idk if this helps
#help-23
round tiger
and this is like a related example of what i’m trying to do
but basically im trying to create an equation that would suit a predicted population of a city
do you think something like this would work?
this is what bing ai is suggesting
but what do you think?
ples come back
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willow gust
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marble moss
i need help with solving the fist interval
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i need help with solving the fist interval
bright nacelle
Domain is correct but in range it should be (-4,-1)U(3,8]
marble moss
-1 should have a ] because its including it
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rotund harbor
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rotund harbor
How is this done?
frank glen
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wanton remnant
Yo guys how do I find the range again
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Yo guys how do I find the range again
little mesa
do you know how to find the vertex
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wanton remnant
do you know how to find the vertex
Tbf I initially thought the vertex was (4, -9)
wanton remnant
☠️☠️☠️
flat frigateBOT
Spooderman
little mesa
k
wanton remnant
Yo guys how do I find the range again
So what do i do here
little mesa
ohh i didn't even notice the domain restriction
for x<3, the parabola ends at y=-7
which is why y>-7
flat frigateBOT
Spooderman
little mesa
wanton remnant
Yoooo
I just plugged 3 into the thing
How do I determine the inequality sign again
quasi bison
posting chatGPT output is a bannable offense
<@&268886789983436800> 2 channels of this crap
twilit moat
wanton remnant
posting chatGPT output is a bannable offense
Damn I thought blud was onto something
quasi bison
i'm not a guy.
- that's a question you should take up with the moderators
- please edit out the "guy" in your message.
wanton remnant
Wait could u help me real quick
quasi bison
honestly i dont have much energy for that sorry
wanton remnant
Yo guys how do I find the range again
How do I determine the direction of the inequality
Oh
quasi bison
will wait for @rotund harbor to fix his misgendering of me tho.
oh so you're openly transphobic
fuck you then
wanton remnant
quasi bison
<@&268886789983436800> get this transphobe out of here please
quasi bison
<@&268886789983436800> double ping but please deal with the transphobe here
wanton remnant
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exotic nymph
how to find the domain?
safe radishBOT
how to find the domain?
icy lance
when could y not be defined
autumn iris
as long as the denominator is not equal to 0, that’s ur domain
so in this case as long as x is not equal to 5 or -5
tiny wraith
*and the inside of the sqrt isn't negative
exotic nymph
so in this case as long as x is not equal to 5 or -5
whaa how did u get that, i got 9 xD
alr i will try again
ok i got 5
so its D: [3,5] or (-infinite, -3] or [5, infinite)
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undone stirrup
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undone stirrup
How would I go about solving these type of questions? Graphing calculators are allowed for these questions.
elfin sinew
how to find the domain?
11th grade?
Identify the type of function and substitute the values
elfin sinew
how to find the domain?
Same thing Herr also
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manic heart
I have a question, like this equation is normal
x + 2y = 2 and 3x +5y = 4
manic heart
I know how to do that but
the teacher added another number to the equations
which doesn't include a variable
like for example
3x + 5y - 13 = 0
and
2x - y + 5 = 0
as I always thought there's only supposed to be x and y =
glass carbon
you can always move the numbers to the another side
to get it
like
3x + 5y = 13
and
2x - y = - 5
quasi bison
another question, if I get x as a fraction, how would i get y
it makes no difference at all whether x is a fraction or not
unless you're allergic to fractions or don't know how to do arithmetic with them
manic heart
so if we use 3x + 5y = 13
so for example, if we know the x value, how would we figure the y? as you'd have to plug in many numbers in your calculator to figure it out
quasi bison
you don't need your calculator at all
do you know how to isolate y in the equation 3x + 5y = 13?
manic heart
yes
you'd have to put 3x to the other side
and then divide y by 5 and the others by t
5*
quasi bison
you would subtract 3x from both sides and then divide both sides by 5.
to get y = (13 - 3x)/5
notice that at no point did you need to know whether or not x was a fraction
manic heart
you would **subtract 3x from both sides** and then **divide both sides by 5**.
why would you subtract 3?
