lusty reef
and half of the diameter is the radius
#help-13
crimson sedge
need help
cosmic steppe
need the problem
obsidian tinsel
What did u try?
manic acorn
First just divide
crimson sedge
divide by?
manic acorn
Divide the polynomial in the numerator by the polynomial in the denominator
crimson sedge
by long division method?
manic acorn
Yea
This would have been so much more epic if the nr and the dr polynomials swapped places
crimson sedge
ok i did it
manic acorn
ok i did it
Now you should be able to integrate
crimson sedge
is there any other method?
manic acorn
Idk, this seems the most obvious way to me
crimson sedge
I have to find the ama of a wheel and axle system AMA=Fe/FL
cedar kilnBOT
I have to find the ama of a wheel and axle system AMA=Fe/FL
crimson sedge
Is it wheel diameter over axle
or opposite
wheel diameter=0.118m
axle diameter=0.025m
so 0.118m/0.025m?
cedar kilnBOT
@crimson sedge Has your question been resolved?
crimson sedge
<@&286206848099549185>
delicate patio
i don't know how to convert it in this form
okay so
you can subtract and add 1
in the numerator
and then split whole expression in two parts
delicate patio
yupp
simple yoke
it results in ln(2) * ln(5)?
delicate patio
ln2 - ln5
simple yoke
yes
delicate patio
yeah that would be ln(2/5)
delicate patio
no. its ln(2/5)
simple yoke
thanks a lot
delicate patio
yep log2/5
yup
delicate patio
thanks a lot
np np
simple yoke
and sorry for the late response
simple yoke
can i ask sth else?
delicate patio
in other channel
simple yoke
ok
cedar kilnBOT
@crimson sedge Has your question been resolved?
crimson sedge
I have to find the ama of a wheel and axle system AMA=Fe/FL
.
Is it wheel diameter over axle
or opposite
wheel diameter=0.118m
axle diameter=0.025m
so 0.118m/0.025m?
cedar kilnBOT
@crimson sedge Has your question been resolved?
torpid urchin
how would i do question 2 (this is a previous midterm i am not writing it currently)
torpid urchin
im not sure how to come up with the two functions for the squeeze theorem
dense kayak
probably start with an interval (containing zero)
might have to do this twice since you have an x^3 but maybe you can make a symmetry argument i think both sides of this will be the same
using the zero function for one of the functions should help to start
torpid urchin
right i think im going to need to look at the functions cosx^2/x^2 and 1/x^3
because the other one is 0
would i say something like |cosx^2/x^2| is between 0 and 1?
would i do something like this?
i dont think this is right
i am confused on how to find the interval now because i dont think i can leave out the second function
torpid urchin
right
dense kayak
so you're looking at [0, oo) atm
torpid urchin
but can i find an interval for the whole function?
dense kayak
you can squeeze on the left with 0
now find a function that also has a limit to zero which is always greater than or equal to that big nasty that you started with
torpid urchin
so i came up with that value correctly?
dense kayak
on the interval you want g <= f <= h
and you have g(x) = 0 which is the easiest choice for g
dense kayak
you have to choose g and h
dense kayak
well we want to show the limit of f goes to zero
and we know f is always non-negative
dense kayak
so bounding below is easy if we just choose the constant function 0
dense kayak
yaya
dense kayak
yep! sorry i gtg but maybe someone else can step in!
dense kayak
i graphed it and 2x works, but maybe there is something more clever?
torpid urchin
ok
sleek condor
decompose the binomial coefficient into the factorial form
and use the recurrence hypothesis on both uk and un-k
white delta
decompose the binomial coefficient into the factorial form
Yh it shows someting like n!* sum(ak*an-k) with ak = uk/k!
white delta
and use the recurrence hypothesis on both uk and un-k
Can you explain tho
I dont get it
sleek condor
white delta
Ty so much btw
sleek condor
de rien
white delta
.close
cedar kilnBOT
sleek condor
recurrence forte du coup
cedar kilnBOT
Available help channel!
crimson hare
this is a bit of a big ask but i was wondering if someone would be able to review my calculations for a psmt !
crimson hare
completely understand if not because its a tiring and lengthy process
sleek condor
psmt?
crimson hare
its leslie matrix - population growth
crimson hare
yes i asked my question above c:
sleek condor
no but
post the maths
if you want people to review your work post your work
and possibly the assignment
crimson hare
oh i see i intercommunicated this, it was like if i could call them or something
but i understand ! ill just post a page
sleek condor
can you explain exactly what this is about? to me it seems like theres a vector representing population from age class and a matrix that dictaters the evolution
rate of growth would be the rate of growth of the sum of the cordinates of the vector?
