Helpers are just people volunteering their time to help you. Be polite.
#help-0
lone heartBOT
gray isle
i'm making an effort to stop this line of behaviour as are you going to be asking
"is this option correct" for the next 1000 questions?
grim berry
gray isle
for every single question that you do "in your head"
grim berry
Helpers are just people volunteering their time to help you. Be polite.
them harassing me isn't helping imo
vale wigeon
"boohoo im getting told not to do shit in my head this is clearly harassment"
gray isle
if you aren't confident with your mental arithmetic, do it on paper
vale wigeon
^^^^
gray isle
until you get to a point where you are confident with your mental arithmetic
thorn tapir
them harassing me isn't helping imo
It's not about harassment, we're simply suggesting you to use a calculator or hit a bot if you're asking for correctness in a numerical solution.
grim berry
It's not about harassment, we're simply suggesting you to use a calculator or hi...
I wasn't even talking about you guys
no need to be an asshole over a simple question
@pale kestrel
pale kestrel
pale kestrel
We're all literally saying the same damn thing
A calculator or bot will give you your "yes" or "no"
vale wigeon
shuri said, and i quote,
This server isn't here to be your answer checker
We can check if your steps to get to the answer are correct.
We're not here to be "yes" "no" to your homework / test / quiz
Don't treat us as checker bots. help-12
That's not how this server works
what part of this is them being an asshole to you @grim berry
pale kestrel
We can help with answer verification - but that's with your working and the steps you took to get there.
vale wigeon
well you're acting kind of entitled, is all.
grim berry
i'll just close the ticket and you can move on with whatever you were doing
worn fox
Could've submitted your answer by this point and found out if you were right 
grim berry
.close
lone heartBOT
grim berry
Could've submitted your answer by this point and found out if you were right <:b...
or you could've just said yes or no
pale kestrel
you're taking up channel space with off-topic questions.
lone heartBOT
Available help channel!
alpine sable
why exactly is this 0? when I calculate it i get 1/4
lone heartBOT
why exactly is this 0? when I calculate it i get 1/4
alpine sable
the antiderivative is sin^8(x)/8
upbeat hornet
Did you alter the bounds correctly
alpine sable
while typing out the calculation step by step I realized my mistake
echo socket
You don't even need to find the antiderivative, this is clearly an odd function being integrated over a symmetric interval, hence it's 0
alpine sable
You don't even need to find the antiderivative, this is clearly an odd function ...
what are criteria of an odd function?
echo socket
f(-x) = -f(x) for all x in the domain
alpine sable
alr
okay yea makes sense ty
I would listen to @echo socket here. Just make sure you understand WHY it’s zero.
That is, why the symmetry renders it zero
alpine sable
I would listen to <@348696743388381195> here. Just make sure you understand WHY ...
yes that is clear
the area under the curve cancels out because we're mid peak
,w graph sin^7(x) * cos(x) from -pi/2 to pi/2
ocean sealBOT
alpine sable
yea exactly it cancels
As you can see, it cancels out
yep
thank you for the explanation
.close
lone heartBOT
lone heartBOT
Available help channel!
lone heartBOT
ocean sealBOT
1shero1
lone heartBOT
lone heartBOT
Available help channel!
celest herald
My answer here was 1/2, but the correct answer is -1/2 and im not sure why
languid bolt
!show
lone heartBOT
Show your work, and if possible, explain where you are stuck.
wind cloak
I mean you have positive/negative so you can't be getting a positive answer anyways
celest herald
i divided numerator and denominator by x
then ignored the terms that had a fraction with x as the denominator
wind cloak
when you take x inside the square root
you need to write it as -|x|
And keep the minus outside
it's something that people tend to forget which is why I recommend replacing x with -u
That way it tends to positive infinity and you don't have to deal with the crappy negative square root situation
celest herald
you need to write it as -|x|
why's that?
wind cloak
$\frac{\sqrt 2}{-1}$
ocean sealBOT
neonperseus
wind cloak
What does this equal
celest herald
$-\sqrt 2$
ocean sealBOT
cubopia
wind cloak
$\sqrt{\frac{2}{(-1)^2}} = \sqrt 2$
ocean sealBOT
neonperseus
wind cloak
oh my god -sqrt(2) = sqrt 2
languid bolt
🙀
wind cloak
what I just did is incorrect
$\frac{\sqrt 2}{-|-1|} = - \sqrt{\frac{2}{(-1)^2}} = -\sqrt 2$
ocean sealBOT
neonperseus
wind cloak
This is the right way to do it
so whenever you take something negative inside a root you need to rewrite it as -|x| before doing that
celest herald
ah so squaring x and putting it under the sqrt makes it the absolute value of x?
wind cloak
not necessarily
you can only take a positive number inside the square root
|x| is positive
And for negative x, x = -|x|
|x| is positive so that can be taken inside the root without making mathematicians cry
celest herald
whats actually written in the root would still be x^2 no? regardless of whether its negative or not when you initially put it in
wind cloak
I'm sorry?
celest herald
Putting a number under a square root is like taking the square root of the square of the number right?
