8?
#help-0
cyan token
thorny iris
Basically you need to make a 5 letter word
You have 5 slots
There are no repeating letters
So in the first slot you have 8 possible letters
After you use that letter you now only have 7
After you use one letter there you only have 6
And it goes on till 5 letters are used
8x7x6x5x4
Because no repeating is allowed
You only have 3 letters left which you can’t make a word with
Because it’s a 5 Letter word
cyan token
except if its 8! then isnt that combinations, not words
they need to be real words not just random combos
thorny iris
Combinations is when order does not matter
In this case you have to arrange the words a certain way
So it’s permutations
It’s not like explicitly finding the amount of words
Is this a textbook problem? Like do you have the answer to it?
cyan token
the question: From the letters in the word "Numeracy" how many 5 letter 'word' arrangements can be made?
yes I do, but I don't want to look at the answer key just yet
thorny iris
Yeah the answer should be 8x7x6x5x4
They shouldn’t expect you to know every word in the dictionary to answer, most likely the answer to the question is not factually accurate
The amount of words there really are for 5 letter arrangements of numeracy is probably not what your textbook will have the answer as
But if it is then I got no clue how
cyan token
I think your approach is the most logical, it seems unreasonable for math to expect a student to know every obscure word
thorny iris
Yeah that’s what I would think
cyan token
Do you know what the exact numerical value is if you don't mind?
thorny iris
6720
cyan token
yeah you got it right congrats
thorny iris
Yeah but in actuality there probably isn’t 6720 word arrangements lol
cyan token
scrabble says 22
alpine sable
can someone walk me thru this one
cyan token
put it through mathway
manic quail
you can multiply the exponents.
manic quail
you get 2^6 in the denominator
manic quail
and 2^(-3)* something^(-4*-3) in the numerator
you multiply the exponent of the denominator with the exponent of the outside
ionic jewel
put it through mathway
not only does this not help him, mathway is an inferior program
spiral bloom
In a normal distribution where µ = 100 & σ = 12, what's the probability that a random outcome exceeds 124?
<@&286206848099549185>
thorny iris
In a normal distribution where µ = 100 & σ = 12, what's the probability that a r...
124 is the x value, use that to find your z score, than get the area of the z score, and subtract that from 1 to get the probability
serene moon
alpine sable
that's simple, no? you just do a(x-1)(x-1) which is exactly 1 root
misty vigil
umm
alpine sable
(because if you dupe a root you basically have one root no?)
alpine sable
Do you know what's a factored form in a quadratic equation?
misty vigil
ya, so our teacher doesn't give us formulas like that, rn all we have is
ax^2+bx+c=0
@alpine sable ?
alpine sable
<@456226577798135808> ?
I'm currently searching if my method is wrong and/or trying to adapt it.
misty vigil
ah
all good
ya
but do you square both x and three on the other side
or just x
both no?
i get x=14
manic quail
Forget what I said, I am a moron. Isn't as nice as I thought xD
alpine sable
,w plot y=x^2
misty vigil
but answer key says 7
ocean sealBOT
alpine sable
isnt this one root
alpine sable
isnt this one root
yes
misty vigil
what does this even mean?
we don't use graphing for this
at least not yet
wait im wrong
alpine sable
u could use quadratic formula to verify it if u want
alpine sable
at least not yet
ok, draw a graph with your formula but it's f(x) = 1x²+0x+0
alpine sable
or any other method to get zeros
misty vigil
ok, draw a graph with your formula but it's f(x) = 1x²+0x+0
no idea how to graph that
alpine sable
no idea how to graph that
when x is 0, it'll hit the x-axis right?
ocean sealBOT
misty vigil
ah
smart
i wish there was an answer in the answer key for that one
but google docs is dumb
alpine sable
it's ok I'm in pre calc too
misty vigil
so f(x) = 1(0)+0x+0
this seems complex
alpine sable
it's 1x²+0x+0
misty vigil
oh
alpine sable
f(x) is basically y
sinful flare
Anyone can help me with Vector Analysis here?
misty vigil
isn't that physics?
alpine sable
(AKA: function of x which means wtf is y when x is whatever)
slow cargo
misty vigil
Anyone can help me with Vector Analysis here?
