Ok
#help-13
surreal plume
buoyant latch
And IR is ℝ meaning the real numbers
So -5, -3, -0.7261584, 0, sqrt2, pi, 500000000000
Any real number is in ℝ
The set notation is a little harder to explain if you’ve never seen it before
But we “build” sets with conditions
For example, {x | x ∈ ℝ, -8 <= x <= 8} is saying
Consider the set (that’s what {} means)
This set contains something we will name x
| means such that:
x ∈ ℝ means x is an element of the real number set
surreal plume
x such that x is an element of the real number set?
buoyant latch
And -8 <= x <= 8 just imposes more restriction on this x
And any x that satisfies this will be an element of the set
buoyant latch
x such that x is an element of the real number set?
First part is naming our variable
The set includes all the x’s, where x is an element of the reals
But also satisfies -8 <= x <= 8
buoyant latch
We want to name it because you could have something like
{(x, y) | x,y ∈ ℝ, y = x²}
And that’ll give you the set of all points on the curve y = x²
So it’s specifying the things in this set have the form (x, y)
Also ℝ is often written as a normal capital R, then you add a line inside the R
So the top connects the 2 vertical lines
And it doesn’t just look like IR
dull shard
I have a really stupid question
cedar kilnBOT
I have a really stupid question
dull shard
can someone just explain to me how 1-(1-sin²∅) is sin²∅
long arrow
No such thing as a stupid question
muted bear
distribute the minus then combine like terms
tropic oxide
can someone just explain to me how 1-(1-sin²∅) is sin²∅
1-(1-a) = a
btw do not use the empty set symbol as a substitute for theta
buoyant latch
Just use x
long arrow
θ
buoyant latch
Or that
sick fable
Hi
dawn junco
what do you mean ?
sick fable
what do you mean ?
Is this correct?
wraith daggerBOT
open vine
Where did i go wrong here?
cedar kilnBOT
Where did i go wrong here?
muted bear
Not writing y' somewhere
But like actually lemme look
Product rule first, chain rule second
open vine
Product rule first, chain rule second
didnt i do that?
runic garnet
||LOG DIFF AAAAH||
upper garnet
||LOG DIFF AAAAH||
muted bear
Not a bad idea, but also 🙅🙅🙅🙅🙅🙅
open vine
What are your two functions for product rule?
(2x^2-1)^3 and (x^4+3)^5
muted bear
Ok, now what is the derivative of each?
open vine
Ok, now what is the derivative of each?
right?
muted bear
OH SORRY
Yes you did
You went wrong when you factored out the 4x
12x does not become 3x
cedar kilnBOT
muted bear
Sorry about that
cedar kilnBOT
Available help channel!
bronze pivot
any tips on how to find the smallest coefficients possible for the normal vector
bronze pivot
in b specifically
im asked to graph the plane so i would like to know how to get the smallest coefficients posisble in the point normal equation
dreamy sleet
Have you found the plane?
bronze pivot
yeah but I got a big coefficient
dreamy sleet
And what is the point of intersection of the lines
Can you show the equation you got?
mighty drift
And what is the point of intersection of the lines
To make sure they define a plane
bronze pivot
-12(x-5)-8(y-2)-16(z+1)=0
bronze pivot
Can you show the equation you got?
here
mighty drift
That's fine
dreamy sleet
yeah but I got a big coefficient
oh, I thought you meant something big like 6174 or something
dreamy sleet
-12(x-5)-8(y-2)-16(z+1)=0
you could divide by 4?
bronze pivot
ahh yeah I can
mighty drift
Then you get coprime integers which is considered optimal
bronze pivot
And what is the point of intersection of the lines
(-3,-2,7)
dreamy sleet
Is your issue resolved?
bronze pivot
yeah
runic garnet
<@&268886789983436800> @crimson sedge oddity
cedar kilnBOT
@pallid tundra Has your question been resolved?
cedar kilnBOT
@pallid tundra Has your question been resolved?
cedar kilnBOT
hard merlin
.reopen
cedar kilnBOT
✅
cedar kilnBOT
cedar kilnBOT
Available help channel!
limber stone
cedar kilnBOT
limber stone
So if they ask me for the co ordinates that maximises the standard maximisation problem
what am I going to answer?
the method here is simplex
cedar kilnBOT
@limber stone Has your question been resolved?
limber stone
.close
jolly sapphire
The diameter CE of a circle, exscribed around a triangle ABC, is perpendicular to AB and intersects it in D. Find the sine of the angle at C if CD = a and DE = b
long arrow
sine law
jolly sapphire
can you elaborate?
long arrow
generally
it's about finding AB
because sine law gives
$$\frac{AB}{\sin \alpha}=2R=a+b$$
wraith daggerBOT
modus7591
jolly sapphire
Here's another problem: 2 circles with radii of 7 and 3 have perpendicular internal tangent segments (whatever this means). Calculate the distance between their centers.
provide some sketch if possible
cedar kilnBOT
@jolly sapphire Has your question been resolved?
dreamy zenith
evaluate sin(690degrees)
cedar kilnBOT
evaluate sin(690degrees)
south tundra
Yes
dreamy zenith
can i subtract 360 every time im evaluating degrees higher than 360 ?
what if its odd
south tundra
You can do it whenever you want
dreamy zenith
You can do it whenever you want
so the fact you are just pulling 360 out to subtract doesn't have any other implications outside of getting you a number inside 360
crimson sedge
can i subtract 360 every time im evaluating degrees higher than 360 ?