crimson hare
alrighty !
my survival and birth rates were provided so i substituted that into my matrix
so in order to determine future population values i multipled my initial population by my leslie matrix
sleek condor
okay
crimson hare
alright so now all that was solved i had to now suggest a recommendation where my population would not exponentially increase
crimson hare
so with that i multipled my original matrix by the reciprocal of the growth rate
sleek condor
and what would that translate in the real world?
crimson hare
is this a good way for my population to platau or is there a smarter way, is there also a way i can use desmos to verify my growth rate
sleek condor
yeah this is essentially normalizing the matrix
depending on how is defined growth rate
crimson hare
is there any way i can verify this on technology
crimson hare
im saying its awful
sleek condor
if you are allowed to do anything you want numerically
i would diagonalize this matrix numerically
everything will be simpler after that
crimson hare
i would diagonalize this matrix numerically
im not sure what that means are you able to explain further c:
sleek condor
there are algorithms/calculators
that give you the diagonalized matrix
and the change of basis matrix associated
which will make your calculations easier
crimson hare
are you by any chance able to send me one
yeah with these psmts everything is just left to your interpretation, all you have to do is meet the critea and then easy 20/20
also gonna quickly delete those pictures cause if by any chance someone copies
sleek condor
lom
lol*
yeah i dont think for your matrix size anything is useful
unless you know some coding
to prove your solution works you juste have to compute the growth rate of your new matrix
crimson hare
AHHHHHHHHH i hate psmts
okay i think im just gonna leave it there then but i really appreciate all your help
i think unknowingly (or maybe knowingly) you helped me understand everything in this task a lot more too
thank you thank you
cloud egret
Given the f(x)=e^（x^3）+ln(1+x),
seek the 2019—order derivative of
f(0)
cedar kilnBOT
Given the f(x)=e^（x^3）+ln(1+x),
seek the 2019—order derivative of
f(0)
@cloud egret Has your question been resolved?
bitter olive
i need an equation that outputs 1 if the input is not equal to 0, and 0 if the input is equal to 0
normal remnant
can you use a piecewise function?
bitter olive
i dont care i just need an equation for it
normal remnant
not sure how to do the proper notation through discord unfortunately
im also waiting for help haha
one sec using an equation editor
solid juniper
f(x) = 1 - 0^|x| 🙃
normal remnant
impressive
solid juniper
just make sure whatever is parsing the function knows 0^0 = 1
solid juniper
haha thanks ^-^
bitter olive
and i assume that this is not computationally expensive right
normal remnant
shouldn't be, hopefully
bitter olive
imma use it then, thank you @solid juniper
solid juniper
yay
bitter olive
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
limber snow
If the question is askin tk find where the vertical axis would b 0
limber snow
would this b right
since the slope would b nearly 0
in these arras
areas
when it gradually increasing/decreasing
cedar kilnBOT
@limber snow Has your question been resolved?
cedar kilnBOT
@limber snow Has your question been resolved?
limber snow
Where the vertical axis would be 0?
Oceanographers define layers of the ocean by patterns in the density. There are three layers to the Labrador Sea - the mixed layer (near the surface), pycnocline layer (below the mixed layer), and the deep layer (below the pycnocline layer).
The derivative dρ/dz is nearly zero (or small) in the mixed layer and also in the deep layer. Use your derivative graph to find the boundaries between the layers (approximate answers are enough). Draw horizontal dotted lines on Romina’s density plot at the approximate locations of the two boundaries. Then write a sentence or two describing the derivative dρ/dz in the pycnocline layer, and how the density changes in each of the three layers.
I assumed that was what the quesrion was asking
cedar kilnBOT
limber snow
.reopen
cedar kilnBOT
✅
cedar kilnBOT
@limber snow Has your question been resolved?
cedar kilnBOT
@limber snow Has your question been resolved?
spark orbit
cedar kilnBOT
crimson sedge
(x+1/3)/2 +4/3 = 19
crimson sedge
what is not there
cedar kilnBOT
@spark orbit Has your question been resolved?
clear veldt
it's D
upbeat lotus
,w {(x+1/3)/2}+4/3= 19
clear veldt
but why it's {(x+1)/4}+4/3= 19
wraith daggerBOT
hard tree
for (a-b)^2 = a^2-2ab+b^2, do we include the signs of a and b ?