^]
alpine sable
isn't that physics?
no, that's just a math function.
misty vigil
oh we did vectors in physics
sinful flare
misty vigil
this is getting cluttered
sinful flare
Im having a hard time figuring 10-12
sinful flare
Sorry, I'm a little desperate.
misty vigil
ok
misty vigil
(AKA: function of x which means wtf is y when x is whatever)
lol
what is the answer to a
I get 14
which is wrong
alpine sable
i get -x²-x+14=0
yeah
alpine sable
by inspection 7 is a solution to a
sinful flare
Anyone got any ideas how to go about my problems?
manic quail
@slow cargo , you already had the right idea. Here, I plotted the first one for you.
The overlap of the areas represents the solutions.
ocean sealBOT
Chai T. Rex
native remnant
100a +10b + c = 47 ( a + b + c)
ocean sealBOT
Chai T. Rex
native remnant
im confused on this part
oak chasm
Well, it says the tens digit is half the hundreds, right?
native remnant
yeah
ocean sealBOT
Chai T. Rex
native remnant
b = 0.5a
oak chasm
Right. Now, do that for the specified relationship between the tens and the unit.
native remnant
b = c - 1
ocean sealBOT
Chai T. Rex
native remnant
so like 100a turns into 50b
native remnant
a = 2b
ocean sealBOT
Chai T. Rex
native remnant
c = b + 1
ocean sealBOT
Chai T. Rex
native remnant
200b + 10b + b + 1 = 47(2b + b + b + 1)
native remnant
so b = 2
oak chasm
,w 200b + 10b + b + 1 = 47(2b + b + b + 1)
ocean sealBOT
oak chasm
Right.
ocean sealBOT
Chai T. Rex
oak chasm
What's the number?
native remnant
423?
oak chasm
,w 423 = 47(4 + 2 + 3)
ocean sealBOT
oak chasm
Looks good.
native remnant
thank you
oak chasm
You're welcome.
cyan token
Question: In the word “Numeracy” how many 5 letter “word” arrangements can be made if it must start or end with a vowel?
alpine sable
what is a 5 letter "word" arrangement in a word?
cyan token
Disregard that, it’s redundant.
alpine sable
no really, i dont know exactly what it means lol
cyan token
It has to be 5 letters, and must either start or end with a vowel
alpine sable
,w 560 = 57 (5 + 6 + 0)
ocean sealBOT
alpine sable
How many possibilities are there for a vowel?
thorny iris
Basically you have 5 slots still. But now the first and last slots are only vowels. This question deals with addition since “or”. In numeracy there are a e u (3 vowels). So the first case is 3 x 5 x 4 x 3 x 2 and then the second case is 5x4x3x2x3
You get the 5 from subtracting 3 from 8 (since after you use a vowel you can’t use it again)
So then just add the two cases (first case where it starts with vowel, 2nd case where it ends with vowel)
alpine sable
,w 560=56 (5+6+0)
ocean sealBOT
alpine sable
Shouldnt it be 7 slots after you use 1 vowel?
cyan token
Thank you. I just didn’t think it made sense because that’s the exact same number as if it was to start AND end with a vowel
alpine sable
,w 423 =47(4 + 2 + 3)
ocean sealBOT
alpine sable
,w 6×6×5×4=720
ocean sealBOT
cyan token
Yes.
oak chasm
No, click the blue link to go there.
cyan token
@thorny iris what would you do if the question asked for all the vowels to be together then?
ocean sealBOT
thorny iris
If all the vowels had to be together in the word?
Like in one word together
It would be 1x1x1x5x4
but then you need to group and arrange
cyan token
Yeah like all the vowels had to be together all 3 of them
thorny iris
It would be !3x3!
You have 3 groups
5, 4, and the 3 vowels
And then you need to arrange 3, as the vowels can be together, but order is not specified
alpine sable
3×3=9
thorny iris
Yeah so each vowel gets one spot, and then there is 2 slots remaining
Within those two slots are non vowels
alpine sable
,w 56.8³×4=
thorny iris
You have 5 non vowels left so you put them there
cyan token
Last question: What about the number of arrangements that can be made with the letter “y”?
