yes
#help-0
autumn pasture
you can express as a single fraction
$\frac{sinC - sin(C) cos^{2}(C)}{cos^{2}C}$
ocean sealBOT
duckiescute!
grizzled cliff
OHH Okay
grizzled cliff
uh
grizzled cliff
uhh
autumn pasture
if I have $x-4xy$
ocean sealBOT
duckiescute!
autumn pasture
there’s x common right
grizzled cliff
yeah
ocean sealBOT
duckiescute!
grizzled cliff
?
grizzled cliff
YES
grizzled cliff
that's equal to
autumn pasture
the thing
grizzled cliff
sin^2(C)
grizzled cliff
okay wait wait
autumn pasture
okay okay 👍
grizzled cliff
okay there
autumn pasture
YES
grizzled cliff
YES
autumn pasture
👏
okay
now we can write that in a split fraction form
as two things multiplied together
if I have $\frac{x}{2}$ I can write it as x(\frac{1}]{2})$
ocean sealBOT
duckiescute!
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
autumn pasture
ahhh nooo
grizzled cliff
huh 💀
autumn pasture
wait let me rewrite that
grizzled cliff
okay
autumn pasture
if I have $\frac{x}{2}$
ocean sealBOT
duckiescute!
ocean sealBOT
duckiescute!
autumn pasture
so the denominator becomes 1
grizzled cliff
oh
grizzled cliff
then that's
autumn pasture
and what is 1/cos^2
grizzled cliff
autumn pasture
WOO
grizzled cliff
WE DID IT
autumn pasture
YOU DID IT
grizzled cliff
TYTYTYTYTY
grizzled cliff
Thank you so much 😭
autumn pasture
no problemoo 😌
grizzled cliff
oH
autumn pasture
so like
autumn pasture
oh yea you don’t hahahah
there’s a - in between them
so if $\frac{3}{4} - \frac{1}{4}$
ocean sealBOT
duckiescute!
autumn pasture
I can write that as $\frac{3-1}{4}$
ocean sealBOT
duckiescute!
autumn pasture
no probbb! and nooo HAHA there’s much smarter people here
autumn pasture
tqtq
grizzled cliff
.close
lone heartBOT
autumn pasture
byeee
lone heartBOT
Available help channel!
lone bronze
I'm working on a game and am trying to work out how many unique 'build' possibilities exist for the player based on a few variables and have no idea where to start.
There are 9 weapons in the game. The player can choose two weapons.
There are 8 equipment items in the game. The player can choose two equipment items.
There are 45 perks in the game. The player can choose up to 23 different perks.
With the above in mind - how many unique perk/equipment/weapon combinations exist in the game and what is the process to prove this?
karmic rapids
,, {9 \choose 2} {8 \choose 2} {45 \choose 23}
alpine sable
ocean sealBOT
illuminator3 (#eric4honorable)
ocean sealBOT
lone heartBOT
@lone bronze Has your question been resolved?
lone bronze
Thanks @karmic rapids
limpid thunder
I feel like i have been doing this wrong big time but is this solution true?
limpid thunder
ornate condor
,w solve 9x+3=3(3x+1)
ocean sealBOT
limpid thunder
9x + 3 = 3 (3x + 1) - 3
fluid basin
that's the equation?
merry depot
The solution isn’t true. You added 9x across the equals instead of subtracting.
limpid thunder
So its a trick question?
fluid basin
no, just one that has no solution
autumn pasture
the question
autumn pasture
is saying 0=3??
limpid thunder
J.
autumn pasture
OH MY
ornate condor
ok whats at the top
fluid basin
the lhs and rhs are the same except for a constant, and that situation is an "inconsistent system" with no solutions
limpid thunder
Those are other question each alphabet is a different Equation
fluid basin
if the lhs and rhs are exactly the same you get a singular system where everything is a solution
i is singular; in i everything is a solution
limpid thunder
It says solve the equation in which way you find easiest
limpid thunder
But in the end J. is a mistake?
