It’s a question I received in advanced functions (a class taught before calculus)
#help-13
weak berry
livid hound
i suppose for this you could first identify the slope of the secant
the tangent line equation will be in the form
y = -2x + b
and consider when that line intersects with the the curve once
using properties of the discriminant
cedar kilnBOT
@weak berry Has your question been resolved?
weak berry
using properties of the discriminant
Could you please elaborate? What would the steps be to solve this using the discriminant of the curve?
livid hound
use the discriminant to determine when there'll be a single solution
weak berry
use the discriminant to determine when there'll be a single solution
So you would set the discriminant of the rational function equal to y=-2x+b to find the solution?
livid hound
set
2x/(x-4) = -2x+b
convert that to a quadratic and use the discriminant of that
weak berry
set
2x/(x-4) = -2x+b
convert that to a quadratic and use the discriminant of tha...
I didn’t get the right answer
Perhaps I simplified wrong, when you solved it was (3,6) your answer
livid hound
show work
weak berry
Sorry for the poor quality I’m not home at the moment @livid hound
weak berry
Just realized that as I was checking whoops
weak berry
b * -4 is -4b not 4
I’ve tried redoing it now but I don’t see how it affects the question for the discriminant
livid hound
what values are you getting now
weak berry
Oh I see, thanks!
How did you know to come up with this answer?
Or overall strategy
weak berry
18 works too
18 as an x value yields a secant line to the function
livid hound
18 for the b in
y = -2x + b
cedar kilnBOT
@weak berry Has your question been resolved?
restive plover
cedar kilnBOT
crimson delta
well you could give the greatest lower bound explicitly
first show that it is indeed a lower bound
and then show it is the greatest, i.e. taking a bigger one is not possible
restive plover
Ohh but how , should i Start with the epsilon delta definition
But this a set not a function
Idk where to start, could you tell me?
bitter finch
Idk where to start, could you tell me?
if u have 1/n with n being a natural number what’s the lowest it can be?
for example, it can’t be 1 because 1/2 is less than that
it can’t be 0.0001 because 1/10000000 is less than that
restive plover
0
bitter finch
yea so that’s the greatest lower bound
restive plover
But I want to write down as a prooof
bitter finch
yeah u have to formalise it
bitter finch
ok so first actually show it is a lower boun
d
how to do this? prove 1/n can’t ever be < 0
restive plover
Yea cuz we are dividing by natural numbers
bitter finch
exactly
for the second part u gotta prove that there’s no lower bound bigger than 0
i guess you gotta prove that
for a given b, b>0 exists n such that 1/n < b
restive plover
exactly
How can i write it like a proof, or can i just write we are driving by natural numbers so it can never be less than 0
cedar kilnBOT
@restive plover Has your question been resolved?
bitter finch
How can i write it like a proof, or can i just write we are driving by natural n...
proof by contradiction:
assume 1/n < 0
n is a positive integer so multiplying each side of the inequality by n won’t change the direction of the inequality
=> 1<0 which is obviously untrue
green belfry
Rotate 90
green belfry
Please someone hel9
runic garnet
,rotate
wraith daggerBOT
hushed spoke
Question statement?
green belfry
hushed spoke
How do i prove tba5 doce is cyclic
You mean DFEC?
I can’t say if DOCE is cyclic
@green belfry
hushed spoke
So why do you need the other one
hushed spoke
Opposite angles add to 180
green belfry
But dfoe is cyclic
hushed spoke
Is it?
worldly glacier
hushed spoke
Any progress?
hushed spoke
Can any of you figure it out
Not really
cedar kilnBOT
@green belfry Has your question been resolved?
cedar kilnBOT
@green belfry Has your question been resolved?
crimson sedge
.help
cedar kilnBOT
Commands:
clopen: .close, .reopen, .solved, .unsolved
consensus: .poll
factoids: .tag
help: .help
Type .help <command name> for more info on a command.
