#help-0
lone heartBOT
cunning bloom
should it not only be x^2 and (x-1), where did A/x come from?
alpine sable
\begin{align*}
\f{A}{x} + \f{B}{x^2} &= {\c z \f{x}{x} {}\cdot{}} \f{A}{x} + \f{B}{x^2} \
\f{A}{x} + \f{B}{x^2} &= \f{Ax}{x^2} + \f{B}{x^2} \
\f{A}{x} + \f{B}{x^2} &= \f{Ax+B}{x^2}
\end{align*}
ocean sealBOT
lone heartBOT
lone heartBOT
Available help channel!
twin drum
what is the sequence for this? 1, 3, 7, 11, 13, 17, 31, 37, 71, 73
fiery cliff
what is the sequence for this? 1, 3, 7, 11, 13, 17, 31, 37, 71, 73
Ig All are prime numbers
twin drum
fr?
twin drum
oh i probably missed a number
twin drum
Shouldn't it be, 1, 3, 7, 11, 13, 17, 31, 33, 37, 71, 73 ?
wait but 33 aint prime
what would be the sequence for that tho?
fiery cliff
wait but 33 aint prime
Yes...! As I said all are prime numbers
wild trail
oh, maybe it's all primes formed by 1, 3 and 7
wild trail
as in all primes which only use numbers 1, 3 and 7
twin drum
oh ok that would make sense
wild trail
although, to be nit-picky 1 is not a prime
inner path
not necessary primes
small elbow
@twin drum once again check the sequence??
twin drum
<@999854344365154455> once again check the sequence??
yuh this is it "1, 3, 7, 11, 13, 17, 31, 37, 71, 73 "
so the next number can be like 131
wild trail
seems like it
modern sedge
113?
twin drum
oh i guess 113 then 131
modern sedge
yep, and then 137
twin drum
173
311
thank you guys
maybe the rule is that it can be formed by 1,3,7 and it has to only be divisible by 1 and itself
since 1 isnt prime
fiery cliff
maybe the rule is that it can be formed by 1,3,7 and it has to only be divisible...
That's the only logic holds true
jade dagger
lone heartBOT
jade dagger
Is this right? Or am I doing it wrong?
jade dagger
I was wondering if it was intentional or a printing error, so if they are unrelated I can take these as constants right?
naive valley
if u is not a function of t, then $$\lim_{t \to \infty}\frac{e^{u/10}}{u^3}$$ is just $$\frac{e^{u/10}}{u^3}$$
ocean sealBOT
Bungo
naive valley
no differentiation involved
lone heartBOT
lone heartBOT
Available help channel!
granite ore
help
cinder spindle
vave
granite ore
this one
cinder spindle
,rrtw
cinder spindle
,rotate
ocean sealBOT
cinder spindle
you have a good start
ocean sealBOT
chromium
cinder spindle
and the expansion i'm going to assume is correct
granite ore
ye
cinder spindle
now
hollow shale
You've expressed f as a polynomial. Using the remainder theorem, you know that f(4) = 20.
granite ore
yes
cinder spindle
hang on
before we got to that we should address k
because that is quite easy to figure out
granite ore
oh
cinder spindle
the question tells us that the coeffiecent of x^3 is -2
hollow shale
And if you expand the above product of brackets, what is the coefficient of x^3?
hollow shale
If you scale a polynomial by some constant, do the values of its roots change?
granite ore
i think so
hollow shale
Do they?
granite ore
i dont know
hollow shale
Try messing with some polynomials on desmos.
cinder spindle
i think you fucked up your expansion
granite ore
omg
granite ore
aaaa
cinder spindle
-x^2
granite ore
oh
granite ore
ocean sealBOT
granite ore
idk
granite ore
ok
cinder spindle
$f(x) = x^3 + kx^2 - x^2 - kx - 2x -2k$
ocean sealBOT
chromium
cinder spindle
$f(4) = 4^3 + k4^2 - 4^2 - k4 - 24 -2k = 20$
ocean sealBOT
chromium
cinder spindle
because they told us the remainder of x - 4 is 20
granite ore
yes
cinder spindle
fuck up
granite ore
.-.
