Channel closed
Closed by @ruby musk
Use .reopen if this was a mistake.
#help-36
spiral hill
Would appreciate some help with b.
final saddleBOT
Would appreciate some help with b.
final saddleBOT
@spiral hill Has your question been resolved?
spiral hill
<@&286206848099549185>
final saddleBOT
spiral hill
.reopen
final saddleBOT
✅
final saddleBOT
@spiral hill Has your question been resolved?
rare cradle
Would appreciate some help with b.
First of all, can you argue that $\lambda(n) \ge \omega$?
soft zealotBOT
giannis_money
rare cradle
How would you justify this?
spiral hill
Hm, the order can only be less or equal, if not then the rest would not be 1 but bigger.
I think I’m way out on grasping the entire thing doe.
Thus it make sense?
soft zealotBOT
giannis_money
rare cradle
and the order of $[a]$, $\omega$, is the smallest positive integer st. $[a]^{\omega} = [1]$
soft zealotBOT
giannis_money
rare cradle
because $\omega$ is the smallest such positive integer, it follows that $\lambda(n) \ge \omega$
soft zealotBOT
giannis_money
rare cradle
$[a]^{\lambda(n)} = [1]$ AND $[a]^{\omega} = [1]$
spiral hill
and if ${\lambda(n)} = m then we for sure know that m divides ${\lambda(n)}
soft zealotBOT
giannis_money
rare cradle
and if ${\lambda(n)} = m then we for sure know that m divides ${\lambda(n)}
what's m
m is only used to define $\lambda(n)$
spiral hill
sorry ment $\omega$
rare cradle
and if ${\lambda(n)} = m then we for sure know that m divides ${\lambda(n)}
yes
but that might not be true
say $\lambda(n) = q\omega + r$ where $0\le r < \omega$ and $0\le q$
soft zealotBOT
giannis_money
spiral hill
Ohh 😲
I think I kinda see it now
Then [a]^r = [a]^(lambda(n)-wq)
Trying to think this through a little while, maybe a can figure out the rest. otherwise I'll type here. thx!
tranquil pine
final saddleBOT
junior pebble
because it is not true for EVERY angle
it is only true for a couple of very specific angles, and then false for all of the infinitely many other ones
frail loom
I don't see what the answer is because all statements are true for some or all values of alpha
We are looking for a statement which is false for all alpha
tranquil pine
what does the negation of the set mean? (x) means for "all x" and phi is a propositional function
final saddleBOT
what does the negation of the set mean? (x) means for "all x" and phi is a propo...
tranquil pine
fickle dove
bro is this a prank
tranquil pine
no?
fickle dove
did you look up the hardest problem on the internet or something
is this discrete math?
tranquil pine
this is actually page 15 / 720 of the book ;-;
ye more specifically boolean algebra
tranquil pine
.close
worldly bane
If i want to rationalize a polynomial from the denominator how would i do it. Not sure what conjugate to use
final saddleBOT
If i want to rationalize a polynomial from the denominator how would i do it. No...
dry light
Just multiply by $\frac{\sqrt{x^2+x-2}}{\sqrt{x^2+x-2}}}$
soft zealotBOT
Umbraleviathan
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
dry light
Not really
Because you have a square root
You can easily get rid of it by multiplying it by a manipulation of the value 1
In this case, that
dry light
Not really
worldly bane
or am i going about this in the wrong way
worldly bane
denom >= 0 right?
or wait
cause the radical cant be negative
i guess one step at a time
dry light
Yeah take this one step at the time
f(x) is undefined whether the denominator = 0
So to find discontinuities, we need to set the denominator = 0
$(2x-3)\sqrt{x^2+x-2} = 0$
soft zealotBOT
Umbraleviathan
dry light
What is x?
worldly bane
im not sure whaat you mean by that since we arent given a value for x
dry light
Okay I'm back
@worldly bane what did you get
I had to find a way to get wifi, being stuck in a brick building where the reception is literal dogshit
worldly bane
wait can i not just do 2x-3 =/ 0?
since it will multipy by the radical anyways
or does that violate some math law
dry light
Wdym by =/
worldly bane
not equal
dry light
≠?
worldly bane
yea
dry light
Yeah that violates
Well
Lemme think
If you're finding areas of domain, then yes, but if you're finding discontinuities (which is easier), then stick to =
worldly bane
man this question is confusing me
dry light
**Umbraleviathan**
So what values of x makes this true
worldly bane
oh wait
you want me to set it =0?
not =/?
