stewart calculus numer 2.1 exercise 1 . helpm with letter c
#help-0
rotund crater
lone heartBOT
stewart calculus numer 2.1 exercise 1 . helpm with letter c
lone heartBOT
@rotund crater Has your question been resolved?
opal jolt
Empieza por graficar la función.
Sabes que P es el punto (15, 250).
Llama Q1 al punto (5, a), Q2 al punto (10, b) etc
lone heartBOT
@rotund crater Has your question been resolved?
flat vale
what do we call tenth, hundreds, thousands, and so on?
lone heartBOT
what do we call tenth, hundreds, thousands, and so on?
flat vale
like a word for that
coral flower
what do we call tenth, hundreds, thousands, and so on?
units?
atomic harbor
Place values?
flat vale
like order of magnitude
powers of tenth
i need a concice name for my program
for one of my variable
idle bay
It’s called a place value
lone heartBOT
@flat vale Has your question been resolved?
stuck ruin
lone heartBOT
vale wigeon
!status
lone heartBOT
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
also what are you asked to do with this
vale wigeon
i strongly suspect this might be as far as you can simplify it
also i suspect there might be something you have mistakenly cropped away
stuck ruin
wwolfram alpha said the other
lone heartBOT
@stuck ruin Has your question been resolved?
stuck ruin
ccan i ask other ppl?
opal jolt
can you provide the full instructions of the question?
opal jolt
Done. Next question?
stuck ruin
?
opal jolt
If there's nothing more on that, that's the simplest form that number can take.
Thus, it's simplified, and you're done.
stuck ruin
bruh
wwhy does wolfram alpha said its can be simplified more????
????
bruh
can i ask other ppl or just wait for the answer?
surreal trail
Try and do the math, show us your progress and then we can help
lone heartBOT
@stuck ruin Has your question been resolved?
thorn pebble
can anyone help me create two triangles with two equal sides and one equal angle? but they cant be congruent
coral flower
that not possible
coral flower
coral flower
its the same thing
thorn pebble
no
frank briar
If the angle not between them they are not necessarly congutent
thorn pebble
first one is impossible second one is possible,
i need two triangles that have two equal sides and one equal angle that are not congruent
near apex
Look closely. Isosceles so others angles also become equal.
thorn pebble
theyre not isosceles tho
thats not the point
when i say two equal sides i mean between the triangles
like a triangle with sides 3,4,5 and one with sides 2,4,5
they have two equal sides
(4 and 5)
near apex
Okay. Yes, i get it. I misunderstood.
thorn pebble
no problem
tardy stag
what i tend to do with these is imagine a physical model
near apex
I still find it hard to imagine if that would be possible.
tardy stag
with like sticks and springs
thorn pebble
i mean im trying, i used my imagination a bunch on this question
thorn pebble
I still find it hard to imagine if that would be possible.
it is, SSA is not a congruency case
near apex
Okay. I got how you can do it. Angles don't have to be corresponding.
tardy stag
hint: it won't work with a right triangle
thorn pebble
hint: it won't work with a right triangle
yeah cuz of that special case
thorn pebble
Okay. I got how you can do it. Angles don't have to be corresponding.
wdym by that
near apex
Actually, it's only possible if angle is not corresponding.
near apex
wdym by that
Let's assume that equal sides are a and b.
tardy stag
i don't think it will work with isosceles either
near apex
Draw a side of a for one triangle. Draw b for another one. Then draw equal angle for both. Take a on angle arm for one. On another side for another.
tardy stag
hint: SSA does not constrain you to one triangle, but it nearly does
thorn pebble
you mean it almost constrains to scalene?
thorn pebble
Draw a side of a for one triangle. Draw b for another one. Then draw equal angle...
ok drew a for one triangle and b to another
same angle for both
wdym by "take a on angle arm for one. On another side for another"
tardy stag
I'm not sure
what i would do is choose an angle and two side lengths and then construct a triangle with that in that order, paying attention to where you're making hidden assumptions
thorn pebble
i think i did it?
first proving sides are equal
then proving A is the same angle on both, though not quite let me see if i can fix that
i think thats good enough and sides are still equal
thx for the help
near apex
lone heartBOT
@thorn pebble Has your question been resolved?