limpid thunder
Ah i see, then its probably a trick question my teacher gave me to challenge me
He is probably having a laugh rn
fluid basin
i dunno if i'd call i a trick so much as an object lesson
fluid basin
"not all equations can be solved"
fluid basin
no, if you get 0=1, then the solution set is empty
limpid thunder
Yep i think that is the question, it cant be solved because it results in 0
fluid basin
yes, one way is right, the other is not
ornate condor
yes, one way is right, the other is not
fluid basin
np
limpid thunder
.end
ornate condor
.close
lone heartBOT
limpid thunder
Oh yea sry lol
ornate condor
💕
lone heartBOT
Available help channel!
alpine sable
Help
alpine sable
Do you know the form of the equation of a line
Nope
y = ax+b
So for the point A (x,y) you have y=ax+b
Oo
What do you have for (-1 ,1) and (5 ,-6)?
E
Uh
I think I'm too bad at it to understand
Maybe you have a lesson you can work on
E
If not you can find one with google
Can u get the answer 🧍♀️
I*
I have 15 minutes to submit it to my teacher 💀
lmao
is this a test?
Naur homework
This is my last chance to summit the homework
But if you don't learn how to do it you'll never know
I'll learn it later
Sure thing
for the second line you isolate y and it's done
Nvm I can't solve it on the website too
yes
You have (-1 ,1) and (5 ,-6)
Aaaaa
enter -1 ,1
and 5 , -6
Okay
Wait this site is trash
Let me find a better one lol
☠️
ornate condor
LOL
alpine sable
Damn they're all a bit hard to use
I'll give you the answers lol
Kk
Tysm
first is y=-7x/6 -1/6
or y=-7/6 * x -1/6
Ooo
second one is y=18/29 * x - 9/29
or 18x/29 - 9/29 it's the same thing
O
Tysm
Last one is y= 17/16 * x -113/8
O:
Then you isolate y
You can do it? for the 3 left
I don't think so
x-2y=7
We want y=....
We can substract x for both side
-2y=7-x
Then we divide both side by -2
y=(-7+x)/2 = x/2 -3.5
O:
I gave you an example now do it for the 2 next
Kk
Ty
lone heartBOT
@alpine sable Has your question been resolved?
topaz stirrup
I'm crap at division
Like absolute dogwater mixed with crap and piss
Teach me division
HELLO!?
My friend sent me this telling me it would help my math
This ain't helping shit, you don't even reply
solemn juniper
This ain't helping shit, you don't even reply
topaz stirrup
I already have
It says say my problem here and then I get helped
I've done that
And no help
topaz stirrup
It said post in help 0, that's what I'm bloody doing
solemn juniper
topaz stirrup
It said post in help 0
unkempt reef
lone heartBOT
unkempt reef
Can you help for the last question
trim wagon
,rccw
ocean sealBOT
unkempt reef
Can you help
lone heartBOT
@unkempt reef Has your question been resolved?
lone heartBOT
lone heartBOT
Available help channel!
obsidian juniper
vocal lion
in question one, either a is positive and c negative or the other way around
same goes for a and b in question 2
that's bc if you want a negative product, you need a positive and a negative factor since 2 positive gives positive and 2 negative cancel each others' negativity out so they become positive
ornate condor
hi again
thats
is an element of
shortening the stuff to their abbrev
{A,D} is an element of enrolled
iff
in enrolled theres
{{A,D}, ...stuff}
but in enrolled iirc its
{A,B,C,D}
thrs no element {A,D}
like it has A and D, but it does not contain a set of 2 elements
no
like
an element that contains {A,D} as an element would for eg be
{A,B,C,D, {A,D}}
yes
A and D are both individuall enrolled
but the set of A,D is enrolled
eh idk
normally we dont use subset for elements
A isnt a set
some1 else can prob ans it btr
vale wigeon
vale wigeon
no obviously not
vale wigeon
the people's names should be treated as atoms here imo
they are not themselves sets
thus it makes no sense to ask whether i am ann is a subset of anything
ornate condor
would it be false or undefined or?