I been trying to do this for not equal to zero
didn't realize you said =
dry light
Yeah it's =
dry light
It's easier to find where the function is discontinuous
worldly bane
okay, makes sense
dry light
And then take those values out of the domain of all reals
Basically we're finding "restrictions"
worldly bane
that makes so much more sense
idk im still stuck
maybe ive been doing math for too long
been doing limits questions all day
and im stuck on a damn domain question
this is quite discouraging
might have to just take a break and come back with fresh eyes
dry light
Yeah take a break
If you've done a lot, take a break
Burnout makes you blind
Not like actually blind
But ya know
worldly bane
yea
ok, thank you for your helpo
im gonna eat and watch a yt vid then try again
glhf ❤️
.close
final saddleBOT
Available help channel!
sturdy raven
whats the definition of a solvable group? i have one in my notes saying a finite group G is solvable if all its composition factors are cyclic of prime order. But i've seen another definition that says G is solvable if it has a subnormal series with abelian factors. these aren't equivalent are they?
final saddleBOT
whats the definition of a solvable group? i have one in my notes saying a finite...
@sturdy raven Has your question been resolved?
final saddleBOT
@sturdy raven Has your question been resolved?
final saddleBOT
@sturdy raven Has your question been resolved?
final saddleBOT
@sturdy raven Has your question been resolved?
silver dew
When G is finite then they are equivalent
By structure of finite generated abelian groups
sacred smelt
okay, I'm really lost with this one:
i(x) = 3x^4 + ax^3 - 39x^2 + bx + c
i(x) / (x^2 - 5) = q(x) with remainder (12x -84)
q(1) = 18
find a, b and c all real numbers
final saddleBOT
okay, I'm really lost with this one:
i(x) = 3x^4 + ax^3 - 39x^2 + bx + c
i(x) /...
gray vortex
$i(x) = 3x^4 + ax^3 - 39x^2 + bx + c \
i(x) / (x^2 - 5) = q(x) with remainder (12x -84) \
q(1) = 18$
soft zealotBOT
Asagao 朝顔
sacred smelt
$i(x) = 3x^4 + ax^3 - 39x^2 + bx + c \
i(x) = q(x) (x^2 - 5) + (12x -84) \
q(1) = 18$
soft zealotBOT
guillew
gray vortex
think of what "i(x) / (x^2 - 5) = q(x) with remainder (12x -84)" implies
sacred smelt
i(x) = q(x) (x^2 - 5) + (12x -84) ?
sacred smelt
i(1) = 18 (1 - 5) + (12 - 84)
3+ a - 39 + b + c = -144
a+b+c = -108
dont know what to do now
$i(1) = 18 (1 - 5) + (12 - 84) \
3+ a - 39 + b + c = -144 \
a+b+c = -108$
soft zealotBOT
guillew
final saddleBOT
@sacred smelt Has your question been resolved?
sacred smelt
?
tranquil pine
looks like an exam we cant help
sacred smelt
**guillew**
I am struggling to continue from here, anyone available?
vital crag
what is your question
vital crag
**guillew**
why can't you continue here
sacred smelt
**guillew**
ive gotten here
i do not know what to do with that equation
I thought about replacing one of the variables in the original function in terms of the other ones but did not get anywhere
something like this
$i(x) = 3x^4 + ax^3 - 39x^2 + bx - a - b - 108$
soft zealotBOT
guillew
sacred smelt
and then
$$3x^4 + ax^3 - 39x^2 + bx - a - b - 108 = q(x) (x^2 - 5) + (12x -84)$$
soft zealotBOT
guillew
sacred smelt
but it lost me there
soft zealotBOT
guillew
vital crag
Write q(x) = r x^2 + s x + t
vital crag
and you know q(x) because i(x) = q(x) * (x^2 -5) + (12x - 84)
sacred smelt
oh
so
$$3x^4 + ax^3 - 39x^2 + bx - a - b - 108 = q(x) (x^2 - 5) + (12x -84)$$
$$3x^4 + ax^3 - 39x^2 + bx - a - b - 108 - 12x + 84 = q(x) (x^2 - 5)$$
$$\frac{3x^4 + ax^3 - 39x^2 + bx - a - b - 108 - 12x + 84}{x^2 - 5} = q(x)$$
$$q(x)=\frac{3x^4 + ax^3 - 39x^2 + (b-12)x - a - b - 24}{x^2 - 5}$$
soft zealotBOT
guillew
vital crag
Write q(x) = r x^2 + s x + t
do this
sacred smelt
but what would be the r, s and t values? or jus new variables
vital crag
they're unknowns that you can solve for
sacred smelt
I genuinely do not get what you are talking about
vital crag
which part
vital crag
$$3x^4 + ax^3 - 39x^2 + bx - a - b - 108 = q(x) (x^2 - 5) + (12x -84)$$
$$3x^4 +...
plug the q i suggested into the second equation here. the rest are pointless
soft zealotBOT
guillew
$$3x^4 + ax^3 - 39x^2 + (b-12)x - a - b - 24 = (r x^2 + s x + t) (x^2 - 5)$$
sacred smelt
what can I do with these 3 new unknowns?