I got y = 13/5 - 3/5x
normal moss
Moving a term from one side to another is actually substracting or adding it to both sides of the equation
manic heart
I got y = 13/5 - 3/5x
so this is correct?
normal moss
So, if you've got $y + x = 0$
flat frigateBOT
USS-Enterprise
manic heart
oh
normal moss
To isolate y, you move x to the right (and change its sign), but this means you substract both sides of the equation by x
quasi bison
that's the proper way of saying what you phrased as "putting 3x on the other side"
manic heart
that's the proper way of saying what you phrased as "putting 3x on the other sid...
ohhh
it would turn into -3x
quasi bison
you should never think of this as "putting stuff to the other side". it's (a) horribly ambiguous, and (b) breaks down with the slightest increase in complexity
manic heart
I got y = 13/5 - 3/5x
is my answer incorrect
quasi bison
yes of course
dapper cradle
$x^2 - 1 +(x+(-x)) = 0 \Rightarrow x^2 - 1 +x+(-x) = 0$
can i just do that or is that some axiom
flat frigateBOT
aaaaaaaa
dapper cradle
in a proof btw
peak estuary
well you need associativity. but that's assumed anyway cause otherwise you would need much more brackets here
dapper cradle
$x^2 = 1$
We can add the additive inverse to both sides
$x^2 + (-1) = 1+(-1)
\Rightarrow x^2 - 1 = 0$
As we know 0 is an additive identity we can add it to the equation
$x^2 - 1 + 0 = 0$
Note that $x+(-x)$ equals 0 so,
$x^2 - 1 + (x+(-x) = 0$
flat frigateBOT
aaaaaaaa
$x^2 = 1$
We can add the additive inverse to both sides
$x^2 + (-1) = 1+(-1)
\Rightarrow x^2 - 1 = 0$
As we know 0 is an additive identity we can add it to the equation
$x^2 - 1 + 0 = 0$
Note that $x+(-x)$ equals 0 so,
$x^2 - 1 + (x+(-x) = 0$
```Compilation error:```! Missing $ inserted.
<inserted text>
$
l.62
I've inserted a begin-math/end-math symbol since I think
you left one out. Proceed, with fingers crossed.```
peak estuary
no you would need brackets around x^2-1
dapper cradle
which line
$x^2 = 1$
We can add the additive inverse to both sides
$x^2 + (-1) = 1+(-1)
\Rightarrow x^2 - 1 = 0$
As we know 0 is an additive identity we can add it to the equation
$x^2 - 1 + 0 = 0$
Note that $x+(-x)$ equals 0 so,
$x^2 - 1 + (x+(-x) = 0$
$x^2 - 1 +x+(-x) = 0$
$(x^2 + x) + (-1 + (-x)) = 0$
$x(x+1) -1((1+x) = 0$
$(x-1)(x+1) = 0$
flat frigateBOT
aaaaaaaa
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
dapper cradle
i didnt add explnaations
need help with adding them
im stuck
idek if my other explanatiosn are correct
have to use thiw
flat frigateBOT
aaaaaaaa
dapper cradle
@peak estuary is this good
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molten hawk
struggling with an epsilon-delta proof
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struggling with an epsilon-delta proof
molten hawk
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wintry holly
wintry holly
I got 1 and 1/2 but the website is telling me its wrong
flat frigateBOT
NEON
pseudo scroll
I got 1 and 1/2 but the website is telling me its wrong
You should get a set of values not two discrete ones
wintry holly
can you please help show me the work because I'm confused
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jovial orchid
What theorem says if a=b and b=c, a=c
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What theorem says if a=b and b=c, a=c
lean otter
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lean otter
Is this right? Someone double check por favor
Just to be clear Is horizontal asymptote where the numerator equals 0
All values that make it 0
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lean otter
honestly, i just started learning vertical asymptotes, but wouldn't the restrictions just be 7 and -2
im prolly not qualified though
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lean otter
Is this correct ?
safe radishBOT
Is this correct ?
rocky ferry
if the LHS doesn't use f'(t) but rather f(t) then i believe so
lean otter
what is the LHS ?
rocky ferry
left hand side
lean otter
No it wouldn't be correct
celest ember
rocky ferry
i think hes referring to this part of FTC
lean otter
i think hes referring to this part of FTC
No I know this theorem but I wanted to know if the reverse was true
if the integral cancels the derivative
but it doesn't since Kushu pointed out that it shall be f(x) -f(0) on rhs
sad but that's the way
Thank you
.close
errant rain
I've been stuck on this for a while, I got help earlier, still didn't get it.
errant rain
rocky ferry
by set of solutions does it want a parametric vector eq?