lone heartBOT
lone heartBOT
Available help channel!
alpine sable
hello
alpine sable
can anyone help me with the following problem
frozen compass
alpine sable
A bouncy ball is thrown horizontally off 45-meter building
how long will it take to hit the ground, and if it bounces 65% its original height, how long will it take to reach this height
languid bolt
ignoring friction and air resistance?
alpine sable
yes
languid bolt
and other stuff?
gilded sedge
Gravity will pull it down at g.
So time for accelerating at g for 45m
alpine sable
g^2/2
gilded sedge
I don't have means to do calculation
No just acceleration by time .
It give you speed at t
You integrate one more time.
F(t)
To have distance.
f'(f)=g to f(t)=.... to F(t)=...
And you find t for F(t)=45
long axle
~~and other stuff?~~
What other stuff is there? pressure or smth?
gilded sedge
g=9.81m/s^2 in your exercice?
alpine sable
9.8
alpine sable
yes it is
olive sentinel
@alpine sable the ball is thrown. Does that mean it's projected with a velocity or just free fall.
olive sentinel
Ah ok so it's a projectile question
gilded sedge
f(t) is velocity.
alpine sable
Ah ok so it's a projectile question
yes
I can do the first part no problem
but the second part stumped me
gilded sedge
<@456226577798135808> the ball is thrown. Does that mean it's projected with a v...
Horizontale velocity is not mentioned, and we don't need it, if I understand the problem.
olive sentinel
Yeah we dont
gilded sedge
Everything goes done at g.
olive sentinel
the time of flight is root(2h/g) iirc
gilded sedge
I have a file who does that, I start pc and confirm your result.
olive sentinel
u can find the final vertical velocity using v = g times root(2h/g)
alpine sable
do I need it tho to determine the time in which the balls rebounce reaches 65% of 45
olive sentinel
total time should be the appropriate one
but it could be only the rebound time as well
alpine sable
well time taken for the ball to hit the ground the first time is 3.03 seconds
olive sentinel
yeah
olive sentinel
that should be right
alpine sable
yea it is
so what can I do for the second part
it bounces back up and follows a different parabolic trajectory reaching a max heigth of 29.25m
olive sentinel
exactly
you have the projection velocity of the rebound too
as the horizontal velocity doesn't change, its constant, and the vertical velocity at the time of rebound is g times t in the first part
damn this is a good question it might come in my exams
alpine sable
yea it's a good question but its tough considering the amount of approaches
olive sentinel
ok I think I get it
olive sentinel
time of flight in the second projection after rebound is 2v/g so the time taken to reach the maximum height is v/g
where v is the vertical velocity after rebound
gilded sedge
Need to go.
olive sentinel
let me bring out my notebook and I'll do this wait a sec
gilded sedge
Speed is average not final speed
alpine sable
the valocity of the ball in the first throw is 14.85m/s
olive sentinel
@alpine sable
is the answer 6.06s?
total time taken to reach 65% of initial height from initial launch
alpine sable
thats what is confusingm, is it from initial launch or after bouncing on the ground
alpine sable
no
olive sentinel
yea well there u go
alpine sable
what has to be found is the time taken for the ball to reach 65% of the inital height
olive sentinel
assuming the collision is elastic with the ground
and there's no loss of momentum
then once u have the final vertical velocity of the initial launch, u can find the time taken by forming a quadratic equation
alpine sable
vertical velocity should be 14.85m/s
alpine sable
how can we find final vertical velocity
olive sentinel
the horizontal velocity is 14.85
alpine sable
oh yea i read it wrong mb
olive sentinel
the final vertical velocity = initial vertical velocity + g*(time taken to hit the ground the first time)
initial vertical velocity is 0
olive sentinel
we get 2 times because the ball hits 65% of height while going up, then also while coming back down in the projectile path
the smaller one should be the answer i think
alpine sable
yea but this is only for going up
olive sentinel
it will reach the lesser height again, but in more time
yeah
thats why we reject the 4s
olive sentinel
this is technically a free fall
since we don't give any initial vertical velocity
alpine sable
yeaaa, youre right
olive sentinel
horizontal projection or simply dropping the body will take the same time
in this situation
olive sentinel
however if it's not a horizontal projection
alpine sable
not archimedes
olive sentinel
u can't do what I did there
alpine sable
it was someone else
olive sentinel
yeah
alpine sable
cant remember the name
alpine sable
no not newton
alpine sable
hi
lone heartBOT
@alpine sable Has your question been resolved?
