I don’t get what this means tbh
#help-13
raven fox
zealous compass
I’m telling him he missed brackets
jaunty mural
It was wrong, and I'm tyring to demonstrate why it was wrong.
because clearly this point is being misunderstood
jaunty mural
Earlier, you did it correctly for 2.
wraith daggerBOT
raven fox
Yes I did
wraith daggerBOT
jaunty mural
No, forget 5n first
zealous compass
Oh I see what ur trying to demonstrate mb
wraith daggerBOT
jaunty mural
The point is, the (1+1) should always happen
before you do anything else with it
you can consider it one unit
zealous compass
Sheri is talking about the brackets
raven fox
Yes
zealous compass
Shuri*
jaunty mural
And it makes sense if you first compute the 1+1 = 2
raven fox
So do you mean I would do the exponent first
jaunty mural
So now you should see what was wrong with 5n
raven fox
Or something
jaunty mural
So do you mean I would do the exponent first
No, you do 1+1
which is 2
then do the exponent
raven fox
So 25n^2-5n????
zealous compass
Yes
jaunty mural
yes
The safest substitution is to put brackets in always
,,f(x) = x^2 - x = (x)^2 - (x)
raven fox
Fs but what do I do now
wraith daggerBOT
raven fox
Do I need to factor or sum
jaunty mural
I don't know what the question asks
jaunty mural
So 25n^2-5n????
this is done
jaunty mural
well u have
jaunty mural
yes the value is in terms of n
raven fox
👍
jaunty mural
hopefully when u did 34, you remembered the (...)
otherwise u'd get the wrong answer
raven fox
I didn’t have to do 34 only 36 and 40 for that section
jovial glacier
Lets say I have a record of every time an Airplane has flown overhead.
How would I calculate the probability of a plane flying overhead for every 5 minute interval of the day?
What statistic functions/theorems would I use for that
cedar kilnBOT
Lets say I have a record of every time an Airplane has flown overhead.
How woul...
@jovial glacier Has your question been resolved?
jaunty mural
You would likely model with a Poisson distribution
raw spoke
How do I factorise this by grouping?
cedar kilnBOT
How do I factorise this by grouping?
slate lintel
if it doesn't seem to work the first way you try, swap some terms and try again
raw spoke
The answer given is but idk How it gets there
ancient valley
Well to start what are some groupings you can make out of the terms in the numerator?
jaunty mural
How do I factorise this by grouping?
well ngl, the denominator is a hint
raw spoke
well ngl, the denominator is a hint
Ik
jaunty mural
The question is likely laid out so that it cancels with something on the denom, so at least try it first
ok
wraith daggerBOT
jaunty mural
And then you deduce term by term what must be in the 2nd bracket
raw spoke
Ye I see that but the problem is it says by grouping and I don't know what the steps to it that way are
raw spoke
no I dont I just want to know how to
slate lintel
it's a little hard to see but it's worth it
jaunty mural
The answer given is but idk How it gets there
If you multiply out the numerator, you get 6 terms, 2 of which cancel
That makes it hard(er) to group (working backwards from the answer)
slate lintel
i'll give another hint here that you don't have to rearrange any terms, just group the first two and the last two
then factor each one by whatever means you can
raw spoke
then factor each one by whatever means you can
I see
I would have never done it that way
slate lintel
i didn't realize it until i tried the others
slate lintel
yeah exactly
crimson estuary
how do i do 5c?
smoky stump
C
smoky stump
Could someone please clarify to me about taylor series
Why does |x| < 1?
wouldn't it still be valid for x to be any value?
cedar kilnBOT
@smoky stump Has your question been resolved?
cedar kilnBOT
cedar kilnBOT
Available help channel!
hybrid wren
if i have a piece of steel thats 8' x 0.5" x 3.5" and i cut the pieces into pieces that are 3.5" x 0.5" x 3.5" how many pieces do i have?
smoky idol
!status
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
2
i believe since the 0.5 x 3.5 doesnt change i dont have to worry about that too much
so then do i just divide the 8ft in 12 inches?
then divide that by 3.5?
smoky idol
I think that's correct. Just remind me, is " feet or inches?
hybrid wren
i believe we are working with ft in inches in this one
i believe the final answer would be in inches
and we are starting in feet
smoky idol
oh that's not what I meant. I just can't remember if " means feet or inches
gentle flower
single apostrophe for feet and double apostrophe for inches
smoky idol
Okay then yeah your thinking is correct. Convert the 8ft into inches and do your division
hybrid wren
im trying to first convert feet to inches
smoky idol
Cause you see Atlas, there are 12 inches in each feet. And you have 8 feet
gentle flower
hybrid wren
then determine how many cuts i can make
vestal bear
so then do i just divide the 8ft in 12 inches?