celest herald
no
wind cloak
then you can't put it into a root either
celest herald
I had $\sqrt{\frac{4x^2-3x}{x^2}}$ as my numerator after multiplying it by 1/x
ocean sealBOT
cubopia
wind cloak
yes but x is negative here
You cannot take -1 inside the square root
So let it be outside
ocean sealBOT
cubopia
wind cloak
yes when x is negative
crimson saddle
i need help knowing what # is for
lone heartBOT
i need help knowing what # is for
languid bolt
can you give an example?
crimson saddle
idk what # is for like i said
languid bolt
where have you seen it?
limpid spade
We need context
limpid spade
then wikipedia can tell you?
crimson saddle
oh
languid bolt
this?
crimson saddle
yes
languid bolt
i believe it has included the definition
limpid spade
sure wikipedia knows better
tawny lava
lone heartBOT
tawny lava
b makes no sense i dont know hw to do it
unborn saddle
What's the goal of the problem? Are you simplifying it, drawing a number line, or something else?
tawny lava
It says to solve it but b doesnt make snese its suposed to be an inequality but like i dont know how im supposed to do it
merry depot
it's a typo, missing the inequality sign.
You can either put your own in or just not do it.
mellow grail
can u explain how you get 1
brave stratus
I tried this:
t=(x+1)/(2x-1)
x=(t+1)/(2t-1) and then substitute t with 2 and get x=1, so then f(2)=1^2018-2×1^2017+1=0 and f(0)=1
mellow grail
I tried this:
t=(x+1)/(2x-1)
x=(t+1)/(2t-1) and then substitute t with 2 and get...
Tht seems correct..altho u might be better off finding f(x)
$f(\frac{x+1}{2x-1}) = x^{2018}-2x^{2017}+1$
ocean sealBOT
itzkraken.
mellow grail
**itzkraken.**
have u tried taking something common
try rewriting using x+1=u and (2x-1)=p
eh nvm
ur solutions seems correct
must be a problem with the answer key
lone heartBOT
Available help channel!
violet ore
IBP for the indefinite integral cos(lnx)dx
lone heartBOT
IBP for the indefinite integral cos(lnx)dx
violet ore
I have no clue how to start because there is no product of functions
tacit arch
$1 \cdot \cos(\log(x))$
ocean sealBOT
rie.mann
violet ore
Hmm I will try this
since the if dv = dx, v = x, and du has 1/x factor in it, uv will have cancelation
Give me min
Ahh I see now, thank you
That worked out nicely after doing IBP twice then an algebraic manipulation
it was in the form I = ... - I do then I had 2I = ... And found I
.close
warped topaz
lone heartBOT
https://i.imgur.com/AG1uCmg.png
warped topaz
I got the correct answer but im wondering something
Is there a reason they gave it in a factorized form? First thing I did was change them both back to polynomials but it seems weird that they gave it in this form, was I supposed to do it a different way?
vale wigeon
change them both back to polynomials
they always have been
you expanded them and changed the num and denom to standard form
warped topaz
Ah ok nice
So I guess they were just giving me extra work to convert them haha
.close
tender anchor
I'm really struggling with this problem I don't understand how my answer is wrong
tender anchor
I think i tried C and E too for the graph and they were wrong
tacit arch
lone heartBOT
@tender anchor Has your question been resolved?
tender anchor
https://www.khanacademy.org/math/old-ap-calculus-ab/ab-derivatives-analyze-funct...
im still so confused though. from x0->2 is the slope increasing so the derivative graph would then be and start positive? then it slopes out to 0 then after that does the slope decrease or increase til it slopes out again? like i'm confused bc its the same shape line sloping out to 0. i see it as the slope is increasing then stops increasing bc it goes to 0 does that mean it's slowing down and the derivative would be negative as it reaches 0 again? does the derivative graph ever go negative? sorry that probably doesn't make sense im just confused
Wait on the x-axis from 0-2 does the slope increase til it hits 2 on the y axis then decrease after that point as it approaches the still slope at y=4
vapid shuttle
x'(t) does not represent the acceleration of the car
it represents the velocity of the car
Don't think about whether or not the slope is increasing, think about whether or not the function is increasing
over intervals of the function increasing, the velocity (x'(t)) will be positive
over intervals of the function remaining stationary, the velocity (x'(t)) will be 0
over intervals of the function decreasing, the velocity (x'(t)) will be negative
@tender anchor
Because the derivative of position, is velocity (not acceleration) and the graph you are given is the position of the car
tender anchor
Ah
tender anchor
over intervals of the function increasing, the velocity (x'(t)) will be positive
Ok so from x 0->2 the function is increasing and x't is positive? then from 3-5 its decreasing so negative? then from 7-9 increasing & positive and 10-12 decreasing & negative
vapid shuttle
I don't see the function decreasing anywhere
tender anchor
wait im so lost lmao
vapid shuttle
tender anchor
yeah so its always increasing
tender anchor
yeah
vapid shuttle
it just doesn't decrease
tender anchor
so the derivative graph is always above the x-axis
vapid shuttle
for this function in particular, the graph of the derivative should be always above the x-axis, or 0
tender anchor
so its D then?