cedar kilnBOT
Commands:
clopen: .close, .reopen, .solved, .unsolved
consensus: .poll
factoids: .tag
help: .help
Type .help <command name> for more info on a command.
cold oxide
hello
cold oxide
can someone help me out here
I am studying velocity
and velocity=displacement/time
and it gives a result in m/s
but surley this is just an average distance travlled in a second
cosmic steppe
Yes that is average displacement over time
cold oxide
and in order to get an accuarte result you need distanced trravlled overr an infitessiamly small period of time
cosmic steppe
Yeah so you need to differentiate the position function
cold oxide
ahh
ok
i do not know what that means, I am too stupid for that
thank you for calrifiying
.close
cedar kilnBOT
jade charm
and in order to get an accuarte result you need distanced trravlled overr an inf...
You can approximate velocity by averaging over smaller and smaller time intervals. And then calculus lets you "average over an infinitesimally small period of time" to get the true velocity.
Hence "differentiate the position function"
cedar kilnBOT
Available help channel!
ivory delta
Can someone just find the answer to this? Change the base
cedar kilnBOT
Can someone just find the answer to this? Change the base
velvet mortar
What is a base
ivory delta
Bro💀
ivory delta
3^4
runic garnet
Do the same to 49 with 7
ivory delta
7^2
runic garnet
So now we have: (Lemme write it visually)
We can now distribute the external exponent to the numerator and denominator
ivory delta
Why do we have to distribute? Isnt the form already consisiting of 3/7?
@runic garnet
runic garnet
Rn our base is (3^4)/(7^2)
We wanna get it so that the numerator and denominator have the same exponent
So instead of 3^4, can we rewrite 81 with a base of 9
Lemme check smth rlly quick
Ok well
There’s no perfect way for us to have a base of 3/7
We ultimately end up with (3^2/7)^4a
Which is (3^8a)/(7^4a)
Idk if that still counts, but there’s no perfect form for 3/7 base
cedar kilnBOT
@ivory delta Has your question been resolved?
velvet mortar
√5 * √2 = √(5*2) = √10 right? How is √-1 * √-1 not √1?
cedar kilnBOT
√5 * √2 = √(5*2) = √10 right? How is √-1 * √-1 not √1?
wraith daggerBOT
Kihei
gray blade
so that rule can't apply here
ivory delta
Idk if that still counts, but there’s no perfect form for 3/7 base
Does it matter if I do the distribution of 4a?
wraith daggerBOT
Kihei
cedar kilnBOT
@velvet mortar Has your question been resolved?
velvet mortar
so that rule can't apply here
Oh thanks
runic garnet
Add the x to the right then square both sides
crimson sedge
Someone asked me to figure out the following and I don't really know what I'm supposed to do with it but I know someone in here would be able to aid me 🙂
The quarrel:
87,5 x divided by 80 should be a whole number (i.e: 1, 2, 6, 25 whatever no commas)
What is X?
I plotted 87.5x/80 and I get a line but then what lol, should I just make y2, y3, y4 etc 1, 2, 3, 4 ,5 ,6 ,7 and see which one it hits?
In other words 87.5x/80 whenever it hits a whole number should give back x
tight epoch
I'm very stuck on this problem I can't figure out where the slope equals zero
cedar kilnBOT
@crimson sedge Has your question been resolved?
livid hound
start by simplifying your fraction
crimson sedge
right, simplification, so then 87.5x/80 would simplify to i.e. x80 so thats 7000*80x?
