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#help-39
tranquil badger
slender viper
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For a given ring $R$, construct the polynomial ring $R[x]$, where the elements are \textbf{formal} sums $\sum_{i=0}^na_nx^n$. Quadratics are elements in the polynomial ring. Given a map $R\to S$ of rings, the evaluation map $\operatorname{ev}_s:R[x]\to S$ is the map induced by $R\to S$ and $x\mapsto s\in S$
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I don't think you need to find zeros to plot the parabola. You can always evaluate for $y$ at given points $x$ and then plot those points.
tranquil badger
uhhhh is that discreet math?
jolly parrotBOT
Element118
slender viper
uhhhh is that discreet math?
Yeah, the polynomial ring is a concept quite beyond this. In short, polynomial and polynomial functions are two different concepts.
tranquil badger
o H
alright
thank you for explaining that.
Still, this describes my understanding of it, and I don't think that that is necessarily important to it.
The main question, again, was regarding how this was equivalent due to how they were graphing the parabola which is from the behavior of the quadratic of course.
slender viper
> The main question, again, was regarding how this was equivalent due to how the...
My guess is that they are trying to graph $f(x)=ax^2+bx+c$.
Changing it to $f(x)=x^2+bx/a+c/a$ only scales the graph vertically.
Changing it to $f(x)=x^2+bx/a$ only shifts the graph vertically.
jolly parrotBOT
Element118
slender viper
The other possibility is that they are trying to find roots
which they are trying to show the "complete the square method"
but getting rid of the c/a term so that it is easier to present the next step
tranquil badger
https://www.youtube.com/watch?v=UTuxHsaH-gQ&list=PLybg94GvOJ9FoGQeUMFZ4SWZsr30jlUYK&index=37 (this explains what theyre doing)
1. Well, clearly, by subtracting c/a which logically is apart of the behavior of the problem and thus removing it would make the behavior when graphed different to the original quadratic they wanted to graph the behavior of
so this leaves me with two possibilities that they rather are removing it and it somehow isnt that important what the quadratics components are or that they somehow arent and its still somehoe equivalent to the original.
2. what is the difference between scaling and shifting vertically? Do you mean multiplication vs adding?
3. My very first question was the what values correlate to X or Y and which values get what.```
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slender viper
https://www.youtube.com/watch?v=UTuxHsaH-gQ&list=PLybg94GvOJ9FoGQeUMFZ4SWZsr30jl...
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The motivation of subtracting $\frac{c}{a}$ from both sides is to clean up the left-hand side to get $x^2+\frac{bx}{a}$. I think introducing graphs into this might complicate things. Doing the same reversible operation to both sides leaves you with an equivalent equation to the original.
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That seems to be implied by trying to plot it out on a graph.
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When solving $f(x)=0$, there's no $y$ to be concerned about. The point appears to be that doing a reversible operation preserves what $x$ satisfies the equation.
jolly parrotBOT
Element118
tranquil badger
1. The motivation of subtracting $\frac{c}{a}$ from both sides is to clean up th...
5 - 15 + 5 = -5 ---- 5 + 5 = 10
so is it not equal but because you can undo it it makes it equal?
and how does one go about undoing it?
slender viper
In general "doing the same thing to both sides" preserves equality.
tranquil badger
5 - 15 + 5 = -5 ---- 5 + 5 = 10
that does not appear to be the result.
slender viper
if a = b, then f(a) = f(b). Being able to undo it, by adding back c/a to both sides, ensures that the final equation doesn't lose information the original equation had.
Say $a=b$ and we square it, we get $a^2=b^2$. But the solutions to this final equation are $a=\pm b$, which is different from the original equation. That's because squaring cannot be reversed.
jolly parrotBOT
Element118
tranquil badger
if a = b, then f(a) = f(b). Being able to undo it, by adding back c/a to both si...
so it is not equal?
only this half is?
and that part is perserved for the formula
and then c/a is added back after
?
slender viper
Doing a reversible operation on an equation preserves the set of solutions. Doing an irreversible operation on an equation may increase the set of solutions.
"Subtracting c/a" can be reversed by "adding c/a"
"dividing by a" can be reversed by "multiplying by a" (assuming a is not 0)
tranquil badger
Does that imply that I was correct?
it is unequal until reversed? (removing c/a is unequal until reversed after operations are complete)
slender viper
Does that imply that I was correct?