torpid kestrel
Hello, I have some data ranging from 0 to 1 that I'm trying to convert to weights (range doesn't matter, but 0-1 is preferred). And I want the weights to be more extreme (see example below). As in to make large numbers bigger and small numbers even smaller. What would be the most general function for performing this transformation.
torpid kestrel
Currently I'm using this logistic function:
[\frac{1}{1+e^{\left(-cx+0.5c\right)}}]
ocean sealBOT
LucasYerz
torpid kestrel
c is a constant that in my case ranges from 10 to 50.
mortal trellis
well there are a lot of options. you could even use something as simple as x^2
torpid kestrel
well there are a lot of options. you could even use something as simple as x^2
very true.
I mostly what a function that besides c will also have another parameter for a bias.
to change the skewness of the graph.
something like this b
but for the logistic function
mortal trellis
you could take the whole logistic function to the power of b?
torpid kestrel
you could take the whole logistic function to the power of b?
really? yeah, you're right, that kinda works.
mortal trellis
or you could take x^b inside the logistic function
torpid kestrel
or you could take x^b inside the logistic function
hmm
still not getting that exponential shape in the middle
how can I transform the logistic into x^2
and x^b
like take the average between the functions
mortal trellis
well average just means adding them up and dividing by 2
torpid kestrel
lets try that
mortal trellis
not exactly sure what you mean by transforming the logistic into x^2
mortal trellis
well could do a weighted average. a*logistic + (1-a)*x^b or something
torpid kestrel
yup that should do it
I'll use an optimization procedure to select the b, c, and w.
torpid kestrel
well could do a weighted average. a\*logistic + (1-a)\*x^b or something
thanks a bunch!
this is what I wanted
.close
heady void
help how do I do this one
lone heartBOT
help how do I do this one
echo socket
Quotient rule
But if you're unfamiliar with it, then just represent tan as sin * (cos)^-1
So that you can apply product, power and chain rules
echo socket
You forgot about the chain rule
heady void
Where
heady void
You forgot about the chain rule
I don’t see it
echo socket
When you differentiated the (cosx)^-1 you forgot about it
heady void
ok how do I get this
lone heartBOT
ok how do I get this
heady void
1/cos(x)
echo socket
Derivative of (f(x))^(-1) is -(f(x))^(-2) * f'(x) according to the chain rule
gray isle
$$\frac{1}{\cos(x)} = (\cos(x))^{-1}$$
differentiate using a combo of power and chain rule
echo socket
Are you familiar with the chain rule?
ocean sealBOT
ℝamonov
heady void
Are you familiar with the chain rule?
not much, but I know how it works
gray isle
doing a substitution like u = cos(x) may make the application clearer for you
lone heartBOT
@heady void Has your question been resolved?
silk frigate
is my answer correct
lone heartBOT
is my answer correct
karmic rapids
yes
silk frigate
ok thanks
wise thistle
No
silk frigate
i need to fix
karmic rapids
@silk frigate jesus christ wtf is up with your about me
wise thistle
HOLY SHIT
alpine sable
help
karmic rapids
dw about that
????