rocky ferry
yes
rocky ferry
row operations
errant rain
Do I divide the first row by -2
rocky ferry
errant rain
Ok so:
| 1 -1/2 -1 0 | -1/2 |
| 0 0 -3 1 | -4 |
rocky ferry
seems like you understand, show me your reduced matrix when you're done.
errant rain
Divide second row by -3
| 1 -1/2 -1 0 | -1/2 |
| 0 0 1 -1/3 | -4/3 |
rocky ferry
its not in RREF yet.
errant rain
Add R2 + R1
rocky ferry
good
with row operations you always want to mark where you are placing the result
R2 + R1 -> R1
i've also seen R1 -> R2 + R1. whichever you prefer.
errant rain
| 1 -1/2 0 -1/3 | -1/2 |
| 0 0 1 -1/3 | 4/3 |
rocky ferry
Divide second row by -3
| 1 -1/2 -1 0 | -1/2 |
| 0 0 1 -1/3 | ...
double check this result
errant rain
4/3
rocky ferry
it also changes the result of R2 + R1
errant rain
| 1 -1/2 0 -1/3 | 5/6 |
| 0 0 1 -1/3 | 4/3 |
rocky ferry
alright, so we have our reduced matrix. do you know what to do next?
errant rain
So we solve for x1, x2, x3, x4, right?
rocky ferry
right, technically we already did
we found Ax = b by virtue of reducing the matrix.
only thing to do is write it out in the form you want
errant rain
Okay so first row:
x1 - (1/2)x2 - (1/3)x4 = 5/6
Second row:
x3 - (1/3)x4 = 4/3
There is more than 1 variable, what should I do?
rocky ferry
we have x2 and x4
what happened to those
to get it into the form you showed me we have to write out all 4
you might be wondering "how do i write out x2 and x4 if they aren't defined?" easy we just write x2 = x2 and x4 = x4
whatever they are doesn't matter to us, we just know they are a part of the solution
rocky ferry
Okay so first row:
x1 - (1/2)x2 - (1/3)x4 = 5/6
Second row:
x3 - (1/3)x4 = 4/...
so we have x2 and x4, now you take these equations you found and solve for x1 and x3
errant rain
So x2 = s1 and x4 = s2
rocky ferry
yes, thats what they are asking you. since there are infinitely many solutions ( there are 1 or more free variables ). in this case we got 2
so now solve x1 and x3
errant rain
First row (x1):
x1 - (1/2)s1 - (1/3)s2 = 5/6
-> x1 = (1/2)s1 + (1/3)s2 + 5/6
Second row (x3):
x3 - (1/3)s2 = 4/3
-> x3 = (1/3)s2 + 4/3
rocky ferry
yes, good. but conventionally, we always keep the constants as the first terms
rocky ferry
errant rain
So question.
rocky ferry
shoot
errant rain
Infinite solutions means that there are ONE or MORE free variables (the number after the pivot)
rocky ferry
yes, one or more free variables means infinite solutions if the resulting matrix is consistent.
free variable is any column without a pivot
errant rain
Ok got it. Thanks for the help
rocky ferry
np
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heavy glade
why do we care about the mass of m1?
safe radishBOT
why do we care about the mass of m1?
heavy glade
for acceleration
jaunty owl
because
both boxes are accelerating
so we need to factor in both masses
it's not only m2 that is moving
heavy glade
yeah but I thought since the table is frictionless no matter the mass of m1 it will accelerate the same
jaunty owl
if I'm pulling on two objects attached by like a string on a flat frictionless table
I need to consider both masses
it's the same thing here except now I'm not pulling on the system, gravity is.
and the force with which it is doing so is = m2g
heavy glade
okay so since Fg is interacting with m1 we just use sum of m for F?
I think I get it now thank you
.close
mystic marsh
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mystic marsh
How do I solve this equation?
Quadratic formula?
Factoring by grouping?
Factoring?