That are also 5 letters
I assume theres more
alpine sable
thorny iris
So there is only 1 Y
cyan token
Yeah there aren’t any repeats
alpine sable
,w av
cyan token
@alpine sable what are u doing
ocean sealBOT
thorny iris
So you need to find what it is with one Y in the word, then multiply by 5
Basically right, Y could be anywhere in the word
But it can only be in 5 spots
cyan token
Yeah
alpine sable
<@456226577798135808> what are u doing
What do u mean
thorny iris
So if you find what the value is when it’s in any spot
And multiply it by 5
That’s your total amount
cyan token
Much appreciated
thorny iris
Np
winged vine
Anybody know what i need to do here
alpine sable
,w 90¹+56-6=
ocean sealBOT
winged vine
?
alpine sable
,w 3x+4×2 2×-3×2=
ocean sealBOT
alpine sable
Anybody know what i need to do here
winged vine
I still don’t get that
ocean sealBOT
alpine sable
I still don’t get that
-288
alpine sable
Negative 288
alpine sable
What grade r u in
winged vine
I know
That it’s easy just don’t even know where do I start
There’s nothing on google
cyan token
@hardy geyser use ratios
winged vine
Your correct
alpine sable
That it’s easy just don’t even know where do I start
The answer is 28
cyan token
Actually looking at the question, that’s the right answer
hardy geyser
@cyan token I know but I guessed
winged vine
The answer is 28
What were you got that 28 from
alpine sable
Easy
winged vine
How you solved it
alpine sable
What were you got that 28 from
Add and subtract
winged vine
But it dosent tell me what the variable is equal to so how you took out the x
alpine sable
How you solved it
Add subtract
winged vine
But there not equal so you can’t use that methot of
winged vine
The x is a variable
winged vine
Who you talking too
alpine sable
U
fading delta
can someone help me?
cyan token
@fading delta yes
alpine sable
There no multiple choice in my question
I know but witch one is it
fading delta
yes
alpine sable
Do u think it's 16 or 28
winged vine
cyan token
It’s 4 @fading delta
fading delta
thankyou
alpine sable
Somebody help @winged vine
winged vine
Yeah
winged vine
Yeah
winged vine
Ohhh that’s all
alpine sable
Solve for the area?
That's exactly what I was saying to the boy but he is not listening
cyan token
We all learn at difference paces : )
alpine sable
True
winged vine
So it’s 6x-12
winged vine
You add them or multiply them
winged vine
Cuz it will be 5x+1
alpine sable
I believe u multiple
alpine sable
12 24 36 48 60 72
winged vine
I put the x as 3 and solved it and then it didn’t give me the same thou
alpine sable
Ok now I’m confused again
That's okay
gray isle
sum and product of roots would be the simplest way
also you've messed up your copmplex conjugate
-1 + sqrt(3)i is not the complex conjugate of 1 + sqrt(3)i
,w expand (x - (1+ sqrt(3)i))(x - (-1+ sqrt(3)i))
ocean sealBOT
gray isle
results in stuff with i which isn't what you want
first fix your other root first
and then like i said
sum and product of roots would be the simplest way
you could expand and distribute if you want but it can get a bid tedious with all those terms
carmine lion
is this channel free
gray isle
no
carmine lion
alright
gray isle
the complex conjugate of
a + bi is
a - bi
whut?
why are you square rooting the i?
the complex conjugate of
a + bi is
a - bi
oak chasm
@mint swallow You change the sign of the part with i in it.
gray isle
change the sign being multiplied to the term with i from pos to neg or neg to positive
the complex conjugate of $\red{a} + \blue{b}i$ is $\red{a} - \blue{b}i$ \
for your question you have: $\red{1} + \blue{\sqrt{3}}i$
gray isle
no
what's your other complex root?
you really need to identify that first before you're able to move on
reread the tex i made above
and really try NOT to overthink it
do you understand the first line i wrote?
and the difference between
a + bi and a - bi
no
we still haven't even reached that point yet
$\red{a} + \blue{b}i$ and $\red{a} - \blue{b}i$ are complex conjugates.
can you identify the difference between them?
ocean sealBOT
ℝamonov
gray isle
for your question you have: $\red{1} + \blue{\sqrt{3}}i$ \
similarly what would be the complex conjugate of that? \
(which will be your other root)
ocean sealBOT
ℝamonov
quick token
how do you find the surface area of a rectangular prism
charred flint
whats the question
winter bay
charred flint
😓
gray isle
the explanation for the complex conjugate has been typed like 5 times already
charred flint
oh
gray isle
what exactly don't you still understand about it
i've even inserted colours
to try and make it more clear
you've also even identified the difference when i prompted you
ocean sealBOT
NDY
gray isle
no you're jumping ahead again
and still not doing it properly
forget about x
completely
worry only about getting the complex conjugate nothing else
the complex conjugate of $\red{a} + \blue{b}i$ is $\red{a} - \blue{b}i$ \
$\red{a} + \blue{b}i$ and $\red{a} - \blue{b}i$ are complex conjugates.