wise thistle
dw about that
worrying bruv
karmic rapids
its just a symbol chill
dude do you know how many people died due to the nazis
wise thistle
you becoming the next art sch reject
wise thistle
hey @silk frigate where can i get that symbol
karmic rapids
no it's not
wise thistle
i want it
silk frigate
For india
karmic rapids
that's the other way around
silk frigate
Im an indian
karmic rapids
the Hindu luck symbol is the other way around
silk frigate
there
wise thistle
that was a joke
karmic rapids
hail hitler
<@&268886789983436800>
silk frigate
hail hitler
bro
wise thistle
IT WAS A JOKE
keen plinth
y'all are overreacting to possibly an honest mistake
silk frigate
sorry
autumn pasture
what is happening..
autumn pasture
hail hitler
uhhhh
keen plinth
yeah just ignore that
silk frigate
well is it correct?
keen plinth
i think so
silk frigate
ok thank u
keen plinth
,w simplify (a+2)/2 - (a-4)/4
night geyser
fyi, "its a joke" does not excuse the behaviour.
ocean sealBOT
oblique lichen
Can anyone tell me the answer of 7X x 14X x Z/28
frozen zodiac
how do i prove that the angle between two intersecting lines is an invariant under the set of all translations?
untold vigil
Can anybody solve this problem of set theory?
fluid basin
Can anybody solve this problem of set theory?
https://math.stackexchange.com/q/...
this channel is already in use, please move to an open channel
frozen zodiac
<@&286206848099549185>
<@&286206848099549185>
<@&286206848099549185> please helppp
lone heartBOT
@frozen zodiac Has your question been resolved?
lone heartBOT
@frozen zodiac Has your question been resolved?
frozen zodiac
.close
rough ice
lone heartBOT
rough ice
How does this become (1-cosx)(cscx)^2
naive crystal
See
rough ice
?
naive crystal
What
rough ice
what do u mean see
naive crystal
No
rough ice
???
naive crystal
Show full question
rough ice
Why do u need the full question
naive crystal
How does this become (1-cosx)(cscx)^2
That can't happen
rough ice
naive crystal
Use the chain rule ig
tiny cosmos
Why do u need the full question
Because we needed to see the derivitive sign there
the original question is impossible
rough ice
oh
naive crystal
Ye
rough ice
So how is it solveable
Btw that’s y=sinx/1+cosx not just sinx/1+cosx
Ya’ll wanna see how i solved it and got to that point?
naive crystal
,w d/dx ((sinx)/(1+cosx))
naive crystal
Ya’ll wanna see how i solved it and got to that point?
Show
ocean sealBOT
rough ice
ocean sealBOT
Basudev
rough ice
The top is the same as the bottom so i can simplify
rough ice
I multiplied by 1-cosx/1-cosx so 1-cosx could become on top
rough ice
Yea but where did the cscx^2 come from
naive crystal
You can write
rough ice
Write what?
naive crystal
$(1-\cos(x))×\frac{1}{(sinx)^2}$
ocean sealBOT
Basudev
naive crystal
Them 1/(sinx)^2 = (cscx)^2
naive crystal
K
rough ice
.close
blissful shale
1/-4?
pale lance
1/-4?
Close, try looking at how much it rises and divide it by how much it moves right
If it goes up. by 3, and right by 2, what would the slope be?
blissful shale
2/3?
alpine sable
lone heartBOT
alpine sable
How should I approach this trig sub problem? I tried to see if I could get rid of the x with du for possibly an inverse trig solution
but that got me nowhere.
Do I need to utilize long division? If so, how does that work with the sqrt?
echo socket
Is the problem telling you to use trig sub?
alpine sable
Or is this a simple trig sub problem with x^2 - a^2 where x = asec(theta)?
alpine sable
Is the problem telling you to use trig sub?
yes
We get points off for not doing so
Although, this is just practice for the exam next week.
echo socket
Try x = 2sec(theta)
alpine sable
I will give that a go.
alpine sable
go away lol
alpine sable
whys this integral under trig sub
Maybe this is unrelated, but our math department is quite poor.