just convert 8ft to inches
hybrid wren
so i got 96 ft
inches
rofl
then i divide that by 3.5
and thats how many pieces i can make
smoky idol
Right
hybrid wren
so 27.42857142857143 pieces
gentle flower
each piece has to be 3.5 x 0.5 x 3.5 so you’ll only count whole numbers, i think?
hybrid wren
sweet so if i wanted to make a total of 108 parts
i would then take that 27 '
and divide 108 by it
vestal bear
yeah round down
vestal bear
i would then take that 27 '
no
vestal bear
convert 27ft into inches divide it by a variable x and set it equal to 108
hybrid wren
if i can make 27 parts with that
piece of steel
and i wanted 108 parts
i would need 4 pieces of steel
hybrid wren
lowkey no og problem
vestal bear
if i have a piece of steel thats 8' x 0.5" x 3.5" and i cut the pieces into piec...
seems like its more than this
hybrid wren
im trying to learn the conversion
vestal bear
from feet to inches?
hybrid wren
well not exactly
i was just trying to understand how many parts i would have to make
and the process of deducting that
my bad how much material
**
vestal bear
is this some kind of project youre doing?
hybrid wren
yes!
vestal bear
brackets?
yes
what's the whole thing
some kind of structure?
do you have to make these by hand?
or do you have machines?
hybrid wren
i have a iron worker
hydraulic press
i just come here often for other math problems and i was just trying to make sure i got the correct amount of material
its for a gazebo
vestal bear
ooo cool
I got a gazebo one time that came with all the lumber and hardware
they're a bitch to put up
the roof pieces need to be almost exact and the wood was warped in places
hybrid wren
oooof i seen this meme about the home depot forest lol
it was a bunch of gnarled trees haha
hybrid wren
youd assume their transit has alot of moisture content
vestal bear
I did some work for this one guy who made his own shed and he wanted some baseboards and trim around the inside
all the trim he provided was warped and he built the structure with more warped wood
nothing went together properly
maybe some incompetence on his end
vestal bear
youd assume their transit has alot of moisture content
yeah
cedar kilnBOT
@hybrid wren Has your question been resolved?
hybrid wren
all the trim he provided was warped and he built the structure with more warped ...
thats never a good idea haha definitely incompetence
slate lintel
hola debe empezar su propio canal, use #help-2 o #help-7｜zen1thxyz
upbeat zealot
Ablas espanol?
slate lintel
si pero vayase asi
rigid gulch
cedar kilnBOT
rigid gulch
actually
wondering if i am doing this right
i am told to prove that this vector field is conservative
and then generate a potential function for the given vector field
dire geode
Problem is really small
cedar kilnBOT
@rigid gulch Has your question been resolved?
solid juniper
Problem is really small
here use this 🔍
rigid gulch
wait seriously you cant read it?
rigid gulch
cedar kilnBOT
rigid gulch
may someone help with this problem please
im having a hard time figuring this one out
slate lintel
not sure what they even want here, are they asking you if it's a sphere / plane / paraboloid / etc?
cedar kilnBOT
@rigid gulch Has your question been resolved?
rigid gulch
Well
They’re asking what surface it is
And I’m having trouble determining that and my professor said not to graph it
Just use what you’re given
slate lintel
i mean it's like... that sure is a surface alright, and it's a pretty good description of it
but what more do they want?
cedar kilnBOT
@rigid gulch Has your question been resolved?
cedar kilnBOT
cedar kilnBOT
Available help channel!
uneven forum
help me this question
cedar kilnBOT
help me this question
uneven forum
we have b=7 c=5 cos a = 3/5 find height ha
umbral dew
can you show me the diagram?
tropic oxide
consider finding side a if you haven't already
uneven forum
consider finding side a if you haven't already
i has been find a :v
uneven forum
can you show me the diagram?
nah i don't have the diagram
tropic oxide
i has been find a :v
then think about the area of ABC
uneven forum
then think about the area of ABC
i solve all of this question but i find in the internet they have the answer different me
tropic oxide
ok then show your work and show what you found on the internet
tropic oxide
is this yours or from the internet?
cedar kilnBOT
@uneven forum Has your question been resolved?
ripe wasp
cedar kilnBOT
ripe wasp
Only help in part a
sonic thicket
!status
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
What did you try?
sonic thicket
Try making a equation using the volume of cube instead
ripe wasp
(1000,0) (125,70) ?