thorn pebble
ok i see they share two sides, but are you sure angle A is divided into two equal parts?
wait they dont even have two equal sides
thorn pebble
parallel lines what?
near apex
AB and CD are parallel
thorn pebble
yeah but so what?
near apex
Alternate angles made by a transversal intersecting two parallel lines are equal.
thorn pebble
well only one equal side and no equal angles
OOh i see
C is equal to A
top C and bottom A
yeah im dumb
two equal sides and one equal angle
alpine sable
hey
alpine sable
i dont get 3d
alpine sable
agreed, therefore
8* 7* 2 ??
alpine sable
well it can start with 5
it can't start with 5 because 5 must be the last digit
tacit arch
it can't start with 5 because 5 must be the last digit
wot
alpine sable
i mean
tacit arch
are you saying 510 is not divisible by 5
alpine sable
it has to be divisible by 5
no wait
you're right
but my solution isn't correct
for some reason you have to split it
one calculation includes 0 being the last digit
the other one is 5 being the last digit
but i dont see it
the sense
tacit arch
agreed, therefore
8* 7* 2 ??
doesn't this include 0 or 5 as the last digit
alpine sable
it does
tacit arch
well it can start with 5
this is what you're missing
alpine sable
i think it has to do with the fact that 015 is not a three digit number
yes it has to do something with this
but i still dont see why 8x7x2
isnt correct i mean
tacit arch
but i still dont see why 8x7x2
this calculation misses 510
so you need to add those cases to 8 * 7 * 2
so identify how many of them there are
lone heartBOT
@alpine sable Has your question been resolved?
dull prawn
.solved
brave stump
lone heartBOT
Available help channel!
alpine sable
pls chelp me what is this monstrosity
lone heartBOT
pls chelp me what is this monstrosity
@alpine sable Has your question been resolved?
lone heartBOT
@alpine sable Has your question been resolved?
lone heartBOT
@alpine sable Has your question been resolved?
alpine sable
d
wary stream
You didn't need to close your previous channel
lone heartBOT
<@&286206848099549185>
Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
@alpine sable Has your question been resolved?
rocky grove
@alpine sable do you need this channel?
wary stream
.close
lone heartBOT
wary stream
They have #help-34
lone heartBOT
Available help channel!
heady tendon
lone heartBOT
heady tendon
algebra 2
lavish cedar
Okay what is the question?
heady tendon
okay so i need 2 equations since this is elimination
25x +10y = 180
for time
but where do i get the second equation
heady tendon
it’s elimination
heady tendon
i have to eliminate either x or y to single out a single variable
that’s why i need a second equation
i can show u a previous problem of u need me to
heady tendon
yeah i did too but 12 and 180 are two different variables
that’s why i get confused
i’ll solve that and see if the answer makes sense
lavish cedar
So what would you like me to do?
What are you confused onto available
On so I can help you
pulsar spire
lone heartBOT
pulsar spire
f(x) = x^2 − 3x
Im trying to find the domain of this function, but Im not sure where to go from here, or if i even did it right.
placid zinc
,w graph x^2 - 3x
ocean sealBOT
placid zinc
Make sure you know the definition of "domain"
placid zinc
You'll need a more specific definition
pulsar spire
its a set of inputs, that are allowed in a function
pulsar spire
what would be your first step in getting the domain to this? I am not sure if " = 0" was correct, or not
placid zinc
You don't need to do any rearrangements
What values can you plug into f(x) = x² - 3x?
Or to ask the opposite, what values "mess this function up"?
pulsar spire
i see
ima try it, one min
yea im lost
i know how to find domains to something like this, but its the multiple x’s that are confusing me
@placid zinc
placid zinc
So x = 4 is an element of the domain, since you can plug it in
What can't you plug in?