cinder spindle
$f(4) = + k4^2-6k = -4$
ocean sealBOT
chromium
cinder spindle
$f(4) = 10k = -4$
ocean sealBOT
chromium
cinder spindle
k = $\frac{-4}{10}$
ocean sealBOT
chromium
hollow shale
lol
granite ore
what
granite ore
yeh
granite ore
how to do
cinder spindle
lets start from scratch
granite ore
ok
cinder spindle
$f(x) = x^3+kx^2-x^2-kx-2x-2k$
ocean sealBOT
chromium
hollow shale
For some $f(x) = (x - a)(x - b)(x - c)$, define $g(x) = kf(x)$. We know we can express f(x) as a product of its roots, giving us: $$g(x) = k(x - a)(x - b)(x - c).$$ To find the roots of g, set the LHS to be 0: $0 = a(x - a)(x - b)(x - c) \Rightarrow 0 = (x-a)(x-b)(x-c),$ Thus, the roots of g and f are the same.
ocean sealBOT
Castroploiin
hollow shale
So, (generally) scaling a polynomial does not change its roots.
granite ore
hm-
cinder spindle
seems like a lot of waffle
hollow shale
The coefficient of x^3 without a constant at the front is 1. To get from that to -2, you multiply by -2.
cinder spindle
đ§
granite ore
everything by -2?
hollow shale
Yes.
hollow shale
So $f(x)$ now becomes $-2(x + 1)(x - 2)(x + k)$
ocean sealBOT
Castroploiin
hollow shale
And now you use that f(4) = 20.
hollow shale
No?
hollow shale
**Castroploiin**
Re:
cinder spindle
so the remainder would be different
hollow shale
No.
You're assuming that f(4) = 20 with the polynomial you wrote earlier.
But you're presupposing what the polynomial is, which is indeed "illegal."
cinder spindle
fuck my ass
say, @hollow shale , need help with a vector question, will make a channel now, feel free to check it out đ
hollow shale
While you're at it, try being nicer than saying "fuck up."
cinder spindle
don't be rude now
hollow shale
.close when you're done.
granite ore
okay
do i sub in
the
f(10) into he (x+1)(x-2)(x-5) or
the expanded equation
@hollow shale
help
hollow shale
Either.
granite ore
but
hollow shale
The product one will be nicer to work out.
granite ore
i got different answers for both
hollow shale
f(10) into he (x+1)(x-2)(x-5) or
Did you forget the -2 here?
urban sorrel
Hello, i am doing functions rn. I got a function:
f:x -> x²
And
-f(-5)
I know I need to do f(-5) = (-5)² = 25
But i am confused about the -f , i have never seen this before.
hollow shale
It should just mean -f(x), no?
pliant cedar
-f(x) is just f(x) multiplied by -1
viscid pawn
so it's -((-5)²)
pliant cedar
If you know what f(-5) is equal to, that number multiplied by -1 is -f(-5)
viscid pawn
if i translate it mathematically
urban sorrel
If you know what f(-5) is equal to, that number multiplied by -1 is -f(-5)
So the anwser is -25?
pliant cedar
Yes
urban sorrel
Lol
viscid pawn
So the anwser is -25?
yes
urban sorrel
Okay bcs it was weird bcs every negative number had -f(-"somenumber")
viscid pawn
Because the function isn't linear lmao
urban sorrel
So i was confused
quasi vector
you can treat f(x) effectively as a variable
urban sorrel
If u had 2f(x), that would just be 2 Ă f(x)
Thx now i get it
viscid pawn
urban sorrel
How can i close this case?
viscid pawn
quasi vector
.close
lone heartBOT
urban sorrel
.close
pliant cedar
Type .close
viscid pawn
done
urban sorrel
Thx
lone heartBOT
Available help channel!
river salmon
In isosceles right angle â˛ABC, the top angle â BAC = 100°, extend AB to D, make AD=BC, and find the degree of â BCD. help plz
lone heartBOT
In isosceles right angle â˛ABC, the top angle â BAC = 100°, extend AB to D, make A...
pliant cedar
You can't have an isosceles right triangle with one angle being 100
river salmon
eh yes
so it is not a right angle
In isosceles â˛ABC, the top angle â BAC = 100°, extend AB to D, make AD=BC, and find the degree of â BCD.