vapid shuttle
looks like based on our criteria C is also an option
so figure out which one it is
tender anchor
I think i guessed C and it said it was wrong before
Unless it is c i mightve changed it before i submitted it i dont remember
vapid shuttle
you should be able to figure it out without guessing though
match up the intervals of your function, to the derivative graphs
wherever your function is flat, the derivative graph should be 0
see if that is true for D, or C, or both
tender anchor
wherever your function is flat, the derivative graph should be 0
so D then? Cause for c at 6 it should be at x 0 for x 5 and x 7
vapid shuttle
at x=6, the graph of the derivative should have y=0, which C does not
so it can't be C,
tender anchor
Yeah
o shoot yeah the 6 doesn't line up it's above 0
And for the 2nd part the true ones would be E, F, G?
vapid shuttle
looks good to me
tender anchor
Ty for the help
vapid shuttle
no problem!
tender anchor
.close
lone heartBOT
lone heartBOT
Available help channel!
umbral portal
From a mountain that 5 km high, you can see the horizon with a 87.73° angle. Determine radius x km
umbral portal
Initially, I tried doing
x+5/x= cos 87.73
= -5.2
And since its obviously wrong, im wondering how I should continue
quiet vector
well with the given angle
which are the known sides?
cos probably isnt the relation u r looking 4
u do remember the trig definitions right?
umbral portal
I think so
quiet vector
so u know the side opposite to the angle and the hypotenus
umbral portal
Yeah
quiet vector
whats their relation
umbral portal
?????
lone heartBOT
Please read #❓how-to-get-help
quiet vector
sin(87.73) =
x/x+5
seems like u havent understood basic trig
whats the definition of cosine of an angle
umbral portal
the nearby side/hypotenus
quiet vector
ok i see the problem
u dont define any sides as the nearby sides; start looking with respect to the given angle
one is opposite to the given theta
or simply opposite
then opposite the right angle or hypotenus and then the base
umbral portal
my mother tounge isnt english thats why
umbral portal
Yea
quiet vector
even if u've understood i dont undersatnd anything when you say nearby side
umbral portal
why not cosin though
quiet vector
the base is the side opposite to the unknown angle
its clearly not known
remember this
if u rotated that figure
would ur "base"
change?
would ur answer change?
if so u are clearly doing something wrong
only one answer in maths
fair wyvern
It doesn't say which direction is positive
lone heartBOT
It doesn't say which direction is positive
fair wyvern
But I assume the direction going up is, right?
So this is right?
And in part 2
There's no longer work pulling it up
And total energy is always the same, the only difference is whether or not it's potential or kinetic
lone heartBOT
@fair wyvern Has your question been resolved?
fair wyvern
<@&286206848099549185>
fair wyvern
What?
fair wyvern
what u need
I'm not sure my answers are correct because I don't know which direction of work is positive
wild owl
whats the problom
fair wyvern
It doesn't say which direction is positive
two part problem
fair wyvern
And in part 2
and this
unborn saddle
Work is positive when the force vector is in the same direction as the displacement of the object. Like if I push a box, and the box moves i the direction I push, work is positive.
On the other hand, work is negative if the force vector is in the opposite direction as the displacement. Like with friction forcing a sliding object opposite the direction of motion. This work is negative.
wild owl
I'm not sure my answers are correct because I don't know which direction of work...
its all right
fair wyvern
Work is positive when the force vector is in the same direction as the displacem...
so that would mean up is positive, right?
wild owl
yea\
unborn saddle
Yup
wild owl
yep
fair wyvern
is it positive
I assume the box gets more potential energy, so it's positive
No idea about the second part :(
I don't think there are non-conservative forces because it's in free fall
unborn saddle
I'd have to agree, it doesnt seem there are any non-conservative forces
fair wyvern
I guess the work on the conservative forces is positive because now the box changed direction
unborn saddle
However, since gravity IS doing work on the box, and the box is moving in the same direction. Work should be positive.
unborn saddle
I guess the work on the conservative forces is positive because now the box chan...
yeah
silent monolith
correct?
tardy stag
doesn't seem right to me (how could it be way bigger than AB + BC?); how did you get that?
lone heartBOT
@silent monolith Has your question been resolved?
worn fox
tell us what work you're doing
silent monolith
ok
so im doing
pythag
and i got this so far
5^2 + 8^2 = 89
5^2 + 8^2 = AC^2
89 = AC^2
tardy stag
okay, if you think about this physically the answer of 64 should make no sense
just thinking about triangle ABC
tardy stag
well... if you have $89 = \bar{AC}^2$ then you should be able to solve for $\bar{AC}$
ocean sealBOT
Hayley
silent monolith
oh so 89 is ac
i jus brainfarted lol
i thought i had to find AC but 89 is AC
worn fox
AC is not 89
worn fox
5^2 + 8^2 = 89
5^2 + 8^2 = AC^2
89 = AC^2
look at your last line here
silent monolith
89 = ac^2 i see it
worn fox
so AC = ?
silent monolith
its not 89^2
right
like multiply 89 x 89 thats not AC right
bc u said 89 is not AC
worn fox
$\overline{AC}^2 = \overline{AC}\cdot\overline{AC} = 89$
ocean sealBOT
ΣΑC
worn fox
AC squared is 89, so what is AC
silent monolith
7921
worn fox
if x^2 = 9 then what is x?
silent monolith
u talking to me?
silent monolith
if x^2 = 9 then what is x?