sonic thicket
Yup
And since they said it decreases at a constant rate
Slope is constant
Do you know what shape that is?
ripe wasp
Straight line?
ripe wasp
y2-y1/x2-x1
sonic thicket
And what would slope represent in this case
ripe wasp
The rate at the ice block melts
sonic thicket
There you go
ripe wasp
Still not right
sonic thicket
What's your ans?
ripe wasp
-0.08
sonic thicket
,calc 5^3-10^3
wraith daggerBOT
Result:
-875
,calc 875/70
wraith daggerBOT
Result:
12.5
Check your work
wraith daggerBOT
Result:
-12.5
harsh garden
Hi guys
vague rapids
So your goal was to find sum and product of roots?
lunar lynx
Does my answers we're correct?
Yeah
vague rapids
Yup, all are correct
harsh garden
So your goal was to find sum and product of roots?
Yes
Thank you so much guys💖
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
forest carbon
Is there a name for a graph (graph theory), like a lattice graph, where there's a repeating 'pattern?'
forest carbon
More formally, maybe some subgaph size n is isomorphic to at least some number of other subgraphs
stiff totem
a periodic graph?
forest carbon
I googled that, actually! I wasn't 100% about its definition on wikipedia though
Because I don't understand half of it
I guess I will do some further reading and see if it's right; thanks!
.close
cedar kilnBOT
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Available help channel!
inner elbow
One of the properties of congruency is that if a≡b(mod n), then ac≡bc(mod n). What's the proof for the truthfulness of this?
dusk finch
hint: a≡b(mod n) if and only if a = kn + m and b = ln + m for some integers k,l,m
or other way to rewrite it is a≡b(mod n) iff a = kn + b for some integer k
inner elbow
If a=kn + b, could we say that b is the remainder when a is divided by n?
dusk finch
If a=kn + b, could we say that b is the remainder when a is divided by n?
not exactly, a = kn + b means, that a = b + some multiple of n
e.g. 5 ≡ 13 (mod 4) means that 13 = 5 + some multiple of 4
upbeat forge
One of the properties of congruency is that if a≡b(mod n), then a*c≡b*c(mod n). ...
I would choose another definition. If a≡b(mod n) then n | a - b. Then multiplying it by some c will get us n | c(a-b)=ac-bc from which we get ac≡bc(mod n)
dusk finch
!nosols
cedar kilnBOT
As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.
dusk finch
but yeah, that definition works too
depends on what definition of modular congruency are you familiar with
inner elbow
I would choose another definition. If a≡b(mod n) then n | a - b. Then multiplyin...
Ohhh that does make sense
Because a-b is divisible by n, so c(a-b) would be divisible by n too, right?
upbeat forge
yes
cedar kilnBOT
cedar kilnBOT
Available help channel!
molten quartz
cedar kilnBOT
molten quartz
integrate that function wrt x..... is what i did right?
cuz ans isnt matching....
can someone help pls
junior dome
that is the correct answer
cedar kilnBOT
cedar kilnBOT
Available help channel!
wild belfry
** A cylinder of volume V has height (5pi)/2, and radius r. f(x) = [2sin(2x - 4pi) + 184]^(1/2). This function makes a solid when revolved around the x axis. The volume of this function is the same as V in the domain pi/2 to (3 * pi)/2. Find the radius of the cylinder.**
I squared [2sin(2x - 4pi) + 184]^(1/2) then integrated and got 184x - cos(2x)
Putting in the domain pi/2 and 3pi/2 gave me 184pi
Multiplied by pi gives 184(pi^)2
Is this the answer?
wild belfry
I dont really know what they wanted me to do with 'cylinder of volume V has height (5pi)/2'
tropic oxide
so you found the volume of that solid of revolution and you got it as 184pi, yes?
wild belfry
Yeye
tropic oxide
multiplying it by pi was pointless
you're told that this volume you just found equals V
$V = \pi r^2 h$ and you're told $V = 184\pi$ and $h = \frac52 \pi$, and you're asked for $r$
wraith daggerBOT
Ann
wild belfry
But dont I need to multiply by pi at the end after squaring and integrating the function
I thought that was the method for solids of revolution
tropic oxide
?
oh wait no hold up
i got confused sorry
the way you've written the problem is a little strange with the order things are put in
and the way you laid out your work
ok wait hold on
wild belfry
My bad haha
tropic oxide
,w int[pi/2, 3pi/2] pi * (2 sin(2x) + 184) dx
wraith daggerBOT
wild belfry
So r = √(V / (πh)).
r = √184π^2 / (5/2)π^2
Thats the answer?
I think it is so I will close this
But thank you!