[
\map \sin\alpha = \map \sin{\theta + 360n} \implies \map \sin \alpha =\map \sin \theta
]
for any integer n, this will always hold true for any theta
wraith daggerBOT
south tundra
so the fact you are just pulling 360 out to subtract doesn't have any other impl...
In this context, yes
dreamy zenith
what does this mean
grand heath
cedar kilnBOT
woven depot
Hi I would like to ask how do I know the trN is equals to 6+3t
The trace is the sum of the elements on the diagonal of N
i.e. 6 and 3t
crimson sedge
cedar kilnBOT
crimson sedge
I'm very confused here
I put speeding up, and I don't see why it's wrong
for the grey one
mighty drift
it probably meant in absolute speed
which is always ambiguous
it's slowing down because it's speed is getting closer to 0
it's slowing down in reverse
crimson sedge
it's slowing down because it's speed is getting closer to 0
I see
from my understanding acceleration is the same thing speeding up / slowing down
so I thought since acceleration is the derivative of velocity, it would be speeding up here, I'm guessing something might be wrong then I don't see what exactly it is
mighty drift
which is always ambiguous
these are kind of ambiguous
crimson sedge
these are kind of ambiguous
I see so it is the interpreting "speeding up" as acceleration that is wrong
mighty drift
it's slowing down because it's speed is getting closer to 0
but arguably this should be morally more correct
just look at acceleration as the derivative of |v|
cedar kilnBOT
mighty drift
depends on context/exercise though
cedar kilnBOT
Available help channel!
junior timber
cedar kilnBOT
junior timber
where do i start exactly
so the glass has to be at least 60 cents
-10 for his sister
cedar kilnBOT
@junior timber Has your question been resolved?
junior timber
<@&286206848099549185>
cedar kilnBOT
@junior timber Has your question been resolved?
ashen terrace
cedar kilnBOT
ashen terrace
<@&286206848099549185>
dire geode
!15m
cedar kilnBOT
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.
ashen terrace
i have been waiting for an hour in another chanel
@dire geode
please may you help me i need this question done and ive been waiting for so LONG!
finite raven
!show
cedar kilnBOT
Show your work, and if possible, explain where you are stuck.
ashen terrace
i dont have any work for this question because i dont know where to start
can you explain it to me for me to do it
finite raven
Start by callind B = number of costumers at breakfast, L = number of costumers at lunch and D = number of costumers at dinner. See if you find some relation between these
ashen terrace
i know what you mean but i cant remeber what else to do
all i have done so far is write out D:B:L and then put the numbers underneath
but idk what to do next?
<@&286206848099549185>
cedar kilnBOT
@ashen terrace Has your question been resolved?
ashen terrace
Please help
<@&286206848099549185>
<@&286206848099549185>
IVE BEEN WAITING FOR AN HOUR
<@&286206848099549185>
tight thicket
IVE BEEN WAITING FOR AN HOUR
Nobody here owe you sm
ashen terrace
Yeah its just id like some better communication
you could have let me know that your busy or given me a reason as to why your ''helper'' role isnt being fufilled
finite raven
Start by callind B = number of costumers at breakfast, L = number of costumers at lunch and D = number of costumers at dinner. See if you find some relation between these
B/L = 11/6, B/D = 7/4, L = D-10
dire geode
you could have let me know that your busy or given me a reason as to why your ''...
!volunteers
cedar kilnBOT
you could have let me know that your busy or given me a reason as to why your ''...
Helpers are just people volunteering their time to help you. Be polite.
ashen terrace
B/L = 11/6, B/D = 7/4, L = D-10
im a bit confused what to do next
@finite raven
<@&286206848099549185>
rain cloak
Okay. Can you be polite first.
ashen terrace
of course sorry if i came accross as rude that wasnt my intention
rain cloak
Np, I get it. What problem are u stuck on?
ashen terrace
its the last one that i sent i will send it again for you quickly
rain cloak
Okay. Thanks.
ashen terrace
rain cloak
Let me read it.
ashen terrace
ok take your time
rain cloak
Thanks.
Okay so, Let:
B = Breakfast
L = Lunch
D = Dinner
The ratio of breakfast to lunch: B:L = 7:4.
B/L = 7/4
B = (7/4) L
The ratio of breakfast to dinner: B:D = 11:6.
B/D = 11/6
B = (11/6) D
(7/4) L = (11/6) D
Does that make more sense? If not I can help more.
ashen terrace
yes that does help but the bit that i am stick on is it says ''the number of customers at lunch was 10 less than the customers at dinner'' however the number is smalller at dinner?
rain cloak
Did you multiply both sides by 12 yet?
ashen terrace
no what do you mean by that?
rain cloak
If you multiply both sides by 12, you get
21L = 22D
Substituting this into the previous equation
21L = 22(L - 10).
ashen terrace
oh thank you
ashen terrace
wait im being so stupid...
rain cloak
wdym?
ashen terrace
can you give me a minute to think. my mind is blank i dont even know what is going on but im forgeting simple mathamatics (i have dyslexia so sometimes the easier stuff is harder than the hard stuff)
ashen terrace
really?!
fair play if you do you seem really good at maths ngl
do like does 1 = 10?
because 22-21
@rain cloak
ashen terrace
what is it that you have to sub
like i dont know what number to sub into the original
<@&286206848099549185>
@rain cloak
<@&286206848099549185>
please i really need to finsih this question
nova glacier
@ashen terrace what's the problem? you have 3 equations... just solve
ashen terrace
i think im overwhelmed on this question ive been on it for 3 hours
tight thicket
please i really need to finsih this question
According to my calculations this is 210.