livid hound
no
crimson sedge
why not? getting rid of the division by timing it to the rest is part of simplifying no
livid hound
you essentially multiplied your expression by 80^3
crimson sedge
i dont really know then how to simplify an equation where i dont have the other side of the equals if you get what i mean
livid hound
$\frac{87.5x}{80} \neq 7000\cdot 80x$
wraith daggerBOT
ℝamonov
livid hound
not equation
expression
simplify in a similar way you'd simplify something like
$$\frac64$$
the presence of an equation or equal sign isn't relevant
wraith daggerBOT
ℝamonov
livid hound
yes
you can put the x aside for now and focus on expressing
87.5/80 as a fraction of two integers
crimson sedge
right
how does 87.5/80 ever boil down to two integers. anything i try to the 87.5 makes the 80 a comma number
wait 12.5 works
no fuck
im just guessing things here i dont know how to do this mathematically im not a very schooled maths guy. all i know is there should be like a calculative way to boil 87.5/80 down to less numbers i dont know how to do it
livid hound
first start by multiplying the numerator and denominator so you actually have a fraction of two integers
in this case this can be achieved by multiplying the numerator and denominator by 2
$\frac{87.5}{80} = \frac{87.5\times 2}{80\times 2}$
wraith daggerBOT
ℝamonov
crimson sedge
riiiight i see
no its probably still the same problem id have to guess numbers to divide it by
i dont see it
livid hound
do you know your times tables?
crimson sedge
never above 144 xD
crimson sedge
errrr
livid hound
for 2,3,4,5,6,8,9,10
crimson sedge
could you give an example english isnt my first language
livid hound
yes
so overall your original fraction simplifies to
$$\frac{87.5x}{80} = \frac{35x}{32}$$
wraith daggerBOT
ℝamonov
crimson sedge
Right. then what should i try to do from there
crimson sedge
but isnt that the same as 87.5x/80 i dont know where to go hah
livid hound
did x also need to be an integer or not?
crimson sedge
i dont think so
wraith daggerBOT
ℝamonov
crimson sedge
so then if i isolate x is should get it right
livid hound
yeh, and then plugging in any integer value for y will get you the respective x value
crimson sedge
so that comes down to x = (y/32)/35?
crimson sedge
x=y/35?
livid hound
wdym by divided by 32
crimson sedge
so 35x/32 = y -> get rid of /32 by timing everything by 32
1120*32x = 32y
and then from there /32
livid hound
wheres 1120 * 32 x coming from now
livid hound
no
you're not multiplying properly
you don't multiply to both the numerator and denominator like that
crimson sedge
you dont?
livid hound
$a \times \frac bc = \frac{ab}{c}$
wraith daggerBOT
ℝamonov
livid hound
35x = 32y
would be the correct result of multiplying both sides by 32
why do you plan on dividing by 32, undoing what you just did
crimson sedge
cuz i wanna go to 1 y
livid hound
divide both sides by 35 yes
crimson sedge
32/35 is that
livid hound
just leave 32/35 as 32/35
given an integer y, you'll know exactly what x is
and not have an approximation
crimson sedge
thanks. thats the problem solved then right
any int i put for y i get x for that equation
livid hound
yes
crimson sedge
❤️ thanks man sorry that it was such a tough one for me and probably peanuts for you
torpid urchin
how am i supposed to isolate for y here?
cedar kilnBOT
how am i supposed to isolate for y here?
torpid urchin
):
muted bear
What ddo you need to find
torpid urchin
y'(-2)
muted bear
Use implicit
torpid urchin
ok let me try this out
will return shortly
@muted bear the issue is that i still have the e^y
o
derived wrog
one sec
wrong
torpid urchin
You plug in your known values (x,y)=(-2,2)
where u get this at
muted bear
From the question statement
muted bear
Yes
torpid urchin
i think it makes sense but
is there any way u could explain
the way i am understanding it is
i have dy/dx
and values from an original function
and those values will also be true in the derivative?
torpid urchin
all u know is it works
muted bear
Yes and i have a rough understanding that lets me be comfotable with using it
torpid urchin
i think
it may have to do wit the fact that is is
e^y
and derivative e^y
is e^y
muted bear
3blue1brown made a video on it but its my least favorite in the calc series
muted bear
Yeah
gaunt hamlet
and those values will also be true in the derivative?