Helps to look at the graph
,w graph x^2 - 3x
ocean sealBOT
pulsar spire
you can plug in any domain
placid zinc
You can plug in any point, yes!
placid zinc
Note that every polynomial has "all real numbers" as a domain
Not a waste at all. Thx for thinking through it with me
pulsar spire
.close
ripe stone
lone heartBOT
jagged cobalt
the way youve written it is saying: -3<x<-inf or 3<x<=0 which doesnt really make sense
the numbers are right but youve written it wrong
ripe stone
the numbers are right but youve written it wrong
whats the correct order lmfao
jagged cobalt
the left one for example should be (-inf,-3)
left boundary goes on the left, right boundary on the right
jagged cobalt
[0,3)
lone heartBOT
@ripe stone Has your question been resolved?
main cedar
how do I solve these? (probability)
lone heartBOT
how do I solve these? (probability)
lone heartBOT
@main cedar Has your question been resolved?
lone heartBOT
@main cedar Has your question been resolved?
graceful pawn
i can try to help @main cedar
if 5 specific persons insist on following each other, their order is fixed
so take the 5 specific people as one person
main cedar
why?
graceful pawn
they insist on following each other
so they stick to each other and their order is fixed
so they are "one" value
main cedar
so 5! x something. right?
graceful pawn
why is it 5!
main cedar
because any sequence of those 5 people need to be accounted for?
graceful pawn
really?
main cedar
idk
graceful pawn
because I thought that the 5 people have a fixed arrangement
main cedar
its fixed, but that doesnt change the fact that the question wants all possible ways of arrangement.
graceful pawn
because any sequence of those 5 people need to be accounted for?
if they have a fixed arrangement, why do we need to account for the sequence of those 5 people?
main cedar
I'm sorry, are you testing me, so I can give the correct justification even though i have the right answer? Or am I actually wrong?
graceful pawn
no, I'm also confused about what the question is asking for
I need to understand what it means by the 5 specific persons insist on following each other
main cedar
it could mean that they have to be adjacent in line to one other, and the fact that they could change the order theyre standing in line together, means there are 5 x 4 x 3 x 2 x 1 ways they could stand in line together
graceful pawn
they have to be adjacent
can they change their order while staying adjacent to one another?
main cedar
yeah
graceful pawn
ok so, if they can change their order, the no. of combinations, as you said, is 5!
now, treat the five people as one entity
main cedar
ok
main cedar
so that means there are 4 total entities?
graceful pawn
yes
main cedar
5! X 4!
graceful pawn
that should be correct 
main cedar
i just submitted the answer on my class's hw page and it came out correct. Thanks man i appreciate it!
main cedar
Thanks to your help, I already solved it: 8! - 2!7!. It uses quite the same logic.
.close
charred dock
so
charred dock
is there an infinite number of point slope forms
because you can get y2-y1/x2-x1 as like an infinite number of varriations right
in the same line
because any point can be either x1,y1 or x2,y2 right
tell me I'm not crazy
gray isle
missing a lot of (), but yes
using the slope and any random point on the line will give a point-slope form for that line
gray isle
yes. though in questions they'd usually ask you to use a specific point
remote heron
I need help with this guy
lone heartBOT
I need help with this guy
remote heron
Show that $(x+1+O(x^{-1}) )^x = ex^x + O(x^{x-1})$ as $x \to \infty$
ocean sealBOT
jan Niku
remote heron
? to get $\qty( x \qty( \frac{x+1}{x} + O(x^{-2})))^x$
ocean sealBOT
jan Niku
ocean sealBOT
TooManyCooks
forest cobalt
But more to the point
forest cobalt
You have $x^x (1+1/x)^x$
ocean sealBOT
TooManyCooks
forest cobalt
Limit as x-> infinity that parenthesis is e
remote heron
it should be $\qty( x \qty( 1 + \frac 1x) + O(x^{-1}) )^x$ still
ocean sealBOT
jan Niku
remote heron
what happens to the rest of the expansion
forest cobalt
x goes to infinity
the behavior is dictaed by the leading term in the expansion
which is x^x
remote heron
the behavior is dictaed by the leading term in the expansion
how do you know this?