3
worn fox
okay what if x^2 = 10?
worn fox
5x5 is not 10
silent monolith
yea no thats 25 i brainfarted
silent monolith
okay what if x^2 = 10?
nothing
worn fox
you dont think there is any number that squares to 10?
silent monolith
well 5
worn fox
not even the square root of 10?
worn fox
but we want (something)^2 = 10
or in the case of your actual question, (something)^2 = 89
silent monolith
ohh i see
its not something times 2 right
its something that when multiplied by itself
gives 89
right
worn fox
yes
worn fox
have you heard of square roots?
tacit arch
nothing equals 89
have you heard of irrational numbers?
silent monolith
nope
silent monolith
square root
tacit arch
silent monolith
2
tacit arch
,calc sqrt(2)
ocean sealBOT
Result:
1.4142135623731
rose sigil
,calc (1.4142135623731)^2
ocean sealBOT
Result:
2
u get 4
silent monolith
u said square 2
tacit arch
u said square 2
read both sentences
tacit arch
Result:
```
1.4142135623731
```
this is the decimal approximation to sqrt(2)
tacit arch
AC *squared* is 89, so what is AC
does that answer this question for you
silent monolith
7921
alpine sable
Let ${a_n}$ be a sequence of positive integers defined as follows: $a_1 = 1$ and for $n > 1,$ an = a{n-1} + \left\lfloor \frac{n}{\sqrt{a_{n-1}}} \right\rfloor, where $\lfloor x \rfloor$ denotes the greatest integer less than or equal to $x.$ Determine the smallest positive integer $k$ such that there exists a term in the sequence $a_k$ satisfying \left|\frac{a_k}{k^2} - \frac{1}{\sqrt{2}}\right| < \epsilon, for any positive real number $\epsilon > 0.$
Specifically, there is an issue with the step where we substituted $\frac{n}{\sqrt{a_{n-1}}}$ as $\frac{k\cdot n}{\sqrt{k^2a_{n-1}}}.$ This substitution is not valid and has led us astray in our analysis. I need help because i can't get an answer
next brook
Let ${a_n}$ be a sequence of positive integers defined as follows: $a_1 = 1$ and...
This channel is in use. Please claim one that is available or your question, as explained in #❓how-to-get-help.
tacit arch
2 squared is 4
you're making this mistake again
tacit arch
but that's not what you're computing
.
tacit arch
AC *squared* is 89, so what is AC
read this slowly
ocean sealBOT
Result:
9.4339811320566
yes
silent monolith
ok my fault like when i hear square
tacit arch
Result:
```
9.4339811320566
```
what happens when you square this number
ocean sealBOT
Result:
3.0659419433512
Result:
3
see?
tacit arch
what happens when you square this number
read this slowly
tacit arch
,calc sqrt(89)
.
silent monolith
ok?
lone heartBOT
@silent monolith Has your question been resolved?
wary stream
ok?
You should review the difference between square root and square, that's what riemann is pointing out
silent monolith
.close
lone heartBOT
lone heartBOT
Available help channel!
olive citrus
given a point on a vector field how do i get the equation for its trajectory? are there any tutorials on this?
acoustic wharf
it depends on what the vector field signifies
for example if it's a force field then the point will move according to the diff eq md^2OM/dt^2=F(x,y,z), where m is its mass
lone heartBOT
@olive citrus Has your question been resolved?
olive citrus
it depends on what the vector field signifies
for any vector field
for example the guy in this video draws what the equations are but doesnt say how to actually obtain them https://www.youtube.com/watch?v=f1f4VNTo0Gs&ab_channel=DrBrainWalton
tacit matrix
Help me by proving it
lone heartBOT
Help me by proving it
vague coral
the dot is multiplication ?
tacit matrix
the dot is multiplication ?
Yes
acoustic wharf
Help me by proving it
you can find a closed form for AB
vague coral
then to prove its a closed set, you can prove that A.B contains the limits of all his converging sequence
🤔
acoustic wharf
lol thats overkill
tacit matrix
sequence not required
vague coral
never said it was the only method
tacit matrix
But A and B are Set not Sequence
tacit matrix
Can you solve it and send me using the paper .. 🌸
vague coral
I dont have paper where i am rn
acoustic wharf
if 1<a<2 and 2022<=b<=2023 then where does ab lie ...?
vague coral
if 1<a<2 and 2022<=b<=2023 then where does ab lie ...?
thats definitely not something that justify a closed set
acoustic wharf
it's in order to find A.B explicitely
from there it would be easier to tell its nature
yk if it's an interval then you'd be able to easily tell just by looking at it
tacit matrix
🥲
lone heartBOT
@tacit matrix Has your question been resolved?
native temple
https://cdn.discordapp.com/attachments/486841106298961930/1124516223988801658/image.png My book doesn't have answers for this question how do I know if I got it correct?
tender anchor
so for this problem i think its discontinuous at x=3 and x=-1 so its continuous at all real nums besides those 2 how do i put my answer in interval notation?
naive valley
how many intervals will you need?
tender anchor
ok i did (-inf,-1)U(3,inf) but its wrong is my original answer wrong?
naive valley
your original answer is right, but you haven't expressed it correctly in terms of intervals
tender anchor
oh
naive valley
for example, is zero in either of those intervals?
naive valley
yep that's right
tender anchor
thanks
tacit matrix
<@1057955116017266738> Has your question been resolved?