What are you asking?
torpid urchin
uhhh
how do i word it
so
why does using (-2,2)
work in y'
when it is from y
gaunt hamlet
You have the derivative in terms of x and y
x is just, well, x
y represents the original function
Which is 2 when x = -2
gaunt hamlet
y represents the _original function_
Well, represents the original function solved for y
gaunt hamlet
Which can't be done probably
torpid urchin
so because the derivative is at -2
it will be the same
?
because y=2 when x=-2
gaunt hamlet
Yes
cedar kilnBOT
frail mesa
honest sable
okay I'm waiting
honest sable
😥
cedar kilnBOT
@honest sable Has your question been resolved?
cedar kilnBOT
@honest sable Has your question been resolved?
cedar kilnBOT
cedar kilnBOT
Available help channel!
true garnet
How do I do it?
cedar kilnBOT
How do I do it?
haughty wraith
How do I do it?
I think the answer would have to be like a series approximation like integral of x^x
not sure though someone smarter can probably help
true garnet
And how donibsolve the integral of x^x?
haughty wraith
And how donibsolve the integral of x^x?
weak mountain
If I have a series $\sum a_n$ that is convergent and nonnegative $a_n\geq 0$, is $\sum \sqrt{a_n}$ convergent as well?
wraith daggerBOT
Mirinim
sacred grail
harmonic series
thank you
cedar kilnBOT
cedar kilnBOT
Available help channel!
sacred peak
how
sacred peak
like literally how
yes i know what ur gonna say
chain rule
definition of sine
but try calculating it yourself with the chain rule
you shouldnt get that answer. i did it myself and i used mathway and both of them are giving a different answer
solemn torrent
npnp
sacred peak
.close
stray raven
you have a pulley and two blocks attached to the rope each pulling on the rope, why is T the same such that you can cancel it out??
Here we have a mass on an inclined ramp attached to a pulley, and another mass hanging from a pulley;
the mass on the ramp must have a Tension force from the hanging mass pulling it towards the pulley.
the mass hanging from the pulley must have a Tension force from the mass on the ramp sliding downwards.
Why are these two tension forces equal?
stray raven
I thought that each Tension force would be its own force
stray raven
but like
obsidian coral
So it wouldn't be two different tensions
stray raven
if m2 (the hanger) was like, pulling with a thousand gravities
then the T force on M (the ramp block) should be a thousand gravities
and then M is pulling on m2 with a few gravitys
soooo
T is defined as a shared force?
basically the difference between those two forces?
because M still gets pulled with a thousand gravities, but it also pulls back with a few of its own gravities
obsidian coral
and then M is pulling on m2 with a few gravitys
No, because the gravity would be the same
stray raven
i mean the force
in newtons is like 1000g
ignore the units the guy used
sorry
i mean like pretend m2 is pulling on the rope with 1000N
m1 is pulling with 10N
obsidian coral
The tension would be the same between the two because it's attached to the same rope
stray raven
we don't say tension force on m2 is 10N and tension force on m1 is 1000N
but the total tension force would be 990N, if i understand it correctly?
ok let me try saying it this way
why can't i have individual tensions? like T_1 and T_2
how can the rope be pulling on both masses at the same time with the same amount of force? is that what tension is?
a magnitude directed towards a center point, and anything attaches experiences that magnitude?
runic garnet
1 rope
obsidian coral
If you tied a rope to two different objects on each end of the rope, why would they have different tensions?
If it's attached to the same rope
stray raven
because object 1 is pulling with force A and object 2 is pulling with force B
so object 1 should be pulled by force B
and object 2 should be pulled by force A
obsidian coral
So? Doesn't matter, the masses are attached to the same rope
obsidian coral
why doesn't it work the way i think it would
And this defies Newton's third law, I think, or second. Because if you have one rope, with to two different forces, it's not equal and opposite
runic garnet
Think it’s 3rd
stray raven
so i can't do something like
T_1 = Fg_2 and T_2 = Fg_1, assuming we have two masses hanging by a rope from a pulley hanging freely, because tension is the same throughout the rope. If it wasn't the same, then the rope would move. So tension exists when the rope is not moving? no, that's wrong. Tension exists on the object that is being pulled. So if m1 is heavier, it will pull m2 with a tension force equal to Fg_1, but m1 will not experience any tension force.