I'm not sure exactly how you are correct.
tranquil badger
im saying that by removing c/a which is a component of the problem and its behavior
it isnt equal to the original equation until you reverse it and add c/a back
but while its gone
you gain access to certain forms
allowing access to quadratic formula etc
is this true?
if not explain
because throughout this entire time the idea of it being unequal hasnt been touched because you havent actually said anything on the matter (difference between fact stating and technical resolving)
no matter how much you say something is or is not true or if something equates to something
if my fundamental concept is off by even a little bit i will interpret the same information you gave differently
slender viper
Firstly these two equations are equivalent
$x^2+\frac{bx}{a}+\frac{c}{a}=0$
$x^2+\frac{bx}{a}=-\frac{c}{a}$
We can get from the top to the bottom by subtracting $\frac{c}{a}$ from both sides and bottom to top by adding $\frac{c}{a}$ to both sides.
jolly parrotBOT
Element118
slender viper
equivalent, meaning
"(a, b, c, x) makes the top equation true if and only if this (a, b, c, x) makes the bottom equation true"
tranquil badger
define top and bottem
slender viper
top equation: $x^2+\frac{bx}{a}+\frac{c}{a}=0$
bottom equation: $x^2+\frac{bx}{a}=-\frac{c}{a}$
in this case
jolly parrotBOT
Element118
slender viper
equivalent, meaning
"(a, b, c, x) makes the top equation true if and only if th...
there's a small caveat here, that we already assumed a is not 0.
tranquil badger
**Element118**
so
the last way i can interpret this
is that
they are unequal but also not
in that the definition of equality was wrong
tranquil badger
i always meant it in that the problems essential structure
would be unchanged
in that if you removed fundamental pieces of the problem
it would have to be incorrect.
because you lost the original data and behavior the zeroes described
but
what i get from that
is that
your idea of equal is completely different
in that
any formation of the same data even if subtracted to form a different result that isnt the zeroes
so long as it utilizes the same set of numbers
is still equal in the sense it is another expression of the same data
in that the subtraction to remove itself WAS the expression of that component
rather than that component not existing
slender viper
equivalent, meaning
"(a, b, c, x) makes the top equation true if and only if th...
hmm, it might be equivalent to my definition here
it doesn't fundamentally lose any piece of the problem because the set of solutions remain the same
that's what we care about when we are trying to solve for x
the "if and only if" is doing a lot of the lifting here
tranquil badger
alright
i cannot continue
it is 3:09
am
ive been at this for hours and i cannot understand what you mean by alot of that.
also, no offense but, is english not your first language?
oh well
.close
pearl pondBOT
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Available help channel!
sharp smelt
This basically means that the cardinality of the set is non- finite , right
rustic gate
that's not all there is
sharp smelt
I know
but that's the part I'm concerned about
It basically means A is an element of the set containing the elements of the powerset of P(\N)
rustic gate
being not finite is not sufficient to be an element of that set
{2, 4, 6, ...} is not contained in that set
sharp smelt
I know
rustic gate
so it does not "basically mean that the cardinality of the set is non-finite"
that is not an equivalent description
sharp smelt
As I said, that was the part that confused me
rustic gate
what are you confused by? you haven't specified
sharp smelt
what are you confused by? you haven't specified
I was confused by $|\overline X|<\infty$
rustic gate
it means the cardinality of the complement of X is finite presumably
jolly parrotBOT
Veni, vidi, perii
sharp smelt
it means the cardinality of the complement of X is finite presumably
Yes, that's what I wanted confirmed
thanks
.clsoe
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mild reef
A travel company organizes a tour with a price of 500 $ per customer for 30 customers. Starting from the 31st customer, for each additional customer, the price of the tour decreases by 𝑎 $
(where a is a positive integer). The number of additional customers cannot exceed 15. It is known that if the number of additional customers ranges from 1 to 8, the total revenue increases as the number of customers increases. Find the maximum value of a. I need help with this problem
pearl pondBOT
A travel company organizes a tour with a price of 500 $ per customer for 30 cust...
@mild reef Has your question been resolved?
low crystal
Is 1/lnx considered continuous function?
pearl pondBOT
Is 1/lnx considered continuous function?
low crystal
It's obiviously not continuous when you have x<1 but do we call it non-continuous just because it's not between specific range
what do you need to have to say a function is not continuous
worthy lance
The function is continuous wherever is defined except at x=1
From (0,1) and (1, inf)
And is discontinuous at x=1 cause it is undefined
Because of division by 0
low crystal
The function is continuous wherever is defined except at x=1
only x=1 ?
worthy lance
Where else?
low crystal
is it not undefined ln(-5)
worthy lance
The function is continuous wherever is defined except at x=1
Here
When x<0 is not defined
Ln over reals is only defined when x>0
low crystal
Ln over reals is only defined when x>0
So you're saying it's because definition of domain of a logarithmic function ?
worthy lance
Check the function
low crystal
Like it's not defined 0<x at the first pplace
worthy lance
,w plot lnx
jolly parrotBOT
low crystal
yeah
worthy lance
Because 1/0 is undefined
low crystal
so when we call a function continuous?