Breakfast - x
Lunch - y
Dinner - z
tight thicket
you could have let me know that your busy or given me a reason as to why your ''...
I am not receiving money for this, that count as reason ?
tight thicket
Do your homework and take responsibility
Nevermind, it is people
nova glacier
,w {B/L = 11/6, B/D = 7/4, L=D-10}
wraith daggerBOT
verbal wigeon
<@693147328097419384>
hi
anyone need math help
p mme
i am done high school
and have finsihed math with all A's
i love math so much
ashen terrace
yes please may you help
verbal wigeon
yes please may you help
ofc
nova glacier
Here you have the answer
ashen terrace
IVE DONE IT
IVE FUCKING DONE IT
I CANT BELIEVE IT
THANK YOU ALL FOR THE HELO
HELP
IDK IF YOU DO PROMOTIONS OR ANYHTING OR REWARD GOOD HELPERS BUT IF YOU DO HUGE SHOUTOUT TO AIDEN FIELD
tight thicket
IDK IF YOU DO PROMOTIONS OR ANYHTING OR REWARD GOOD HELPERS BUT IF YOU DO HUGE S...
I am waiting for my money than
ashen terrace
haha lol thanks alot mate
tight thicket
You should take care this next time by yourself and not lay on random people. That is not the right way
verbal wigeon
?
verbal wigeon
You should take care this next time by yourself and not lay on random people. Th...
its fine
?
where is everyone
verbal wigeon
?
dont get mad at him
we r here to help each other
not to yell at each other
worki together
for god sake
tight thicket
dont get mad at him
That is just rules of the life, no more
And the most simplest answer on this all
verbal wigeon
That is just rules of the life, no more
bruh
tight thicket
we r here to help each other
Of course, lets keep it up than
verbal wigeon
🙂
cedar kilnBOT
@ashen terrace Has your question been resolved?
halcyon axle
I don't understand the solution to this problem
cedar kilnBOT
I don't understand the solution to this problem
iron saffron
Do you know what average means?
iron saffron
Then, where are u stucked in this problem?
halcyon axle
i dont understand how x=4/-5
cunning loom
dont listen to archimonde he died in hellfire citadel years ago
iron saffron
lol
halcyon axle
how did (x+5)(x-4)=0 become 4 or -5?
heady solstice
how did (x+5)(x-4)=0 become 4 or -5?
Because one of them must be 0
iron saffron
no prob
iron saffron
this one?
cosmic steppe
They're factoring (x-1) out
halcyon axle
nope the one after it
halcyon axle
wow just realized i dont remember much of the math i learned in school
is there any way to quickly catch up to precalc level?
iron saffron
Study
halcyon axle
any resources you can point me to?
cedar kilnBOT
@halcyon axle Has your question been resolved?
dim sail
is this correct?
slate lintel
looks right to me
note that you didn't need to calculate the intercept of the second one since you don't particularly care about it
dim sail
note that you didn't need to calculate the intercept of the second one since you...
so idc about b = -13? everything else matters?
slate lintel
did you use that value in your answer?
dim sail
no
slate lintel
well there you go
dim sail
well there you go
okay, ty. is it okay if i ping you to check some more answers once i've finished?
slate lintel
I mean you can keep it, no harm, but faster for next time 
slate lintel
okay, ty. is it okay if i ping you to check some more answers once i've finished...
sure, but I might be driving
dim sail
okay
cedar kilnBOT
@dim sail Has your question been resolved?
dim sail
sure, but I might be driving
are these 2 questions correct?
slate lintel
first one is right, good reasoning, nice
second one doesn't seem to be, B and C aren't on the plane
dim sail
first one is right, good reasoning, nice
second one doesn't seem to be, B and C ...
how do you know they aren't on the plane?
slate lintel
because they don't satisfy the equation
dim sail
because they don't satisfy the equation
wait, where exactly did i go wrong?
slate lintel
idk what those equations are for m1 but they don't seem to make sense
dim sail
idk what those equations are for m1 but they don't seem to make sense
its to find the direction vector, its B - A
slate lintel
that's m1
dim sail
that is wrong
slate lintel
reasoning seems right otherwise
dim sail
let me redo it
dim sail
reasoning seems right otherwise
okay, i tried again
slate lintel
does it fit all three points?
dim sail
does it fit all three points?
wdym by fit?
slate lintel
like do all three points satisfy the equation
slate lintel
I can't check your numbers rn but if they work then that's right
dim sail
like do all three points satisfy the equation
which equation did you mean?
dreamy sleet
i think so
have you substituted all the values into the equation in the box on your piece of paper?
dim sail
have you substituted all the values into the equation in the box on your piece o...
um, i subbed in 2, 4, -1 into the equation and got 53
dreamy sleet
um, i subbed in 2, 4, -1 into the equation and got 53
and not 0?
dim sail
and not 0?
no
dreamy sleet
oh wait, i forgot to put in -53
knew it
dreamy sleet
i get 0 now too
now try all other points
dreamy sleet
got 0 for all of them
what this means is that your equation is right
dim sail
now try all other points
can you help me with this question pls? not sure how to approach it.
how do i convert the first plane to a cartesian equation?
dreamy sleet
how do i convert the first plane to a cartesian equation?
do you know how to convert cartesian to parametric?
dim sail
do you know how to convert cartesian to parametric?
no, i don't remember
but i need to convert from vector to cartesian right?
dreamy sleet
but i need to convert from vector to cartesian right?