I am still confused by what tension is. I do not really understand why tension is the same. I am not satisfied. I'll study it up but recommend some sources would be great.
Or is this wrong, and m1 does experience a tension force?
gritty viper
both will experience tension force
stray raven
wait the tension force wont be equal to fg_1 because fg_2 does exert some kind of force
oh.
gritty viper
both will experience the same amount of tension force
this will be enough force to accelerate the lighter weight upwards
but the heavier weight will still accelerate downwards
stray raven
Tension
If you pull on a rope, the rope pulls back on you with the same force, by Newton’s third law. The magnitude of this force is called the tension in the rope. As far as the direction of the tension goes, the question, “At a given interior point in the rope, which way does the tension point?” can’t be answered. What we can say is that the tension at the given point pulls leftward on the point just to its right, and pulls rightward on the point just to its left. Equivalently, the tension pulls leftward on someone holding the right end of the rope, and it pulls rightward on someone holding the left end of the rope.
still not getting it but ill read it later
thanks all
cedar kilnBOT
@stray raven Has your question been resolved?
ornate sage
help
ornate sage
my channel disappeared
cedar kilnBOT
cedar kilnBOT
Available help channel!
calm ocean
Idk why this is wrong
cedar kilnBOT
Idk why this is wrong
calm ocean
bold vine
Do you have work?
livid hound
note the one obtuse angle in bold
calm ocean
note the **one obtuse angle** in bold
What would that mean for that problem?
livid hound
consider the ambiguity of the law of sines;
that x = arcsin(c) isn't the only solution to
sin(x) = c
calm ocean
It's really confusing to me since my professor didn't explain properly. Do you have any resources about the law of sines in general?
livid hound
look up ambiguity of sine law/rule
calm ocean
Alright, thanks 👍
cedar kilnBOT
Available help channel!
solemn torrent
aye aye
cedar kilnBOT
toxic moat
hm
sacred grail
just product rule
cedar kilnBOT
Available help channel!
spark birch
I'm making a video player thing and I need to get the percentage of people who liked a video.
Say the video get's 5000 views, and 234 likes. How can I get the percentage of people who liked? For example 13%
sullen spire
gray blade
cedar kilnBOT
gray blade
I drew this diagram but I'm just not sure where to go from here
the problem is idk x either
toxic moat
so much stuff
muted bear
15=y
toxic moat
whats y btw
muted bear
ues similar triangles
toxic moat
well
u can think of this as some triangle stuff
with lamp height as 0
and use triangles
and translate all accordingly
with some neg height itll act the same way as that with pos height
well at least Shadow wld b the same
gray blade
hmm
I don't really get what you mean but
I drew some triangles
and made a ratio 10 / 30 = (15 - x) / 10
to get x?
idk
okay i dont think that works
toxic moat
hm
u can extend x n 15 to 25
make a rect
see sim tri
n how rate of change wld change
cedar kilnBOT
@gray blade Has your question been resolved?
cedar kilnBOT
@gray blade Has your question been resolved?
oblique loom
need help with a quadratics question
cedar kilnBOT
need help with a quadratics question
oblique loom
i got up to 2(x^2 + 12x + 36) but unsure what to do next
oblique loom
need help with a quadratics question
5J*
tropic oxide
x^2+12x+36 is a perfect square
zealous tapir
how do u find a?
cedar kilnBOT
how do u find a?
craggy oriole
$log_a(b)=c \Leftrightarrow a^c=b$
wraith daggerBOT
ralvrz
cedar kilnBOT
@zealous tapir Has your question been resolved?