opal basin
that doesn't matter, because (-x)^2 = x^2
lethal jackal
certainly, (b-a)^2 = (a-b)^2
but it is definitely not true that (a-b)^2 = (a+b)^2, i.e. you can't just randomly negate a and b
opal basin
nvm, thought you said it wasn't
cedar kilnBOT
@hard tree Has your question been resolved?
nova ruin
helllo everyone can someone help me or guide me on how to solve this or suggest any youtube video thatll guide me in solving please , its really difficult for me
valid yacht
hmmmmmmm
(1) find derivative of the curve
(2) calculate derivative (/slope) at (-1,3) by substituting x=-1 & y=3
(3) then find the equation
something like that
south tundra
Rephrasing the question: Find a and b such that y = ax + b passed through (-1, 3) and the system of equations y = ax + b, x^2 + 4y^2 - 4x - 8y + 3 = 0 has only one solution
So b = a + 3
y = ax + a + 3
Plug this into the equation of the circle
You'll get a quadratic equation in x where you need the discriminant to be 0 so that there is only one intersection
And solve for a (which will have 2 solutions) and then b
cedar kilnBOT
@nova ruin Has your question been resolved?
nova ruin
And solve for a (which will have 2 solutions) and then b
THANK YOU SO MUCH SIR! ill be searching more about discriminant since i dont know about it
cedar kilnBOT
@nova ruin Has your question been resolved?
solid juniper
“for all”
not sure :c
backwards e is “there exists”
could the circle dot be exclusive or?
there must be more context
like what’s S?
sorry idk what the questions are then :c
runic zealot
I think that symbol is xnor
tropic oxide
$\odot$ has no established meaning but from this it appears that it refers to a relation
wraith daggerBOT
Ann
tropic oxide
it appears you are asked to translate these logical statements into properties of \odot that have English names
such as it being reflexive, symmetric, transitive, that kind of thing
hello
...
wait can you share the entire question again
with the answer options and all instructions
...oh, so the images are not displaying properly
okay so what's the question tho
you've shown instructions & some sentences written in logical symbols
ah.
so you need to tell which of these sentences mean "odot is irreflexive"
it's the only one that is the definition of transitivity lol
all the others talk about properties that are not transitivity and do not imply nor are implied by it
you misunderstand
this is basically just a vocabulary test
you need to know the meaning of the math-english words "reflexive", "symmetric", "transitive", etc. and you need to match each word to its definition(s)
no, but you can look up each individual term on various resources such as Wikipedia
or maybe your textbook has an alphabetical index of these
for most of these yes
except that 4 and 5 are the same thing (as explicitly explained) so they go together
"there exists an x such that x odot x" vs "x odot x is true for ALL x"...
there is a very clear difference between "for all" and "exists"
"someone in this house wears a red shirt" vs. "everyone in this house wears a red shirt"...
what's a "direct inversion"?
no
4 and 5 are literally the same thing. they are not negatives of each other, they are ONE AND THE FUCKING SAME.
$x \not\odot y$ means the same thing as $\neg (x \odot y)$...
wraith daggerBOT
Ann
cedar kilnBOT
@plain bridge Has your question been resolved?
Available help channel!
@crimson sedge Has your question been resolved?
Available help channel!
elfin kindle
Given the distribution of a random variable at different discrete points in time, what can you infer about the stochastic process itself without making any further assumptions? I don't think you have enough information to get the joint distribution of the variable at different points in time but maybe you can get some bounds on autocorrelation for example?
lethal jackal
Given the distribution of a random variable at different discrete points in time...
don't you have absolutely nothing, because the marginals say almost nothing about the joint distribution?
literally X_1 could be totally different from X_2 or could be the same
You have things like E[XY] <= E[X]E[Y], but all of these have to apply to any two random variables
cedar kilnBOT
@elfin kindle Has your question been resolved?
finite pollen
what is this property of logarithms called?
cedar kilnBOT
what is this property of logarithms called?
hollow minnow
patent cape
the official name i have no idea
cedar kilnBOT
hybrid glade
crimson sedge
Okk
cedar kilnBOT
Available help channel!
woven bison
From A' ∩ B = ∅ follows B ⊂ A
so i have to show this for the first part i have already written down {x: x is not element of A and x is element of B} or would it just be written down as {} since it is empty?
woven bison
and for be b is subset of a i would have written down x is element of b and a
cedar kilnBOT
@woven bison Has your question been resolved?
grim flower
From A' ∩ B = ∅ follows B ⊂ A
so i have to show this for the first part i have a...