No
limpid turret
lone heartBOT
@native temple Has your question been resolved?
lone heartBOT
tacit arch
It's closing. Just wait
lone heartBOT
Available help channel!
native temple
It's closing. Just wait
You're here? can you answer my question?
lone heartBOT
You're here? can you answer my question?
native temple
https://cdn.discordapp.com/attachments/486841106298961930/1124516223988801658/image.png My book doesn't have answers for this question how do I know if I got it correct?
lone heartBOT
@native temple Has your question been resolved?
lone heartBOT
cinder sundial
The geometric definition of derivative is “slope”
So I assume that what I wrote on the paper is correct?
tacit arch
So I assume that what I wrote on the paper is correct?
No
cinder sundial
Why?
tacit arch
Because it's not? You can't just make up your own definition of slope
You have to prove it equals the original definition
cinder sundial
The original definition in geometry is just the slope of a tangent line.
What I wrote above is also the slope of a tangent line
They are same in geometric meaning
tardy stag
it's not though
tacit arch
The original definition in geometry is just the slope of a tangent line.
It has a formula
tardy stag
I mean it's tangent to something but not to what you think it is
cinder sundial
I mean it's tangent to *something* but not to what you think it is
That means I couldn’t consider the derivative as the slope of a tangent line
tacit arch
That means I couldn’t consider the derivative as the slope of a tangent line
No
The original one is. Look up the formula
tacit arch
Not your made up one
cinder sundial
I know what the formula is, but I wanna consider it in the geometric way!
tacit arch
The original one has a geometric meaning
cinder sundial
The original one has a geometric meaning
I wrote it clearly on the paper, mine is also has a geometric meaning
cinder sundial
Which is different from "the derivative"
Do you agree what I wrote is the slope of a tangent line
When h approach 0 it’s the slope, do u agree
tacit arch
When h approach 0 it’s the slope, do u agree
Slope of what
tardy stag
it's the slope of something but that something is not f
cinder sundial
Slope of what
The tangent line which through the point (1,f(1))
tacit arch
All numbers represent some slope, so it's meaningless to say the number you're writing is a slope
iron pine
cinder sundial
it's the slope of *something* but that something is not f
What do you mean “not f”
tacit arch
The tangent line which through the point (1,f(1))
No. "the tangent line" is reserved for the definition of the derivative, not your made up one
cinder sundial
All numbers represent some slope, so it's meaningless to say the number you're w...
That makes me more confused
cinder sundial
No. "the tangent line" is reserved for the definition of the derivative, not you...
Ohhh
tacit arch
Yours is a tangent line of something, but not the original definition
Just your own made up line
cinder sundial
Just your own made up line
So it’s a “strict” definition
tacit arch
All definitions are strict
You can't just make stuff up and call it something that already exists
cinder sundial
All definitions are strict
I thought it’s just P and Q almost overlapped then take the slope of PQ
cinder sundial
I thought it’s just P and Q almost overlapped then take the slope of PQ
That wouldn’t be derivative right?
tacit arch
That's too vague to be a definition
cinder sundial
That's too vague to be a definition
But that’s what I being taught
tardy stag
that's intuition and analogy not a definition
cinder sundial
that's *intuition* and *analogy* not a definition
God I didn’t know that
rose sigil
You can't just make stuff up and call it something that already exists
why not 
all my definitions are mutable
tacit arch
,w definition derivative
ocean sealBOT
tacit arch
@cinder sundial that's a definition
tacit arch
The original one is. Look up the formula
Which I said to look up
cinder sundial
Which I said to look up
Ohhh
cinder sundial
To conclude, to get the value of A I can only compare it with the true definition of derivative
Rather than using the definition that I made up
rose sigil
all my definitions are mutable
definition: an integer m is even if m = 3^k for some positive integer k
theorem: 27 is even
proof: trivial
lone heartBOT
@cinder sundial Has your question been resolved?
rose sigil
<:what:1113954135692279929>
you can't deny it
tacit arch
you can't deny it
rose sigil
yea idk if this one is my style
keen plinth
you can't deny it
well, if you define even like that...
rose sigil
well, if you define even like that...
i said what i said
native temple
https://cdn.discordapp.com/attachments/486841106298961930/1124516223988801658/image.png My book doesn't have answers for this question how do I know if I got it correct?
quiet vector
wait free body diagrams dont require resistive forces?
lone heartBOT
@native temple Has your question been resolved?
native temple
wait free body diagrams dont require resistive forces?