❤️
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
umbral pulsar
If I want to point out n^5/2, is it correct? I am not sure with the 4 at all.. thank you
cosmic perch
1/2-5/2=-4/2=-2 so it should be 1+4/n^2 in bracket
cedar kilnBOT
@umbral pulsar Has your question been resolved?
wintry wasp
I was trying to do this example by myself and got stuck at the part where i got -ln|10-x|, i dont get why x>10 for all t and i dont get the books explenation. Does someone understand?
wintry wasp
Also dont understand why -ln|10-x| suddenly becomes ln(x-10)
royal loom
if x cannot equal 10
and the initial condition of x(0)=50
then at the initial condition, we already are above 10 (we are at 50)
in order to cross below 10, we would have to equal 10 at some time
but x cannot equal 10
because ln(0) is undefined
wintry wasp
if x cannot equal 10
oh okey i thought we were trying to establish this to show that this differential equation is the right one for this function. I get it now thank you
wintry wasp
Also dont understand why -ln|10-x| suddenly becomes ln(x-10)
what about this?
wintry wasp
and the initial condition of x(0)=50
wait but ln of a negative number is also not defined and 10-x is necesarrily negative since x>10
radiant fjord
what about this?
they multiply the negative one over to the other side
wintry wasp
they multiply the negative one over to the other side
but the order of the subtraction changes
radiant fjord
wait but ln of a negative number is also not defined and 10-x is necesarrily neg...
which is why they change it to ln(x-10)
because |10-x|=x-10 for all x>10
wintry wasp
which is why they change it to ln(x-10)
How is that justified
o
oh yeah
lol
Thanks alot ahaha, exam stress is making me miss stuff like this
radiant fjord
no you're good! good luck
cedar kilnBOT
cedar kilnBOT
Available help channel!
subtle horizon
How do i accurately draw curves
cedar kilnBOT
How do i accurately draw curves
subtle horizon
so as to accurately get their integratin
area
i mean
for example $$ x(x-1) and x(2-x) $$
vestal bear
what
wraith daggerBOT
Brian
vestal bear
just integrate it I'm not sure why you need to graph it?
subtle horizon
to know bounds
cedar kilnBOT
vestal bear
that will give you your bounds
you can make a little sketch too if you want
but it doesn't have to be elaborate
cedar kilnBOT
Available help channel!
drifting ridge
7 + (-3) + (-5) - 10
cedar kilnBOT
7 + (-3) + (-5) - 10
drifting ridge
i keep getting -25 as my answer
ancient valley
Could you show your work?
upper ruin
7 + (-3) + (-5) - 10
Is it 7 or -7 at the beginning?
drifting ridge
7
upper ruin
Could you show your work?
This is the best thing you can do @drifting ridge so that we can help you
drifting ridge
yes let me get a picture
ancient valley
!nosols
cedar kilnBOT
As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.
ancient valley
All good, you should delete the answer though
upper ruin
17 + (-8) is the same as 17 - 8
twilit knot
There is no multiplication
drifting ridge
17 + (-8) is the same as 17 - 8
the answer is supposed to be -11
upper ruin
Oh you also copied the wrong sign for 10 in the second row
twilit knot
So 7-3-5-10, do you get this part?
drifting ridge
So 7-3-5-10, do you get this part?
yea i get this
drifting ridge
yes
twilit knot
Try now
drifting ridge
my book only told me to change subtraction to addition, never said anything about changing the + to a -
weird
ancient valley
If it helps:
1+(-1) = 1-1
1+(+1) = 1+1
1-(-1) = 1+1
1-(+1) = 1-1
These are just examples btw not pertaining to your problem
drifting ridge
idk i understand this question but i dont think i can remember when and what to change the symbols to
drifting ridge
If it helps:
1+(-1) = 1-1
1+(+1) = 1+1
1-(-1) = 1+1
1-(+1) = 1-1
These are just ...
why dont the questions just ask whats on the right? whats the point of the left version
twilit knot
Life will not be kind with you and give you simple questions
upper ruin
idk i understand this question but i dont think i can remember when and what to ...
Rule is: if in front of the brackets there's a plus you remove the brackets and leave the signs as they are, otherwise you remove the brackets but change all the signs inside it
twilit knot
In nature/physics/maths, you will find difficult stuff
twilit knot
1 - (-1) = 2?
Yes
twilit knot
I have a (complex) proof but i think intuition is better
Imagine turning around
And turning around again
You're facing straight
They cancel out
drifting ridge
Rule is: if in front of the brackets there's a plus you remove the brackets and ...