What you have written down here is correct.
woven bison
i think i forgot to write down the symbol for empty set behind the first part woops
grim flower
Yes 🙂
But other than that you're on the right track.
So given that this correct do you have further questions?
woven bison
technically yes but for something else:
grim flower
Then just ask
woven bison
so this the diagram for a ⊃ b but what would it look like for a' ⊃ b' would there just be a or nothing?
woven bison
i think so , so like B'∩A' and a' ⊃ b' are the same?
grim flower
For $B' \cap A' = \emptyset$ yes
wraith daggerBOT
djuji
grim flower
i think so , so like B'∩A' and a' ⊃ b' are the same?
Wait
No
Would you be fine if we switch this to German?
woven bison
sure :)
grim flower
Ok es ist nicht ganz das selbe wie deine Aussage oben. Wenn du B' und A' gleich leere menge hast dann folgt daraus nicht das B' eine Teilmenge von A' ist. Sondern, wie bei deiner aussage oben das B' eine Teilmenge von (A')'.
Ansonsten ist das richtig so.
grim flower
i think so , so like B'∩A' and a' ⊃ b' are the same?
Du musst also hier schauen das du die richtigen mengen benutzt.
woven bison
vielleicht bin ich nur grad verwirrt oder hätte es anmerken sollen a' ⊃ b', das gehört nicht zur oberen aussage - ist was seperates, um genau zu sein ist es komplett "A ⊂ B genau dann, wenn a' ⊃ b' "...
grim flower
Ah OK ja das macht sinn 🙂
Trotzdem kannst du aus b' teilmenge von a' nicht folgern das a' geschnitten b' die leere menge ist.
Das ist nämlich falsch.
scenic garden
I can only get one value (2.1) but I’m not sure how to get the other one
cedar kilnBOT
I can only get one value (2.1) but I’m not sure how to get the other one
@scenic garden Has your question been resolved?
crimson sedge
Need help with this final question
cedar kilnBOT
Need help with this final question
crimson sedge
can i haver the first few steps and i can attempt to finish it off
floral forge
divide by 2 pi d and square both sides, also close your other channel
crimson sedge
ok one sec
when i divide by 2 pi d wat does the right side turn into
@floral forge
floral forge
show me what you think it becomes
floral forge
step 2
crimson sedge
when i square it will i have h squared + d squared on the right side
crimson sedge
then i take away d suared and square root evrything
floral forge
yep, dont forget the plus minus sign when taking the square root
crimson sedge
ok thanks
floral forge
np
crimson sedge
do i close this now? @floral forge
floral forge
yes, unless you have any more questions
crimson sedge
can i show u my final answer?
floral forge
go ahead
crimson sedge
is it the square root of s squared/4 pi squared d squared - d squared = h
@floral forge
floral forge
👍
floral forge
ok thanks have a good day
you too
crimson sedge
.close
elder elm
Okay so for this problem, the answer would be that the function is continuous over the interval [0,1]?
south tundra
Not only that
elder elm
elder elm
Not only that
Oh..
south tundra
You have to show that it's negative somewhere and positive somewhere else
On that interval
In order to apply ivt theorem
Oh wait you've shown that already
Yeah that's it then
elder elm
You have to show that it's negative somewhere and positive somewhere else
What do you mean? I thought I was meant to substitute the values given to us in the interval into the function and see if the results make an appropriate inequality?
south tundra
In this case that works yeah
But it doesn't work in all of the cases so keep it in mind
Here mentioning that f is continuous and that f(0) > 0, f(1) < 0 is enough
So yeah that's it
elder elm
So yeah that's it
Could you give an example where it wouldn’t work?
Like another problem I’ve been tryna find some
south tundra
For example if I gave you the function f(x) = x^2 - 1 and the interval [-2, 2]
As you can see f(-2) = f(2) > 0 in this case
So instead of plugging -2 and 2, you have to present a value of x between -2 and 2 for which f(x) < 0
In this case x = 0 works for example
f(0) < 0 and f(2) > 0
So there's a zero between 0 and 2
(and, yes, there's another zero between -2 and 0 coming from an analogous argument)
elder elm
For example if I gave you the function f(x) = x^2 - 1 and the interval [-2, 2]
Wait let’s recap. How would such a question be phrased? Would they just give me the function and the interval and I’d be on my own?