ocean sealBOT
ℝamonov
gray isle
do you understand that? yes/no?
edgy wharf
gray isle
well that's the definition of the complex conjugate
as mentioned/implied multiple times by multiple people
to get the complex conjugate, you change the sign in front of the imaginary term form pos to neg (or from neg to pos)
ocean sealBOT
NDY
gray isle
not the issue here
though the difference of two squares is the reasoning behind why conjugate root theorem is applied to get a polynomial with real coefficients
this is purely about getting the actual conjugate nothing else
$\red{a} \underbrace{+}_{\text{to get the complex conjugate, change this to a -}} \blue{b}i$
ocean sealBOT
ℝamonov
gray isle
alternatively if you have: \
$\red{a} \underbrace{-}_{\text{to get the complex conjugate, change this to a +}} \blue{b}i$
ocean sealBOT
ℝamonov
ocean sealBOT
NDY
gray isle
no
stop fking skipping ahead
because it's pointless if you don't get the first step correct
if by IT you mean the sign being applied the the part with i
yes, you change that to get the complex conjugate
you really shouldn't be overthinking this
ocean sealBOT
NDY
gray isle
no
stop fking skipping ahead
because it's pointless if you don't get the first step correct
forget about x
at this point completely ignore that variable or any other part of the question
no
not even that
focus only on finding the complex conjugate of
1 + sqrt(3)i
currently I'm only after the very FIRST step ONLY nothing else
the complex conjugate of
1 + sqrt(3)i is:
and the complex conjugate is the only thing I want to see.
no extra crap
no skipping ahead
no xs
ocean sealBOT
NDY
gray isle
i mean still fkn skipping ahead...
but apart from the missing parentheses at the end
you actually did it properly
your complex roots are
1 + sqrt(3)i and 1 - sqrt(3)i
and to expand the above, you could distribute but that can get tedious
alternatively you can use the sum and product of roots which will make this a lot simpler
ocean sealBOT
NDY
gray isle
(x - p)(x-q) = x^2 - (p + q)x + pq
the value of (p + q) should be very easy to obtain
and pq will just the difference of two squares
also wait
since i was a bit pissed
i overlooked where your square roots were
ocean sealBOT
NDY
gray isle
the radical shouldn't extend over the i
wdym by key
sqrt(3) is just a number
wdym
as stated multiple times
conjugate root theorem
and definitiion of the complex conjugate
by DEFINITION, the COMPLEX CONJUGATE of a + bi is a - bi
by (complex) conjugate root for your polynomial to have real coefficients,
if a + bi is a root, a - bi will also be a root
here you are told that
1 + sqrt(3)i is a root
and by that theorem (conjugate root theorem)
1 - sqrt(3)i will also be a root
(since if you were to compare 1 + sqrt(3)i to a + bi the a=1 and b=sqrt(3)),
does that make sense so far?
yes. as stated almost 10+ times already, those are complex conjugates
and for the past two hours that was literally all i wanted you to apply
regardless, does everything that I've just typed make sense so far?
ok.
now you wanted to expand your factors with complex roots
$$(x - (1 + \sqrt{3}i))(x - (1 - \sqrt{3}i))$$
ocean sealBOT
ℝamonov
gray isle
expanding normally can be a bit tedious, so you can consider the sum and product of roots
consider:
$$(x-p)(x-q) = x^2 - (p+q)x + pq$$
where:
$$p =1 + \sqrt{3}i$$
$$q =1 - \sqrt{3}i$$
ocean sealBOT
ℝamonov
gray isle
yes, but its more tedious
what i just wrote
instead of manually expanding
(x - (1 + \sqrt{3}i))(x - (1 - \sqrt{3}i))
consider what happens when you expand
(x-p)(x-q)
then consider the values of your roots
their sums and products are relatively easy the calculate
ocean sealBOT
NDY
gray isle
yes
(x+5)(x - (1+ sqrt(3)i))(x - (1- sqrt(3)i)) does indeed expand to that
though you should consider a scaling factor (to be determined using f(-2) = 36)
outer plaza
i have this question quys
how do i work it out?
could someone message me privately
yeah totally doing a test while in discord...
i live in Australia, our classes are in person lol
im so confused
what?