jade hollow
In isosceles â˛ABC, the top angle â BAC = 100°, extend AB to D, make AD=BC, and fi...
did you try making a diagram?
river salmon
do you wantďź
jade hollow
do you wantďź
yea
river salmon
lone heartBOT
@river salmon Has your question been resolved?
lone heartBOT
@river salmon Has your question been resolved?
lone heartBOT
@river salmon Has your question been resolved?
lone heartBOT
@river salmon Has your question been resolved?
lone heartBOT
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Available help channel!
uncut smelt
hi i would like some help on the following
lone heartBOT
hi i would like some help on the following
alpine sable
u ignore it. this type of math homework should be illegal. Only to be solved in the classroom where a professional aka "professor" is able to help
wild trail
shouldn't be that hard, just check all the conditions for subgroup
uncut smelt
idk how to
wild trail
Do you remember the conditions for subgroup?
uncut smelt
yeh theres an for a,b element of H ab is also elemt of H then there is an a such that inverse a^-1 is also elent of H
and the identity e is also elent of H
wild trail
yeah then just check if these conditions are satisfied for the sets given
uncut smelt
im struglling to appply to q tho
like for example part b
theres no e such that we get mapped to itself
wild trail
theres no e such that we get mapped to itself
Didn't quite understand what you're saying
uncut smelt
then if we take s1 and s2 elents of H then s1 composed s2 is s1(s2(3))=s1(1)=?
uncut smelt
Didn't quite understand what you're saying
the identity element
idk why im finding it very vague
wild trail
Yeah I know e is the identity element but what confusion do you have with (b)
uncut smelt
sigma 3 is mapped to 1
we dont know if there is a sigma that gets mapped to itself
wait a min lemme show u
wild trail
I vaguely understand what you're trying to say but you need to put it more clearly
uncut smelt
this what i tired
its bit messy
but like for b idk how to make sense of it
cuz i feel like with that question not much to go off
wild trail
looks correct to me
wild trail
but like for b idk how to make sense of it
I think you're overthinking, lemme help you out
Notice that e doesn't belong to H in (b)
So, (b) is NOT a subgroup
hope this helps
wild trail
wdym counter example?
you're first condition says that e should belong in the set
It doesn't so it is not a subgroup
uncut smelt
like usually when you want to say its not u come up with counter example
wild trail
A counter example is an example to disprove some hypothesis
This is straightaway, violation of what it means to be a subgroup
uncut smelt
ok then lol
i mean it makes sense now
i think was over thinking too much
Thank you soooo muchhh- honestly I appreciate it a lot!!
wild trail
suree
tribal lily
lone heartBOT
tribal lily
in the b part
1/2x + 2 > -2 it simplifies to x > 2 ?
and what happens to the + 3 ?
echo socket
x/2 + 2 > -2 solved is x > -8
echo socket
and what happens to the + 3 ?
The +3 does not affect the domain of that, it only affects the range
tribal lily
oh yea thx can you tell what happens in the range bec i am struggling with that a bit
echo socket
I like to think of it this way:
Since we are given that the range of f(x) is (-5, 10), it means that -5 < f < 10
tribal lily
okay then
echo socket
So, in this case, -3 * 10 + 3 < -3f(x/2 + 2) + 3 < -3 * (-5) + 3
Meaning -27 < y < 18
tribal lily
so the range is -27 < y < 18
echo socket
Right
tribal lily
and domain is -8
tribal lily
Meaning -27 < y < 18
it should be 12 instead of 18 right ?
echo socket
Why?
tribal lily
ohh yea - - cancel out
echo socket
x > -8*
tribal lily
thx
faint edge
Asked this yesterday but I had to leave before I could understand the answer.
In a card game where the probability of drawing a winning card is set at 0.58 and is independent of each successive draw, the player receives a payout 100x^2 where x is the number of winning cards drawn before a losing card. What is the expected value of winnings?
faint edge
My work includes calculating the probability of losing, 1-0.58 = 0.42
keen pasture
What have you tried?
faint edge
Then the expected value of the number of plays before the first loss would be 1 / 0.42 = 2.381
vale wigeon
the player keeps drawing until they draw a losing card, right?
faint edge
the player keeps drawing until they draw a losing card, right?