Idk what to do
twilit spindle
are you setting this equal to 0?
twilit spindle
that x-2 in the denominator is making things very unfortunate
are you only interested in real solutions? i.e. where it intersects the x-axis?
twilit spindle
ah ok then
mystic marsh
I don’t know how to
twilit spindle
so first we have $x^2-2x+1+\frac{5}{x-2}=0$
flat frigateBOT
FancyBredFries
twilit spindle
now we can multiply everything by x-2 :)
mystic marsh
Wtf
twilit spindle
which looks like this
$\displaystyle x=\sqrt[3]{\left(\frac{-b^3}{27a^3}+\frac{bc}{6a^2}-\frac{d}{2a}\right)+\sqrt{\left(\frac{-b^3}{27a^3}+\frac{bc}{6a^2}-\frac{d}{2a}\right)^2+\left(\frac{c}{3a}-\frac{b^2}{9a^2}\right)^3}}+$\$\displaystyle\sqrt[3]{\left(\frac{-b^3}{27a^3}+\frac{bc}{6a^2}-\frac{d}{2a}\right)-\sqrt{\left(\frac{-b^3}{27a^3}+\frac{bc}{6a^2}-\frac{d}{2a}\right)^2+\left(\frac{c}{3a}-\frac{b^2}{9a^2}\right)^3}}-\frac{b}{3a}$
mystic marsh
What is the cubic formula
flat frigateBOT
FancyBredFries
mystic marsh
twilit spindle
so I'm assuming you don't wanna use that 
mystic marsh
😭
mystic marsh
Ahh thank you!!!!
twilit spindle
mystic marsh
Well before i had no idea what to do
twilit spindle
here is the full solution Wolfie gives
mystic marsh
Ah i see
twilit spindle
but the Quintic doesn't exist fun fact
the Quartic is the highest you can you can solve "in radicals"
you can prove that with something called "Galois Theory" which is a very advanced mathematical field
twilit spindle
Is that gonna be covered in pure math in college
after Ring Theory, Group Theory, Linear Algebra, etc.
mystic marsh
How long do those take for someone to fully comprehend/understand the concept?
Like a whole semaster?
twilit spindle
depends Galois made the field at age 18
mystic marsh
Or a year?
twilit spindle
after Ring Theory, Group Theory, Linear Algebra, etc.
but it can take years to learn all about these things ^
twilit spindle
really depends on how mathematically intuitive you are
twilit spindle
I still have long way to go
same my friend 😅 :)
mystic marsh
twilit spindle
trying out Calc III/Complex Analysis rn
and I've doing it for like a year on and off
but yeah you got Alg II, PreCalc, Calc I/II/III, Stats, Combinatorics, Set Theory, Linear Algebra, Analysis (Complex, Real, Functional), Number Theory, Group Theory, Ring Theory, Topology, Category Theory, Galois Theory, Differential Geometry, etc
mystic marsh
Ah
Ummm
After all those
What do you get
A job?
Do you become a mathematician
My life will be miserable if i become a mathematician ngl
I just want a job that utilizes math not studies math😭
Imagine working for math after 6 years of math in university
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mystic marsh
anyways thanks for your help with cubic formula! @twilit spindle
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devout shale
@twilit spindle
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What step are you on?
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6. None of the above
@twilit spindle Has your question been resolved?
devout shale
@twilit spindle
twilit spindle
twilit spindle
actually kinda
You see, I have: $\frac{\sum_{n=0}^{\infty}\frac{n^{p+1}\cdot2^{n+1}}{3^n}}{\sum_{n=0}^{\infty}\frac{n^p\cdot2^{n+1}}{3^n}}\approx\frac{2(p+1)}{\ln3}$ but I'm interested in: $\frac{\sum_{n=0}^{\infty}\frac{n^{p+1}}{3^n}}{\sum_{n=0}^{\infty}\frac{n^{p}}{3^n}}$
flat frigateBOT
FancyBredFries
twilit spindle
any chance I could get the desired ratio?
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devout shale
sorry minor typo
twilit spindle
bro why was the bot typing a whole ass essay 😭
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twilit spindle
damn was trying to confuse the bot 😭
worthy hemlock
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?
twilit spindle
all helpers just got tagged in this aneurysm of a channel 
devout shale
@wraith prism
twilit spindle
Guys how do I solve tangent(radical(x+5))=pi/2
PLEASE HELP
HELP
@worthy hemlock
@tepid walrus
tepid walrus
are you good...?
worthy hemlock
Guys how do I solve tangent(radical(x+5))=pi/2
2 = 2
twilit spindle
are you good...?
i need help 🥺
tepid walrus
i see that..
safe radishBOT
hardy lion
.reopen
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✅
twilit spindle
AUGHHHH
hardy lion
We need to stop fooling around ohmy god
devout shale
bruh
safe radishBOT
twilit spindle
.loose
hardy lion
.roopen
twilit spindle
.noose
worthy hemlock
.reclose
twilit spindle
.clopen
devout shale
.reoplaeena
twilit spindle
.reclopen
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Please don't repeatedly close and claim a new channel with the exact same question. This erases all previous progress made towards your problem and is confusing for helpers, making it more difficult to help you. Please be patient, even if your channel has not received much attention.
twilit spindle
Please don't repeatedly close and claim a new channel with the exact same questi...