Is it when there is only one undefined point or something like that
worthy lance
And at x<0 the function is also undefined because ln(neg) is undefined
We can say it is continuous in two (idk the word in english) parts
(0, 1)
And (1, inf)
And there is a discontinuity at x=1
low crystal
does that mean there is no general referring like "f(x) is continuous but g(x) is not"
worthy lance
But the function is not continuous over the whole spectre
worthy lance
does that mean there is no general referring like "f(x) is continuous but g(x) i...
Not sure I get this question
Can u say with an example?
low crystal
Not sure I get this question
Is there no such a thing like calling a function discontinuous or continuous as a whole or general?
worthy lance
You can say f(x) = x is continuous
There is no undefined point in this function
But in 1/lnx you cant say that
Cause there are 1 point and 1 side undefined
low crystal
So you're basically saying "to say if a function is continuous or not we need to include where we're talking about"
no?
worthy lance
Yes
You specify what are you talking about
That will make clear the context better
low crystal
Yes
okay get it. So is it correct to say that 1/lnx is continuous at 1<x while It's not at 0 and x<0 ?
worthy lance
I see redundancy
low crystal
okay
worthy lance
And is undefined for x<0
low crystal
And is undefined for x<0
so do we say discontinuous only when there are undefined point or points in a continuous interval which is breaking it or something?
because I thought that we can still say it's discontinuous at x<0?
but you just said "undefined"
worthy lance
When a function is not defined at certain points like for x < 0, we do not consider those as points of discontinuity, the concept of discontinuity applies to points within the domain of the function where the function’s behavior breaks down.
low crystal
When a function is not defined at certain points like for x < 0, we do not cons...
ohh okay so my problem arose due to definitions I guess
worthy lance
Yes, definitions are the first thing to check
low crystal
because I was thinking like when you try to go back from point 0, you are not allowed which must mean It's discontinuous
.cllose
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pearl pondBOT
pearl pondBOT
Available help channel!
livid bolt
pearl pondBOT
livid bolt
integer that is positive and odd?
how would i find part B
every number is divisible by 8?
livid osprey
yep
for (c) just take m to be some positive odd integer 2k+1, and show that the result is still divisable by p
livid bolt
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hollow parcel
pearl pondBOT
light helm
double angle identity
is a special case of the compound angle identity
which can be derived from clever construction of similar triangles
hollow parcel
😮
vestal tapir
hollow parcel
damn they expect me to remember this while doing integrals
light helm
trig should've been a pre-requisite for calculus
livid osprey
if u need a easy way to derive it on the spot u can use the addition formula
hollow parcel
yes but
in college not so much trig
economics college
so it very much in the dark
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pearl pondBOT
pearl pondBOT
Available help channel!
wooden merlin
Use Moivre's formula to express $cos4\theta$ and $sin4\theta$ by $sin\theta$ and $cos\theta$
jolly parrotBOT
Good
wooden merlin
For $cos4\theta$, I got $2cos^2\theta-1$
jolly parrotBOT
Good
wooden merlin
For $sin4\theta$, I got $$(1-sin^2\theta)(4cos\theta sin\theta +2sin^2\theta)+4cos\theta sin^3\theta$$
jolly parrotBOT
Good
wooden merlin
Is there any way to keep factorize? Or is this enough?
pearl pondBOT
@wooden merlin Has your question been resolved?
deep bane
pearl pondBOT
deep bane
hi how do i go about solving these? any hint or a particular method
crisp ravine
since this is calculus, us a CALCULATOR
desert nebula
since this is calculus, us a CALCULATOR
hello can you help me in #help-36
pearl pondBOT
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deep bane
<@&286206848099549185>
arctic carbon
The bearing of point B from point C is $254^\circ$. The bearing of point A from point C is $344^\circ$ The bearing of point A from point B is $32^\circ$ If the distance from A to C is 780 miles, find the distance from A to B to the nearest meter.
jolly parrotBOT
snooze
arctic carbon
I need some help visualizing and drawing this out
pearl pondBOT
@arctic carbon Has your question been resolved?
pearl pondBOT
@arctic carbon Has your question been resolved?
pearl pondBOT
@arctic carbon Has your question been resolved?
dark sparrow
I have been staring at this question for the longest time and I Dont really know how to even begin. this is about probability going from a point to a point.
dark sparrow
$P(E_{1})=\frac{2}{5}$, $P(E_{2})=\frac{3}{4}$, $P(E_{3})=\frac{2}{3}$, $P(E_{3}\mid E_{2})=\frac{4}{5}$, $P(E_{1}\mid E_{2}\cap E_{3})=\frac{1}{2}$.
jolly parrotBOT
Totalani
dark sparrow
First question asks what is the probability someone can go from A to B if he has to pass C ?
nevermind got the first question, very simple
Second question askes the prob from A to B
pearl pondBOT
@dark sparrow Has your question been resolved?
dark sparrow
Any help with this?
plush bramble
Second question askes the prob from A to B
In how many steps?