forest cobalt
Think of it this way
remote heron
sorry my teacher is not very good
forest cobalt
If I had $(x+1)^2$ I get $x^2 + 2x + 1$
ocean sealBOT
TooManyCooks
remote heron
oh youre using leading to mean something different than what im thinking
okay
i get what you mean
forest cobalt
ok good
remote heron
so wait
forest cobalt
yeah that's all i meant
forest cobalt
Sure
remote heron
i wanna write some more out so i have a good example
@forest cobalt so the order of the error would be the next term? thats $$\qty( x \qty(1 + \frac 1x ) ) ^{x-1} O(x^{-1})$$
ocean sealBOT
jan Niku
remote heron
but this doesnt seem like its going to match the RHS
forest cobalt
why is the power to x-1
remote heron
wouldnt this have order $O(x^{x-2})$?
ocean sealBOT
jan Niku
remote heron
why is the power to x-1
you miss one by not being in the leading term
the leading term takes the ^x
the next one which hits O(x^-1) loses a power of the other factor, right?
like (x+3)^3 would have leading term x^3 + O(x^(3-1))O(1)
@forest cobalt 
forest cobalt
lmao wait
lone heartBOT
@remote heron Has your question been resolved?
forest cobalt
I promise I'm still thinking this through
forest cobalt
ye
remote heron
then wouldnt x^(x-2) be O(x^(x-1))?
forest cobalt
I'm trying to get the $+O(x^{x-1})$
ocean sealBOT
TooManyCooks
forest cobalt
I have (1+ $+\frac{O(x^{-1})}{x+1})^x$
ocean sealBOT
TooManyCooks
forest cobalt
i fucked up the + sign. wtver
remote heron
$(x + O(x^{-1}) )^2 = x^2 + O(x^0) = x^2 + O(x^{0+1})$
ocean sealBOT
jan Niku
remote heron
i think im really abusing notation here
forest cobalt
Lemme type what I have
$(x+1+O(x^{-1}))^x = x^x (1 + \frac{1}{x} + O(x^{x-2}))^x = x^x (1+\frac{1}{x})^x (1 + \frac{O(x^{-1})}{x+1})^x$
ocean sealBOT
TooManyCooks
remote heron
I mean can we agree up to $\qty(x+1 + O(x^{-1}) )^x = ex^x + O(x^{x-2})$
ocean sealBOT
jan Niku
forest cobalt
What?
forest cobalt
my intuition says yes
remote heron
just use binomial thm
that term will be $C \qty( x \qty(1 + \frac 1x) ) ^ {x-1} O(x^{-1})^1$ right
ocean sealBOT
jan Niku
forest cobalt
i can sort of bs my way through it
remote heron
this is an applied math class bs is fine
forest cobalt
$(1+ \frac{(O(x^{-1})}{x+1})^x \approx (1+ \frac{(O(x^{-1})}{x})^x = (1+ O(x^{-2}))^x \approx (1+ O(x^{-2}))$ in the limit as $\x\to\infty$
ocean sealBOT
TooManyCooks
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
forest cobalt
to be honest i'd turn that shit in hahahaha
remote heron
**TooManyCooks**
Compile Error! Click the <:errors:504266556054962196> reaction ...
im not sure i agree with this
or not
but ill mark this as resolved i guess
thanks for the help @forest cobalt
.close
upbeat hornet
How do you do this? I tried replacing each of the derivatives with the limit definition, but now I have 2 h’s going to 0
vapid shuttle
:p
upbeat hornet
actually I ended up helping for an hour before asking this question
upbeat hornet
have you tried any Lhop
No, I’ll try it
opaque heart
What is this called?
lone heartBOT
What is this called?
opaque heart
I know why this works but is there a name for this thing that was used to get rid of the 6 on the bottom?
hard mountain
Cancelling out numbers?
opaque heart
Is that all it's called?
tardy tapir
its an operation of dividing both the numerator and denominator by 6, sometimes called 'cancelling'
hard mountain
You could also say that youre reducing the fraction to its lowest terms
By cancelling out common factors
opaque heart
Got it
"cancelling" or "cancelling out common factors in a fraction"
thank you!