anyway
i mean i didnt know helping with studying was cheating
gray isle
be more civil
outer plaza
but i guess this is the wrong place then
tame shell
don't use sarcasm wrt cheating
people will 100% take it the wrong way
as people who do attend in person classes still cheat @outer plaza
outer plaza
idk how this goes in the US or wherever you guys are from
our teachers take our phones before our exam
and we put our bags at the front of the room
tame shell
lol I wish they did that
gray isle
some places do tests online and it may be hard to confirm that
there are concerns when people specifically request for stuff to be dealt in dms immediately
tame shell
yeah
outer plaza
i want it in DMs because i wanted to be walked through it
and not clog up this channel
gray isle
so if you want help you should be able to get it within this server, there are plenty of free channels to use, that's what they're for
outer plaza
i literally wanted to ask questions and go over some stuff in details because i just dont get it. I have used the Python Discord and The Cisco discord to great success with many helpful people hopping in chats with me sharing their screen and walking me through some stuff i just dont understand. i understand i have more leeway in those discords as ive been in them for a while, and i just entered this one.
However its definitely not very welcoming when the first people you have messaging you are people like NDY, Why tf would i feel comfortable in this server when i have people accusing me of doing things from my very first msg
sly mantle
@mint swallow can stand to soften their tone toward other users, even users who they think are breaking server rules. heads up however @outer plaza this server takes academic honesty very seriously, and as per universal laws of online chats, if there's potential for sarcasm to be taken seriously, it WILL be taken seriously by someone
alpine sable
lost geyser
so like what is 'area bounded' even asking for then
im not quite sure
this is riemann sums, should i just find the area for each rectangle without the formula
is that what its asking essentially?
gray isle
yes
lost geyser
i see.
gray isle
pretty much
lost geyser
so how would i find the are abounded then
gray isle
have you drawn a pic?
lost geyser
yep
jagged imp
huh no not rectangles, think triangle
gray isle
the question you posted doesn't really involve reimann sums
lost geyser
iinteresting
because the question i posted is relating to riemann sums, let me show you the previous question
wicked ember
yes but
gray isle
regardless the part you posted does not
gray isle
the full region will be a simple trapezium
wicked ember
here it’s clear to see you can find the exact area
just with area of trapezium
or trapezoid if that’s what you call it
lost geyser
okay wait i think im understanding it
so take out the rectangles, find the area between the x axis and the line that was given
but on the intervals 1, 4
wicked ember
no here don’t use rectangles
again they gave “using basic geometry”
no Riemann sums
lost geyser
yeah i said throw the rectangles away, i outlined the part in red, im just finding the area for that?
or am i completely misinterpreting this
gray isle
assuming those boundaries are at x=1 and x=4, that's pretty much it
lost geyser
ah okay, they are
gray isle
lost geyser
yep yep i understand that now
have you found a solution for it?
the answer i worked out to is 30, not sure if thats correct
disregard my 30
24 was my new answer
gray isle
neither is what i'm getting
gray isle
you should probably label the lengths of the sides you're actually using.
i suspect you made an error with the length of the edge that's at the x-axis
gray isle
i suspect you made an error with the length of the edge that's at the x-axis
lost geyser
oh my god
gray isle
🙂
lost geyser
21?
gray isle
no
gray isle
show work and reasoning when you do
obsidian plover
e has to be 40 due to 360-220=140, and ae and ec are tangents so arc ac and aec have to be supplementary
gray isle
yes
though you should really be using capitals
and clearly mention that
360-220=140 gets you the measure of arc AC
obsidian plover
alright
safe bison
Hi,
I've got this problem
u < 4 / u-3
What's shown as the correct way to do this is
u - 4 / u-3 < 0
(u^2 - 3u - 4 )/u-3 < 0
(u-4)(u+1)/u-3 < 0
But if I tried it this way
u < 4 / u-3
u (u-3) < 4
u^2 - 3u - 4 < 0
(u-4)(u+1) < 0
the denominator is just straight up gone, what went wrong here?
gray isle
um...
do you have a pic of the work?
it feels like there's a gross disregard for parentheses
that makes it near impossible for me to follow
tight locust
@safe bison nothing is wrong
both are correct lines of reasoning
the first one is just missing an extra step
(u-4)(u+1)/u-3 <= 0, so (u-4)(u+1) <= 0
the difference being that u cannot be 3
which you should account for
gray isle
is that u-3 supposed to be part of the denominator?