Isn’t that what f is?
quiet vector
so u made the same one for friction and other resistive forces ig
np
u wanted what the maths checked
stark tiger
hey guys
stark tiger
A level studet here
i have some math probems and i kinda need help
are there any voice channels cause i would really like a good explaination
kindred anchor
lone heartBOT
@stark tiger Has your question been resolved?
lone heartBOT
lone heartBOT
Available help channel!
gentle coyote
What is the number of ways to arrange the numbers 1,2⋯,6 in a circle so that every two consecutive numbers are not
Side by side?
gilded magnet
!show
lone heartBOT
Show your work, and if possible, explain where you are stuck.
@gentle coyote Has your question been resolved?
unborn ridge
lone heartBOT
lone heartBOT
@unborn ridge Has your question been resolved?
vale wigeon
what do i do from there?
what do you have on the LHS currently?
if you've done it correctly, at this point you can do some binomial expansion.
or a bit more tinkering to make your own life easier.
unborn ridge
what do you have on the LHS currently?
idek if im doing this right but
vale wigeon
better to have $z^{-1}$ rather than $\overline{z}$
ocean sealBOT
Ann
unborn ridge
oh okay
vale wigeon
also $\sin(\theta) = \frac{z-z^{-1}}{{\color{red}2i}}$
ocean sealBOT
Ann
lone heartBOT
lone heartBOT
Available help channel!
viscid coral
dumb question, why is fourth root of 81 equals to 3, and fourth root of 0.81 is not equal to 0.03, but 0.948683298
mortal trellis
0.03^4 = 0.00000081
viscid coral
oh
lavish glacier
You can write 0.81 as 81 * 1/100
Take the 4th root of each and multiply
The 1/100 term is where the weird decimals come from
viscid coral
The 1/100 term is where the weird decimals come from
i like this explanation!
lavish glacier
It's basically the same reason why sqrt(100) is a nice number but sqrt(1000) isn't
viscid coral
Thanks guys, i acutually kinda know why but im just trying to find a way to justify why exactly
viscid coral
It's basically the same reason why sqrt(100) is a nice number but sqrt(1000) isn...
yeah makes sense
.close
wide trout
lone heartBOT
wide trout
I don't understand this guys
pliant wedge
are they defined in 0.25?
wide trout
no
pliant wedge
conclusion of Intermediate Value Theorem is: there exists some c in [a,b] so that f(c) = u for any u in [f(a),f(b)]
in the first example 0.25 is the c, but f is not defined there. So for value u = 2 there is no such c
wide trout
what is the diffrence in the second one
echo socket
If f in the first graph satisfied the conclusion of the theorem, f would take on any value from (1, 3) on the interval (0, 1), but at no point is f(x) equal to 2, so it's not satisfied (the reason is that the premise of the theorem is unsatisfied, as f is not continuous on the interval)
In the second graph the function does take any value from (1, 3), even despite it being undefined for x = 0.25
pliant wedge
I believe they are looking at the value u = 2 only...
pliant wedge
If f in the first graph satisfied the conclusion of the theorem, f would take on...
the value from interval is always on the image of f. So the second example is not (1,3) but [f(0.25),f(1)] since f(0.25) is minimum
echo socket
(f(0.25) *
I meant to say that f(x) = a where a is in (1, 3) for 0 < x < 1 always has a solution in the second graph
pliant wedge
i mean if you consider the theorem completely (not just the conclusion), the function has to be continuous. Which in both cases is not. So it does not guarantee the existance of such c in [a,b]
echo socket
Yeah the premise is unsatisfied in both cases but the conclusion is false in the first one and true in the second one because the implications F -> F and F -> T are true
wide trout
ok guys I'll look into it thx all
lavish tiger
lone heartBOT
subtle birch
!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
!show
lone heartBOT
Show your work, and if possible, explain where you are stuck.
lavish tiger
equilateral triangle formula was applied and it’s solved now but there’s another question I’m having a touble with
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
2
subtle birch
and show your work
teal ember
@lavish tiger
- calculate the area of the square first
- calculate the area of triangle DFC and triangle ADE
teal ember
- add the areas of those two triangles... suppose the area as S
teal ember
- minus it from the area of square
teal ember
thankyou thankyou , I got it bow
welcome
lavish tiger
you’re Indian right , u guys are so smart
thankyouuuu soooo much
fbsjeidhbs
.close
safe tartan
is tan (arctanx)=x?
lone heartBOT
is tan (arctanx)=x?
teal ember
exactly
teal ember
but -1 <=x<=1
safe tartan
woo
safe tartan
As long as arctan(x) is defined
yeah i thought it was this, and i still do. Why does this pass the condition?
modern sedge
arctan(x) is defined for all real x
safe tartan
oh yeah makes sense
teal ember
minus pi/2 to pi/2
happens when arcsine(sinx)=x
modern sedge
happens when arcsine(sinx)=x
here x must be between pi/2 and -pi/2
safe tartan
yeah cuz the range for arcsin is that right
its quite confusing for me
then for sin(arcsinx) does that one always = x with no conditions?