!noclopen
safe radishBOT
Please don't repeatedly close and claim a new channel with the exact same question. This erases all previous progress made towards your problem and is confusing for helpers, making it more difficult to help you. Please be patient, even if your channel has not received much attention.
safe radishBOT
Please don't repeatedly close and claim a new channel with the exact same question. This erases all previous progress made towards your problem and is confusing for helpers, making it more difficult to help you. Please be patient, even if your channel has not received much attention.
Please don't repeatedly close and claim a new channel with the exact same question. This erases all previous progress made towards your problem and is confusing for helpers, making it more difficult to help you. Please be patient, even if your channel has not received much attention.
Please don't repeatedly close and claim a new channel with the exact same question. This erases all previous progress made towards your problem and is confusing for helpers, making it more difficult to help you. Please be patient, even if your channel has not received much attention.
Please don't repeatedly close and claim a new channel with the exact same question. This erases all previous progress made towards your problem and is confusing for helpers, making it more difficult to help you. Please be patient, even if your channel has not received much attention.
Please don't repeatedly close and claim a new channel with the exact same question. This erases all previous progress made towards your problem and is confusing for helpers, making it more difficult to help you. Please be patient, even if your channel has not received much attention.
Please don't repeatedly close and claim a new channel with the exact same question. This erases all previous progress made towards your problem and is confusing for helpers, making it more difficult to help you. Please be patient, even if your channel has not received much attention.
Please don't repeatedly close and claim a new channel with the exact same question. This erases all previous progress made towards your problem and is confusing for helpers, making it more difficult to help you. Please be patient, even if your channel has not received much attention.
twilit spindle
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twilit spindle
edgy pendant
What happened here?
twilit spindle
What happened here?
no clue
safe radishBOT
What happened here?
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).
twilit spindle
.close
twilit spindle
$\int_{0}^{\infty}\frac{\sin(x)\cdot e^{-x}}{\sqrt{x}}\dd x$
flat frigateBOT
FancyBredFries
twilit spindle
may as well ask a question
how do I evaluate this integral?
I tried $\sqrt{x}=u$
flat frigateBOT
FancyBredFries
twilit spindle
this gives $\int_{0}^{\infty}\frac{\sin(u^2)\cdot e^{-u^2}}{2u^2}\dd u$
flat frigateBOT
FancyBredFries
twilit spindle
but now I have no clue how to proceed
safe radishBOT
twilit spindle
.reopen
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✅
worthy hemlock
Oh
twilit spindle
lmao
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@twilit spindle Has your question been resolved?
twilit spindle
.close
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Available help channel!
sick cape
How do i solve the bottom part to find the value of a, also a note that the value is a number without variables
safe radishBOT
How do i solve the bottom part to find the value of a, also a note that the valu...
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@sick cape Has your question been resolved?
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Available help channel!
glad agate
help
sudden forum
u know the formula for cos a cos b + sin a sin b
lean otter
teh asnwer is B ig
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As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.
sudden forum
$\cos a \cos b + \sin a \sin b = \cos (a + b)$
flat frigateBOT
n11
glad agate
teh asnwer is B ig
no its C
lean otter
Oh
glad agate
$\cos a \cos b + \sin a \sin b = \cos (a + b)$
this is a thing!?
where do you learn this?