vital crag
two polynomials are equal if and only if their coefficients are equal
sacred smelt
$$3x^4 + ax^3 - 39x^2 + (b-12)x - a - b - 24 = r x^4 - 5 r x^2 + s x^3 - 5 s x + t x^2 - 5 t$$
sacred smelt
if that is correct then I think I can handle the rest
@vital crag sorry to bother but thanks a lot!
final saddleBOT
@sacred smelt Has your question been resolved?
tranquil pine
can anyone help me with my homework i cant understand a single thing one example for a and b will do
final saddleBOT
can anyone help me with my homework i cant understand a single thing one example...
strong orbit
Do you know sohcahtoa?
tranquil pine
nope
strong orbit
What garde are you in if I may ask?
tranquil pine
grade 8
strong orbit
Have you learned about sin?
strong orbit
Ok so I take it you are learn a set of special triangles
tranquil pine
yes
strong orbit
So for example 45,45,90
tranquil pine
right triangle
strong orbit
This is the idea of the trianlge
And you have one other triangle the 60,30,90 triangle
tranquil pine
i cant do this can i cancel it imma try ro learn solo if i dont get something i will come back i feel so stupid
tranquil pine
.close
final saddleBOT
tranquil pine
sorry
final saddleBOT
Available help channel!
round otter
hi, could someone help me with this question? i seriously cant understand it
tired walrus
do you understand where the angle you're asked for is situated on the diagram?
round otter
okay so this is what i tried, so ik that angle of depression, you can take it to the opposite side of the adjacent line
therefore, i tried to find the lenght of d to b
and then use tan to find the lenght from c to d
but lenght of c to d was shorter than b to d
@tired walrus
tired walrus
okay so you did not answer my question at all, but
you somehow got that CD < BD? that's definitely wrong.
round otter
yeah
i just dont know how to find the angle of depression from d to b
like enough as it is to find DC, i dont know how to find an angle
tired walrus
well to find an angle it helps to know where on the picture it is
it's a little hard to notate here, but if we take a point somewhere on the horizontal dotted line right of D and call it E, then the angle of depression from D to B is angle EDB
do you understand this?
tired walrus
C does not play a role at all here
angle EDB equals angle DBA (since AB and DE are parallel), and it should be clear that tan(DBA) = DA/AB = 168/126
round otter
how would i arithmetically prove that though,
wait i think i have to find the angle of d to its right most lenght
tired walrus
what do you mean by "arithmetically prove"
round otter
from d to outer most right to b
tired walrus
does it matter how far it's extended? it shouldn't.
do you understand this:
angle EDB equals angle DBA
yes or no?
round otter
oh yeah i suppose
tired walrus
there is no "i suppose", you either understand it or you don't.
round otter
E being the angle, EDB is what im trying to find, if EDB = DBA, then i dont understand for sure
tired walrus
please type the names of points as capital letters.
no, E isn't the angle. E is a point somewhere on the dotted line. the only reason why i'm introducing E is to give a name to the angle we want to find.
and you still haven't given a simple yes or no answer to my question
round otter
....no
tired walrus
could have said that at the beginning
okay, so let's roll back a bit.
DE and AB are parallel lines. do you understand this, yes or no?
round otter
yes
tired walrus
AB is a transversal line that cuts both DE and AB.
in doing so, it creates the pair of alternate interior angles EDB and DBA.
do you understand this, yes or no?
round otter
i cant recall
plush cosmos
i remember that they are the same angle though
round otter
do you mean elevation and depression
plush cosmos
wait its alternate
tired walrus
no i don't mean elevation and depression
plush cosmos
elevation and depression is for trig no?
tired walrus
either way, you have to somehow find out that angles positioned like this are equal
round otter
oh?
round otter
there is not much to be said about it
okay, thank you for the help, i think id like to hear from another person to see if they have anything easier to digest
tired walrus
you didn't need to be so polite in saying "thanks for explaining absolutely nothing, you slimy little mathematician fuck"
but you're welcome.
round otter
you didn't need to be so polite in saying "thanks for explaining absolutely noth...
I mean idk what you read, I was being honest, I'm sure you're correct and I'm just not being able to understand it, but I'm not accepting that solution because one, I haven't learned that during this course, so idk how sus its gonna look that I whip this out, and second, I simply just don't get it lol. I'm sure there's a very elementary way of solving it and I just cant figure it out right now
<@&286206848099549185> could someone help me figure out how to solve this question?
abstract gale
Ok so do you know about alternate interior angles?