teal ember
here x must be between pi/2 and -pi/2
exactly what I ve said
teal ember
then for sin(arcsinx) does that one always = x with no conditions?
also does there
without conditions
means for all values of x
teal ember
sin(arcsin), cos(arccos), tan(arctan), sec, cosec, cot....... in these cases it is equal to x for all values of x
modern sedge
sin(arcsin), cos(arccos), tan(arctan), sec, cosec, cot....... in these cases it ...
you sure?
teal ember
sure..
modern sedge
sin(arcsin(x)) is equal to x for -1<=x<=1
teal ember
but generally
modern sedge
in reals it would be non-sense (undefined)
safe tartan
then x shouldnt be all values right
teal ember
or would that be 5
cant happen
safe tartan
alright
so only tan does not have these conditions
since the domain is inf
what values of x then is arcsin(sinx) defined?
safe tartan
oh right cuz sinx is -1 to 1 which is in the domain of arcsin
teal ember
what values of x then is arcsin(sinx) defined?
[-pi/2,pi/2]
modern sedge
https://www.desmos.com/calculator/que76ivhjs
in the left panel, you can type your own formulas and see what happens, it might be easier to understand when you see it graphed
modern sedge
[-pi/2,pi/2]
??? It's defined for all values of x, it's just not equal to x for all values of x
teal ember
??? It's defined for all values of x, it's just not equal to x for all values of...
yeah .. I misspelled then 😅 .. I apologize
safe tartan
[-pi/2,pi/2]
that would be the range i tiink
modern sedge
Do you understand graphs? If you do, I would really try to play with graphing calculator for a while.
safe tartan
but arcsin(sinx) would not always equal to x since arcsin has a restricted range
yeah i proabbly should
i think i have a better understanding now thanks
.close
fierce delta
lone heartBOT
fierce delta
heres what i tried
I messed up somewhere, maybe even at the beginning, can someone help me find where I messed up?
hasty hill
bro..
fierce delta
It’s obvious isn’t it
safe tartan
well the 2nd last and last lines
fierce delta
Gimme a sec
safe tartan
what
hasty hill
a - b / c - a
fierce delta
In the 3rd step,
hasty hill
u can't remove a from numerator and denominator just like that
hasty hill
a - b / c - a
it won't be 1 - b / c - 1 at all
fierce delta
I used the in the 3rd step 1-sin(theta)*cos(theta) from the bottom to cancel out the one on the top
safe tartan
you did everything right until the last 3 lines including the ...
hasty hill
your basics are a bit messed up I feel..k * m / k * n = m / n when k is not equal to 0
safe tartan
yeah try get rid of the 1 using pythagorus identity, which then you can factor out certain terms to leave you with tanx
hasty hill
is this clear to you now?
safe tartan
well you couldve used it in the first step
all you did in the first 4 lines was rearrange for no reason
3 i meant
hasty hill
she meant sin^2 theta + cos^2 theta = 1
fierce delta
Cuz there’s a 1 and a -cos^2(theta)
Yeah I know what the identity is, but haven’t done much practice
safe tartan
idk what that means but the first 3 lines was not necessary, couldve simply converted 1 into sin^2x + cos^2x from the begginning
ornate ginkgo
Well yeah getting rid of the 1 would be the first step
ornate ginkgo
Cuz there’s a 1 and a -cos^2(theta)
$1 - cos^2\theta = sin^2\theta$
ocean sealBOT
coldtee
hasty hill
Okay I suggest only one of us to help him out..otherwise he might get confused
I am leaving
ornate ginkgo
Me too
hasty hill
someone take the lead and help him out
marsh rapids
that sounds like an attempt to help better turning out terrible
marsh rapids
**coldtee**
using this, you get
sin² x - sin x cos x / sin x cos x - cos² x
then it's one more line (or 2) and you're done
fierce delta
Yeah I’ve got it out to be
Nvm
After using the Pythagorean identity when replacing the 1
The sin^2 + cos^2 should be in a bracket right?
marsh rapids
it's more so that 1 - cos² = sin² and 1 - cos² = sin²
that's how it's often used in practice too
fierce delta
I didn’t do that and paid for it with 7 years of my lifespan
lhs = 1 - sincos - cos^2 / sin^2 + sincos - 1
= sin^2 + cos^2 - sincos - cos^2 / sin^2 + sincos - (sin^2 + cos^2)
that bracket at the end was what i was talking about, i didnt put it and ended up getting sin(sin - cos) / cos(sin + cos)
marsh rapids
at least now you know
We learn from our mistakes
warped kindle
Hi guys, just wondering can someone help me with this question? I can't seem to get the numbers right. For the variable i think it's correct.
mortal trellis
dont upload random files
safe tartan
prolly some virus lma
subtle birch
Hi guys, just wondering can someone help me with this question? I can't seem to ...
send a screenshot of your problem
wind cloak
prolly some virus lma
Probably isn't but we won't download files just to be safe
warped kindle
lone heartBOT
Show your work, and if possible, explain where you are stuck.