south tundra
"Show that f(x) = x^2 - 1 has a zero on the interval [-2, 2]"
latent rover
Also $f(x)=\frac{1}{x-0.5}$ wouldn't work for [0,1] but for a different reason
south tundra
Yeah, cuz of discontinuity
elder elm
"Show that f(x) = x^2 - 1 has a zero on the interval [-2, 2]"
So wait. I shouldn’t plug 2 and -2 into this because it wouldn’t get me there, thus I’d need to find a value between the values in that interval?
south tundra
Yes, for which f(x) < 0
elder elm
Yes, for which f(x) < 0
Okay this might sound dumb but by f(x)<0, do you mean for which there will be a value lower then 0 and greater then 0 in the inequality f(x)<0<g(x)?
south tundra
What's g?
elder elm
What's g?
A value greater then 0?
I might be getting functions denotations confused with a value
south tundra
If you mean in this case f(0) < 0 < f(2) then yeah
You just need to find one value of x for which f is negative and some other value of x for which f is positive
elder elm
If you mean in this case f(0) < 0 < f(2) then yeah
It could be one as well, right?
As in value 1
south tundra
Well f(1) = 0
elder elm
You just need to find one value of x for which f is negative and some other valu...
For your example btw
elder elm
You just found the zero itself
Wait so
elder elm
"Show that f(x) = x^2 - 1 has a zero on the interval [-2, 2]"
Alright I’m still confused on this problem. What would a answer be?
It’s 0?
south tundra
f(x) = x^2 - 1 has a zero on the interval [-2, 2] because f(x) is continuous on [-2, 2] and f(0) < 0 < f(2)
elder elm
f(x) = x^2 - 1 has a zero on the interval [-2, 2] because f(x) is continuous on ...
Okay but why did we get the 0?
south tundra
No, it's not asking you to find the zero
It's asking you to prove that it exists (preferably using the ivt theorem)
Or, sure, you could have just shown that f(1) = 0
But I showed this question for the sake of applying the ivt theorem
elder elm
But I showed this question for the sake of applying the ivt theorem
So there’s no actual computation involved?
south tundra
No, the only computation is behind f(0) < 0 and f(2) > 0
cedar kilnBOT
@elder elm Has your question been resolved?
unkempt cargo
can someone help? its a surprise question i lit forgot these 😭
crimson sedge
Hiii
violet rapids
draw a picture
crimson sedge
Welcome back
unkempt cargo
hiiii
strange fulcrum
hi celineeee
unkempt cargo
sorry loll ive got a geometry final in a frw days
crimson sedge
Anyways, try and draw a square first
crimson sedge
Okay now draw another rectangle next to it
unkempt cargo
rectangle drawn
crimson sedge
Okay so now go back to the square and label each side as 'a'
Because all the sides of the square are equal
crimson sedge
Okay now that's where u r gonna come in and start thinking
So now, you take half of that square and fold it in half to become the rectangle you got on the right
What do u think the sides of this rectangle are going to be, in terms of a?
unkempt cargo
equal to each other?
unkempt cargo
hmmmm
crimson sedge
Like, what do u notice?
unkempt cargo
theyre right?
crimson sedge
Hmm okay here is a hint
Compare the top and bottom sides of the rectangle and square
Actually can u show me the two shapes u drew? I wanna see if u drew them right
unkempt cargo
okayy
crimson sedge
In case u r confused because of that
crimson sedge
Ah! That's where u made ur mistake
toxic moat
Ah! That's where u made ur mistake
sad
unkempt cargo
very much sad
crimson sedge
Actually, can u get a tissue paper yourself and fold it in half? @unkempt cargo
toxic moat
u unfortunately
crimson sedge
Nothing better than a visual
toxic moat
drew the square
unkempt cargo
ive got one right next to me
crimson sedge
Yeah do it
toxic moat
Nothing better than a visual
amazing
toxic moat
another tissue wasted
crimson sedge
Okay draw the full tissue and the folded thing
toxic moat
another planet destroyed
unkempt cargo
another tissue wasted
noo im using it to erase on my whiteboard
toxic moat
good job lieutenant
crimson sedge
another planet destroyed
We love it!