I don’t understand, can you do the steps according to this method so I get it?
dim sail
I don’t understand, can you do the steps according to this method so I get it?
?
idk how to do this question at all
dreamy sleet
?
idk how to do this question at all
Can you convert from vector to cartesian first?
dim sail
Can you convert from vector to cartesian first?
no, thats what idk how to do
dreamy sleet
can you help me with this question pls? not sure how to approach it.
here’s an approach I thought of: find the normal vector to both planes, then the answer will come out
dim sail
here’s an approach I thought of: find the normal vector to both planes, then the...
here, this is an example i did in class but it was already given in cartesian equation form
dim sail
Can you convert from vector to cartesian first?
i think i did it?
dreamy sleet
i think i did it?
Looks like you did it
dim sail
Looks like you did it
for this question, how do i find the value of k so its parallel?
idk what im doing
dreamy sleet
for this question, how do i find the value of k so its parallel?
Find them so that the normal vectors are scalar multiples
dim sail
Find them so that the normal vectors are scalar multiples
Did I even need to do the cross product?
cedar kilnBOT
@dim sail Has your question been resolved?
dreamy sleet
<@&268886789983436800>
outer heart
cedar kilnBOT
lapis maple
what is the formula for thearea of a triangle
crimson sedge
if i take a word " N U M B E R " and if i determine 3 letter words that can be formed using this letters (repetition allowed ) then it will be 6 * 6 * 6 = 216
crimson sedge
will this be considered as permution?
solid juniper
wdym considered as permution?
crimson sedge
i mean will it become perumution only when different objects are selected?
solid juniper
btw it's permutation (and oops i didn't even notice when i copy pasted lol)
but yes the 3-permutations of N U M B E R are the distinct 3 letter words from those letters
slate lintel
"repetition allowed" and "permutation" don't generally go together
cedar kilnBOT
cedar kilnBOT
Available help channel!
crimson sedge
cedar kilnBOT
crimson sedge
Is this correct?
dreamy sleet
Is this correct?
you can check your answers by drawing it out on graph paper
but neither of them are correct
crimson sedge
but neither of them are correct
How do I do it correctly?
dreamy sleet
How do I do it correctly?
Do you know how to find the vector equation of a line?
wooden sigil
@dreamy sleet was your name meant to be sarcastic?
dreamy sleet
<@661915034888175618> was your name meant to be sarcastic?
so it’s like this: I saw people in #groups-rings-fields making their names obviously false statements like “a subring of a field is always a field” and “the p-adics have characteristic p” to confuse algebra students preparing for their exam, so I also made my username a false statement to confuse algebra students preparing for their exam
flint plinth
<@661915034888175618> was your name meant to be sarcastic?
wow that was spammier than i expected
crimson sedge
Anyone?
solid juniper
https://en.wikipedia.org/wiki/Freshman%27s_dream
you can press the X on the embed to make it less spammy yknow
flint plinth
you can press the X on the embed to make it less spammy yknow
how did i never notice that before?
solid juniper
haha
crimson sedge
Do you know how to find the vector equation of a line?
I don’t think so
What is it
dreamy sleet
I don’t think so
Have you been taught it?
crimson sedge
We’ve been taught vectors but I haven’t heard of vector equations specifically
What is it? maybe I have idk
wooden sigil
so it’s like this: I saw people in <#496784958430380033> making their names obvi...
Why should you confuse em?
dreamy sleet
We’ve been taught vectors but I haven’t heard of vector equations specifically
the first blue box on this page should be what you’re looking for
https://tutorial.math.lamar.edu/classes/calciii/eqnsoflines.aspx
crimson sedge
the first blue box on this page should be what you’re looking for
https://tutori...
Nope I haven’t seen that before
I’ll ask my teacher
How do I do part a then? @dreamy sleet
dreamy sleet
How do I do part a then? <@661915034888175618>
Subtract instead of adding
dreamy sleet
If you draw it on a graph, it may become clear
crimson sedge
So to find direction vector you subtract them all the time?
dreamy sleet
So to find direction vector you subtract them all the time?
yes
cedar kilnBOT
@crimson sedge Has your question been resolved?
magic solar
The information of the diagram is on the right and my working follows. Im not quite sure what I did wrong if anyone could correct me
cedar kilnBOT
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
You’ve done a i and a ii?
those aren’t equations
those are equations for force
what ial past paper is this
What unit?