If not we can go another approach
abstract gale
If not we can go another approach
Which is to find the measure of angle ADB by using inverse tangent (opposite/adjacent) and then subtract that value from 90 degrees
final saddleBOT
@round otter Has your question been resolved?
round otter
Which is to find the measure of angle ADB by using inverse tangent (opposite/adj...
i was doing that
currently finding the tangent theta
round otter
wow really?
abstract gale
Yep that’s it
abstract gale
What do you mean by how?
round otter
but i just want to know how you simplified it from alternate interior angles to just find theta tangent and then subract 90 to find angle of depression
sorry my brain is just a jumbled mess
abstract gale
Oh there’s 2 ways that I know of to find the answer to this
I made a sketch
So the first way of alternate interior angles would be the red
Blue is what you just did
They are different methods but they end up at the same solution
abstract gale
Nice job
abstract gale
No problem
round otter
.close
vague loom
hiya
final saddleBOT
vague loom
.reopen
final saddleBOT
✅
raw sluice
I solved it
deft ravine
Note that 32 = 2^5
deft ravine
Firstly, you bring it on one side, and the ones with numbers as exponents on the other.
vague loom
what does slowing a number mean tf
raw sluice
4096
deft ravine
You basically want to reach here 2^x = 2^x meaning you have an linear equation.
soft zealotBOT
r^2=x^2+y^2-2xycos
tranquil pine
First stuff u need for this
tranquil pine
Second stuff
$a^b=a^c$
$\implies b=c$
soft zealotBOT
r^2=x^2+y^2-2xycos
vague loom
yep
deft ravine
I am right right <@774739847608139796>
.Well, by "slowing" the number down you make it more difficult. It doesn't mean you're wrong.
tranquil pine
So u have
$2^{12}÷2^{\frac{k}{2}}=32$
$\implies 2^{12-\frac{k}{2}}=32$
soft zealotBOT
r^2=x^2+y^2-2xycos
tranquil pine
Try to convert 32 to base 2
vague loom
2 to the 5
tranquil pine
Yup
raw sluice
2^k/2 =128
deft ravine
Oh, that's even shorter than my solution
tranquil pine
$2^{12-\frac{k}{2}}=2^5$
soft zealotBOT
r^2=x^2+y^2-2xycos
tranquil pine
$\implies 12-\frac{k}{2}=5$
soft zealotBOT
r^2=x^2+y^2-2xycos
vague loom
wait huh
tranquil pine
Now u have a quite straightforward equation
tranquil pine
**r^2=x^2+y^2-2xycos**
This rule
vague loom
mb im not very good at this
tranquil pine
**r^2=x^2+y^2-2xycos**
U have this
tranquil pine
tranquil pine
mayb i need some more time on it
Lemme show you wait
raw sluice
Two try my way
vague loom
Lemme show you wait
kk
tranquil pine
So u have
$2^{12}÷2^{\frac{k}{2}}=32$
$\implies 2^{12-\frac{k}{2}}=32$
$\implies 2^{12-\frac{k}{2}}=2^5$
$\implies 12-\frac{k}{2}=5$
soft zealotBOT
r^2=x^2+y^2-2xycos
vague loom
**r^2=x^2+y^2-2xycos**
yep...
raw sluice
Teo just think about as a normal equation after that
vague loom
Now u have a linear equation
yeah thats ez
but its the first part
with the combine and all that ig
raw sluice
But this person finished I think
vague loom
DUDE GO TO ANOTHER CHANNEL HOLY SMOKES U HAVE LITERALLY GHOSTED MY CHANNEL FOR SO LONG CAN U PLS GO AWAY
IM NOT BRUHHHHHHH
i would dot close it if i was
tranquil pine
But this person finished I think
Let him close first
raw sluice
Kk
tranquil pine
i would dot close it if i was
Ok so which part are you confused of?
vague loom
**r^2=x^2+y^2-2xycos**
so is it because of the rules that u can go from the first equation to the second?
tranquil pine
**r^2=x^2+y^2-2xycos**
Something here?
tranquil pine
so is it because of the rules that u can go from the first equation to the secon...
Ya
The two rules which I mentioned before
vague loom
Ok so which part are you confused of?
hmmm that first part when it turns into 2 to the power of 12-k/2 = 32
vague loom
The two rules which I mentioned before
yeah i should probably try to understand them better
tranquil pine
**r^2=x^2+y^2-2xycos**
This rule
vague loom
**r^2=x^2+y^2-2xycos**
ahhh isee
tranquil pine
$\frac{a^b}{a^c}=a^{b-c}$
Second stuff
$a^b=a^c$
$\implies b=c$
soft zealotBOT
r^2=x^2+y^2-2xycos
tranquil pine
I just write in one place
vague loom
I just write in one place
wdum
i think its starting to make sense....
thanks so much for this
it was a big help
.close
fresh musk
final saddleBOT
final saddleBOT
fresh musk
.reopen
final saddleBOT
✅
fresh musk
my question is
why do you reject one of them
its + and -
but you reject the -
what is the significance of the - result ??
i know its not equal to cos(2pi/5) cuz i typed it in and its diff
but whats the significance of it
outer peak
why do you reject one of them
cos(2pi/5) is positive since 0 < 2pi/5 < pi/2
,w cos(4pi/5)
soft zealotBOT
outer peak
hmm so thats cos(4pi/5)
fresh musk
hmm so thats cos(4pi/5)
yh i realized its that but like
whats the significance of it
why does it appear in the equation
outer peak
because its also a root to z^5 = 1
fresh musk
oh yh i guess so
alright ig that makes sense, easier than i thought lol. thanks.