Yes
vale wigeon
the probability of drawing exactly $n$ winners followed by a loser is $0.58^n \cdot 0.42$
ocean sealBOT
Ann
faint edge
So I square that 2.381 and get 5.669 multiplied by 100 and get 566.9 round up to 567.
But it says it is wrong.
Wouldnât the probability of n be an infinite sum?
Doing it in numbers right now to see what I get.
vale wigeon
Wouldnât the probability of n be an infinite sum?
bad wording
vale wigeon
So I square that 2.381 and get 5.669 multiplied by 100 and get 566.9 round up to...
where do these numbers come from...
okay, so like
oh, alright, yeah, i see what you're doing and why it's wrong.
if we let, say, X be the random variable representing the number of winners drawn before the first loser,
you say E[X] = 2.381, and what you're looking for is E[100X^2], but you are calculating 100(E[X])^2.
these are not the same.
faint edge
I wasnât squaring the 100, but yeah. Thatâs what I was doing pretty much.
How do you know to use 100E(x^2) vs. 100E(x)^2?
I would think the latter is the correct choice because you want to know the payout which is equal to 100 multiplied by the number of winning cards drawn squared.
But because we donât know the number of winning cards drawn, we calculate the expected value of the number of winning cards drawn.
Which is where I am getting E(x) = 2.381
Then, because we expect to win 2.381 draws, we square that number of draws and then multiply by 100.
So I ask again, why is this wrong? And how do you know when to use E(x^2) vs E(x)^2?
Okay, so using numbers for my phone, I got E(x^2) = 5.1949 for using 0-29 as the number of winning draws. Which is very close to the answer. So I now know how to find the right answer, but I am still lost on how to determine using E(x^2) be E(x)^2. Thatâs the last clue to my puzzle.
vale wigeon
well, maybe we should think of a different example
let's say you're rolling a dice, and your score is the square of the number that comes up.
and let's again use the letter X for the random variable that results, i.e. the dice roll
your average score is (1 + 4 + 9 + 16 + 25 + 36)/6, of course
and this is the same as rolling a die that is inscribed with the numbers 1, 4, 9, 16, 25 and 36
does that make sense to you
faint edge
Not exactly. Would not rolling the second die lead to an expected score of (1+16+81+256+625+1296)/6?
vale wigeon
no...
okay, maybe i phrased this in a way that left nonzero room for misinterpretation
let's say you have two games
game A and game B
in game A you roll a standard die (i.e. with the numbers 1 through 6 inscribed on it), and the score is the square of the number that shows
in game B you roll a die with the numbers 1, 4, 9, 16, 25 and 36 inscribed on it, and the score is the number on the die itself
you agree that game A is entirely equivalent to game B, yes?
lone heartBOT
@faint edge Has your question been resolved?
faint edge
Yes
faint edge
Okay. That doesnât make sense. Because B has 1, 4, 9, 16, 25, and 36 inscribed, so x^2 would be the squares of those numbers, would it not?
vale wigeon
the numbers recorded on dice B are already squared
X is the roll of the dice from game A
...
i don't know how to explain it any better.
faint edge
Oh. Okay. That makes more sense then.
Sorry I am distractedly responding.
So X is the number of wins, not the expected number of wins, which is why I use E(x^2) here?
So I should use the expected number of squared wins vs the expected number of wins squared. Yesno?
Also, if I have a second question I am confused on, should I just put it here as well, or close this one and start a new post elsewhere?
leaden aspen
lone heartBOT
leaden aspen
I'm a bit confused about the combination of "plane" and all Reals squared here - can someone explain what they probably mean?
ie. is the 'plane' just the set of all squared Reals ?
fast lichen
$\mathbb{R}^2=\mathbb{R}\times\mathbb{R}$
ocean sealBOT
Køter
fast lichen
so every point (a,b) is in $\mathbb{R}^2$ thats why its the plane, where $a,b\in \mathbb{R}$
ocean sealBOT
Køter
leaden aspen
ok so would the first set a. be a patition of R^2 ?