unkempt cargo
okok done
crimson sedge
Can u show me ur new shapes
unkempt cargo
boom
toxic moat
OH WAIT ITS A WHITEBOARD LOL
unkempt cargo
unkempt cargo
OH WAIT ITS A WHITEBOARD LOL
SJSJSJSJJS
toxic moat
what r the lengths
unkempt cargo
my geometry final is so close 💔
crimson sedge
Okay but like draw the top one as an actual square 😭
unkempt cargo
what r the lengths
they said the perimter is 15
unkempt cargo
they said the perimter is 15
MY TISSUE IS A RECTANGLE STOP 😭
toxic moat
lol
crimson sedge
Okaaayy fineee
Just draw a full square okay
And like
Imagine u cut it in half in the middle, that's ur rectangle
unkempt cargo
okok drawn
crimson sedge
Show
crimson sedge
Yeah like, it needs to be the same length width wise
crimson sedge
Because if u take a square paper tissue and fold it in half, it's gonna be the same widh
unkempt cargo
draw with my amazing art skills
artist! we love to see it
crimson sedge
And yeah just show us circle lmao
unkempt cargo
my drawing shapes skills are so bad 😭
unkempt cargo
omg im there 🙈
crimson sedge
I defined the full square's side as a so let's keep it as that
unkempt cargo
okk
toxic moat
wow
toxic moat
I defined the full square's side as a so let's keep it as that
but
its weird numbers
i meannn
crimson sedge
Ehh it's fine let me just draw them seperately so it can be better visualised
unkempt cargo
okays
unkempt cargo
apple pie
toxic moat
now that ive stolen u as a student
toxic moat
well work with this
unkempt cargo
me
unkempt cargo
15
crimson sedge
unkempt cargo
oh
toxic moat
ignore lex
crimson sedge
This is basically what is being talked about
toxic moat
lol
crimson sedge
Woww
unkempt cargo
i am an actual idiot
toxic moat
they have a weird diagram
unkempt cargo
I DREW A VERTICAL RECTANGLE
unkempt cargo
popcorn
toxic moat
do u want more headroom in ur cage
or more space to roll around about
but its still a half rectangle
so it works
unkempt cargo
me personally i would choose more space
crimson sedge
they have a weird diagram
It's just showing the full paper and the folded one separately wdym lmao
toxic moat
ur
variable names
is diff
n idl that
back to this
whats the red bit perimeter in terms of a
unkempt cargo
i forgot these last time i took them i was in 6th
unkempt cargo
perimeters is all lengths added tgt
i couldve said that 😭
unkempt cargo
IS IT WRONG
unkempt cargo
DAMN 😄
toxic moat
toxic moat
ok
unkempt cargo
i feel like an idiot im so sorrg
toxic moat
just use + for now
unkempt cargo
OH
toxic moat
yea
unkempt cargo
so 2a^4
toxic moat
no
imma just say
its
a + 2a + a + 2a
= 6a
idk why u used ^ as well
^ means exponential
like
unkempt cargo
i js made everything complicated
toxic moat
$a^b$
unkempt cargo
like exponents
unkempt cargo
yes
toxic moat
u want multiplication here
unkempt cargo
uhhhhh
toxic moat
and find (2a)*(2a)
those r the original lengths of the tablecloths multiplied together
toxic moat
perimeter of red cage = 6a = 15
unkempt cargo
one sec
toxic moat
solve for a
toxic moat
find area of square = 2a * (2a) = ?
toxic moat
yes
unkempt cargo
THANK UUU 😊
toxic moat
unkempt cargo
🫶🫶🫶🫶
toxic moat
np
unkempt cargo
.close
cedar kilnBOT
toxic moat
💕
cedar kilnBOT
Available help channel!
earnest kettle
can someone please explain factoring it in the last step and why
earnest kettle
crimson sedge
They just divided the expression by x^4 and pulled it out, more or less
As to why, you don't have to do it, but it would be useful for finding possible 0's and it looks nicer ig
earnest kettle
But they moved 5
next to cosx
and took away
x^5
and reduced it to just x
how
and why
solid juniper
it might be helpful to multiply out the thing at the very bottom by distributing the x^4 to each of the terms in the parentheses
to see how it’s equal to the thing above it
earnest kettle
okie
also
could you please explain
I got the derivative part
But I don’t understand how they got to the next part
as in how they got the answer after deriving using the product rule
solid juniper
so like the simplify part?
earnest kettle
oui oui
solid juniper
one thing they used is cos*tan = cos*(sin/cos) = sin
so that’s how you get to sin(x) + sec^2(x)sin(x)
then factoring out the sin(x) completes it
solid juniper
yay 🙂
earnest kettle
what rule am I supposed to be applying with this
why do they only find the derivative of the 1st and last
but keep the 5csc in the middle?
oh
nvm
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
remote dust
cedar kilnBOT
remote dust
could anyone help me with this? statements like these are confusing to me.
cedar kilnBOT
@remote dust Has your question been resolved?
remote dust
<@&286206848099549185>
cedar kilnBOT
@remote dust Has your question been resolved?
warm bone
could anyone help me with this? statements like these are confusing to me.