.close
final saddleBOT
fresh musk
heello i need help
final saddleBOT
Available help channel!
feral dock
<#488120190538743810>
hwllo
feral dock
i need help
final saddleBOT
@feral dock Has your question been resolved?
fresh musk
final saddleBOT
fresh musk
i thought you would multiply by i because 90 degree rotation but tahts not quite right
i cant quite tell what you do
silver dew
((2+3i)-(1-i))i +(1-i), ((2+3i)-(1-i))i +(2+3i) is a pair
-((2+3i)-(1-i))i +(1-i), -((2+3i)-(1-i))i +(2+3i ), is another pair
Because rotate -π/2 is multiplication by -i
fresh musk
((2+3i)-(1-i))i +(1-i), ((2+3i)-(1-i))i +(2+3i) is a pair
im sorry i cant understand whats going on here
weary wharf
Have you learned that if you multiply a complex by $e^{\frac{\pi}{2}i}$ then you will rotate that complex number anti clockwise by 90 degrees
soft zealotBOT
azeem321
fresh musk
thats just multiplying by -i
i thought it was i tbf, but ok its -i
wiat no
it is i
im being sleepy sorry
yh multiplying by i is 90 degree anti clockwise
multiplying these by i does not give the correct ans tho
weary wharf
So we have our square. We can find a complex number representing the line segment joining (1-i) to (2+3i) by doing 2+3i-(1-i) = 1+4i
fresh musk
oh your saying i should just do it with vectors?
weary wharf
kinda, yh like a vector approach
now we have the complex number representing that line segment
we can multiply it by exp(ipi/2)
and exp(-ipi/2)
fresh musk
and exp(-ipi/2)
i dont understanrd this
so now your multiplying by -i
i can do it with vectors
via mostly inspection
but i dont really understand the maths behind it is my issue
if i was to get a different shape in an exam
normally i multiply by the angle but multiplying by i does not work here
probably due to different arguments
oh your saying you multiply the line segment by i
thats weird to think about
then u add it on?
basically by the way the reason for so many questions suddenly today - doing OCR A papers (my normal board is OCR B), so very different questions from what im used to but i mean they should mostly still be on spec.
weary wharf
If you multiply i, you get the top dotted line. if you multiply by -i you get the bottom dotted line. so this should result in 4 possible points if i am not mistaken
not sure why mark scheme only given 2
weary wharf
i was confused for a sec lol
So yeah
You rotate by both i,-i
You get the resulting line
and then u subtract of the 1-i term to get the point
Something that might be helpful, in general to rotate a complex number any angle $\theta$, you multiply by $\exp(i\theta)$
soft zealotBOT
azeem321
fresh musk
yes i get it
my mistake was multiplying the numbers themselves by i, but now i understand you multiply the vectors, then add or subtract the vectors from the points
thank you as always 🙏
.close
weary wharf
my mistake was multiplying the numbers themselves by i, but now i understand you...
Yyh multiplying the complex numbers by i, would be rotating them about the origin
final saddleBOT
Yyh multiplying the complex numbers by i, would be rotating them about the origi...
weary wharf
.close
random grotto
8th grade math
When A is increased by 20% and B is decreased by 2%, the resulting values are equal. What is the ratio of A to B?
Thank you.
final saddleBOT
8th grade math
When A is increased by 20% and B is decreased by 2%, the resultin...
grim badger
<@&286206848099549185>
One, please read #❓how-to-get-help because you are supposed to wait at least 15 minutes before pinging helpers
Two, don't abuse the ping, you used that 3 times in less than 15 minutes
fresh musk
final saddleBOT
fresh musk
i believe they help
i did
i realize its the same thing if you put 1/2pi - theta into it
if theta = pi/2 - theta
2theta = pi/2
theta = pi ?!?
no
thats incorrect
strong atlas
f(x) = f(π/2 - x)
fresh musk
oh
i did basic math wrong
what i was saying was correct, right?
you get pi/4 = theta
fresh musk
same value of r for like +- the number?
strong atlas
if f(k - x) = f(k + x), x = k is a line of symmetry
consider the case for f(-x) = f(x), for example
f is even, f is also symmetric across the y-axis
strong atlas
if f(k - x) = f(k + x), x = k is a line of symmetry
this is the generalisation
strong atlas
f is even, f is also symmetric across the y-axis
y-axis is just x = 0
fresh musk
final saddleBOT
fresh musk
what is
i know what sum(ab) is
sum(ab) is ab + bc + ca
but the squared
idk how that works
strong atlas
??