7 + - 3 + -5 -10?
cedar kilnBOT
@drifting ridge Has your question been resolved?
rigid gulch
cedar kilnBOT
@rigid gulch Has your question been resolved?
weary vessel
Did you try to do it in rectangular coordinate system?
heady mountain
cedar kilnBOT
cedar kilnBOT
@heady mountain Has your question been resolved?
heady mountain
<@&286206848099549185>
torpid urchin
cedar kilnBOT
torpid urchin
is the most efficient way to check to rref the matrix
check rank(A)=n
im jw since its worth so little marks ):
actually obviously 1 is independant of 4, 2 is independant of 4, 4 is independant of 3, 1 is independant of 2, and then i can check 1 and 3?
slate lintel
annoyingly it's possible for three vectors to be independent in pairs but dependent together
rref is indeed fastest
as far as I know
stiff totem
annoyingly it's possible for three vectors to be independent in pairs but depend...
intuitively, this happens when the vectors are contained within a hyperplane
so pairwise, each vector adds a new dimension, but all together, they're still constrained into a subspace
torpid urchin
annoyingly it's possible for three vectors to be independent in pairs but depend...
oh right that is true
i was just looking at the signs and drawing conclusions based on that
but i guess when you have so many vectors you can make weird combinations
stuck in r3 lol
thank you
.close
calm bronze
i need help with how to get started with this question
cedar kilnBOT
i need help with how to get started with this question
stiff totem
you can find the vector from O to B by adding the OA to AB
the question then gives you the unit vector that has the same direction, so you can compare the i and j components of these vectors
calm bronze
Oh omg thanks ill try that
So when comparing do i include the root 17/ 34 bit or only what's inside the brackets?
stiff totem
include it
it's the same as $\frac{\sqrt{17}}{34}(3a+2)\mathbf{i}+\frac{\sqrt{17}}{34}b\mathbf{j}$
wraith daggerBOT
Desync
calm bronze
And then do i multiply the root 17/ 34 with the 3a + 2 or leave it as it is
calm bronze
So I added OA and AB to find OB
And now in tryna compare the unit vector of OB and the unit vector parallel to OB that is gives in the question
But I'm stuck with the comparing ig
stiff totem
right, so you want to find the unit vector of OB, right?
stiff totem
unit vector has unit length (length 1)
they point in the same direction
you have the direction vector OB from OA+AB, and the question gives you a scaled version of that same vector with length 1
so you can try scaling down your vector OB to have unit length as well
then that should be equal to the unit vector given in the question
calm bronze
How do I scale down
stiff totem
do you know how to find the length of a vector
calm bronze
No I don't think so not yet
calm bronze
Can you tell me how
stiff totem
yeah, sure
so, you have the components of the vector from O to B
in terms of i and j
calm bronze
Mhm
stiff totem
terrible drawing, but
you have a right angle triangle here
and you know the i-component and the j-component
you can use the pythagorean theorem to find the hypothenuse, which is the length of the vector OB
and you want the vector OB of length 1, so if you scale this vector by this 1 over this length, you get the unit vector you want (say it has, for example, length 20; if you scale it down by 1/20, then it has length 1)
calm bronze
So for OB which i got (b+4) i + bj
I do (b+4) squared plus b squared to get the c squared( and then square root to find hypotenuse)
stiff totem
yep, looks good
calm bronze
And then that's the length?
stiff totem
yeah
calm bronze
And then I do 1/ length to scale it down to length 1
stiff totem
yep
and that should be the same as the unit vector in the question
so you can then compare components
calm bronze
Ohh okay ill do that and get back to you, thankyouu
stiff totem
I just did this and I'm getting some pretty gross numbers, but it looks like it works out
stiff totem
what are you solving for?
we don't have an equation yet, we've just multiplied a vector by a scalar
unless you mean you've set
\begin{equation*}
\frac{\sqrt{17}}{34}\bigl((3a+2)\mathbf{i}+b\mathbf{j}\bigr)=\frac{1}{\sqrt{2b^2+8b+16}}\bigl((b+4)\mathbf{i}+b\mathbf{j}\bigr)
\end{equation*}
calm bronze
Ahh okay
wraith daggerBOT
Desync
stiff totem
then you just compare the i components and j components
I would first rewrite $\frac{\sqrt{17}}{34}$ to be $\frac{1}{2\sqrt{17}}$
wraith daggerBOT
Desync
stiff totem
makes the fractions out the front easier to compare
and also start with the j component, because they're a lot closer in form
calm bronze
Wdym by compare 🥲
stiff totem
they're the same vectors
so the i components must be equal
and the j components must be equal
calm bronze
Right right
stiff totem
so we have
\begin{equation*}
\frac{1}{2\sqrt{17}}b=\frac{1}{\sqrt{2b^2+8b+16}}b
\end{equation*}
for the j components
calm bronze
Ohh
wraith daggerBOT
Desync
stiff totem
that lets you find an explicit value for b
then sub it into the i component to find a value for a
calm bronze
Okay so i got b = 3.477 and then i jist sub that into the vector i got for OB ?
