx Has your question been resolved?
jovial lynx
<@&286206848099549185>
obtuse pebbleBOT
@jovial lynx Has your question been resolved?
jovial lynx
!status
obtuse pebbleBOT
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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
2
chrome crypt
Alright Renato so I observed that the function is not linear, and for non-linear functions there is a different way as to how you would solve them regularly with a linear interval.
jovial lynx
min()? 😮
chrome crypt
So basically what I did to understand your problem better was to observe a simpler scenario and really question it. Essentially with non linear functions we have to take the minimum at times and I am going to explain why. I'm going to now complete the epsilon delta proof for your question.
Also Renato, I know it may be hard but have fun with enjoying this math proof. Isn't it interesting that we are actually proving a limit? 🙂
It may be hard to gauge some ideas but I promise with practice and dedication that you will do good. I'm going to do the best of my ability to help you, but I would like you to get another pair of eyes to verify just in case although I am sure its correct.
If you are struggling though with the general idea of epsilon delta proofs now is the time to tell me as I want to make sure not only you understand, but that you understand it where in the future you will not be memorizing it and can explain it to someone else.
jovial lynx
$\lim_{x\to x_0}f(x) = a \Longleftrightarrow \forall \varepsilon > 0, \exists \delta > 0, \forall x\in (x_0-\delta,x_0+\delta), |f(x)-a|<\varepsilon$
warm shaleBOT
renato (ping if reply)
chrome crypt
im still here just solving it for you.
jovial lynx
:’v
chrome crypt
it takes a while my friend I am still here. This is by far the biggest epsilon delta definition of a limit I have done so bear with me please.
chrome crypt
After what has seemed to be an eternity I believe I have solved it. However I would like you to clarify with someone as I am not 100% sure as this was quite tedious. I checked the algebra and everything, referred to a website and it seems to check out, but still confirm with a professor or friend you know.
This was the website I refered to.
Now I am going to give my full explanation to ensure you understand it.
So in order to prove the definition of the limit with epsilon delta proofs, I like to refer to this proof as the four key word method. Given, Choose, Suppose, Check.
Now when dealing with epsilon delta proofs for linear functions with a single variable x is fairly easy to solve as we deal with a single variable and can often times use the algebraic property with absolute values where IabI = aIbI
However the problem with functions that are not linear (to the power of 1) is that we cannot use this property often times to solve for what delta is.
and so then what often times what we need to do is lets say we have I f(x) - L I < E, such that we cannot factorize the function where we can use the general product rule for absolute values. What we do know is that we need to ultimately obtain I x - c I < delta where delta is defined in terms of epsilon.
For starters what we do know is that according to the definition of an absolute value where y = I x I --> { x, if x >= 0 & -x, if x < 0
what we then do is break up f(x) - L into these 2 cases.
We consider the first case where (f(x) - L) is greater than or equal to 0 which would result in f(x) - L < E. Now lets consider case 2 where f(x) - L is less than 0, so
-(f(x) - L) < E --> f(x) - L > -E
Then we mash the 2 cases together we have
-E < f(x) - L < E
now f(x) - L is some function could be (sqrtx) - 2, where we observe the limit as x approaches 4 (Arbitrarily example for showing this proof)
then we would have -E + 2 < (sqrtx) < E + 2. Whatever we do to one of the terms in the equality we must prepare that same operation to the other terms or else it would be disproporionate and the inequality would not hold true.
Next we would say (-E +2) < (sqrtx) < (E+2)
now we square the function to get x by itself and we do the same for the other 2 terms.
(-E + 2)^2 < x < (E + 2)^2
Now we know that once we obtain I x - c I < delta, we can say
-delta < x -c < delta
In our case c is 4 so (-E +2)^2 - 4 < x - 4 < (E+2)^2 - 4
Now here is the exact reason we have to choose a minimum. I'm going to make a graph to show you why we have to do this.
Hmmmmmmm for this type of question I did not have to take a minimum, but rather had to consider the fact that one delta was outputting a negative result so we cannot choose that delta, and must use the other delta instead.
Here is the intuition behind choosing minimum delta
So let delta 2 > delta 1. In this graph we observe the neighbourhood x values of c where we are given the exact amount to be within epsilon. And on the righthandside lets say we initially had a delta 2 where that particular interval is within epsilon as well. Now a problem arises, because we ultimately need to choose a singular delta, not multiple, just one. We need to ensure that the epsilon holds true for whichever delta we choose. Now we observe the smaller delta and see that if we chose that to be our delta we no that c - delta 1 and c delta 2 will not change the fact that f(x) is within L + E. However lets say we chose delta 2 instead to be our delta which would mean c + delta 2 and c - delta 1. We would observe that for the righthandside that the fact that f(x) < L + E will hold true. But on the left-handside if we chose delta 2 we would be outside of the maximum interval delta 1 for that epsilon, so f(x) > L - E would not hold as its outside epsilon and the entire epsilon delta proof would not work. But we do know if we chose the minimum delta that no matter what the statement will hold true therefore it works, hence we choose minimum.