lean otter
yea xd
glad agate
like at what level of school
sudden forum
i do believe u have to use that property to find the answer
glad agate
i have an olympiad in a month idk where to prepare all these topics our schoolt eaches us nothing
wet wigeon
$\cos a \cos b + \sin a \sin b = \cos (a + b)$
cos(a-b) NOT +
light shoal
$\cos a \cos b + \sin a \sin b = \cos (a + b)$
a - b
sudden forum
check your textbooks perhaps
wise oyster
glad agate
i do believe u have to use that property to find the answer
ill try ty
glad agate
check your textbooks perhaps
its an olympiad qs
glad agate
im asking for general advice how do i learn these theorems properties and where from cuz im confused. i have an olympiad and it cant be done using gcse maths only
im in AS
thin bridge
khan can give you a basic intro
wet wigeon
You can google proof of angle formulas
thin bridge
you'd pretty much want to be well versed in basic stuff
and then fancy tricks for olympiad level stuff
glad agate
You can google proof of angle formulas
ty. i get that but there r hunderds of other things that are missing from my knowledge. like where did you learn this?
glad agate
you'd pretty much want to be well versed in basic stuff
and then fancy tricks fo...
yeah but where do i learn the basic stuff im confused over that
thin bridge
khan can give you a basic intro
glad agate
> khan can give you a basic intro
!?
thin bridge
or look up dedicated you tube videos
glad agate
OH KHAN ACADEMY
wet wigeon
Its taught in high school in my country
glad agate
sorry
wet wigeon
In grade 12
glad agate
Its taught in high school in my country
im in 11
i wanna learn stuff early to win comps
wet wigeon
So its not a secret of a sort
thin bridge
prof leonard / organic chem tut come highly recommended
fluid token
you shouldve done trig by now, if youre in year 11
glad agate
prof leonard / organic chem tut come highly recommended
thank you!
glad agate
you shouldve done trig by now, if youre in year 11
i know basic trig and add maths trig
our year just started
wet wigeon
you shouldve done trig by now, if youre in year 11
Not every country teaches angle formulas in grade 11
Turkey is one
fluid token
true i guess
fluid token
i know basic trig and add maths trig
add maths, youre doing olevels?
glad agate
i know indentities cos2x+sin2x waghaira
glad agate
add maths, youre doing olevels?
done with o levels, just started a levels
fluid token
oh ok
glad agate
wanted to take further maths but its really time intensive i have phy math cs and chem alr
fluid token
good luck with those lmao
glad agate
thank you
fluid token
alevels is on another level
glad agate
(im gonna die)
fluid token
real
glad agate
alevels is on another level
yeah but so far stuff has been okayis
fluid token
its pretty much first year uni math
glad agate
its pretty much first year uni math
ive done add maths so some topics thankfully are easier
feeling for the ppl who didnt 👆💯
.close
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Available help channel!
dire escarp
can someone explain how to do
safe radishBOT
can someone explain how to do
dire escarp
ping me if youre here
quasi bison
!status @dire escarp
safe radishBOT
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
1
quasi bison
do you know how to write down the equation of motion for an object in free fall
quasi bison
"the 4 equations"...?
quasi bison
you only really need the first two here
do you know what $x_0$ and $v_0$ stand for, and (separately) what their values are in this problem?
flat frigateBOT
Ann
quasi bison
x_0 is 24 m but v_0 isn't 0 !
the bolt falls off the rising rocket, and that matters.
quasi bison
the rocket is rising steadily, not in freefall
dire escarp
then 20?
quasi bison
the bolt, upon detaching from the rocket, shares its upward velocity of 20 m/s
flat frigateBOT
Ann
dire escarp
will final velocity be negative then
quasi bison
acceleration due to gravity is -9.8 m/s^2
dire escarp
if it goes up then positive?
dire escarp
$x = 20 + 24t - 4.9t^2$
wait shouldnt this be $x = 24 + 20t - 4.9t^2$
flat frigateBOT
cake
quasi bison
if it goes up then positive?
our "x" axis faces upward
quasi bison
no, the bolt did not travel only 24m
dire escarp
oh did it continue going up before falling down
quasi bison
of course it did...
safe radishBOT
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Available help channel!
polar forge
hello I need help with a question in maths :
Let f(x) = integrate e^(-(t²/2)) dt from x to +∞.
Calculate for all A > 0, the integral of f(x) dx from 0 to A in terms of f(A).
grim plover
hello I need help with a question in maths :
Let f(x) = integrate e^(-(t²/2))...
$f(x) = \int_{x}^{\infty} e^{-\frac{t^2}{2}} dt$
flat frigateBOT
ItzKraken
grim plover
to find $\forall A \int_{0}^{A} f(x) dx$ in terms of f(A)
flat frigateBOT
ItzKraken
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unreal stump
how is 6x-x^2 = x(6-x) = -(u+3)(u-3) if u= x-3?
safe radishBOT
how is 6x-x^2 = x(6-x) = -(u+3)(u-3) if u= x-3?
unreal stump
holy shit
im in college and have never though of it that way
wtf
im shit at factoring HAHA
thanks!