it seems like that contains all possible reals and has elements outside of the set of R^2
Thank you for response but that just restates the info the in question
fast lichen
i dont understand how it would have elements outside of R^2. remember it is a subset
fast lichen
which of the following subsets are partitions. This requires that the subsets cover R^2 and that the elements in those subsets are disjoint
leaden aspen
Ok i see now - so since the first contains all reals, it must also be a partition of R^2?
fast lichen
thats the 1st requirement what about the 2nd one
leaden aspen
that x + y = c ? , it gives no Universal set for x,y though right?
fast lichen
no i mean the requirement i gave of something being a partition
the subsets have to be disjoint
leaden aspen
that they are disjoint?
fast lichen
yes
leaden aspen
ok I'm reading this: https://faculty.uml.edu/klevasseur/ads/s-partitions-and-law-of-addition.html
I'm not sure if there's something I'm missing I've gone through it a ton and seem to still be missing the basics of this my apologies
fast lichen
ye so b.
leaden aspen
do you know better resources to learn this ?
fast lichen
if $i\neq j$ then the two subsets have to be disjoint
ocean sealBOT
Køter
leaden aspen
that refers to different cardinalities right?
fast lichen
something being disjoint means that $A_i \cap A_j=\emptyset$
ocean sealBOT
Køter
fast lichen
that they have nothing in common
sly mantle
i,j are indices corresponding to sets in the collection
fast lichen
the intersection of the two sets are empty
leaden aspen
ok that refers to just each subset being disjoint from each other ?
they're both partitions (subsets ? ) of the first set R^2
sly mantle
essentially any pair of sets with different indices must be disjoint
the collection in part a) is $\brc{A_c}_{c\in\bR}$ where $$A_c=\brc{(x,y):x+y=c}$$
ocean sealBOT
RokettoJanpu
sly mantle
this collection being ``pairwise disjoint" means that $A_c$ and $A_d$ are disjoint whenever $c,d\in\bR$ and $c\ne d$
ocean sealBOT
RokettoJanpu
fast lichen
yes so the subsets of $\mathbb{R}^2$ constructed as they tell you in a. would be a partition if 1. the subsets cover $\mathbb{R}^2$ and 2. the subsets are pairwise disjoint
you have already claimed that for a. the 1st requirement for being a partition is satisfied now you have to show that 2. is aswell
sly mantle
yep, specifically the collection covers $\bR^2$ if
$$\bigcup_{c\in\bR}A_c=\bR^2$$
fast lichen
so do you atleast understand now what the excercise is asking of you? because then we can continue
lone heartBOT
lone heartBOT
Available help channel!
quiet kestrel
this was from the MIT 2022 integration bee finals (number 3)
How do i evalaute this?
quiet kestrel
I've been thinking of using a Dirichlet kernel to transform the two sines into 1+2[insert cosine series] but that didnt really help
using a contour integral didnt help (wth z=e^(ix)) due to the insane powers int eh denominator lmao
?
que
<@&286206848099549185>
lone heartBOT
@quiet kestrel Has your question been resolved?
lone heartBOT
@quiet kestrel Has your question been resolved?
sinful dome
But thatâs clearly not right
ocean sealBOT
pseudo ice
How'd you get this?
lone heartBOT
@sinful dome Has your question been resolved?
finite forge
@
lone heartBOT
@grizzled raptor Has your question been resolved?
agile path
Could someone please explain nth terms to me?
lone heartBOT
Could someone please explain nth terms to me?
gray isle
plugging in a value for n, gives you
that-th value in the sequence
eg plugging in n=1, gives you the first term
plugging n=2 gives you the second
n=567 gives the 567term
lone heartBOT
@agile path Has your question been resolved?
agile path
Iâm still doing it
agile path
n=567 gives the 567term
Aah
lone heartBOT
@agile path Has your question been resolved?
agile path
plugging in a value for n, gives you
that-th value in the sequence
How do you find 7th and 12th term?
I understand now
U7 or U5 are the numbers you substitute in Un equation
gray isle
5 and 7 themselves are you value you sub in
substituting in 5, (replacing all n with 5)
gives you the equation telling you what the 5th term is
agile path
Okie
I also donât know how to do this
What do they mean by âmake y the subjectâ?
Somebody?
Is it like this?