Write out your thoughts
paper pumice
cedar kilnBOT
paper pumice
can someone quickly look over this work and see if there are any mistakes?
idk why it sent sideways at first
weird
.close
tender estuary
can someone do this for me
cedar kilnBOT
can someone do this for me
short blade
can someone do this for me
start with the first one
wintry prism
no
tender estuary
start with the first one
can u just do it
wintry prism
can u just do it
no
tender estuary
k
tender estuary
can you put x+5y=-1 into slope-intercept form?
no
short blade
do you know what slope-intercept form is?
tender estuary
yes
short blade
you can put it in slope intercept form by isolating the y
tender estuary
k
short blade
let me see what you get once you've done it
cedar kilnBOT
@tender estuary Has your question been resolved?
winter lion
cedar kilnBOT
winter lion
Question and What I have tried. Relating to proofs and relations
I am unsure if I did the proof for symmetric and transitive correctly
crystal raptor
What is n?
winter lion
i don't believe I need that i tried following an example but it doesn't make much sense for there to be n
sick summit
can someone help
cedar kilnBOT
can someone help
winter lion
if you notice first your answer is not a degree 4 and rather a degree 5
livid hound
you have both x and (x-0)
winter lion
i am unsure why you have a 0.4 too
if this helps:
multiplicity 2 at x = 4 is (x-4)^2
multiplicity 1 at x = 0 is (x-0) = x
multiplicity 1 at x = -3 is (x+3)
now that you can assemble the 4 degree polynomial you need to account that it goes through points (5, 24)
cedar kilnBOT
@sick summit Has your question been resolved?
crimson sedge
How do I simplify the second term t2 ….(ignore question it’s translated wrong lol)
cedar kilnBOT
How do I simplify the second term t2 ….(ignore question it’s translated wrong lo...
crimson sedge
.close
river quiver
cedar kilnBOT
river quiver
,rotate
wraith daggerBOT
river quiver
6u = 6 units
if PQ = 11 and RS = 5 are parallel chords, determine the length of the radius
can someone give me a hint as to how to start this question?
cedar kilnBOT
@river quiver Has your question been resolved?
zinc vortex
cedar kilnBOT
zinc vortex
What does it mean to identify a function represented by the Power Series?
My professor didn't provide an example problem of this
solid juniper
it probably means write it in a form that doesn't have an infinite sum
cosmic steppe
55
Alright
Let's start with that
Make it so it's just one base to the power of k
I can provide an example
solid juniper
n or k?
cosmic steppe
Example:
$$\text{}$
$\sum_{n=0}^{\infty}\left(\frac{x}{7}\right)^n = \frac{1}{1-\frac{x}{7}}, |x| < 7$
Or something like that
I forgot the radius of convergence for that
solid juniper
7?
solid juniper
i meant was that supposed to be 7 or 2 lol
cosmic steppe
No that was an example
solid juniper
oh ok
wraith daggerBOT
Umbraleviathan
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
cedar kilnBOT
@zinc vortex Has your question been resolved?
zenith zealot
I dont understand how to do logical reasoning, I understand how to read it but not complete the truth tables
cedar kilnBOT
@zenith zealot Has your question been resolved?
dense kayak
pinging helpers is enough, sorry no one's come yet
pinging moderators isn't appropriate in this instance
@zenith zealot what is your question exactly?
you want help constructing the truth tables?
zenith zealot
yeah
dense kayak
so you'll want to start with columns for however many arguments are needed, two for p and q in this case
starting with prob 1
then you want all possible inputs for those, and they've listed those out for you already
the following columns are supposed to show the work for later statements
| p | q |
|---+---|
| T | T |
| T | F |
| F | T |
| F | F |
we want to know the value of the negation of q so let's show that work in a column
| p | q | ~q |
|---+---+----|
| T | T | F |
| T | F | T |
| F | T | F |
| F | F | T |
so far so good?
dense kayak
so we also want a column for p <-> ~q, and we should use the columns for p and ~q to help us calculate that
yes sorry i'm using ~ for logical negation
zenith zealot
okay
zenith zealot
so we also want a column for `p <-> ~q`, and we should use the columns for `p` a...
okay
dense kayak
you can compute negation ezpz, but the biconditional is okay?