Mech 1, mech 2, or mech 3
cedar kilnBOT
@crimson sedge Has your question been resolved?
slow rain
im a little confused, how would a graph for this look?
cedar kilnBOT
im a little confused, how would a graph for this look?
crystal raptor
It would depend on what f is
slow rain
f(x)=2^x
crystal raptor
So you're looking for the inverse function to 2^x
slow rain
so 1 divided by 2^x
crystal raptor
bleak crane
Pls help
cosmic steppe
Tabular integration
cedar kilnBOT
@bleak crane Has your question been resolved?
bleak crane
Tabular integration
Any other way? We haven't covered that yet
crimson sedge
Any other way? We haven't covered that yet
what have you covered
runic garnet
Tabular is just integration by parts simplified
fair rock
Hey guys can someone help with this
cedar kilnBOT
Hey guys can someone help with this
long arrow
what have you tried
fair rock
I can't find the linear equation
long arrow
yeah, you can't
but firstly try to depend it on one unknown
let's say 'm'
(using point given)
fair rock
Uhm how
long arrow
line passes through the point = coordinates of the point must satisfy its equation
long arrow
yes
from here c = m +3
so line equation is y = mx + m + 3
idk what's your level but personally I'd use derivatives to solve this
or okay, you can also compare the curves and see when equation has no solutions
fair rock
So if I combine it,it becomes mx+m+3=x power 2 -x +5
long arrow
in other words
when the quadratic equation has no real solutions?
of form ax^2 + bx + c = 0
fair rock
b power 2 - 4ac <0
long arrow
yes, your equation is also quadratic
make it of form ax^2 + bx + c = 0 firstly (coeffs a, b, c might depend on parameter 'm' !!!)
fair rock
Oooh okayy
cedar kilnBOT
Available help channel!
strong nexus
I'm trying to resolve the following limit using McLaurin's expansions: $\lim_{x\to0^+}{\ln(1+\tan x)-\sin x\over e^x(1-\cos\sqrt x)-{x\over2}}$
wraith daggerBOT
protoleo
cunning loom
whoever gave you that question doesnt like you very much
strong nexus
whoever gave you that question doesnt like you very much
I've actually managed to simplify this to $o(x^4)$ but I get $-\infty$ instead of a finite limit like I get in Geogebra mapping the function
wraith daggerBOT
protoleo
strong nexus
I thought that maybe was a really weird narrow deviation towards - infinity but I really do get that limited value
dusty hazel
Write terms till x^3
strong nexus
I used the expansions: $$\begin{align*}
\ln(1+\tan x) &=x-{x^2\over2}+o_0(x^4) \
\sin x&=x-{x^3\over6}+o_0(x^4) \
e^x&=1+x+{x^2\over2}+o_0(x^2) \
\cos\sqrt x&=1-{x\over2}+{x^2\over24}+o_0(x^2)
\end{align*}$$
wraith daggerBOT
protoleo
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
strong nexus
@dusty hazel I've gone for a term higher but it shouldn't be a problem
dusty hazel
ln(1+tan(x)) isn't that??
strong nexus
ln(1+tan(x)) isn't that??
Well, I used the expansion for $\ln(1+x)$ and $\tan x$ both to second degree
wraith daggerBOT
protoleo
strong nexus
And I get that
dusty hazel
Show all your steps.
strong nexus
Show all your steps.
Sure, but be aware I might be typing for a while lol
dusty hazel
Not an issue for me, really.
strong nexus
Ok
So to get that expansion I went for $\ln(1+x)=x-{x^2\over2}+o(x^2)$ and $\tan x=x+o(x^2)$
wraith daggerBOT
protoleo
strong nexus
Of course composing the two I get powers of $o(x^2)$ that reach $o(x^4)$
wraith daggerBOT
protoleo
strong nexus
But the powers of x remain the same
Using the expansions I got from here and above, I get that $\lim_{x\to0^+}{\ln(1+\tan x)-\sin x\over e^x(1-\cos\sqrt x)-{x\over2}}=\lim_{x\to0^+}{x-{x^2\over2}+o(x^4)-\left(x-{x^3\over6}+o(x^4)\right)\over\left(1+x+{x^2\over2}+o(x^2)\right)\left(1-\left(1-{x^2\over2}+{x^2\over24}+o(x^2)\right)\right)-{x\over2}}$
wraith daggerBOT
protoleo
strong nexus
From here I got the rest of the steps @dusty hazel
dusty hazel
Try leaving tan(x) as tan(x) in ln(1+tan(x))
And then use the expansion for tan(x)
Till the second term.
strong nexus
Till the second term.
I mean... I did that already, I just assume in the first expansion x to be tan x
Instead of writing down unnecessary variables
dusty hazel
And I'm asking you to assume first expansion of ln(1+tan(x)) = tan(x) and then use tan(x) = x + x^3/3...
Those are two different things.
strong nexus
ln(1+tan x)=tan x?
dusty hazel
I mean it is not equal to that.
But using the expansion
You can write only 1 term from ln(1+tan(x)) 's expansion
strong nexus
so... using expansions to different degrees?
strong nexus
I mean isn't that what you did as well?
well, I got both expansions to the second degree
crimson sedge
can anyone help me with math
dusty hazel
well, I got both expansions to the second degree
Um yes. But you then only used one for tan(x)
dusty hazel
can anyone help me with math
strong nexus
Um yes. But you then only used one for tan(x)
because the second degree is nul
I get $0+x+0+o(x^2)$
wraith daggerBOT
protoleo
dusty hazel
Sorry, I meant third degree.