if yes, you really should be writing (u-3)
tight locust
it's pretty obvious if you look it for a sec
gray isle
spacing is not a substitute
spacing means nothing to me
anyway the second method is wrong (without proper justification)
tight locust
right because you'd have to split into cases
gray isle
since it is unclear what the sign of (u-3) is, you can't just assume that its positive and that the direction of the inequality won't be affected
and you'd have to explicitly state the extra work that's going to be involved which is a pain
gray isle
i mean you could use $\overset{?}{=}$ to indicate something to be determined
ocean sealBOT
ℝamonov
gray isle
which could be used to do some proofs or ultimately disprove something
alpine sable
how do i find the 50 degrees on the top left?
i'm supposed to use it to create a vector triangle and solve for $V_a$
ocean sealBOT
MyMethLab
alpine sable
safe bison
the difference being that u cannot be 3
thank you so much ❤️
ocean sealBOT
alpine sable
<@&286206848099549185> sorry for ping I gtg to school
ocean sealBOT
lost geyser
question e, included question b in reference
vale wigeon
f(x)=x^2+1 is a parabola, so the region whose area you get is not a polygon nor is it made of polygons and circles
lost geyser
that makes sense
timber geyser
i need help with part of a question, im trying to find the area of the triangle FOC, i used the formula 1/2xbxh cus its a right angle but in the MS they used 1/2absinC, and there answer came out different to mine. why cant i use 1/2bxh for this?
half lotus
i need help with ti82 calculator
idk how to use the lim function and cant find anything online
like lim x -> infinite
how do i input this into calc
timber geyser
@half lotus plz get free channel
olive vale
i need help with part of a question, im trying to find the area of the triangle ...
Why not? You can find FC to be $r/\tan (\theta)$. And the area of FOC is then $\frac{1}{2}\frac{r^2}{\tan(\theta)}$
ocean sealBOT
morpheus
timber geyser
im not sure what you mean, is my method correct?
olive vale
yeah you can very well use 1/2 bh
What's the answer you got and what's the answer they got?
vestal hawk
guys how to express a sine and cosine wave as a single sine wave?
timber geyser
@olive vale i did 1/2 x4x12 to get 24
the value for r is given as 4 and the raidius CA is 12, theta is given as pi/6
olive vale
area of FOC is 1/2 (OF)(FC) and not 1/2(OF)(AC) like you seem to have done
ocean sealBOT
morpheus
olive vale
no worries
tiny field
Decide the equation for the tan in the points which (picture) cuts (y=x+1)
How should i proceed with this one, im supposed to use derivates
dense mirage
Anyone?
wicked ember
Anyone?
uh since delta E is in absolute value it should be positive I think
and both h and c are positive
zealous igloo
try to use quadratic equations
You responding to my question?
dense mirage
and both h and c are positive
?
wicked ember
?
hc / |E| is positive
because h is positive
c is positive
and |E| is always positive whether or not E is negative or positive
I mean they can be 0 but they aren’t
zealous igloo
try to use quadratic equations
How so?
wicked ember
look at the picture I drew just now
try to come up with quadratic equations
or if you want
you can have a circle as well
it really depends on what you want
just need to find two non linear equations
wicked ember
no
basically
E is negative
however
since it’s in an absolute value
|E| is positive
dense mirage
Wdym bby absolutely value
wicked ember
|x| means the absolute value of x
or in order words
the magnitude of x
basically it’s x if x>=0
and -x if x < 0
zealous igloo
Also my bad for interrupting
wicked ember
it’s fine
upper yarrow
anyone know the proof of this?
pale cargo
dense mirage
@wicked ember so if it has | | around it and it's negative it's basically positive?
wicked ember
yep
daring chasm
it's a bit more wonky than that with complex numbers, but otherwise yeah
alpine sable
How do I answer this?
ok thanks
Proposition
Conditional and Biconditional
discrete math
shell widget
@alpine sable you cant think of anything?
shell widget
Okay so i'll do the first one
alpine sable
A false implication with a false conclusion.
My Answer: John did not do his homework, therefore he will fail his grade?
It doesn't provide me anything 😦
I did that that as well
shell widget
we cant say anything about that implication
shell widget
Listen
alpine sable
my classmates did explain this but it did not give "example"
explain like that's the answer
alpine sable
but mine is different?
shell widget
first answer mine
alpine sable
Do you know that?