dark sparrow
Does not say, it just says the probability from A to B
I read that as directly, since last question was about passing C
Going from A to B passing C was 0.6
plush bramble
Why is it not just P(E1) then
dark sparrow
I dont know, thats not what says in the asnwer, it says its 0.7 but im not sure how its getting it
plush bramble
did you read the first two sentences
dark sparrow
yes
plush bramble
Why is it not just P(E1) then
that's why it's not just P(E1)
dark sparrow
the first 2 sentences doesnt matter. it says "in this particular day this and this are the probabilities.." and it gives you the probabilities for that day.
plush bramble
What does it say about A and B in the second sentence
dark sparrow
It says you cant always travel between A and B during winter, but it does not say you cant travel between A and B during this particular day, its even giving you the probability no?
lets assume you cant go directly from A to B then
so you have to pass C
That was already the question for a)
I just want to know how it got to 0.7
plush bramble
I dont know, thats not what says in the asnwer, it says its 0.7 but im not sure ...
yea but you said you didn't know why it's not P(E1)
dark sparrow
No you asked why it wasnt just P(E1)
and im saying it cant be because P(E1) is 2/5 but the answer is suppose to be 0.7
any help with this?
dark sparrow
.close
violet wing
Let A be the set of real numbers R. Express the following proposition
with a simple sentence.
∀ x ∈ A ∃ y ∈ A [(x < y) ∧ (∀ z ∈ A (x < z) ⇒ (y ≤ z))]
Is this proposition TRUE ? If not, is there a set A for which it is TRUE ?
Justify your answer
violet wing
so basically, x<y and z<=z
so no, it is not true, BUT can I also say there is no set A for whicb it is true?
because, for example, integers would be a set such as {1,2,3...}
and so it cannot work because x > y if x = 3 and y = 1
but i don't fully understand sets, so i'd like to know if i'm thinking on the right track
sharp vigil
you need to review the qualifiers:
"for all x in A, there exists y in A..."
violet wing
for all x in A, there exists a y in A scuch that x< y AND for all z in A, if x< z, y <= z
i'm just confsed by the set part
cinder flower
this question has a super simple answer but i don't know how to allude to it without giving it away
cinder flower
i'm not saying coming up with it is simple, just that the (or one) answer is simple
violet wing
the sets of integers are ordered, right?
the issue is i haven't delved into sets at all so i don't understand if they're ordered
cinder flower
A is a subset of the real numbers
so it has an order inherited from there already
but sets are not manifestly ordered in general, no
violet wing
but the requirements for this set is to be ordered
so does that mean no set exists as the sets aren't ordered?
cinder flower
the order used in the question is real number order
the elements of A are real numbers
sharp vigil
and so it cannot work because x > y if x = 3 and y = 1
remember that the statemeent says "for all x, there exists some y such that...". so given x = 3, can you choose a particular y that satisfies the statement?
violet wing
if y>x then it satisfies it, so 4 would work
sharp vigil
what about the second half of the statement?
violet wing
which statement
sharp vigil
the part about z. is it true that any z larger than x has to be at least as big as y?
violet wing
yes, it's true
sharp vigil
which number system is it true in?
violet wing
the set of real numbers R (which is A)?
wait because it's just saying like
every number has a number greater than it, which has a number greater than it
but is infinity included in R?
sharp vigil
the set of real numbers R (which is A)?
consider z = 3.5 then
violet wing
then it wouldn't work
WAITWAITWAIT
so like
as long as they're discrete intervals
like 1,2,3
beacuse x<z and y<=z and
so if x=1 and y=2
z has to be 2 or higher
so it couldn't be the real numbers?
any subset of R then?
sharp vigil
any subset of R then?
not just any subset of R. think about the type of subset that comes up when we talk about "discrete" things
sharp vigil
just like integers, whole numbers, and natural numbers
so let's take the integers, since the other two are subsets of that. does the statement work on the integers?
violet wing
well in some cases. if youve got {-1,0,1} and x=-1 while y=0 it would work
but couldn't x=1 and y=-1, if either can represent any number of the set?
sharp vigil
so the "for all" means that we have to make it work for every x in the set. but the "there exists" means that at least 1 y in the set satisfies the condition. so we don't get a choice of x, but given an x, we get to pick a y (if we can), to make it work
violet wing
OH
I SEE WHAT YOU MEAN
so as long as a y exists that will be greater than x, it will work
sharp vigil
yes, but we also need a guarantee that if z is larger than x, then it is at least as big as y. since we don't get to pick z, we need to make sure there can't be any numbers between x and y
violet wing
and that's why it can't be a real number because it could be a fraction
i'm confused on z still
sharp vigil
well let's say that x = 3, then we could choose y = 3.5. but then we still have the issue of z = 3.25, so it doesn't work
the problem we run into is that we can always find a z that is somewhere between x and y
violet wing
do you mean when x = 3?
sharp vigil
yes x = 3, sorry
sharp vigil
the problem we run into is that we can always find a z that is somewhere between...