Think of it this way
When you'll expand sin(x) then terms will be of degree 1, 3, 5 ...
strong nexus
So... I use ln(1+x) to the first degree and then tan x to the third?
dusty hazel
Try using expansions to such degree such that you get those degree terms.
dusty hazel
So... I use ln(1+x) to the first degree and then tan x to the third?
Yes.
strong nexus
Try using expansions to such degree such that you get those degree terms.
Ah... intriguing
Even if I'm actually in doubt right now... aren't Taylor/McLaurin's expansions unique for each function?
am I not getting two different ones here?
dusty hazel
They are unique, what are you getting two different ones?
strong nexus
you are suggesting me to combine the two functions in a different way to get different terms
dusty hazel
I am.
strong nexus
doesn't this mean the function has at least two different expansions?
I'm not talking about series
Just limited expansions
dusty hazel
This function as a whole will still have 1 and only 1 expansion.
You'll first write terms like tan(x) -tan^2(x)/2 ... For ln(1+x) and then individually expand each term to get the final expansion. Which is unique.
So that is still unique.
But you don't have to do all that to evaluate the limit, is what I said.
strong nexus
Sorry, I think I'm missing something
Unless I'm going over o(x^4), shouldn't I get those same terms?
strong nexus
But you went for o(x^3) for sin(x)
actually I went for o(x^4)
but the fourth degree term is nul
strong nexus
And for tan(x) you only went for o(x^2)
Because I was composing it with another o(x^2)
strong nexus
If it gives you a better approximation
soooo... I can get two different approximations for the same function for the same o(x^n), but when I'm going for the series expansion, all levels out to the same series?
dusty hazel
Yes you can get different approximations.
Because many times these o(x^n) terms are zero.
To get the right approximately, use o(x^n) such that ultimately all the terms have same/similar exponents.
strong nexus
Because many times these o(x^n) terms are zero.
To get the right approximately,...
uhm... so I know what approximation to get only looking at the other expansions in the expression?
cedar kilnBOT
Available help channel!
hallow sundial
hi
hallow sundial
can someone help explain how they transformed this
the thing circled in blue
x^2(x-1)
is it the same with how they got from x^2 = sqrt(x)
jolly sapphire
With the digits 1,2,3,4,5 are written all positive numbers with different digits. What is the probability of a number being smaller than 400 and divisible by 3?
inland fossil
number of permutations isn’t too difficult, just 5!
that’s the total number of outcomes
ooh wait no, you prob need case work
based on number of digits
5 + 5*4 + 5*4*3… so on
jolly sapphire
and then?
inland fossil
then since 400 is quite small you could prob use some form of brute force
jolly sapphire
Yeah this method is the most obvious I was wondering if there's a more intelligent method
inland fossil
hmm
maybe the divisibility by 3 rule
if you place 1 down as the first digit, the next two digits need to sum to 2 mod 3
its still brute forcey and i doubt you could really do better than this
jolly sapphire
what is 2 mod 3?
inland fossil
uh basically, it needs to sum to 2 above a multiple of 3
take 153
5+3 = 8 = 2 + 3*2
kind lagoon
can anyone explain why it is -1 as the last entry of the basis?
kind lagoon
my RREF matrix looked like
100|0
010|0
000|0
to me there isnt a free variable, but my prof said it has something to do with the zero row
crystal raptor
you could have put any number (except 0) in there
crystal raptor
x3 is a free variable
kind lagoon
one second, let me retry it
how about for this one?
the correct answer is 2,1,-1
crystal raptor
you have a free variable again, x3
kind lagoon
but if i enter anything other than -1 for x3 it doesnt work
crystal raptor
anyway the top line does not say x1 = 2
crystal raptor
no it says x1 - x2 = 0
you have the remember the linear system of equations that a matrix is actually representing
kind lagoon
so, where does the -1 come from?
for the third value of the basis
it makes sense to me how 2 and 1 got there, but i'm still unsure about the -1
crystal raptor
your row echelon form is wrong for a start
crystal raptor
it certainly will confuse things yeah
when you do get the right REF
write x1 and x2 in terms of x3 and then pick whatever number you want for x3 since its free (but not zero)
cedar kilnBOT
cedar kilnBOT
Available help channel!
cloud sinew
is root 32 and root 8 irrational?
cedar kilnBOT
is root 32 and root 8 irrational?
violet night
what happens when you multiply a rational number by an irrational number?
is the result rational or irrational?
cloud sinew
idk
violet night
probably a proof I would suggest looking at
barren harness
just prove it
violet night
optimistic considering the original question
cloud sinew
is it?
cedar kilnBOT
@cloud sinew Has your question been resolved?
cedar kilnBOT
cedar kilnBOT
Available help channel!
dreamy zenith
how did they multiply 80cm by the radian
cedar kilnBOT
how did they multiply 80cm by the radian
carmine bronze
how did they multiply 80cm by the radian
They just multiplied, no magic going on here.
dreamy zenith
They just multiplied, no magic going on here.
5x 180 =900/12 =75
carmine bronze
You forgot pi.
dreamy zenith
75 x 80 = 6000
dreamy zenith
You forgot pi.
pi = 180
carmine bronze
pi = 3.14. Radians is the conversion from degrees to length.
dreamy zenith
pi = 3.14. Radians is the conversion from degrees to length.
so when is pi 180
carmine bronze
Degrees is the measure of rotation and radians is the measure of arc length.
dreamy zenith
Degrees is the measure of rotation and radians is the measure of arc length.
im not following
carmine bronze
One moment, let me make a graph to illustrate the difference.