People typically go to the local community college to take math instead of here.
Almost done with the problem tho.
I got sqrt(x^2-4) + C as my final answer. Could someone please check this?
Seems... too short
gray isle
yeh, that's correct
lone heartBOT
lone heartBOT
Available help channel!
wanton crystal
ln(5x)+ln(32)=4, help I’ve a test soon and I don’t know how this question works
sand ermine
olive sentinel
@wanton crystal is the answer e⁴/160
wanton crystal
Oh tysm
zinc geyser
Hi guys, I have a math problem that I have been failing to solve for two days. The function is y=(5*ln(x))/x and I have to try to find a point where the origin line touches the function. I have no idea at all how to solve this.... I tried to see when the function flattens out before the extreme point, but I have no idea how that could work.
karmic rapids
Hi guys, I have a math problem that I have been failing to solve for two days. T...
which origin line
echo socket
What do you mean by origin line?
zinc geyser
What do you mean by origin line?
A Strang line that go through the Point(0|0)
*straigt
alpine sable
so y = x?
echo socket
y = kx for some k?
zinc geyser
y = kx for some k?
Yes
alpine sable
find where they intersect, so set them equal to eachother.
zinc geyser
But how I didn't have the Point and function
echo socket
Yeah you can set the derivative equal to k for the point too
alpine sable
But how I didn't have the Point and function
are you able to show us the whole problem? it sounds like there may be more to it than youre sharing?
karmic rapids
differentiate then find the tangent where the y intersect is 0
zinc geyser
are you able to show us the whole problem? it sounds like there may be more to i...
Yes
zinc geyser
are you able to show us the whole problem? it sounds like there may be more to i...
Green my Graph
I thought maby i the point is P(0|infinity)
zinc geyser
are you able to show us the whole problem? it sounds like there may be more to i...
making that sense or should i try to explain my problem better?
alpine sable
about to drive, sorry
zinc geyser
about to drive, sorry
no problem
or thought too that maybe there is a tool which allows me that i can try every possible function
Can i maybe create infinite origin functions somehow and then look which match is the best
<@&286206848099549185>
lone heartBOT
@zinc geyser Has your question been resolved?
zinc geyser
Or maybe so? That I cut it in half?
zinc geyser
yeah i tried to understand it but i couldn't undestand where i get x_t and y_t? When i want to calculate both
But i think i can caluclate it too with triangels
gray isle
you were given
$$y = \frac{5\ln(x)}{x}$$
$$y_t = \frac{5\ln(x_t)}{x_t}$$
using everything you know
$$f'(x_t) = \frac{y_t}{x_t}$$
can be expressed as an equation in the variable $x_t$
ocean sealBOT
ℝamonov
zinc geyser
**ℝamonov**
f' is the first derivative... right? And x_t and y_t are the coordinates for P?
gray isle
x_t and y_t represent the x and y coordinates of the point of tangency you're interested in
zinc geyser
Yeah
zinc geyser
wait so my first derivative is f'(x_t)=5-5*ln(x_t)
But what should i put into x_t?
Nothing?
zinc geyser
But what is x_t i dind't have it
zinc geyser
yeah i try to find x_t and y_t
gray isle
solving that equation will tell you the value of x_t
zinc geyser
you'll have an equation in terms of x_t
THe normal function?
gray isle
wdym
zinc geyser
What is the equation that tells me the value?
gray isle
do you understand the equation at the bottom?
zinc geyser
The first derivative equals y_t/x_t but i can't simply trow the x away on both sides
gray isle
wdym by trow away
zinc geyser
I must get rid of the x_t right?
gray isle
no?
zinc geyser
what?
gray isle
where did you get that idea
your derivative was wrong
I didn't double check that earlier
zinc geyser
where did you get that idea
idk i want to calculate y_t but i can't solve it whan i have two missing numbers (x_t and y_t)
gray isle
using
$$y_t = \frac{5\ln(x_t)}{x_t}$$
$$\frac{y_t}{x_t} = , ?$$
ocean sealBOT
ℝamonov
zinc geyser
**ℝamonov**
mustn't be the x² under the line?