.close
wise jewel
lone heartBOT
wise jewel
am i being asked to find the derivative?
gray isle
derivative at 3
wise jewel
ok so like
how do i get the 3 out of the parenthesis so i can do the simple power rule
winter shadow
(3-x)^2 = (3-x)(3-x) then expand this
wise jewel
i get $x^2-6x+9$
ocean sealBOT
Black Hat
wise jewel
and then i distribute the 4 and get $4x^2-24x+36$
ocean sealBOT
Black Hat
gray isle
yes
gray isle
yes
wise jewel
but then im not sure what im supposed to do with the point they gave us
just plug it into that equation?
gray isle
yes
wise jewel
hm ok, so, 8(3) - 24 = 2
gray isle
how are you getting 2 from that...
wise jewel
💀
im actually sped
sorry
0
jesus christ
got it
LMAO
tysm
so what exactly does this mean
winter shadow
do you know what a horizontal tangent line is?
lone heartBOT
@wise jewel Has your question been resolved?
exotic ingot
My math book says this is how to start solving the equation. But why can't it be for example -3x = 2x?
vapid shuttle
, rotate
ocean sealBOT
exotic ingot
I know that by why cant it become -3x = 2x, not -3x = -2x
vapid shuttle
it can
exotic ingot
So i just choose
vapid shuttle
3x=2x is the same as -3x=-2x
and 3x=-2x is the same as -3x=2x
so sure, just choose your favorites
the solution guide is making use of the property that cosine is an even function, meaning that cos(-x)=cos(x)
exotic ingot
How about sin. In that case would you also be able to choose which one would be negative
vapid shuttle
np
alpine sable
vale wigeon
i'll send the complete question
why not do that from the get go
alpine sable
cause i thought it won't be necessary as we would have to compute the integral anyway
ocean sealBOT
vale wigeon
no you cannot compute the integral of e^f(x) in general
alpine sable
can we not solve this integral
alpine sable
no you cannot compute the integral of e^f(x) in general
oh
vale wigeon
it is nonelementary even for such tame f(x) as -x^2
alpine sable
okay
young finch
it is nonelementary even for such tame f(x) as -x^2
i love the gaussian integral
alpine sable
thanks
wait i have one more que
why is this is true ?
@vale wigeon
my math teacher just gave it as a note but did not elaborate o it
vale wigeon
a pair of straight lines is $(a_1 x + b_1 y + c_1)(a_2 x + b_2 y + c_2) = 0$
ocean sealBOT
Ann
alpine sable
yes
vale wigeon
ie the product of two general-form straight line equatoins
so like
if you expanded all that, then collected all the coeffs, and went thru the pain of calculating that determinant
thatd be your answer ig
theres probably some kind of clever linear-algebraic way to look at it which i do not currently have the energy to articulate fully
alpine sable
if you expanded all that, then collected all the coeffs, and went thru the pain ...
that's really not intuitive idk why
vale wigeon
yeah it is not
ocean sealBOT
alpine sable
the one that's not ticked
ocean sealBOT
Ann
vale wigeon
we don't know r but we want this thing to have rational solutions...
alpine sable
yes
alpine sable
no it's not
vale wigeon
i wouldnt be surprised if you can fit infinitely many points on it but i do not see how
alpine sable
i wouldnt be surprised if you can fit infinitely many points on it but i do not ...
no way they could ask such questions in an exam with limited time
wary lantern
Hi
alpine sable
there must be a simpler way
vale wigeon
i am drawing a blank here still
alpine sable
can't we do something using parametric coordinates
vale wigeon
@wary lantern hi, if you have a math question of your own then please open your own channel (see #❓how-to-get-help for instructions), otherwise go to #discussion or #chill
alpine sable
@young finch do you know a way to do this
young finch
if ann doesnt know i definitely dont know
alpine sable
so u wont even try
young finch
im not that smart lol
tardy stag
i wonder if it's 1
lone heartBOT
@alpine sable Has your question been resolved?
vale wigeon
@alpine sable can you ping and/or dm me if you do find a solution? i am actually kind of interested what im missing here.
alpine sable
sure
lone heartBOT
@alpine sable Has your question been resolved?