cedar kilnBOT
for a question such as this one
fading summit
would it be the part in red, or the part in blue
because im thinking, in part i) the n/(2n+1), is accouting for all the way down to 1/1*3
so im thinking since in part ii) its not including it, im assuming i minus the extra
fading summit
oh
hollow minnow
For the sum from 1/(1•3) to 1/(9• 11)
livid hound
no
hollow minnow
n is not 10
livid hound
where are you getting 10
hollow minnow
Yeah
cedar kilnBOT
hollow minnow
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Available help channel!
fossil terrace
I need help!
cedar kilnBOT
I need help!
kind wedge
With what?
fossil terrace
Is anywho here, who can speak ukrainian?
kind wedge
uh... not sure.
kind wedge
Try using google translate?
fossil terrace
My PC is ...
kind wedge
Ok nvm try english and if not ill use google
fossil terrace
Discord was opening 2 min!
kind wedge
if i can help with the question that is
fossil terrace
So, I am new here. I am not a student.
I am 10 years old
And I like math
so
Is here something for me?
Ok
kind wedge
Вам має бути більше 13 років, щоб бути на цьому сервері
idk i just used google translate
kind wedge
Is here something for me?
sorry
kind wedge
No problem :) use .close to close this channel if you dont have any other questions
kind wedge
Bye!
fossil terrace
Maybe I will come here when I will be 13+ years old!
kind wedge
Look forward to it!
fossil terrace
Hey wait!
kind wedge
Mhm?
fossil terrace
Go to my chanel plz!
kind wedge
Sure? DM it to me
kind wedge
Sure!
kind wedge
I sent you a friend req already, we shouldn’t use this channel anymore
cedar kilnBOT
@fossil terrace Has your question been resolved?
lethal knoll
cedar kilnBOT
lethal knoll
not sure how to start here, specifically on which fact of symmetry I can use, or how I can simplify that expression
opal basin
notice that x^3 * y^2 is an odd function for x and sin(y^3) is odd for y
I'm pretty sure the entire integral just cancels
@lethal knoll
lethal knoll
trying that now
sharp igloo
genuinely curious can you really look at it that way
it's not the entire function, just the parts that are odd
opal basin
you can split it up into 2 double integrals
lethal knoll
if the integral just cancels, do you mean both integrals evaluate to 0?
opal basin
pretty sure
sharp igloo
you can split it up into 2 double integrals
oh you're right thanks
sharp igloo
if the integral just cancels, do you mean both integrals evaluate to 0?
yeah i think so too
lethal knoll
side question, how are you meant to find the explicit limits for this integral?
since we just have D
opal basin
x goes from -1 to 1 and y goes from -sqrt(1 - x^2) to sqrt(1-x^2) I think
lethal knoll
ah I see
thanks 🙂
I can't see how this depends on the parity of n.
L = (x-y)^n + l(x^2 + 3y^2 - 1)
L_x = n(x-y)^(n-1) + 2xl
(similar for L_y)
So solving I get:
L_x = 0 => n(x-y)^(n-1) = -2xl
L_y = 0 => n(x-y)^(n-1) = 6yl
so -2xl = 6yl, 3y = -x
and sub that into the third equation (L_l if you like) to get two values for x and y each, but nothing involving the parity of n?
presumably something above is wrong
<@&286206848099549185> any ideas?
oh, I think I just plug it back into f and look at all 4 possibilities
crimson sedge
cedar kilnBOT
cedar kilnBOT
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Available help channel!
hollow stirrup
cedar kilnBOT
toxic moat
💕
toxic moat
we can find each triangle separately
by using the fact we know they r of some ratio of the rectangle
aka for the pink one
its l/2 * w/2 * 1/2
= lw/8
so its 1/8 of the rect area
now u try for the other 2 triangles
@hollow stirrup
hollow stirrup
L/2 * w *
hollow stirrup
Ok and the red l/2 *l * 1/2
hollow stirrup
Mb meant w/2
toxic moat
so whatd u get after simplifying it
hollow stirrup
Wl/4
toxic moat
so
now we can let the area of the rectangle be a
so whats the black triangles area in terms of a
toxic moat
for eg
hollow stirrup
Eg?