zinc geyser
it making no sense to me... must the x_t on the other side
gray isle
mustn't be the x² under the line?
not sure what you mean
focus only on that most recent image and nothing else
zinc geyser
> mustn't be the x² under the line?
not sure what you mean
yeah thought this is the first derivative my fault
$$5\ln(x_t) = \frac{y_t}{x_t}$$ ?
ocean sealBOT
DVD
zinc geyser
mhh... i don't get it sorry...
I would do that x_t * y_t = 5*ln(x)
gray isle
don't overthink
this step is basic fraction division
that doesn't tell you what
y_t/x_t is
starting with
$$y_t = \frac{5\ln(x_t)}{x_t}$$
divide both sides by $x_t$
ocean sealBOT
ℝamonov
ocean sealBOT
DVD
gray isle
simplify that
zinc geyser
x_t / x_t is one and everything divided by 1 is the same so i can throw the 1 away
gray isle
no
you're ignoring the order of operations
(a/b)/b isn't the same as a/(b/b)
solving 2x = 1/2
doesn't get you x=1 (which is pretty much what you're implying)
it may help to think of division by x_t as multiplication by 1/x_t
zinc geyser
$$\frac{y_t}{x_t} = \frac{5\ln(x_t)}{x_t²}$$ so this? because devided by x_t can be written as multiply by $$\frac{1}{x_t}$$
ocean sealBOT
DVD
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gray isle
yes
$$f'(x_t) = \frac{y_t}{x_t}$$
assuming you have the correct derivative now, putting all that together gets you
$$\frac{5-5\ln(x_t)}{{x_t}^2}= \frac{5\ln(x_t)}{{x_t}^2}$$
ocean sealBOT
ℝamonov
gray isle
which is an equation with a single variable: x_t
zinc geyser
and now everything on one side?
zinc geyser
which is an equation with a single variable: x_t
ahh and then i get x_t whith that i can then calculate y_t
tf what kind of master brain are you?
Ok maybe dumb question but why is the first derivative now $$f'(x_t) = \frac{y_t}{x_t}$$
ocean sealBOT
DVD
gray isle
that's what I posted at the very start
it didn't sound like you had an issue with that earlier
zinc geyser
it didn't sound like you had an issue with that earlier
i didn't wanted to disturb you with that
gray isle
that's a key component of the process
if you had questions, state them at the start so we don't have to backtrack
zinc geyser
has it a specific name that i can learn it?
zinc geyser
if you had questions, state them at the start so we don't have to backtrack
yeah ok... next time 🙂
gray isle
the LHS is the expression for the slope from the derivative
the RHS is the expression for the slope between the point and the origin which is just the ratio of the y and x coordinates
these will be equal for the tangent line that you want
zinc geyser
ah ok... yes makes sense
zinc geyser
these will be equal for the tangent line that you want
thanks again for your time
zinc geyser
these will be equal for the tangent line that you want
But why exactly this "touching" point of the tangent with our function results from the equation that is not yet so conclusive for me... because $$f'(x_t) = \frac{y_t}{x_t}$$
ocean sealBOT
DVD
gray isle
the LHS is the expression for the slope from the derivative
the RHS is the expression for the slope between the point and the origin which is just the ratio of the y and x coordinates
you're interested in when these are the same
lone heartBOT
@zinc geyser Has your question been resolved?
zinc geyser
you're interested in when these are the same
Yeah
lone heartBOT
@zinc geyser Has your question been resolved?
jaunty needle
if ur making g alone like in this, ge, can you do divided by e cross both e's out, but with out switching the variables like to eg
last ether
Yeah
jaunty needle
they switch ax to xa to divide it by x
last ether
Which is useless
jaunty needle
do i have to do that or can i just keep it as ax and just cross out x
jaunty needle
so there the same i dont need to switch it
im solving for a
its not a math rule right?