Now I know this is a lot to digest so take a breather, review this and tell me if you are at any crossroads or have any questions.
obtuse pebbleBOT
@jovial lynx Has your question been resolved?
chrome crypt
whats your question?
jovial lynx
im sorry im still trying to understand your notes here
chrome crypt
scroll in.
jovial lynx
im still in the scratchwork xd
chrome crypt
mk, so the scratchwork gives us the tool we need to solve the proof
which is delta defined in terms of epsilon
are you confused as to why the epsilon delta proof works the way it does?
jovial lynx
luffy
@chrome crypt
I understoof at the end
everything but the last part, are you evaluating the limit of some way?
yes this looks like a wonderful proof, cheers
your proof is elegant luffy, bravo!
Sorry it tooked me a while to understand, but there was some heavy algebra
chrome crypt
everything but the last part, are you evaluating the limit of some way?
What do you mean evaluating a limit? We already know what the limit is so that would be nonsensical. What I did at the end was use the delta defined in terms of epsilon obtained from the scratchwork we did to obtain what is delta in terms of epsilon. Because for any epsilon I give I want to find the maximum delta (interval) where epsilon will hold true like a game almost, which is exactly what this formula does. At the end of the question it asked to determine the appropriate interval for when Epsilon = 0.01. I plug in epsilon into the two definitions I have for delta and it becomes apparent that one of them doesn’t work and returns a negative answer, while the other one works and returns a positive answer and gives me the necessary interval.
I don’t think you properly understand epsilon delta definition. You need to first learn it and then movie on to more complex versions of epsilon delta definition of a limit.
jovial lynx
I don’t think you properly understand epsilon delta definition. You need to firs...
Im sorry Nodachi, I had only done linear ones, and im quite lost with the material
chrome crypt
Im sorry Nodachi, I had only done linear ones, and im quite lost with the materi...
Oh, that’s good. If you understand how linear ones work thats good, but your question at the end I don’t know if you forgot about the fact that we had to find the delta interval for epsilon 0.01.
jovial lynx
yeah we were given ε = 0.01 but where is the interval?
jovial lynx
Hmmmmmmm for this type of question I did not have to take a minimum, but rather ...
ahhh, what does that mean
jovial lynx
What do you mean evaluating a limit? We already know what the limit is so that w...
why do you say it becomes appearant 
ahh becase δ > 0
chrome crypt
ahhh, what does that mean
read
marble crest
im trying to rotate a perifirom surface around the z-axis
obtuse pebbleBOT
im trying to rotate a perifirom surface around the z-axis
marble crest
can anyone help me?
i would like it to be pointing to the left wall instead of the right
the green represents x, red represents y, blue represents z
this is the equation
knotty gulch
what do you mean the left wall
knotty gulch
sorry i cannot help you, ask someone else <@&286206848099549185>
obtuse pebbleBOT
@marble crest Has your question been resolved?
frosty river
What prevents you from taking x⁴+x³+y²+z²=0?
autumn estuary
obtuse pebbleBOT
autumn estuary
Any video tutorial or solved examples from this type of limits?
I know how to solve it halfway
tardy epoch
Use
a^b = e^(b * log(a))
autumn estuary
I don't think this trick has a name
Ok so in my case can I swap 2x-2 with u?
<@&286206848099549185>
tardy epoch
Ok so in my case can I swap ``2x-2`` with ``u``?
Try it?
tardy epoch
Idk what to do after
Do you know what log(v)/v approaches as v goes to zero
You could do one more sub but it's not absolutely necessary
You know cos(0)=?
tardy epoch
Yes?
warm shaleBOT
Result:
1
so I can write 1 instead of cos(u) now?
tardy epoch
Not quite
The limit as u goes to 0 of cos(u) is 1
Use limit laws to do the rest
,tex .limit rules
warm shaleBOT
riemann
tardy epoch
**riemann**
Product rule for limits
autumn estuary
Product rule for limits
I dont quite understand that
tardy epoch
Why not
hidden compass
I think they are the most intuitive rules for limits actually
hidden compass
I dont quite understand that
One of those in particular?
autumn estuary
One of those in particular?
Well the product rule
the first thing that comes to my mind is to split it into 2 limits
hidden compass
the first thing that comes to my mind is to split it into 2 limits
And then multiplying them, yep. That's what the rule saays
autumn estuary
And then multiplying them, yep. That's what the rule saays
Okay okay
@hidden compass @tardy epoch whats the next step?
1/0 = 0
l hopital?
tardy epoch
No
tardy epoch
Do you know what log(v)/v approaches as v goes to zero
.
autumn estuary
I don't know where cosine went
into 1
tardy epoch
... you really don't need to ping me 3 times in a row
tardy epoch
The limit as u goes to 0 of cos(u) is 1
.
tardy epoch
Split it differently
autumn estuary
Split it differently
how?
tardy epoch
Figure this out first
.
autumn estuary
.
no idea
@tardy epoch @hidden compass I still need help
<@&286206848099549185>
obtuse pebbleBOT
@autumn estuary Has your question been resolved?
obtuse pebbleBOT
@autumn estuary Has your question been resolved?