toxic moat
if we let this be a
then the blue line cuts it in half
the red part is a/2
or half a
the green part is also a/2
toxic moat
hm?
hollow stirrup
What Is A supposed to be
toxic moat
its just whatever we want it to be
toxic moat
here i let it be the rect area
hollow stirrup
Ok
toxic moat
here i also let it be the rect area
but they r diff rectangles
if u feel like u can let it be the area of the triangle instead
u just hv to keep it consistent
sacred grail
@toxic moat has no qualifications
toxic moat
and refining body layer 1 irl
sacred grail
@toxic moat is an amateur
cedar kilnBOT
@hollow stirrup Has your question been resolved?
toxic moat
Ty for the help btw
💕
tidal thistle
cedar kilnBOT
tidal thistle
do i use discriminant
but what would I make it = to
its fine
solved it
/close
ruby lion
its .close
cedar kilnBOT
Available help channel!
smoky wyvern
Could you please help me with this
cedar kilnBOT
smoky wyvern
.reopen
cedar kilnBOT
✅
leaden snow
what did you try?
cedar kilnBOT
@smoky wyvern Has your question been resolved?
leaden snow
what do you do if you want to find the intersection of two functions f and g?
cedar kilnBOT
@smoky wyvern Has your question been resolved?
smoky wyvern
what do you do if you want to find the intersection of two functions f and g?
I don't know sadly
wraith daggerBOT
nvx
potent bough
how come its not H(t-1)(t-cos(t-1)+1)
cedar kilnBOT
how come its not H(t-1)(t-cos(t-1)+1)
potent bough
somehow it drops the 1
cause its the heaviside function times each of the inverse laplaces of the terms right?
so we have t+1, -sin(t+1), 1, and sin(t+1)-cos(t+1)
the sins cancel
oh shoot its -1 frick
.close
hearty lily
How do I find the arclength? I thought the formula to find the arclength was s =r*theta but the answer isn't correct
solemn torrent
aye aye
wassup
uh
yeye
it is
Rθ
what did u try
and how did
u get 12?
hearty lily
I did the radius, 5, * 2.35619449 and then rounded it
I got the second number from 3pi/4
obsidian coral
I did the radius, 5, * 2.35619449 and then rounded it
Use exact numbers, I think that's why it's wrong
Don't use the decimal approximation
Keep it as 3pi/4
hearty lily
ohh, I see
that was right, thanks
ill keep this channel open for any other questions I got
obsidian coral
ill keep this channel open for any other questions I got
My suggestion, if it's going to take a while, just close the channel and open a new one when you need to
hearty lily
.close
torpid urchin
i tried rearranging so i dont have to do a crazy quotient rule but think that may be wrong
fluid crescent
huh
fluid crescent
i-
cedar kilnBOT
fluid crescent
yo
fluid crescent
im on my side hustle shit
man looked fookin stoned
i swear why everyone on the tangent shi
lemme have a look
fluid crescent
lol
fluid crescent
lol
obsidian coral
You were taking a test?
fluid crescent
i did
torpid urchin
i just threw an idea out
torpid urchin
You were taking a test?
top 1 worst things to admit in math discord
fluid crescent
i cant man i forgot i gotta start learning all over again for this one
obsidian coral
That's academic dishonesty
fluid crescent
teacher be like HAHAHAHAHAH SCREW THE CHILDREN
torpid urchin
dldh06 does not fuck around
SOOOOO
does anyone know how to do that
o damn
did he just get banned 😭
fluid crescent
does anyone know how to do that
i looked up google
wait what happened
who got banned lol
torpid urchin
the 5^90 guy
obsidian coral
You need to open a new channel, this is going to close
torpid urchin
ok 😦
obsidian coral
.
fluid crescent
!close"
fluid crescent
HHAHAHAHAHAHA
noble sentinel
fluid crescent
:IRONIC
cedar kilnBOT
Available help channel!