mellow grail
hmm if it was integer coordinates then i would have a solution for this
wait i might have got it
lemme try
$(x - \sqrt{5})^2 + y^2 = r^2$
ocean sealBOT
ItzKraken
mellow grail
$(x - \sqrt{5})^2 = r^2 - y^2$
ocean sealBOT
ItzKraken
mellow grail
$x = \sqrt{5} \pm\sqrt{r^2 - y^2}$
ocean sealBOT
ItzKraken
ocean sealBOT
ItzKraken
mellow grail
where a is any real
ocean sealBOT
ItzKraken
mellow grail
**ItzKraken**
hmmm actually u can put (r,0) in this only
mellow grail
Find r (r = sqrt(5)/2)
mellow grail
**ItzKraken**
If you put x=0 (assuming a point on the circle) if you find all possible rational solutions...that might help
lone heartBOT
@alpine sable Has your question been resolved?
unborn kiln
lone heartBOT
unborn kiln
So basically our lesson here is Mathematical Reasoning
high ferry
hi can someone help me with this
unborn kiln
hi can someone help me with this
Who made that question 😭
high ferry
Who made that question 😭
I DONT KNOW HUHU
unborn kiln
it's so....woke
high ferry
remote iron
high ferry
ohh thank u!!
lilac imp
plush obsidian
What is 5x1
lone heartBOT
What is 5x1
plush obsidian
My teacher said that it is 44
and I confused
Please fast
I type in branli and it say 200
vale wigeon
do not troll.
wind cloak
the heck is branli
vale wigeon
@tepid drum do not feed the troll.
vale wigeon
your teacher could not have said 5 * 1 = 44, unless they lied to you.
or to your brother.
tepid drum
<@990146348517060619> do not feed the troll.
i am not feeding it just telling him that he is troll but as you wish
vale wigeon
<@&268886789983436800>
stray kite
Im 7 years old
Then why are you on discord
gray isle
<@&268886789983436800>
vale wigeon
Im 7 years old
then you can only come back in 6 years, sorry.
hot snow
wow, I am witnessing a true troll
next brook
Hmm, the account has less immature contributions that this, so I'm going to assume it was taken over by a younger sibling or something.
hot snow
isnt this exciting?
next brook
Timing them out for 24 hours while the proper owner has a chance to get it back.
hot snow
and he is gone
next brook
.close
strong drum
lone heartBOT
strong drum
anyone know how to do this?
thick lynx
Which one?
strong drum
Which one?
3rd
the left and right speeds
i got 88 and 0 first
think it was wrong
thick lynx
the left and right speeds
Do you know how you can determine the body's speed at any time t, using the position f(t)?
strong drum
the deriv and just plug t in?
thick lynx
Yes
strong drum
so 88 and 0?
thick lynx
No
strong drum
1/4
thick lynx
so 88 and 0?
No, 88 is wrong, 1/4 too (slightly)
strong drum
let me retry
thick lynx
let me retry
What expression do you get for the derivative at time t?
strong drum
-32/t^3 +4/t^2
thick lynx
-32/t^3 +4/t^2
Yes
thick lynx
Yes, the left endpoint is at t = 1, the right endpoint at t = 4.
thick lynx
Ah, the argument is probably that speeds can't be negative
strong drum
strong drum
Ah, the argument is probably that speeds can't be negative
i gtg to class
can you help me later?
thick lynx
Just ask in a help channel again, like you did, and someone who sees it can help
I might not be here later
strong drum
ok
strong drum
Just ask in a help channel again, like you did, and someone who sees it can help
up to what math dyk?
thick lynx
up to what math dyk?
I don't think there is an "up to"
Some people might know abstract algebra but not linear algebra
It's not that well-ordered
lone heartBOT
@strong drum Has your question been resolved?
wind hill
how can i find the equation of the circle if it is tangent to both axes, and it passes through (1,-8)?
vale wigeon
think this might be ambiguous...
lone heartBOT
@wind hill Has your question been resolved?
strong drum
It's not that well-ordered
well ig do you know calc 1-2?
wheat isle
how do I solve e^x = 2
lone heartBOT
how do I solve e^x = 2
wheat isle
in exact form
tardy tapir
take ln both sides
keen thicket
xn + yn = zn when n is greater than 2, where x,y and z are not equal to each other.