they just have to match
| p | q | ~q | p <-> ~q |
|---+---+----+----------|
| T | T | F | F |
| T | F | T | T |
| F | T | F | T |
| F | F | T | F |
yes this makes sense
dense kayak
great then just one more column for p ^ q
| p | q | ~q | p <-> ~q | p ^ q |
|---+---+----+----------+-------|
| T | T | F | F | T |
| T | F | T | T | F |
| F | T | F | T | F |
| F | F | T | F | F |
okay
dense kayak
do you know how to determine if an argument is valid or invalid?
the truth table work is done
zenith zealot
like
zenith zealot
do you know how to determine if an argument is valid or invalid?
yes and no, i can google quick
i sorta understand it but get confused
dense kayak
there's another step we can do in the table to make it more clear that i used to like to use when i started with these
the gist is that a valid argument is a logical implication that doesn't fail
this link is more detailed https://math.stackexchange.com/a/751709
dense kayak
essentially any time we start with true premises, we want to form a true conclusion
zenith zealot
okay
dense kayak
so looking at the table, whichever row(s) has both premises ~q and p <-> ~q with true values, we should expect to see our conclusion p ^ q with a true value
zenith zealot
did you mean ~q?
dense kayak
oh yes
zenith zealot
okay yeah then row 2
dense kayak
so that's sort of the counter-example
zenith zealot
okay
dense kayak
"you've said this argument but even if everything you start from is true then we have a false conclusion"
aka invalid argument 🙂
zenith zealot
okay that makes sense
zenith zealot
okay gotcha
dense kayak
unless you're a spreadsheet genius haha
zenith zealot
i guess so
dense kayak
you ok for the second one?
zenith zealot
can i ask what software you use to make your truth tables?
dense kayak
sure
zenith zealot
or just some online tool?
dense kayak
i was using the tables with org-mode
i edit text with emacs, and theres a really nice package for note-taking (organizing) that happens to include table stuff
zenith zealot
okay cool im going to have to check that out later bc rn im using pen and paper and its annoying
zenith zealot
you ok for the second one?
yes im ready
dense kayak
tyty
zenith zealot
for ease of access
dense kayak
yea that def helps haha
so are you okay with double negation?
we can show every little step, but sometimes you can do some in your head
i'll more detail by default
zenith zealot
double negation meaning ~(~r) is just r
dense kayak
exactly
| r | s | ~r | ~(~r) |
|---+---+----+-------|
| T | T | F | T |
| T | F | F | T |
| F | T | T | F |
| F | F | T | F |
first and fourth columns are identical
zenith zealot
and ~(~r ^ s) is r ^ ~ s yeah im good with that
dense kayak
we use ~r later on, so i'll keep the column around
zenith zealot
okayt
dense kayak
next column i'll do ~r ^ s
dense kayak
and ~(~r ^ s) is r ^ ~ s yeah im good with that
oh i see now what you have here, it's close
but there's "demorgans" laws
negation distributes but the disjunctions and conjunctions will swap
dense kayak
yayaya
zenith zealot
gotcha
dense kayak
i'll keep going without that simplification, but that's exactly what i mean by kinda doing some in your head
zenith zealot
okay
zenith zealot
next column i'll do `~r ^ s`
f f t f im guessing
dense kayak
| r | s | ~r | ~(~r) | ~r ^ s |
|---+---+----+-------+--------|
| T | T | F | T | F |
| T | F | F | T | F |
| F | T | T | F | T |
| F | F | T | F | F |
nice yep!
then we negate that
| r | s | ~r | ~(~r) | ~r ^ s | ~(~r ^ s) |
|---+---+----+-------+--------+-----------|
| T | T | F | T | F | T |
| T | F | F | T | F | T |
| F | T | T | F | T | F |
| F | F | T | F | F | T |
oof i think three more columns and we're done haha
dense kayak
yeah, it's all up to you how much you want to do in your head
zenith zealot
okay gotcha
dense kayak
reading from two columns and taking the conjunction is the simplest step
| r | s | ~r | ~(~r) | ~r ^ s | ~(~r ^ s) | ~s | ~s v r | ~(~s v r) |
|---+---+----+-------+--------+-----------+----+--------+-----------|
| T | T | F | T | F | T | | | |
| T | F | F | T | F | T | | | |
| F | T | T | F | T | F | | | |
| F | F | T | F | F | T | | | |
i haven't filled that in
but we can take a shortcut if you want and use demorgan on that last column