A little bit honest to goodness
from what I understand false implication is p is 0 and false conclusion is q is 0 meaning p implies q 0 0 1
alpine sable
Propositions
shell widget
@novel field Please leave if u cannot help
vale wigeon
can i see the original problem/question/whatever
shell widget
vale wigeon
@terse iron channel busy please move
terse iron
my bad
vale wigeon
P->Q is false if and only if P=1 and Q=0
otherwise its true
this lets us eliminate some of these points as impossible
alpine sable
<@!332360486207225856> Please leave if u cannot help
So did I do right? I don't understand why some of my classmates have different results of the answer I'm confused.
alpine sable
O.O
vale wigeon
for an implication to be false you need a true hypothesis and a false conclusion
alpine sable
for an implication to be false you need a true hypothesis and a false conclusion
Ok ok I'm beginning to understand
Wait so is it just like this then?
vale wigeon
do you want me to go through each of the other five things and give an example for each
just like what
alpine sable
do you want me to go through each of the other five things and give an example f...
Do 1,3,5
vale wigeon
1, 3 and 5. ok
alpine sable
I'm an odd number my homework
alpine sable
just like what
A false implication with a false conclusion.
My Answer: John did not do his homework, therefore he will fail his grade?
vale wigeon
that's number 1
alpine sable
So wait it is correct?
vale wigeon
and i'd say "if john doesnt do his homework he will fail his grade"
and under the assumptions that john actually DOES do his homework and actually passed his grade
this will be suitable for number 1
alpine sable
A false implication with a false conclusion.
My classmates answer: "The whole explanation of this"
vale wigeon
lmfao
alpine sable
and under the assumptions that john actually DOES do his homework and actually p...
wait how
alpine sable
ok
alpine sable
XD
alpine sable
A false implication with a false conclusion.
My Answer: John did not do his home...
my classmates said that this is wrong but all the sentence I made is p = 0 and q = 0
vale wigeon
"john didnt do his homework" need not be false
like
we dont actually know if this john person did or didnt do their homework yknow
wicked ember
if you did the calculation right yes
dense mirage
I think I did
visual stream
is there a question being asked
desert comet
vale wigeon
have you ever completed the square before?
visual stream
divide everything by 6?
vale wigeon
yup
visual stream
yeah i tried that and something went wrong in the middle lol
manic glade
weird question but whats the english term for placing something in a formula
visual stream
substitution?
visual stream
yeah subsitution
manic glade
alright thanks
pretty annoying we learn math using the local language instead of at the very least english if not proper formal logic
alpine sable
@vale wigeon Are you available to help? 😅
vale wigeon
i dont think i am, sorry
i keep getting tongue-tied every time i try to do that proposition shit
alpine sable
i dont think i am, sorry
it's ok
Ok I don't understand tongue tied? 😅
u got this
vale wigeon
is * a group operation?
alpine sable
multiplying on the right by a constant is a function
manic glade
a simpler explanation maybe? we didnt get to functions yet
vale wigeon
you multiplied by b^-1 on both sides
manic glade
yeah but why is that something i can do in general, is there some fancy term for that?
if x=y why is x+3=y+3
alpine sable
x=y means intuitively that x is the same thing as y
ìf you add 3 to the same thing you get the same result right
ie 1=1 and 1+3=1+3
manic glade
so nothing fancy like "associative/commutative" ?
vale wigeon
is there really a need to be fancy 
manic glade
no idea ^^
alpine sable
the reason is because its a function.. but you said you dont know that
manic glade
alright, and i can just describe it as multiplying despite the operation being nondefined?
alpine sable
its just a name
pulsar willow
Can anyone tell me if this is wrong solution
The 2^(x+4) in original equation is 2^(x+2) on the Note that lines
alpine sable
check the values they get back in original equation
pulsar willow
Yes it doesn't match up the x value, it must've been wrong. Thank you
vale wigeon
Because of + in equation, it is not useful to take log of both sides.
remove this, this line is entirely unnecessarsy
also yeah 2^(x+4) vs 2^(x+2)
worn jetty
Quick linear algebra question
So I have a nilpotent endomorphism of a vector space E with a nilpotence indice of p
(in other words : f^p = 0 and f^(p-1) != 0 )
plain lion
Can someone help me?
worn jetty
we are tasked to show that if rank(f) = n-1 (where n = dimE) then for all k in {0,..,n} ; dim Kerf^k = k
but no matter how I look at it it just feels wrong
because clearly dim Ker f^p = n, but p doesn't necessarily equal n
yes, so my question is.. if the rank of a nilpotent linear application is n-1
does it imply that the nilpotency index is n ?