what subset of real numbers doesn't have this issue? is there a type of number where we can pick two numbers and there aren't any numbers between them?
sharp vigil
doesn't it work with integers since there isn't any "gaps"?
yes
with the integers we can have a "next integer" which we can't have on the real numbers
violet wing
OH BECAUSE
x<y holds true in any sense
and if y<=z, z cannot be less then x, thus x<z
sharp vigil
well the implication is the other way around. we want it to be true that 'if x < z, then y <= z'. in other words, any number bigger than x must be at least y, in other words, we can pick y which is the "next number after" x and there aren't any numbers between them
violet wing
so for example
x=1, and z=2
if 1<z y<=z
so y is 2
okay
i get it
so it does work with integers because y comes directly after x, and no numbers are between them where z=>y
hasty galleon
why is sin the answer shown here and not 5/sqrt61 ?
pearl pondBOT
why is sin the answer shown here and not 5/sqrt61 ?
barren quarry
because u can’t have a radical at the bottom
hasty galleon
this is new to me
barren quarry
so u find the hypotenuse using pythagorean theorem
hasty galleon
ah i see, its 5/sqrt61 but multiplied by sqrt61 so the square root is moved up top
right?
barren quarry
yup
hasty galleon
thank you goat 🙏
pearl pondBOT
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Available help channel!
@velvet wolf Has your question been resolved?
pearl pondBOT
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velvet wolf
any <@&286206848099549185>
pearl pondBOT
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onyx moat
pearl pondBOT
onyx moat
My working so far is that there is 7C3 ways to incorrecty guess the other 7 songs, and 3C0 ways to incorrectly guess the 3 band songs, and 10C3 ways to choose 3 songs from the 10, so my answer is 7C3*3C0/10C3 = 7/24. is this right?
pearl pondBOT
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onyx moat
<@&286206848099549185>
vestal tapir
this makes no sense
oh ok
so like they know all songs, but not the order, one of 10! guesses
yeah 7c3/10c3 makes sense
no not right
they have to guess the exact song, this only "allows" them to guess the band
you gotta do inclusion exclusion
guess first song right: 9!
guess first two songs right: 8!
guess all songs right: 7!
3(9!) − 3(8!) + 7!
pearl pondBOT
@onyx moat Has your question been resolved?
onyx moat
Wait so what would the probability work out to
vestal tapir
,calc 1 - (3(9!) - 3(8!) + 7!)/10!
jolly parrotBOT
Result:
0.73194444444444
Result:
0.73194444444444
Could u elaborate a little bit on the inclusion exclusion
I understand them individually but not all together
Oh nvm I just saw the 1 - lol
I think I get it now
vestal tapir
yeah we find union of outcomes where something was guessed right
onyx moat
I see
Is this just a counting problem? or can we apply a probability distribution somewhere bc that’s kind of the theme of worksheet
vestal tapir
i don't know
well
maybe the idea is you just always have 1/10 chance, instead of choosing a permutation
then it's just binomial
a differetn answer, but it maybe makes sense too
no they said "only once"
so it's clearly about permutation
onyx moat
I was thinking maybe hypergeometric fit in somehow but I’m not sure
vestal tapir
it would make sense if it was about identifying the band, so the same thing you said first
so it's possible, just wrong wording
outer hare
Is the rate of convergance for a taylor series always the highest polinomial you use?
outer hare
Basing it from this:
Ok here is a better question, why is the remainter therum located where it is:
should it not be + error, why is it being multiplied into the last portion?
pearl pondBOT
@outer hare Has your question been resolved?
upbeat ocean
Need help with calculus
pearl pondBOT
Need help with calculus
verbal whale
Be more specific, or just ask directly the exercise/doubt on the theory
upbeat ocean
I want to ask about
The integration with numbers formula
Oh wait
Wth am I doing
Sry sry
.close
pearl pondBOT
mental aspen
Hi guys I am having trouble on what type of angle this is: co interior, corresponding, alternate
@eveyone
<@&286206848099549185>
midnight haven
@mental aspen with what angle
mental aspen
Like identifying what angle it is
verbal whale
<@997055475080253470> with what angle
yes, but the names "cointerior, corresponding ..." refer to pairs of angles
mental aspen
Ok thank you.
midnight haven
Like identifying what angle it is
i think the alternate they are like a Z outside and inside and corresponding like double L
i use that to identify
mental aspen
ok thanks for the tip
pearl pondBOT
Available help channel!