As in I got b + 4 i
So I do 3.477 + 4 ?
Or is that too simple lmao i feel like im missing sumn
stiff totem
**Desync**
I mean sub b into the i component of this
calm bronze
Oh yes the 1/ length
stiff totem
so you have
\begin{equation*}
\frac{1}{2\sqrt{17}}(3a+2)=\frac{1}{\sqrt{2b^2+8b+16}}(b+4)
\end{equation*}
wraith daggerBOT
Desync
calm bronze
Is it the same
stiff totem
I missed a b somewhere in my working, I'll run the numbers again
calm bronze
Ah okay
stiff totem
**Desync**
so just substitute that value of b into this
and solve for a
it also asks for an exact value, so I would use sqrt(30) - 2 rather than a decimal approximation
I get a = ||sqrt(10/3)||
cedar kilnBOT
@calm bronze Has your question been resolved?
calm bronze
Thankyouu sm
icy wyvern
i need help !?
cedar kilnBOT
i need help !?
hoary chasm
Pls don't use such EXPLICIT usernames
icy wyvern
sorry will change
hoary chasm
i need help !?
And just ask.
Don't ask to ask
icy wyvern
give me a momemnt to change my user
solemn torrent
pretty solid username
hoary chasm
pretty solid username
Excuse me sir!
flint plinth
i should not like to drink that cider
icy wyvern
alright we back
vestal bear
nice username
icy wyvern
hoary chasm
Whats wrong with the rest of u
hoary chasm
Whats ur attenpt
vestal bear
??
hoary chasm
Work
icy wyvern
wdym?
vestal bear
wheres the imaginary part
solemn torrent
prolly meant mixed fractions
tropic oxide
Pls don't use such EXPLICIT usernames
trust me 'penisapplecider' is mild
also
can everyone please stop clowning here
flint plinth
real numbers are perfectly valid complex numbers
vestal bear
Whats ur attenpt
^ shoqw work
tropic oxide
STOP CLOWNING @flint plinth
@icy wyvern do you have any progress on any of these four fraction problems?
icy wyvern
i have like zero clue on what to do i had a horrible algebra 2 teacher
icy wyvern
basically learning from scratch
tropic oxide
do you know how fractions work, in general
tropic oxide
okay
tropic oxide
so do you know how to add, subtract, multiply and divide fractions?
icy wyvern
yes
tropic oxide
ok
in that case, you should have no trouble working out $\frac{1 - \frac{1}{3}}{\frac{1}{2} - \frac{1}{6}}$
wraith daggerBOT
Ann
icy wyvern
yes first one is a breeze
i should be more specific on the ones i need help with
the ones i need help with are
2-4
sonic jewel
good effort penisapple
icy wyvern
yes
tropic oxide
$\frac{z - \frac{1}{z}}{1 - \frac{1}{z}}$
wraith daggerBOT
Ann
tropic oxide
there are a couple of different ways you could proceed here
in principle you could just treat z - 1/z and 1 - 1/z as ordinary fraction subtraction problems, work them out, and then do the division.
sonic jewel
u can multiple top and bottom by Z
tropic oxide
...or you could do that
sonic jewel
Yes.
tropic oxide
but lowercase z, not uppercase Z.
icy wyvern
what does multiplying by z do
sonic jewel
it makes it into a non complex fraction.
crimson sedge
are you able to write out in full the solution?
respond with one of:
(A) "Yes, I am able to do it. Give me some time to write it out, then I will ping you."
(B) "I am not sure whether or not I can do it. I will try, but I want you to check my steps partway."