strong atlas
(ab)² + (bc)² + (ac)² + 2 (a²bc + ab²c + abc²) = (ab + bc + ac)²
this is a hint
strong atlas
yes
fresh musk
this is only 2 marks
strong atlas
it’s fairly simple
fresh musk
I have thought about it
Not got an idea yet
I'll continue staring at it
Only way I can think of involves working out the roots
strong atlas
(ab)² + (bc)² + (ac)² = (ab + bc + ac)² - 2abc (a + b + c)
you know the RHS
then done
fresh musk
oh yh, its all good now thought cuz i was making bit of a larger issue.
just gonna see if i get the ans before i close
jesus this is hard to replicate from the start
im gonna have to just memorize the formula
no im still not getting it right 😦
fresh musk
(ab)² + (bc)² + (ac)² = (ab + bc + ac)² - 2abc (a + b + c)
oh nvmd
found my error
.close
final saddleBOT
final saddleBOT
Available help channel!
normal hill
final saddleBOT
final saddleBOT
@normal hill Has your question been resolved?
normal hill
.close
hardy harbor
help
hardy harbor
hardy harbor
for question (d) anyone can explain why x=n cannot be used as the initial estimate?
tranquil pine
Do you know correlation?
strong briar
or is it not possiblr
Alright.
I will help you here. Like petschge said you are missing a two in the term sin^2x/cos x. You can plot it and see it is not the same as the plot of cot x.
hardy harbor
.close
tranquil pine
normal hill
Alright.
I will help you here. Like petschge said you are missing a two in the t...
infront of that should be a 2
lemme see
daring mulch
for a variation to be direct the relationship between the two factors should not be affected by any factor (i.e., mathematically the equation of the line should be y=mx). in this case there is an initial charge (cost=20, time=0), so the variation is not direct (i.e., the equation is y=mx+c).
short tundra
Where can i find, when function drops ? I did for rise but im not happy with x=2. Correct result is [-3,1]. Does anyone knows the solution ?
final saddleBOT
Where can i find, when function drops ? I did for rise but im not happy with x=2...
short tundra
How can i find coordinate for y tangent point ? I got x=2.75. y is -12.8, but i dont know how to calculate this.
final saddleBOT
How can i find coordinate for y tangent point ? I got x=2.75. y is -12.8, but i...
short tundra
Determine the point on the f(x) curve at which the direction coefficient of the tangent is Kt = 3.
Find x0 and y0 coordinats.
final tangle
sub x=2.75 back into the original function
to find the y-coordinate at that location
,w 2x^2-8x-6 when x=2.75
soft zealotBOT
buoyant eagle
What are two sets in R2 where the union of the two sets does not equal the sum of the two sets?
I'm having trouble with this
Like for example would the set contain the vector (1 0) and the set containg the vector (0 1) work
Cause the union is both the vectors in the set and the sum would be (1 1) right?
final saddleBOT
What are two sets in R2 where the union of the two sets does not equal the sum o...
desert mantle
if $A={(1,0)}$ and $B={(0,1)}$, then $A+B={(1,1)}$ and $A\cup B={(1,0), (0,1)}$
soft zealotBOT
Denascite
desert mantle
or do you mean the sum as in the sum of vector spaces?
buoyant eagle
this is the question
I think it is just referring to set sums and union
I was just wondering if my example was correct
buoyant eagle
or do you mean the sum as in the sum of vector spaces?
would you say it is?
desert mantle
well if you just defined A+B as pointwise addition then your example is fine
buoyant eagle
well if you just defined A+B as pointwise addition then your example is fine
I'm using this definition
desert mantle
yup
desert mantle
if $A=\{(1,0)\}$ and $B=\{(0,1)\}$, then $A+B=\{(1,1)\}$ and $A\cup B=\{(1,0), (...
then this is correct
burnt oxide
How do I get started with solving this?
final saddleBOT
How do I get started with solving this?
final tangle
consider what happens when x=1
burnt oxide
But like I don’t see what I’m supposed to get out of it, y=kx+m or y=mx+b. Sure yeah, but like how?
tranquil flume
what is b in mx+b?
final tangle
considerwhat happens when x=1
burnt oxide
y = 8 when x = 1
final tangle
true
but not quite what i'm trying get you to do
look at the second equation you're given about your function
burnt oxide
Aha?
final tangle
sub x=1 into that
burnt oxide
So f(1+2) = f(1)+6 ?
final tangle
not what i'm asking you to do
simplify, don't do other random stuff
don't overthink
burnt oxide
f(3) = f(1) + 6 huh?
burnt oxide
But how do I simplify it with the f(x), god this is so confusing
burnt oxide
yeah 8?