pearl pondBOT
livid bolt
what if i put root 4 and did the same process
cosmic charm
how does doing this prove that its irrational
what part do you not get
livid bolt
what part do you not get
i dont get how showing that it has common factors shows that its irrational
cosmic charm
i dont get how showing that it has common factors shows that its irrational
you assumed that p and q has no common factors
but in the end you end up with p and q having a common factor of 2
livid bolt
you assumed that p and q has no common factors
p^2 = 2q^2
how does this show that p is divisible by 2
cosmic charm
p² is an even number since its 2 times some integer
livid bolt
p² is an even number since its 2 times some integer
5^2 = 25
cosmic charm
and if p² is even, then p has to be even
cosmic charm
and if p² is even, then p has to be even
if you want to prove this on your own go ahead, extremely simple to do
cosmic charm
no sqrt(3)
i remember seeing a proof of this but i forgot
livid bolt
nooo 😭
my test is tmr
and its on complex numbers proof of contradiction and induction
im cooked
livid bolt
https://tenor.com/view/skull-issues-gif-13031152103567454559
hi water beam
do u wanna see what i got for my chem test
livid bolt
wild fable
6/26
livid bolt
..
livid bolt
hey i got this before though..
wild fable
livid bolt
im doing a titration 🫨
livid bolt
cap
dw you'll do fine
u cant do as bad as me
i cant believe
i finished unit 1 and 2 of specialist and i havent dropped it 😭
im so proud of my self 😭
livid bolt
go do normal maths stop doing accelerated!!
NO
😭
if i finish it early
in year 12 i can just cruise through
livid bolt
yes i am
ima finish specialist and methods early
and have sm time to study for others
wild fable
are u good at english
cosmic charm
no sqrt(3)
well i just searched for this online and its pretty similar
livid bolt
i can do mid in it
i cant do like
very well in it
bc i have never finished a book in my life 😭
only the in class ones where the teachers read it to u
livid bolt
well i just searched for this online and its pretty similar
can i see it..
just in case its in my test..
pearl pondBOT
@livid bolt Has your question been resolved?
stoic imp
pearl pondBOT
warped rapids
people who are good at math arent very good at english
Both requires different cognitive faculties
stoic imp
(6x) square is 36x^2
midnight haven
(6x) square is 36x^2
noooo
like whats lim cosx-1 whole /x2
its 1/2
use that logig
pearl pondBOT
@stoic imp Has your question been resolved?
stoic imp
.close
pearl pondBOT
pearl pondBOT
Available help channel!
rose sentinel
33 don’t know how to start, I’m thinking something with conjugates and u sub but I can’t get it to work
slim moss
what did you use as the u sub
rose sentinel
so yes what did you try for the sub
Well I tried y-1 and y+1
Neither seemed to work and no other one seemed relevant
frozen lantern
oh no
yeah it won't
it's a trig sub
think of all the trig identities which look similar
rose sentinel
what did you use as the u sub
I can’t do trig sub yet it’s prior to that
Not meant to be
rose sentinel
Well it very well might but but there must be a non trig sub method
It’s not my instructor it’s a book
Trig sub is another 30 pages from here
compact ridge
frozen lantern
lemme see if i can think of non trig stuff
worthy lance
You can use u sub = the whole thing
compact ridge
I found this by searching on approach0.xyz
frozen lantern
okay but that's even worse 😭
compact ridge
not really
rotund creek
i like that method
worthy lance
yeah it won't
It can be dine like this too
compact ridge
oh they mean u = 1 - x^2 lol
worthy lance
There is no one single way of doing things
rose sentinel
Uhmm
frozen lantern
It can be dine like this too
through that sub?
rose sentinel
I’m lost
frozen lantern
i just dont see it ig
worthy lance
through that sub?
Yes but i don recomment
frozen lantern
Yes but i don recomment
hmm lmaoo
compact ridge
if you sub u = the whole thing you have to do a partial fraction decomposition
rose sentinel
I don’t know that stuff
frozen lantern
i honestly think the cleanest is the trig sub here lmao
worthy lance
Well, what do you know?
frozen lantern
if you know trig i'd recommend trying it just for the lols anyway
frozen lantern
Well, what do you know?
indeed lmao :')
rose sentinel
uhm like everything integration by parts and earlier
Wait what’s du/dx then I can’t do it rn I’m walking to clsss
When you say whole thing you mean everything within the radical or radical included?
rose sentinel
The latter?
worthy lance
It doesnt matter
rose sentinel
What’s du/dx then
rose sentinel
Either
worthy lance
Well you are the one who has to work out on that
rose sentinel
I’m typing on my phone on a sidewalk 😭
worthy lance
Do not try this exercise if you are not in a chair and table
worthy lance
What is that?
rose sentinel
du/dx?
thin
I think
Wait I see how to do it
Conjugate and then just make two fractions
Right?
rotund creek
yes
pearl pondBOT
pearl pondBOT
Available help channel!
pearl pondBOT
simple elbow
Find the values of the constant c for which the line y= x+c is a tangent to the curve y = 3x + 2/x
frozen lantern
What lmao
simple elbow
uhhh how do I solve this
frozen lantern
first you get a separate channel
unkempt yacht
Find the values of the constant c for which the line y= x+c is a tangent to the ...