.close
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narrow vault
anyone here that has taken the dynamics course in engineering and wants to help me out?
safe radishBOT
anyone here that has taken the dynamics course in engineering and wants to help ...
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narrow vault
.close
fleet stirrup
i need help with this question
safe radishBOT
i need help with this question
fleet stirrup
i know i need to find the vertex and can do it on my calculator but cant do it manually
i got a standard form of y=x^2-0x-70
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restive briar
Hey I got this algebra problem for determining the inverse but it uses "completing the square". Im stuck on one of the steps can you help explain it to me?
safe radishBOT
Hey I got this algebra problem for determining the inverse but it uses "completi...
restive briar
After I factored out the 3 I dont understand why we add the +1, -1 and the -3 outside the brackets
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restive briar
<@&286206848099549185>
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proper nymph
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proper nymph
I tried this
fossil shell
proper nymph
yeah i put them up there
fair hound
nope you're wrong, that's why he posted this
proper nymph
so then how would it look
proper nymph
so do i have to find both the adjacent angles
fair hound
you can calc the distance between the 2 rocks directly
that's the length of the horizontal line
proper nymph
tan26=14/x
tan20=14/x1
x+x1
fair hound
yes
fair hound
yes
fair hound
draw a right angled triangle, the rope is the hypothenuse, the pole makes a right angle with the ground
cyan shard
Isn't the rope is supposed to be 56.4 ft away from bottom of pole?
Like the horizontal length
Coz 56.4 isn't the height of the pole
proper nymph
proper nymph
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lean otter
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lean otter
I dont understand what to do
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tight oak
How do I find the domain of square root of -x^2
safe radishBOT
How do I find the domain of square root of -x^2
tight oak
No
Well maybe
I have to find f composed with g
F of x equals square root of 2-x and g of x equals x squared + 2
lean otter
I have to find f composed with g
Why do you need domain for this tho, is it asked?
Yeah f(g(x)) = √(-x²)
@tight oak
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leaden scaffold
Hey! Could I walk through this problem and someone tell me if im on right track?
leaden scaffold
So, so far, I have this approach for a: I'm gonna be using points at t=20 and t=22 months.
From there, I get f_t(20,6) = f(22,6)-f(20,6)/22-20
and from the table, we know f(22,6) = 86% and f(20,6) = 90%
substituting the values, we get ft(20,6)=(86-90)/(22-20) =-4/2=-2
Does this make sense?
So we get: f_t(20,6)≈−2.0
little barn
yes
You could get a possibly better estimate using both the forward and backward difference, but I'm not sure that's needed
leaden scaffold
You could get a possibly better estimate using both the forward and backward dif...
Should I use t=18 and t = 20 as well?
little barn
That would give another estimate. I could only say if I knew more context
leaden scaffold
Okay
little barn
What have you been taught? what does the teacher expect
etc.
I think what you have is good enough
leaden scaffold
What have you been taught? what does the teacher expect
I'll do it just in case. From there, I can the average the two to get a balanced rate of change
little barn
Here's the conceptual picture, but practically, yes, you want the central diff.
or an average of the forward and backward
leaden scaffold
Here's the conceptual picture, but practically, yes, you want the central diff.
Okay, I got -1.5 for ft(20,6). Therefore, this means that, when the concentration of formaldehyde is 6 ppm, the percentage of rats surviving is decreasing at a rate of 1.75% per month around t=20, right?.
I got -1.75 when I averaged both forward and backward
leaden scaffold
i.e. the rats are dying
Got it. Could I ask separate question to another problem?
little barn
yes, but I may not be around to help, gotta go
leaden scaffold
yes, but I may not be around to help, gotta go
no problem, thanks again!
safe radishBOT
@leaden scaffold Has your question been resolved?
lean otter
gentle oak
they're all parallels so 3x-18=5x+14
median totem
someone can help me?
safe radishBOT
someone can help me?
median totem
y = (this shit)
rigid inlet
What's the question?
karmic ocean
can i ask a question here?
rigid inlet
What are you asked to do with this thing?