(C) "I know for sure that I am NOT able to do it."
icy wyvern
between like b and c
crimson sedge
Ok. Wait
tropic oxide
are you able to write out in full the solution?
respond with one of:
(A) "Yes, ...
nice copypaste...
sonic jewel
nice copypaste...
i am very big fan of you
icy wyvern
ok so what would the equation turn into once i multiply by z?
sonic jewel
z^2 - 1 / z - 1
tropic oxide
this is an expression not an equation
tropic oxide
z^2 - 1 / z - 1
MISSING PARENTHESES!!!!!
wraith daggerBOT
Ryаn
sonic jewel
MY BAD GUYS
tropic oxide
(z^2 - 1)/(z - 1) is what it would become.
sonic jewel
MISSING PARENTHESES!!!!!
wdym.
tropic oxide
when you write \verb|z^2 - 1/z - 1| it reads not as $\frac{z^2-1}{z-1}$ but as $z^2 - \frac{1}{z} - 1$
wraith daggerBOT
Ann
solemn torrent
or some other brackets
sonic jewel
focus on the problem
tropic oxide
if you keep up this habit then eventually you will forget what you meant and confuse both yourself and the person you're helping
sonic jewel
But we must focus on the problem.
tropic oxide
and even still this issue needs addressing, and i'm not a fan of how you are doubling down.
sonic jewel
me too
$\frac{z^2-1}{z-1} = \frac{(Z-1)(z+1)}{(z-1)} = {Z+1}$
my bad i made a typo
crimson sedge
LGTM! 👍
tropic oxide
$\frac{z^2-1}{z-1} = \frac{(Z-1)(z+1)}{(z-1)} = {Z+1}$
you made two typos
one of them is pretty fatal
sonic jewel
yea.
tropic oxide
you can and should edit your message
sonic jewel
im not that good with computers
tropic oxide
to amend them BOTH, preferably.
sonic jewel
ok, thanks.
wraith daggerBOT
Ryаn
icy wyvern
proceed to the next please and thank you everyone
sonic jewel
no problem penis apple cider
icy wyvern
i don’t understand 3
hoary chasm
no problem penis apple cider
Excuse sir it's still an explicit or inappropriate term...pls refrain from referring to an individual in this manner
This is not your school friends server
sonic jewel
Excuse sir it's still an explicit or inappropriate term...pls refrain from refer...
i respect people's identities
hoary chasm
i respect people's identities
Yea call them david
sonic jewel
in question 3, mutliple the top and bottom by $x^2 y^2$
wraith daggerBOT
Ryаn
sonic jewel
Yea call them david
thanks my nibber
hoary chasm
thanks my nibber
Im nibberge
sonic jewel
it should become $\frac{y^2-x^2}{y^2+2xy+x^2}$
wraith daggerBOT
Ryаn
sonic jewel
Im nibberge
thanks my nibberge
icy wyvern
yes
hoary chasm
thanks my nibberge
You're welcome ryan7
sonic jewel
Im 7ryan
hoary chasm
You're welcome 7ryan
icy wyvern
i’ll try it myself and see if i get it right king
icy wyvern
ok idk
sonic jewel
$\frac{(y-x)(y+x)}{(y+x)^2} = \frac{y-x}{y+x}$
icy wyvern
wraith daggerBOT
Ryаn
sonic jewel
u just have to know
i mean u can kinda do this
$x^2 + xy + xy + y^2 = x(x+y) + y(x+y) = (x+y)(x+y)$
wraith daggerBOT
Ryаn
sonic jewel
multiply top and bottom by ab
icy wyvern
okay
sonic jewel
thank you ryan
no problem
icy wyvern
what would that turn into
sonic jewel
ab(a+b)/b-a
sonic jewel
that might be the answer
icy wyvern
answer key says it’s -ab
wraith daggerBOT
Ryаn
sonic jewel
and if u take out -1 from the bottom then u can cancel the brackets
icy wyvern
but you’re just left with ab? correct?
icy wyvern
i’m confused
sonic jewel
$ab(a-b)/-(a-b) = ab/-1 = -ab$
wraith daggerBOT
Ryаn
icy wyvern
where did the negative in the denominator come from
icy wyvern
how?
cedar kilnBOT
@icy wyvern Has your question been resolved?
icy wyvern
no
dire geode
.close
thin roost
cedar kilnBOT
thin roost
I've a solution which I'm finding hard to understand
Can anyone pls explain this part
Pls
solid juniper
all prime factors of n less than n are divisors of (n-1)!
thin roost
Hmmm
solid juniper
no integer greater than 1 can divide consecutive integers
sonic jewel
why then are they both squares though?
thin roost
Let's say n=15, n=3×5 so 3 and 5 divide 14!?
thin roost
,w 14!/3
wraith daggerBOT
thin roost
,w 14!/5
wraith daggerBOT
stiff totem
write out the definition of a factorial
thin roost
Nu e
solid juniper
why 👎🏻
thin roost
So, prime factor of less than n divide (n-1)! But not (n-1)!-1
solid juniper
yes
sonic jewel
@solid juniper can u explain why that means both n and (n-1)! - 1 are both squares
solid juniper
still thinking about that one lol
sonic jewel
gotcha
thin roost
But, how does that relate to (n-1)!-1 not having prime less than n
solid juniper
no integer greater than 1 can divide consecutive integers
this
oh it’s because n and (n-1)! -1 have disjoint prime factors and n((n-1)! - 1) is a square
for the next sentence
sonic jewel
ohhhhhh
sonic jewel
disjoint prime factors as in n's prime factors can only be at most n, while (n-1)! - 1 has none less than n
and also because k^2 is a square so they have to both be squares to satisfy?
solid juniper
Can you like provide an example...