!occupied
pearl pondBOT
Find the values of the constant c for which the line y= x+c is a tangent to the ...
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).
latent quail
I dont get it
開一個你的頻道
simple elbow
感谢啦
grand idol
Find the values of the constant c for which the line y= x+c is a tangent to the ...
b^-4ac=0 of y=3x+2/x
simple elbow
还有我的繁体挺差的 xs
grand idol
then c=-x
simple elbow
b^-4ac=0 of y=3x+2/x
oh
latent quail
还有我的繁体挺差的 xs
好吧，我可以转成简体
simple elbow
好吧，我可以转成简体
thank
grand idol
hmm
simple elbow
Heehee
grand idol
you know derivatives?
simple elbow
🤷🤷
grand idol
like dy/dx and shi
simple elbow
Nah we don't write that lol
grand idol
oh
grand idol
ohh
simple elbow
B squared -4ac =0
simple elbow
3x + 2/x=0
grand idol
we know that for a line to be tangent to a curve the y value shud be equal
so equate em
simple elbow
Yes
grand idol
so x+c=3x+2/x
grand idol
that gives $x^2+(c-3)x-2=0$
simple elbow
huh wait let me digest rq
grand idol
3x - x + 2/3
what
jolly parrotBOT
zen
simple elbow
oh
grand idol
get it?
simple elbow
why c-3
simple elbow
to get rid the fraction?
jolly parrotBOT
zen
grand idol
it gives this
grand idol
to get rid the fraction?
yea
simple elbow
alr
jolly parrotBOT
zen
simple elbow
i got the answer tysm
its actually so simple lollll
my dumbass just dont get it but i got it now tysm
grand idol
lol its aight
simple elbow
tysm
also what does The line y = 2x + k is a tangent to the curve x^2 + 2xy + 20
mean
exactly
grand idol
also what does The line y = 2x + k is a tangent to the curve x^2 + 2xy + 20
it only touches the curve in a single point
simple elbow
ooh i got the answers already and also
theres a b) for it
its uh for each of these values of k, find the coordinates of the point of contact of the tangent with the curve
k = 10 or =10
10 or -10
pearl pondBOT
@grand idol Has your question been resolved?
pearl pondBOT
@grand idol Has your question been resolved?
pearl pondBOT
@grand idol Has your question been resolved?
cedar perch
I mean I know it's true because i did a weird repeated integration by parts method to get a form of the integral of the bell curve (too lazy to explain it, it was a pain in the ass 😭 )
but is there like.. a way it telescopes?
Also the L is just supposed to be a standin for the limit as the variable goes to infinity
(desmos doesn't have limit notation.. i think)
$lim_{L \to \infty} \sum_{n=0}^{L} \frac{(2n+1)x^{2n} - x^{2n+2}}{\prod_{k=0}^{n} (2k+1)} = 1$
jolly parrotBOT
Serphic
cedar perch
there we go okay
pearl pondBOT
pearl pondBOT
Available help channel!
latent crescent
help
finite pagoda
youre almost done, just remove absolute value sign, and solve both equations as normal
latent crescent
what are you trying to find
yes
x
@finite pagoda
can u help me solve
@thin bane
@plush bramble
<@&286206848099549185>
@real tiger
latent crescent
bro i need help
plush bramble
!noping
pearl pondBOT
Please do not ping individual helpers unprompted.
finite pagoda
can u help me solve
wait a min
simple jasper
is that $| 3 - \frac{1}{3}x| - \frac{7}{4} = \frac{1}{2}$?
jolly parrotBOT
dragonbreath
chilly sand
I found the solution can I send my work here
latent crescent
ok
chilly sand
2 minutes pls
simple jasper
In your second line where you have the two functions equal to 9/4 and -9/4, drop the absolute values and solve accordingly
simple jasper
For example $|x - 3| = 4$ is equivalent to $x - 3 = 4$ and $x - 3 = -4$
jolly parrotBOT
dragonbreath
latent crescent
thanks
finite pagoda
you're welcome hope you'll understand
chilly sand
I'm getting 9/4 and 63/4 as solutions
chilly sand
you're welcome hope you'll understand
You might have made a mistake somewhere
chilly sand
Is it 9/4 or 3/4?
latent crescent
i don’t get this
finite pagoda
Is it 9/4 or 3/4?