Can someone prove this theorem?
I need help
lone heartBOT
xn + yn = zn when n is greater than 2, where x,y and z are not equal to each oth...
Please read #❓how-to-get-help
vale wigeon
xn + yn = zn when n is greater than 2, where x,y and z are not equal to each oth...
- don't troll
- post in your own chnnel
keen thicket
1. don't troll
2. post in your own chnnel
What troll?
keen thicket
1. don't troll
2. post in your own chnnel
Ok
tardy tapir
i can never beat ann in typing
vale wigeon
i can never beat ann in typing
90 wpm
wheat isle
how
vale wigeon
$\ln(2)$ is the answer to ``$e$ raised to what power gives 2?''
ocean sealBOT
Ann
vale wigeon
no?
you're confusing yourself
and you don't know what logarithms are, or have purposefully erased it from your mind AGAIN.
tardy tapir
how do I solve e^x = 2
just look at this eqn, LHS is e^x other side is 2, which means e was raised to some power to get 2
vale wigeon
it doesnt make sense
because you fucking forgor again
tardy tapir
dude really is MIB character
wheat isle
i never understood that to the what power gives x stuff
tardy tapir
you got me there 
vale wigeon
i never understood that to the what power gives x stuff
ln(x) is the inverse function of e^x
wheat isle
so whats the inverse of a^x
vale wigeon
log_a(x)
again by definition
you know all these
i myself told you that like 10 times
except every single fucking time you consciously choose to forget
wheat isle
Im not doing it on purpose i have a massive yearly test for all of my subjc next week and its a lot of pressure
vale wigeon
ok you might not be doing this on purpose but like
do you not have notes
do you not even have notes of ANY kind from the times we speak
wheat isle
i do but im revising like every single topic for math and whenever i relearn one again i seem to forget another
'
vale wigeon
💀
i mean that's what notes are for...
like you could have a big visible section in your note book titled "EXPONENTIAL EQUATIONS"
to which you could then turn when faced with this equation
frankly this is like a professional runner forgetting how to crawl
idk how to explain to you why ln(2) is LITERALLY BY DEFN the solution of e^x = 2 except repeating it again and again and again and again and again and again and again and again and again and again
vale wigeon
yes
wheat isle
ok
@vale wigeon can you tell me if im correct for solving $\log_{2}\left(x+1\right)+\log_{2}\left(x-1\right)=3$
ocean sealBOT
water beam
ocean sealBOT
water beam
wheat isle
$x^{2}-1=8$
ocean sealBOT
water beam
vale wigeon
so far so good
wheat isle
$x^{2}=9\to x=\pm3$
ocean sealBOT
water beam
vale wigeon
is x = ±3 your final answer?
vale wigeon
yes or no
ocean sealBOT
water beam
vale wigeon
ok then you are wrong in a somewhat subtle way
wheat isle
only plus 3
wheat isle
logs dont like negative i remember that
vale wigeon
indeed, x = -3 throws a log(negative) error if plugged into the original eq.
solar fulcrum
Need help guys
lone heartBOT
Need help guys
Please read #❓how-to-get-help
solar fulcrum
tardy tapir
this channel's occupied
solar fulcrum
I'm sorry I don't know
tardy tapir
np
solar fulcrum
So How should I get help
tardy tapir
# Please read <#488120190538743810>
.
lone heartBOT
@wheat isle Has your question been resolved?
wheat isle
ok wait
wheat isle
i have some idea of what to do but i have trouble with solving for n, do I take the log of it or something and how would i do that
$100=2000\left(1-0.10\right)^{n}$
ocean sealBOT
water beam
wheat isle
@vale wigeon but do i take ln of both sides maybe?
vale wigeon
could do that, but i would have done a little differently
wheat isle
could do that, but i would have done a little differently
how would you do it?
vale wigeon
divide both sides by 2000 first
then you have 0.9^n = 0.05
only then take logs
minimize mistake opportunities
wheat isle
only then take logs
so $\ln\left(0.9\right)^{n}=\ln\left(0.05\right)$?