The blue arc has a measurable length if you were to lay it flat.
The angle is just a measure of the rotation that occurred.
surreal cave
https://www.geogebra.org/classic/t8nshtdw
wow I didn't know GeoGebra could do that
the slider on the graph
obsidian coral
im not following
In other words, degrees is the unit for measure of rotation and radians is the unit for the measure of the arc length
5pi/12 radians is the length of the arc
Kinda like measuring something, like a phone, for example, it's 6 inches. Inches is the unit for the measure of length
carmine bronze
the slider on the graph
It's weird that the slider on the graph actually works better than the slider on the Algebra pane. The precision is much better.
surreal cave
It's weird that the slider on the graph actually works better than the slider on...
ikr and it's so much smoother
carmine bronze
im not following
Does that graph help?
cedar kilnBOT
@dreamy zenith Has your question been resolved?
surreal cave
so when is pi 180
\textbf{Radians} are separate way of measure angles. Radians are much more efficient than \textbf{degrees} because of their practicality in Trigonometry. Degrees have their history in the ancient Mesopotamians and their base-60 counting system. Radians derive themselves from the definition of circumference. The circumference of a circle is $C=2\pi\cdot r$. So a full rotation around a circle is $2\pi$.\~\
Since a full rotation around the circle is $2\pi$red, this equates to 360deg. This means the ratio of the degrees to radians to all circles are $\frac{\theta_{D}}{\theta_{R}}=\frac{360^{\circ}}{2\pi}\implies\frac{\theta_{D}}{\theta_{R}}=\frac{180^{\circ}}{\pi}\implies$\fbox{$\theta_{D}=\theta_{R}\frac{180}{\pi}$}.\~\
As an example one-half rotation around the circle should be 180deg or $\pi$rad. Let's check with our formula. $\theta_{R}=\frac{\cancel{180}\pi}{\cancel{180}}$. Now one can either use this formula or inuition to find $45^{\circ}=\frac{\pi}{4}$ and $90^{\circ}=\frac{\pi}{2}$\~\
Now that you know the definition we know that the arc length of a sector of a circle is the circumference times a section of a circle with that angle so we get $S=2\pi\cdot r\cdot\left(\frac{\theta_{D}}{360}\right)$ in this case we want theta to be dependent upon radians, so we substitute our formula. $S=2\pi\cdot r\cdot\left(\frac{\theta_{R}\frac{180}{\pi}}{360}\right)\implies S=\theta_{R}\cdot r$
wraith daggerBOT
XxMrFancyu2xX
sharp viper
cedar kilnBOT
sharp viper
for a and c i got
a) assume x is pouched mamal
prove x is marsupial
c) assume x is not marsupial
prove x is not pouched animal
r those right?
and im stuck on b
wise python
🤔
buoyant latch
What is a pouched animal and how is it related to marsupials?
royal loom
part (c) your proof isn't a contradiction, it is proving the contrapositive statement
royal loom
is mammal -> is marsupial
is not mammal -> is not marsupial
is the original, and the contrapositive (not a contradiction)
a contradiction of the original would be like
is mammal -> is not marsupial
sharp viper
so an asumption would be
royal loom
and you demonstate that is can't be true (in your proof)
sharp viper
is mammal -> is marsupial?
buoyant latch
If your theorem uses if x is an mammal, then it is a marsupial
Then you use the assumption that mammal implies marsupial-ness
sharp viper
is gpt answers right?
like i got my answers
and gpt had similar
so i thought i got it rigt
buoyant latch
That’s not the same assumptions
astral bay
...ok wait what's the question? what are we trying to prove?
buoyant latch
There’s an assumption for the theorem and then assumptions of how the words connect
sharp viper
oh
buoyant latch
Unless they are really just asking for the first kind of assumption which would be kinda weird imo
dreamy sleet
does indirect proof mean contrapositive?
astral bay
i'm also confused
astral bay
Then you use the assumption that mammal implies marsupial-ness
why would you assume that the theorem you're trying to prove is true
sharp viper
im very confusd
like i mean no disrepsect
but i feel like my answer is right
for a and b
i dont thiink
wut do u think @astral bay
buoyant latch
Not gonna lie I think I misread the question ;-;
buoyant latch
a) assume x is pouched mamal
prove x is marsupial
c) assume x is not marsupial
...
I think Austin was right about the answer to c should be for b
sharp viper
oh
and wut should c be
oh
c is
contradiction
so for assume
i do
x is puched
puched
and prove is not right
since it contradicts
assume x is pouched
prove x is not marsupial
buoyant latch
You try prove the opposing statement and show it leads to a contradiction yeah
buoyant latch
Sorry about that
cedar kilnBOT
@sharp viper Has your question been resolved?
cedar kilnBOT
cedar kilnBOT
Available help channel!
lapis vessel
How to do this question?
cedar kilnBOT
How to do this question?
wind glade
simple the answer is 0% percent Erling Haaland couldn't kick a child if he wanted
lapis vessel
<@&286206848099549185>
slate lintel
feels ambiguous if the kicker picks 1 and the goalie picks 2, is that a goal or not
lapis vessel
I think it is a goal
If the kicker picks 1 and the goalie picks 1, there won't be a goal
But if the kicker picks 3 and the goalie picks 3, the percentage of a goal is 70%
cedar kilnBOT
@lapis vessel Has your question been resolved?