63/4 was right
chilly sand
Yours is correct, the 9 looks like 3 for me so i got confused
finite pagoda
Yours is correct, the 9 looks like 3 for me so i got confused
haha its ok
chilly sand
haha its ok
Lol I have skill issues
finite pagoda
you multiply the numerator in the first fraction times the denominator in the second fraction, then you write that number down. Then you multiply the numerator of the second fraction times the number in the denominator of your first fraction, and you write that number down. So this way you'll remove denominator
finite pagoda
Lol I have skill issues
it happens 😛
chilly sand
it happens 😛
Very relatable lmao
latent crescent
do both negatives cancel out and that’s y they are positive
finite pagoda
yess
latent crescent
thx
finite pagoda
you're welcome
chilly sand
Close if you don't have any doubts
chilly sand
now do i plug the numbers in for x to see if they work
No need
latent crescent
why not
latent crescent
yes
chilly sand
Ok then you do
chilly sand
How do you guys write neatly on a whiteboard?
chilly sand
i use samsung tablet
Ohh
chilly sand
its hard to write with mouse
I tried writing with a mouse but no one was able to understand
chilly sand
I tried writing with a mouse but no one was able to understand
Skill issue btw
finite pagoda
yeah it takes too long and letters or numbers are always edgy
i cant even read what i wrote after some time
latent crescent
@chilly sand
chilly sand
<@809276055411359795>
Yes
latent crescent
it says only negative 1 works but
when i plug -1 in it doesn’t = to the other side
that means they’re both wrong
chilly sand
it says only negative 1 works but
-1 is the only solution
latent crescent
how
i input it to the equation after and it’s not equal to thebotherbside
the other side
@chilly sand
chilly sand
Wait let me explain
You see abs (b+5) is always positive
Take the case as -(b-3) =b+5
You'll ultimately get the answer for this one upon solving this
@latent crescent
chilly sand
Idk whether it's correct , ask her
chilly sand
B<-5, b<3 can this be possible?
chilly sand
I don't want to confuse you
You should take either both as positive or one positive and other as negative
latent crescent
but which one do i know to take as negative
chilly sand
but which one do i know to take as negative
Your wish
chilly sand
if i do it this way it doesn’t work
You apply the answer to the question...
Not with that
latent crescent
to find the solution
chilly sand
It's 2am here
latent crescent
all good
chilly sand
You got the answer?
chilly sand
4=4, hence your solution is indeed correct
chilly sand
4
chilly sand
Anything you put inside the modulus function the output will always be positive
Hasn't your school taught that?
latent crescent
interesting
i didn’t know that
thx
so if i get |-5-5/6|
the answer is
5+5/6
latent crescent
good afternoon for me
chilly sand
If you have any doubts dm me
chilly sand
good afternoon for me
Lol
pearl pondBOT
@latent crescent Has your question been resolved?
copper pagoda
pearl pondBOT
copper pagoda
im not sure if this is right i kind of inferred that deltaY is greater than dy
pearl pondBOT
@copper pagoda Has your question been resolved?
copper pagoda
.close
pearl pondBOT
pearl pondBOT
Available help channel!
abstract rune
bro
abstract rune
am i tripping
plush bramble
Is Pa pascal
abstract rune
yeah
plush bramble
looks right
abstract rune
WHY IS THAT RIGHT
plush bramble
,w si unit pressure
jolly parrotBOT
plush bramble
,w si unit pascal
jolly parrotBOT
plush bramble
WHY IS THAT RIGHT
did you not understand the steps shown?
woeful stump
WHY IS THAT RIGHT
dimensions can indeed seem odd
abstract rune
did you not understand the steps shown?
nah its just pissing me off that im just now realizing this
ill survive, whatever
.close
pearl pondBOT
woeful stump
ohm = kg m^2 s^−3 A^−2
pearl pondBOT
Available help channel!
ripe prairie
I don’t understand how to solve this rational equation
pearl pondBOT
I don’t understand how to solve this rational equation
ripe prairie
ripe prairie
Do I simplify 2x-6 to x-3
verbal whale
2x - 6 = 2(x - 3)
pearl pondBOT
pearl pondBOT
Available help channel!
misty gorge
pearl pondBOT
misty gorge
They hate me because i'm the flash
fluid sequoia
what is Ws and Wt?
misty gorge
partial derivative of W with respect to s and partial derivative of W with respect to t
rough forge
partial derivative of W with respect to s and partial derivative of W with respe...
Do you know the chain rule?
jolly parrotBOT
bacc
misty gorge
O i see
rough forge
F(u(1,0),v(1,0)) = F(5,3)
misty gorge
Thank u
rough forge
no problem
misty gorge
.close
zinc flower
How do i solve this with 2 variables?
pearl pondBOT
How do i solve this with 2 variables?
pearl pondBOT
pearl pondBOT
Available help channel!
midnight haven
don't understand how I am supposed to take y = -1/8x - 3/8 and turn into this form Ax+By=C
chrome plank
don't understand how I am supposed to take y = -1/8x - 3/8 and turn into this fo...
Step 1: Ax+By=C has both x and y terms on the same side. So, how can you manipulate y = -1/8 x - 3/8 to get x and y on the same side?
midnight haven
add -1/8x + both sides ?
chrome plank
yeah, lets try that
midnight haven
1/8x + y = -3/8 ?
chrome plank
yeah, it's almost there though.