ocean sealBOT
water beam
wheat isle
im not sure im just guessing
vale wigeon
$$\ln(0.9^n) = \ln(0.05)$$
or, if you don't like seeing the number 0.9 naked with an exponent,
$$\ln( (0.9)^n) = \ln(0.05)$$
also there is no room to guess here, my instruction was not ambiguous in a way that mattered
i suppose i did not specify the base of the log, but as long as you take logs with the same base on both sides, it doesn't matter. if you are Buridan's ass, then take ln.
ocean sealBOT
Ann
wheat isle
$$\ln(0.9^n) = \ln(0.05)$$
or, if you don't like seeing the number 0.9 naked wi...
hmmm
so I have $2\ln\left(0.9\right)=\ln\left(0.05\right)$
ocean sealBOT
water beam
wheat isle
when am I allowed to drop the logs of both sides?
do I raise both sides by e^x or something?
tardy stag
when am I allowed to drop the logs of both sides?
when you have something that exactly matches the pattern
$\ln(\psq) = \ln(\osq)$
ocean sealBOT
hayley!
tardy stag
do I raise both sides by e^x or something?
sure that'll work
wheat isle
i dont actually know how i would do that
wait
i did something wrong
$n\ln\left(0.9\right)=\ln\left(0.05\right)$
ocean sealBOT
water beam
wheat isle
not 2ln
tardy stag
yeah
wheat isle
i dont know why i put that there
tardy stag
so we're solving for n here right?
wheat isle
yeah
tardy stag
cool, ln(0.9) and ln(0.05) are just numbers
tardy stag
yeah
tardy stag
you haven't done anything wrong
wheat isle
are you sure?
for the x double dot
im confused
there ae no options for acceleration
unless im blind
wheat isle
you haven't done anything wrong
but what would be the correct option
tardy stag
the one that matches what you have
wheat isle
the one that matches what you have
but there is none
last ether
Factor out e^t
e^t * (something)
You're gonna have an equivalent answer but you need to algebraically manipulate your answer to see if it's equivalent to any of the choices
hoary topaz
How do we go from this
lone heartBOT
How do we go from this
hoary topaz
to this
This is the simplified form before we differentiate and I dont understand why both terms are positive
twin nimbus
ah, this is using the even and odd properties of sin and cos
sorry, I was looking at it and disagreeing with it because I thought the differentiation had already happened.
hoary topaz
yah i just realized what are the properties again so i can write them in my notes
is it sin(-x) = -sin(x) and cos(-x) = cos(x)?
twin nimbus
essentially, it's a property of trig that sin(-x) = -sin(x), and cos(-x) = cos(x)
yeah
exactly
hoary topaz
perfect thank you
twin nimbus
yw
bold siren
does anyone knows how to make a inverse graph ?
lone heartBOT
does anyone knows how to make a inverse graph ?
tardy tapir
mirror image along y = x
tardy stag
rewind
what do you mean by inverse
bold siren
i thought inverse means 1 upon :-<
tardy stag
unfortunately math only has so many words
bold siren
you know 1 / sin theta
tardy stag
if you want to graph csc
simplest way is to just graph some points and connect the dots
high sapphire
if you want to graph csc
Sin inverse is not cosec 
bold siren
oh my god i messed up things
can anyone guide in this ques
find the position the word AGAIN in dictionary
dictionary made by only AGAIN letters
high sapphire
find the position the word AGAIN in dictionary
7
Funny thing, one of my classmates asked me the same ques in the morning
high sapphire
yeah correct how did you do it ?
It's simple arranging, first fix A in the first place then next on the 2nd place fix another A, 3 positions are can be filled in 3 factorial ways
Then after fix A in first again, then fix G, then next on dictionary would be A, then 4th letter will be I and last will be N
bold siren
OOh yeah correct thanks
high sapphire
i know same ques my teacher told me today
India's famous ques lmao
Which ques
bold siren
Which ques
AGAIN
high sapphire
U should try MALYALAM
bold siren
.close
lone heartBOT
lone heartBOT
Available help channel!
tiny finch
What do I fill in the blanks with ?
tacit arch
What do I fill in the blanks with ?
do you know how to find the slope of a function?