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
show your process
warped kindle
gray isle
,rcw
ocean sealBOT
gray isle
and what does that simplify to
gray isle
so for the part I circled, you'd have
$${\br{3^{\frac13}}}^{-3}$$
that isn't $3^{27}$
ocean sealBOT
ℝamonov
warped kindle
This is what i get bass on what i understand.
gray isle
${\br{a^b}}^c \redneq a^{\br{b^c}}$
ocean sealBOT
ℝamonov
gray isle
you have what's on the left,
but you're calculating what's on the right
warped kindle
Not so sure what you mean, sorry.
warped kindle
This is what i get bass on what i understand.
So this is wrong right?
gray isle
what you've done there isn't what the question wants
gray isle
the image above outlines that
from the \verb|power of power| exponent law,
$${\br{a^b}}^c = a^{bc}$$
ocean sealBOT
ℝamonov
warped kindle
So what do i do now?
warped kindle
But i still have the power of -3 there
gray isle
wdym
gray isle
apply the proper exponent law above
warped kindle
Is it correct?
gray isle
for that part, yes
warped kindle
Or this?
gray isle
neither
warped kindle
that's exactly what i said you shouldn't be doing
Ok
gray isle
the outer power is -3, not 3
gray isle
you're supposed to use the values you actually have
warped kindle
Then what do i do with the power of -3?
gray isle
that's the value you should have multiplied to the 1/3
warped kindle
Because for thr why i times the y with power of -3
gray isle
power of power law
gray isle
if you want to do the whole thing instead of splitting up the calculations, yes
you can do that directly
gray isle
wdym
warped kindle
I am suppose to make all thr basses 3, and the other 3s have power of 3 and 1 while if i have this as 1/3, it is not 3 already
gray isle
,rotate
ocean sealBOT
gray isle
that was just a pic of the old work
ideally you'd also avoid using a calculator for this
are you aware of this law
$${\br{a^b}}^c = a^{bc}$$
ocean sealBOT
ℝamonov
warped kindle
So, if i want to make the bass as 3 also, how should i do?
gray isle
read above directly above
warped kindle
So this is the final i can get?
warped kindle
I'm sorry which one. I'm kinda confuse already
gray isle
are you aware of this law
$${\br{a^b}}^c = a^{bc}$$
the power of power law i keep mentioning
ocean sealBOT
ℝamonov
warped kindle
are you aware of this law
$${\br{a^b}}^c = a^{bc}$$
the power of power law i kee...
Yes i am aware, and i use it too. But in this context hoe do i apply it?
warped kindle
If (1/3) power of -3 is wrong, then what other way?
gray isle
you have
3 being raised to the power of 1/3 in (), the (a^b)
and that whole thing is being raised to the power of -3, the c
the law above does NOT tell you to raise b to the power of c
warped kindle
Ya
gray isle
the law tells you what you're supposed to do
warped kindle
the law above does NOT tell you to raise b to the power of c
Ok
So, if i want 3 as my bass. The (1/3) power of -3 how should i do it?
gray isle
exactly as the law states
warped kindle
Times it?
gray isle
look at the final power after the parentheses are gone
gray isle
bc is the product of b and c
yes
warped kindle
Oooo i see
gray isle
i also mentioned to not resort to using a calculator
warped kindle
i also mentioned to not resort to using a calculator
Sorry, it was just much more convenient
gray isle
that calculation above takes longer to enter in the calculator than do it by hand
warped kindle
Well, thank you soo much for helping me!
warped kindle
that calculation above takes longer to enter in the calculator than do it by han...
Yaa sometimes
warped kindle
Hi, there's another question i can't seem to figure out.
lone heartBOT
Hi, there's another question i can't seem to figure out.
ocean sealBOT
modern sedge
Translation is below
warped kindle
Sorry, this book consists of duo languages.
upbeat hornet
oh, sorry didn’t see that
vale wigeon
64, 625, 125 and 16 all have something in common
warped kindle
Can be square rooted?
vale wigeon
every number can be square rooted, aside maybe from negative ones depending on what level you're at
but no that isn't what i meant
onyx swallow
Can be square rooted?
what does 625 and 125 have in common
and what does 64 and 16 have in common?
upbeat hornet
consider the factorization of all of these numbers
vale wigeon
what i meant is that ||they are all powers of small integers: 2^6, 5^4, 5^3 and 2^4 respectively||
warped kindle
One is divisible by 5 and another 8?
warped kindle
what i meant is that ||they are all powers of small integers: 2^6, 5^4, 5^3 and ...
Ooo
Sooo
P=4 and q=4 as well?
vale wigeon
that's a huge leap
onyx swallow
Ya it's wrong
you should change the base to 2 and 5
warped kindle
Ok. I have done that
onyx swallow
Ok. I have done that
what do you have?
onyx swallow
8000=8000
but there is multiple solutions
(i think perhaps this is the intended solution)
warped kindle
I mean i had to see whether both sides are equal
onyx swallow
I mean i had to see whether both sides are equal
what i mean is the there are other p,q that works
warped kindle
Then i substitute them into the equation.
warped kindle
what i mean is the there are other p,q that works
I see
Like what else?
What would you have done though?