frosty crescent
Hello
frosty crescent
how do i know when to write ≥ or > in a picewise function?
mental trail
Depends on the function.
obsidian coral
When it includes that value or not
frosty crescent
i dont get when they use them or what they basically mean
frosty crescent
yeah
mental trail
So, if you want to include a bound of your piecewise function into a specific region, you use " ≥". For example, if you want to make the function which outputs 0 for negative numbers and 1 for non-negatives, you say that :
f(x) = { 0 if x < 0
{ 1 if x ≥ 0
sacred grail
double curly braces 
mental trail
Shuush :)
crimson sedge
not everyone is a latex wizard
sacred grail
🪄
crimson sedge
sacred grail
wraith daggerBOT
crimson sedge
hmm so if x=0 then do i evaluate top or bottom
sacred grail
yes
cedar kilnBOT
@frosty crescent Has your question been resolved?
frosty crescent
hmm so if x=0 then do i evaluate top or bottom
good question
cedar kilnBOT
cedar kilnBOT
✅
midnight brook
it got reopened
frosty crescent
what does that mean
quartz frost
the bot asked whether your question qas answered
you said yes
then it autonatically closes the channel
midnight brook
the denominator of a function is (x-1)^2 and I am trying to find vertical asymptote. I set it up so
(x-1)^2 = 0
x^2 + 1 = 0
and got
sqrt(-1)
which Im not very sure what it is.
I already find the domain and by a glance I can tell if x = 1 then there is no value and therefore has an asymptote of 1
cedar kilnBOT
the denominator of a function is (x-1)^2 and I am trying to find vertical asympt...
midnight brook
<@&286206848099549185>
sage forge
Firstly, wait 15 min to ping helpers
Also what is the connection between the first and second line?
midnight brook
The exponent passed into x-1
sage forge
(x-1) (x-1) = x^2 + 1 ???
crimson sedge
Hello
crimson delta
understand what about it
crimson sedge
Why null space of A is zero, if matrix has an inverse.
crimson sedge
understand what about it
What does that mean geomatrically?
crimson delta
well that it doesn't send two different points to the same point
it only maps 0 to 0
no other point
crimson sedge
Okay. Thank you 🙂
shell hearth
I don't understand what he did after applying the product rule
hollow minnow
Factor out cscθ
Then 1-csc^2θ = -cot^2θ
After that its just simplify and taking out cotθ at the end
shell hearth
Thank you
hollow minnow
shell hearth
<:catthumbsup:614540188747563008>
Just one more thing .. when we factor the csc how is csc^2 still in there ( sorry i pretty new to this and i am having a hard time thanks for helping me)
I don’t understand the factor out part
hollow minnow
You have $\csc{\theta}(1-\csc ^2{\theta}) -\csc{\theta}(…)$
wraith daggerBOT
Pure
hollow minnow
Like $a(…)-a(…)=a(…-…)$
wraith daggerBOT
Pure
hollow minnow
I realise this is a bit weird
shell hearth
not rlly 😅
hollow minnow
You see there’s a common factor of csc in both terms of the sum
Then you factored it out
You have $\csc{\theta}(1-\csc ^2{\theta}) -\csc{\theta}(\cot{\theta}(\theta +\cot{\theta}))$
wraith daggerBOT
Pure
shell hearth
csc(x)(1 - csc^2(x) + ( x + cot(x))(-csc(x) cot(x)). where is the comman factory?
hollow minnow
They are both multiplied by csc
hollow minnow
shell hearth
Thank you so much fr
hollow minnow
Np
cedar kilnBOT
@shell hearth Has your question been resolved?
crimson sedge
hearty lily
How would I find the angle from arclength and radius?
cedar kilnBOT
How would I find the angle from arclength and radius?
hearty lily
if the formula to find arclength is s=r*theta, wouldn't finding theta be theta = r/s?
cedar kilnBOT
@hearty lily Has your question been resolved?
hearty lily
<@&286206848099549185>