3 divides 30 so 3 has no chance at dividing 29 because the multiples of 3 are too far apart
thin roost
So you basically mean if k | z => k doesn't divide z-1
thin roost
solid juniper
good on the first highlighted sentence yet?
thin roost
Still wondering why (n-1)!-1 can't have prime factor less than n
solid juniper
the prime factors of n less than n all divide (n-1)!
thin roost
I get that
solid juniper
So you basically mean if k | z => k doesn't divide z-1
by this they can’t also divide (n-1)! - 1
thin roost
Yes I also get that
solid juniper
Still wondering why (n-1)!-1 can't have prime factor less than n
soooo what’s the issue haha
thin roost
So, is it like.... let's say a number 17.... 17 is a prime so atmost the the prime factorization contains 17 in it it can't contain > 17.... so is it same for the (n-1)!-1 is also?
Since (n-1)!-1 < n!
solid juniper
17 has no prime factors less than 17
oh k i see what you mean now maybe
it’s still just… what i’ve been saying all along though
thin roost
P is a prime factor of n, p < n p | (n-1)! And p doesn't divide (n-1)!-1
This is all I get
solid juniper
that’s literally all you need to get
thin roost
But why does p doesn't divide (n-1)!-1 imply (n-1)!-1 has no prime factor less than n...
Wait
I get it now
OK kul
solid juniper
lol ok
solid juniper
solid juniper
let’s say a and b are integers and ab = k^2 for some k
thin roost
Yes
solid juniper
furthermore, a and b share no prime factors
solid juniper
a number is a square iff the powers of all the primes in its prime factorization are even
solid juniper
so both a and b need to have that property for ab to be square
thin roost
Yes
Since they don't have common prime
They have to have even power
a should also have even power
B should also have even power
Right?
solid juniper
the primes in each of their factorizations, yes
thin roost
Yes
How does (n-1)! Is divisible by 4 for n >3
We see that if n=4,(n-1)! =3! Which is clearly not div by 4
solid juniper
less than n
thin roost
?
solid juniper
4 also not prime
solid juniper
How does (n-1)! Is divisible by 4 for n >3
We see that if n=4,(n-1)! =3! Which ...
what are you trying to point out here?
solid juniper
oh lol
thin roost
Says, (n-1)! Should be div by 4
solid juniper
yea
thin roost
How did they conclude 3 mod 4
solid juniper
(n-1)! = 0 mod 4 for n>4
solid juniper
yea
thin roost
So for, n>4 there is no sols
solid juniper
yep
solid juniper
haha sure thing
thin roost
Have a good day/night
solid juniper
you too
harsh garden
Hii
harsh garden
Same goes there with the other side?
native cosmos
In the image, it demonstrates solving for x by saying x^(-1) = u.
By solving for u, you are solving for x^(-1)
And since x^(-1) = 1/x, it is the reciprocal value of x
harsh garden
Okay okay like -3/4 become -4/3
calm helm
is 0.999999999=1
cedar kilnBOT
is 0.999999999=1
south tundra
is 0.999999999=1
0.999999999 no, but 0.9 repeating yes
calm helm
what
vestal bear
0.9 repeating is infinite 9s
calm helm
wait no
south tundra
Yeah, what about it
calm helm
isnt it 1
south tundra
Yes, 0.9 repeating is indeed 1
calm helm
is it exactly 1
south tundra
Yes, no higher no lower
calm helm
my friend says its infinetly closer to one but not actually 1
south tundra
That's when you write finitely many 9's
pliant valley
its just approaching one
but never is 1
think of asymptotes for a visual representation
south tundra
Yeah, introduce yourself to the notion of limits and you may understand what your friend meant
pliant valley
no
south tundra
In uni
vestal bear
after uni?
calm helm
after high school
south tundra
First year calc
pliant valley
its high school too
vestal bear
people don't do limits in highschool? 
calm helm
we do
south tundra
people don't do limits in highschool? <:blobsweat:584506239661113371>
Some do and some don't
calm helm
is 0.999999999=1
howabout this though