slate lintel
i'd start with the case when they pick different zones
lapis vessel
It may be designed to distract people too ._.
rose swan
how many total cases are there?
lapis vessel
16 cases, I guess
rose swan
great
and we can assume each of the 16 scenarios has an equal chance of happening
and basically if they choose different positions, the ball goes in
so we're only analyzing the 4 cases (1,1), (2,2), (3,3), and (4,4)
what do we know about these 4 particular cases?
lapis vessel
For (1,1) and (2,2) the ball is pulled out
For (3,3) and (4,4), the rate of being pulled out is 30%
rose swan
great, so you have the rates of blocking for each of these cases
and you know the probability of each case occuring
so you can multiply, and sum up over the 4 cases
rose swan
do you know what type of problem this is?
lapis vessel
Probability?
rose swan
err..yes but more specifically what concept/formula you might need here
lapis vessel
I don't know how to express it in english, but it's kinda P(tail) = No. tails/total
rose swan
that's part of it
but you have stuff like the number of trials
and a random variable describing the number of "successes"
lapis vessel
Alright, then what next?
rose swan
do you know the binomial distribution?
lapis vessel
Haven't heard of it be4
rose swan
hmmm, you'll have to learn it otherwise you won't be able to solve this
lapis vessel
Can you brief over it?
wispy marten
Have you learned the central limit theorem?
lapis vessel
I think I may have learnt it, but not in english
lapis vessel
Have you learned the central limit theorem?
We don't learn this at school
wispy marten
What did you learn?
rose swan
i could explain it, but it involves a bunch of stuff that you may not be familiar with like binomial coefficients and factorials
i was hoping you'd already seen it before
wispy marten
The point is, even with binomial distribution, how would you answer the question here?
lapis vessel
I've just watch a vid from khan academy, and I think I could understand binomial distribution
rose swan
The point is, even with binomial distribution, how would you answer the question...
using a cumulative distribution function
wispy marten
My question stands, because the sum will get very heavy
rose swan
ah good point, and stuff like a stirling's approximation would probably be too much
i guess you were thinking of applying the normal approximation to the binomial distribution with a continuity correction
wispy marten
While basic understanding of the binomial distribution is definitely required here, I believe they wanted them to use an approximation using the normal distribution indeed, for example the central limit theorem
But it will be very hard, if not impossible, to give you suitable help for your question if we do not know what you've learned in class @lapis vessel
lapis vessel
But it will be very hard, if not impossible, to give you suitable help for your ...
It is said that this question tests knowledge that is not taught at school, so ofc I haven't learnt this
But you can explain, I think I can grasp it
wispy marten
So this is not for a class?
lapis vessel
Hmmm, but this question has both the upper and lower bound
rose swan
you can just subtract
wispy marten
Keep in mind that $P(279 \leq X \leq 321) = P(X \leq 321) - P(X < 279)$
wraith daggerBOT
all matrices are invertible
rose swan
that, and pay attention to the inequality symbols
wispy marten
(and make sure to understand why it has to hold!)
lapis vessel
(and make sure to understand why it has to hold!)
Wydm?
wispy marten
Make sure to understand why this is true:
wispy marten
Excellent then
lapis vessel
Many thanks!
lapis vessel
Excellent then
Btw, I have put a question in #competition-math, can you check it out?
It's adapted from an olympiad so I put there
nova snow
Not sure where to start
cedar kilnBOT
Not sure where to start
dire geode
Find the derivative
nova snow
Of y = sqrt(x)
1/2root(x)?
cosmic steppe
1/2root(x)?
Yeah
tropic oxide
1/2root(x)?
1/(2sqrt(x))
tropic oxide
And I sub in 1/6 for x
no
nova snow
What
tropic oxide
you want to know where dy/dx equals 1/6, NOT the value of dy/dx at x=1/6
nova snow
Oh
tropic oxide
1/6 is the slope not the x-coord of the point of contact
also 1/(2sqrt(6)) is definitely less than 1 anyway
...ok nevermind that
nova snow
tropic oxide
also you should not do any rounding
unless explicitly asked for
which here you are not
yeah ok no 1/(2sqrt(1/6)) is equal to sqrt(6)/2, which is roughly what you said
but again it's not what you're looking for here
tropic oxide
no need to bold the parentheses lol
i only bolded them to draw your attention to them
but yes
nova snow
Solve for x
x=9
tropic oxide
great, are you able to continue from here to get what you're asked for
cedar kilnBOT
@nova snow Has your question been resolved?
nova snow
great, are you able to continue from here to get what you're asked for
I think so
amber hawk
cedar kilnBOT
amber hawk
ive gotten the question to (x - 5) squared - 13, but dont know what to do after that with the root
dusk finch
rewrite 13 as a square and apply difference of square
rain harbor
Help
solemn pawn
cedar kilnBOT
solemn pawn
did they do the algebra right here
crimson sedge
yes
cedar kilnBOT
cedar kilnBOT
Available help channel!
spring coyote
spring coyote
.close
cloud sinew
which is the solution of 3x-x= 7 the option are a (2,3) b (-1,6) c (1.-4) d (0,7)
sonic thistle
Hm