safe radishBOT
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
,rotate
flat frigateBOT
unique bison
Lmao
rigid inlet
So, the sqrt provides a very straightforward domain restriction
Your goal is to find what x values satisfy $2^x - 2^{1-x} \ge 0$
flat frigateBOT
Steakanator
rigid inlet
That's the x value that makes the expression 0, I wouldn't call it "the result"
rigid inlet
This should give you a hint. When is the product of two numbers positive?
safe radishBOT
@median totem Has your question been resolved?
fickle trail
safe radishBOT
fickle trail
is this literally all that an integral means?
the change in y multiplied by the change in x
ΔyΔx
but specifically, the area under the curve, to the derivative axis, in this case dx, so the x-axis
or instead of using variables
ΔheightΔwidth
deep matrix
Integrals are area under the curve
fickle trail
right
deep matrix
But more like sum of the integral areas
fickle trail
and the product of ΔheightΔwidth is how we find them?
oh right
that would always be rectangle
so it's the sum of infinitely small rectangles
all added up
final halo
Go back and look at the riemann sum definition yeah
deep matrix
Yeah
fickle trail
but same premise, just infinitely many rectangles to allow for any curves
deep matrix
That's the rectangle part
fickle trail
does anybody know if Issac Newton or Gottfried Wilhelm Leibniz understood right away that the derivative and integral were one-to-one inverses to one another? or took some time to find that part out
it still kinda blows my mind lol
deep matrix
You ought to read their books to find out
Maybe Newton had a different approach
Idk
fickle trail
(area under the curve)^-1 = (slope at any given point on the curve)
and
(slope at any given point on the curve)^-1 = (area under the curve)
final halo
does anybody know if Issac Newton or Gottfried Wilhelm Leibniz understood right ...
Definitely not, this is the whole point of the fundamental theorem of calculus like I keep telling you
fickle trail
https://tenor.com/view/huh-gif-9646983534577797493
this is still me today, as I do not see the correlation to one another. aside from the calculus to undo each another. but it does not "feel" like an inverse, in the same sense f(x)^-1 is the inverse of f(x) for example
does anybody visualize the inverse when they do inverse of f'(x) or F(x)? or you just follow the math, and trust the math
trying to find out if 3B1B has done a video on this
this is a graph of f(x) to f(x)^-1
this is a graph of f'(x) to F(x)?
(3b1b did do a video)
.close
olive stump
safe radishBOT
olive stump
can i get some help witht he second half
yim pretty sure A is correct but what other boxes appl
i cant really think of anythin
i was thinking about a and e too but it doesnt work
safe radishBOT
@olive stump Has your question been resolved?
gentle valley
hello
gentle valley
I am wondering what does dash or prime indicate, like if we have x, what does x' imply? does it only mean the derivative of x or are there any other meanings?
.close
void cosmos
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void cosmos
Hello there so I answered the question and got it right. I don't think this really matters, but just want to clarify. So in the answer key part a) on my worksheet it shows = x +- (pi)n where n is any integer, and same thing for pi/2 +- (pi)n where n is any integer. Also note I'm using radians. Now everything is fine, except the answer key said x = pi(n) where n is any integer and pi/2 + (pi)n, where n is any integer.
safe radishBOT
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void cosmos
I don't think it matters as the answer key recognized that there are numerous answers and that the answer listed is not always the direct answer.
safe radishBOT
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@void cosmos Has your question been resolved?
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@void cosmos Has your question been resolved?
little mesa
the plus-minus in your answer is not necessary, especially for any integer n, including negatives
void cosmos
the plus-minus in your answer is not necessary, especially for any integer n, in...
Would it be incorrect? Or would it be redudnant?
little mesa
redundant
void cosmos
So it would still be correct, but its just more unecessary work and the goal is efficiency at the end of the day right.
?
I'm just confused chjlamydia cus I scenarios where +- is used and where its not used.
little mesa
in an area of study that appreciates simplicity, elegance and brevity, adding a plus-minus where it doesn't need to be there is goofy
yes it's still correct
weak spire
safe radishBOT
fleet gale
Did u try rationalizing it?
weak spire
Did u try rationalizing it?
It would still be 0 in the denom right?
fleet gale
No try it
There will be 2x³ on numerator i think
U can cancel the x²
Ans should be 0
weak spire
There will be 2x³ on numerator i think
Yeah but what bout the denom
fleet gale
Show me how u rationalized it