final tangle
yes
burnt oxide
so 8 =
final tangle
and hence
f(3) = f(1) + 6 = ?
burnt oxide
f(3) = f(1) + 6 = 8
burnt oxide
Aha? But i don’t see, how do i get that to 3x + 5 ?
final tangle
don't jump ahead
burnt oxide
Alright step by step
final tangle
these were not supposed to be trick questions
and were supposed to take less than 30seconds to answer
burnt oxide
Yeah math teacher told us it was simple, i just dont get it
burnt oxide
I’ve no clue
final tangle
do NOT overthink this
burnt oxide
Oh
final tangle
f(1) + 6 is just 6 added to f(1)
which you know has a value of 8
so f(1) + 6 is just 8 + 6 which is 14
so f(3) = 14
and now you essentially have info about two points
and you can apply the two-point formula and/or otherwise to get your equation
and rearrange to the specified form
burnt oxide
Yeah and how do i do that now again, i take y2 - y1 divided by x2 - x1
final tangle
that will get you the slope (which is part of the two point formula)
you could calculate the slope first separately and then apply the point-slope formula
burnt oxide
And how do i do that, haha i feel so dumb oml
burnt oxide
Yeah and what points do i put in the formula
final tangle
use
f(1) = 8
which you viewed as
y = 8 when x = 1
and
apply the same idea for
f(3) = f(1) + 6 = 8 + 6 = 14
final tangle
yes
final tangle
not like that
you can't just sub in y=8 without doing anything else
y isn't always 8
when is y equal to 8
burnt oxide
no but if i take that point and just do 8=3x1+b
final tangle
is that supposed to be the variable x or multiplication symbol?
burnt oxide
multiplication
final tangle
don't use x for multiplication, especially not in the presence of x
burnt oxide
3*1 ?
burnt oxide
Haha so sorry
final tangle
that'd be more appropriate
burnt oxide
Aha, So let’s see
final tangle
you'd have to sub in both x and y values at the same time for the work to be valid
final tangle
the final line of your work would be
y = 3x+5
burnt oxide
Yeah alright then that’s it.
Thank you so much haha
I’ve got another one:
.close
final saddleBOT
final saddleBOT
final saddleBOT
@tranquil pine Has your question been resolved?
final saddleBOT
@tranquil pine Has your question been resolved?
final saddleBOT
@tranquil pine Has your question been resolved?
final saddleBOT
@tranquil pine Has your question been resolved?
vital crag
.close
final saddleBOT
final saddleBOT
Available help channel!
minor storm
final saddleBOT
minor storm
Helpp
final saddleBOT
@minor storm Has your question been resolved?
minor storm
<@&286206848099549185>
errant junco
worldly vale
final saddleBOT
@minor storm Has your question been resolved?
final saddleBOT
@minor storm Has your question been resolved?
quick mantle
,rotate
soft zealotBOT
quick mantle
Use
$cos (\theta) = dot product (b+kc) and (a) $
For parallel the angle or theta will be zero.
shell mountain
Use
$cos (\theta) = dot product (b+kc) and (a) $
For parallel the angle or th...
This isn't their channel
quick mantle
Oops
final saddleBOT
@minor storm Has your question been resolved?
final saddleBOT
@minor storm Has your question been resolved?
night arrow
wouldnt it create 4 isocles triangles at each of the 4 corners?
from ther eyou can prove their conguency
sorry no
they would not be isoscles
but u could do the same with a bit of trig no
grand kiln
what if you did u=log(x)
minor storm
what if you did u=log(x)
What good would it do?
grand kiln
What good would it do?
idk just experiment with it
if it doesn't work out you can always try something else
I suggested u=log bc you had an x in the denominator and du would be 1/x dx
rare hornet
vernal pewter
candid otter
I recommend you take this in a specific channel
like #calculus
more smart people are likely to help you there
final saddleBOT
@minor storm Has your question been resolved?
minor storm
more smart people are likely to help you there
Oh okay thanks
minor storm
.close
wind lava
final saddleBOT
wind lava
How the fuck do you do this
wind lava
Anyway
wind lava
How do you get the values for 5/17 and 11/17
sturdy cypress
hold on, first i give answer, then i check if it makes sense at all
grim badger
hold on, first i give answer, then i check if it makes sense at all
You're not supposed to give out answers
sturdy cypress
i was warned multiple times, believe me i know
grim badger
Then why are you giving out answers?
sturdy cypress
?
wind lava
@grim badger wdym, I need help
sturdy cypress
does the reason matter?