to switch it
jaunty needle
do i need to switch it?
ocean sealBOT
Umbraleviathan
last ether
No you don't
fading mauve
How do I find domain restrictions?
lone heartBOT
How do I find domain restrictions?
fading mauve
I have part 1 done, f(g) = x and g(f) = x (so they're inverses)
but I don't know how to find the domain restrictions
I'd really appreciate help on this
pallid scarab
when is a rational fraction not defined ? Answer : ||when the denominator gets to 0||
fading mauve
I know that much but I'm still confused
pallid scarab
what is confusing you ?
fading mauve
basically all of it honestly
pallid scarab
let's look at g o f
take any x real number
g o f (x) is not defined when f(x) is not defined
and g o f (x) is not defined either when g is not defined IN f(x)
fading mauve
i think i get like a basic gist of what I need to do but i dont fully understand
im assuming ill need to find the domain restriction to where x cannot be 0 by using f(x) or g(x), i found something about that in my notes
but beyond that im still confused
pallid scarab
example : if x = 0, is g(x) defined ?
pallid scarab
yes
because the denominator is 0
so it would be infinity, which is not possible
now, for now only find the domains of f and g, not the compositions
fading mauve
I think I get it
1/x-4 ≠ 0
Multiply both sides by x-4/x-4.
x-4 ≠ x-4/x-4
x-4 ≠ 1
Add 4 to both sides to get x by itself.
x ≠ 5
The domain is (-∞, ∞) where x ≠ 5
does that look right to you?
pallid scarab
wait
pallid scarab
does that look right to you?
it's not the entire thing that has to be ≠ 0, it's the denominator
fading mauve
could you please show me how i would solve the domain restriction for this problem so i could understand? i dont think im getting it
pallid scarab
ok
let's do it for g (again)
In order for a point x to be in the domain, g(x) has to be defined.
and in particular, g(x) HAS to be finite
so g(x) CANNOT be infinity
when is g(x) infinity ? when the denominator is zero, meaning x = 0
so the domain is (-∞, ∞) where x ≠ 0
try it with f
fading mauve
alrighty
shadow urchin
What is the formula to rotate a 90 degree angle counter clockwise
last ether
What is the formula to rotate a 90 degree angle counter clockwise
Rotate an object 90°?
Like parametrically?
shadow urchin
.....idk I am doing my pre algebra HW and frogot the formula 
raven zinc
econ related but can sme help me
last ether
econ related but can sme help me
#❓how-to-get-help don't take other people's channels
shadow urchin
gilded vessel
very readable thanks
last ether
I think you're thinking of (a, b) -> (-b, a)
_ _
shadow urchin
Thx
steel turret
hello
modest dragon
im pretty sure i need to form 2 permutations
2 combinatios and sum them
steel turret
2 combinatios and sum them
so would that be 9!/(3! * 6!) + 3!/(2! * 1!) ?
modest dragon
yeah 9C3 + 3C2
lone heartBOT
molten steppe
.reopen
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molten steppe
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ornate condor
thats good
molten steppe
now i need to study
ornate condor
good luck
molten steppe
i need help on Estimating Integers it's really hard and i have a quiz tomorrow think you can help me out.
<@&286206848099549185>
hello
ionic agate
need help with indices its a hw due tmr
the question is (3p^4)^-3
hope u can understand it
lone heartBOT
@molten steppe Has your question been resolved?
swift shore
i need help on Estimating Integers it's really hard and i have a quiz tomorrow t...
what
you have to post a problem
lone heartBOT
@molten steppe Has your question been resolved?
short veldt
Is there a way to find the local maxima and minima of a function without graphing it
last ether
Is there a way to find the local maxima and minima of a function without graphin...
Derivative
Or
Well you have a simple quadratic so there's two ways
short veldt
Derivative
I haven't done calculus to there yet