if not, what would a good counter example be ?
alpine sable
i think its true actually, if you look at jordan form all superdiagonal entries will be 1
worn jetty
hmm.. I'll look into it more
but interestingly
I was searching on google for something similar
and I found a pdf
that our maths professor ripped
for this homework problem
: )
and it stated that p = n
: )))))
and it asked to show that rank(f) = n - 1
then this question
so yeah...
alpine sable
i tried to construct counterexample but run into trounle cuz
since the rank is n-1
at each step only one dimension goes to null
and if you mapped more than one dimension to that one
then rank would automatically decrease more
worn jetty
Hmm
I see
give me like.. 10 minutes
If I come up with some counter example I'll share it here with you, I'll try working through it again
thanks for your time though ! I appreciate it a lot :3
alpine sable
due to Jordan form it should be impossible tho, if you know jordan
i think could convert my argument to proof but am lazy lol
worn jetty
haven't actually studied it in class yet but I worked through problems with it
haha, I get that !
alpine sable
Well, what does it mean for two lines to be perpendicular?
ebon cliff
like lines which aren't vertical intersect and form a right angle
alpine sable
what does it mean for two lines to form a right angle?
ebon cliff
The lines are perpendicular
alpine sable
i have no idea what you mean by that
alpine sable
dot product of vectors
jagged imp
i feel like this is probably supposed to be done with the fact that 2 lines are perpendicular iff the product of their slopes is -1
alpine sable
oh that would make sense 111..
ebon cliff
and work frmo there
alpine sable
drawing is not a proof
ebon cliff
ok
alpine sable
but i guess you could do that
ebon cliff
it would take too long wouldn't it because we would have to grpah each line
and we are meant to do questions like these in 30 secs in the exam
alpine sable
did you learn about slopes
ripe ginkgo
Got a linear system with a sparse matrix, the spy/sparsity plot of A looks like this:
b and x are fully dense
any good ways to factorise/solve a system with this sparsity pattern?
similar matrix generated for the problem with n=5 (first matrix is for n=250)
alpine sable
I have a few questions, 38 and 39 that I need help with. I'm not too sure how to do them, as we were never taught how
It's integration, but I just don't know the method. Any ideas?
alpine sable
yeah
i integrate, then what?
What is the point of them giving me y and x values?
Because, I checked the answers at the back of the textbook and I got a different result from just integrating and leaving at that compared to what they did
And they don't have worked solutions
indigo jetty
so what do you get when you integrate 3x^2 - 1?
alpine sable
x^3 - x
indigo jetty
you are missing a term
alpine sable
oh yeah + C
indigo jetty
yes
alpine sable
x^3 - x + C
indigo jetty
yes
alpine sable
thank you
indigo jetty
and that will be the answer
alpine sable
What does In mean In matrix?
glass lichen
What does In mean In matrix?
Context?
alpine sable
alpine sable
Never seen that notation
F##@ me I guess...me neither
alpine sable
Probably just applying the row operation
But they couldve written Rt-->Rs
glass lichen
Or it's their notation for the ele. Matrix associated with the operation
alpine sable
Ok
alpine sable
Hello. I have confusion about these 2 questions. For the 1st one my answer was -(100/q - 1) using p/q/dp/dq.
Did I answer it correctly? Shouldn't point elasticity be a number?
Excuse me kindly see that my question hasn't been answered yet. Please ask yours in another channel.
vale wigeon
you got the point elasticity formula wrong, it's (p/q)/abs(dp/dq)
which would give you $\frac{100}{q} - 1$ as your point elasticity
ocean sealBOT
Ann
vale wigeon
and the elasticity being a number is not really an issue. it's different at different values of the demand after all
alpine sable
I see. Thank you very much.
alpine sable
3 units would cost $1.20, offer being 3 for $1, you save 20 cents
and with the offer, 12 units would cost $4, whereas without the offer $4.80, in this case you save 80 cents
alpine sable
24 units with the offer would be 8 (you do 24/3 * 1 = 8) and without the offer 9.60 (24*0.4)
pallid acorn
help
vale wigeon
the coefficient of x is the number attached (multiplied) to the lone x term in the polynomial
hasty quail
so 2
tired cave
can someone help me with finding a phase spectrum in Fourier series ?
I am getting completely different values than my friends, I don't know what I'm doing wrong
vale wigeon
yeah but it was supahotfire's job to do that, not yours @hasty quail