wind lava
Why can I not receive help @grim badger
grim badger
<@485903210272391178> wdym, I need help
It means what it means. People aren't supposed to give out answers. You're supposed to learn and people here are suppose to engage and let you do the work yourself
sturdy cypress
ok, yeah that's not the wrong answer
after you picked a math book, there are 17 books left, with 5 of them math
it's the same logic as 6/18
the key point is that picking two random books is picking one random book, and picking one again from the remaining books
sturdy cypress
another way is combinatorial i guess you could call it
there are (18 choose 2) ways to pick two books, and (12 choose 2) + (6 choose 2) ways to fulfil the requirement
wind lava
sturdy cypress
they are equally probable
sturdy cypress
they are harder
wind lava
Do you know how to solve them
sturdy cypress
yeah, the first one I would solve with that combinatorial thing
count how many total ways there are to distribute prizes
there are 29 people, choose 3 to receive a prize
= 3654
then add up 4 types of outcomes where it's the same subject
sturdy cypress
it's totally similar to the books, you were right :)
calculator
e.g. google
it's 29×28×27/6 if you wanted to do it manually
n×(n-1)×(n-2)
3 terms total
divided by 3!
sturdy cypress
after you added up the outcomes that are "good" you just divide good by total
that's the final result
wind lava
So total outcomes is 3654
wind lava
How do you get all the good outcomes
sturdy cypress
we're counting how many ways 3 teachers of the same subject can receive the prize
it could be 3 math teachers, then it's (7 choose 3) ways, it could be 3 science then (10 choose 3), we don't care which subject all these outcomes are good
so we add them up
wind lava
How do you get 10 choose 3 and 7 choose 3
sturdy cypress
i'm sorry what do you mean
wooden veldt
If $\sin{A} + \cos{2A} = \frac{1}{2}$ and $\cos{A} + \sin{2A} = \frac{1}{3}$, find the value of $\sin{3A} \newline$ $\sin{A} + 1 - 2sin^{2}{A} = \frac{1}{2}$ solving for sin A, I get $\frac{1 ± \sqrt{5}}{4}$. I understand I have to consider the second equation as well but $\sin{3A} = 3\sin{A} - 4\sin^{3}{A}$, substituting both the values regardless, I get irrational numbers but the answer key states a rational number; where did I go wrong?
final saddleBOT
If $\sin{A} + \cos{2A} = \frac{1}{2}$ and $\cos{A} + \sin{2A} = \frac{1}{3}$, fi...
soft zealotBOT
kinglacto
final saddleBOT
@wooden veldt Has your question been resolved?
wooden veldt
.close
final saddleBOT
final saddleBOT
Available help channel!
wet orbit
confused
balmy condor
me too
fiery wave
tired plume
Ah nice makes sense
final saddleBOT
@wet orbit Has your question been resolved?
final saddleBOT
soft zealotBOT
vov&sons
final saddleBOT
@ebon ginkgo Has your question been resolved?
final saddleBOT
@ebon ginkgo Has your question been resolved?
shell orchid
final saddleBOT
shell orchid
Pour half into 5 gallon jug and you now have 4 gallons
And pour the rest into 3 gallon jug to ensure that you still have an acceptable amount (1 gallon) still in the 8 gallon jug
final tangle
Pour half into 5 gallon jug and you now have 4 gallons
it is implied that you would be unable to get 4 gallons like that
shell orchid
Oh shoot u right
So fill 3 gallon then pour half of the remaining water in the 8 gallon into the 5 gallon (2.5 gallons) and pour half of the 3 gallon into the 5 gallon making 4 gallons
final tangle
it is implied that you can pour out half the contents like that
you can either fill the jug or empty a jug
you can't pour exactly 2.5 gallons out of the jug just like how you can't pour out 4 gallons out of the jug
assume the jugs are irregular with no markings
shell orchid
Hmmmm
final tangle
and all you know is the max capacity
shell orchid
Now I am thinking of filling the 3 gal jug then pouring it into the 5 gallon one
Then refilling the 3 gal so you have 3 by 3 by 2 gals
But I can’t find a way to make it 4 gals
final tangle
consider what you can do with the
5 gall jug that has 3 gall
and the
3 gall jug that's full
shell orchid
Ohhhhhhhhhh
Pour the 3 gallon into the 5 gallon until it is full, resulting in 1 gallon then pour the 1 gallon back into the 8 gallon to make 4 gallons
Correct?
final tangle
close but no
final tangle
note that the 8gall jug had 2 galls at that point
shell orchid
Ahh ur right
final tangle
pouring 1 gall back into that would get you 3 gals
defeating the purpose of what you just did
shell orchid
So instead you pour 5 gallons back into 8 gallons then transfer 1 gallon to 5 gallon bucket and after that filling the 3 gallon back up again and combining in the 5 gallon bucket
4 gals
final tangle
yes
shell orchid
Ahhhh kk thx. Do you have any tips on getting a proof started?
final tangle
that's the proof
proof by example
you successfully showed a (legitimate) way to do it and you're done
dense tundra
final saddleBOT