.close
unique haven
comment on fait la rotation sur cadrillĂŠ?
lone heartBOT
comment on fait la rotation sur cadrillĂŠ?
last ether
What's the urgency
arctic wadi
what is synthetic division?
limpid turret
what is synthetic division?
!help
lone heartBOT
what is synthetic division?
Please read #âhow-to-get-help
@unique haven Has your question been resolved?
unique haven
What's the urgency
its a homework
lone heartBOT
its a homework
gray isle
english?
fallen verge
Go to chat gpt for this đ
bro what
unique haven
Go to chat gpt for this đ
idk wat that
gray isle
translate or give the question in english
lone heartBOT
@unique haven Has your question been resolved?
kind field
vale wigeon
... do you have a question to ask?
vale wigeon
hi @ashen kiln, you'll want to open your own channel to ask your question -- this one's already opened in the name of that jokester.
sudden igloo
hi
vale wigeon
read #âhow-to-get-help for instructions on how to do that.
lone heartBOT
ashen kiln
could you help me in recommending the best pages for mathematical olympics
fallen verge
close it then
next time dont close a random persons channel unless you are sure they are joking
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Available help channel!
cedar pendant
lone heartBOT
cedar pendant
why is this not legitimate PDF?
i found the integral 0 to 2 and got 1
i know when you put 1.9 it gives negative value, which is wrong, but how am i supposed to know that? i cant possible check it with every single number from 0 to 2
lone heartBOT
@cedar pendant Has your question been resolved?
naive valley
i know when you put 1.9 it gives negative value, which is wrong, but how am i su...
you could determine which points x give f1(x) = 0, and then check a single point in each interval between those points
cedar pendant
you could determine which points x give f1(x) = 0, and then check a single point...
could you elaborate?
naive valley
f1(x) = 0 at x=0 and x=sqrt(3)
and f1 is continuous
so for 0 < x < sqrt(3) it can't change sign
and for sqrt(3) < x < 2 it can't change sign
so test a single point x in (0,sqrt(3))
and a single point x in (sqrt(3),2)
cedar pendant
f1(x) = 0 at x=0 and x=sqrt(3)
shouldnt f1(x) = 1 at x =1?
cedar pendant
oh i see now
naive valley
another way, f1 is also differentiable, so you can find its minimum by checking where its derivative is zero, along with the endpoints x=0 and x=2
cedar pendant
and a single point x in (sqrt(3),2)
i should check both and if it is incorrect they will be different signs?
i mean if it isnt PDF
naive valley
if you find a negative value in either interval then you know it's not a valid pdf
cedar pendant
ah right
naive valley
if both test points are positive then you know it's positive (or zero) everywhere
so then it's a pdf as long as it integrates to 1
cedar pendant
thanks a lot
naive valley
sure
cedar pendant
.close
merry depot
so... what is your answer for k?
wintry gazelle
so... what is your answer for k?
k is 14286 x 10^10
Cause i count sum of numbers that is multiple of 8, 64, 512, 4096, ...
And numbers like 64 that can be factorised by 8x8 will be included in both multiple of 8 and 64. So, these numbers will be counted twice
merry depot
so how are you accounting for the double count?
I mean... I can tell you that this value of k seems totally off
merry depot
And numbers like 64 that can be factorised by 8x8 will be included in both multi...
you say, explicitly that these numbers are counted twice, then seem to totally ignore that?
you add the multiples of 64 to the multiples of 8.
Also, all you showed was that p <= to this number, not that p = this number.
At best this shows that p <= 14286x10^10.
Not equality
wintry gazelle
Lemme process
I thought numbers that are multiples of 64 will also be counted in multiples of 8, and not vise versa?
vale wigeon
hang on tho.
merry depot
they are also multiples of 8. So you counted them when you counted multiples of 8
vale wigeon
why are we counting only those numbers in the product which are themselves divisible by 8,
and not ones that have an extra 2 or 4 factor?
merry depot
Think about it like this 2x4x6x8x10 = 2^8)x3x5 = 8^(5)x15
vale wigeon
one would think that we want the exponent on 2 in the prime factorization of $(10^{15})!$, dividing which by 3 and rounding down ought to give us the desired answer
ocean sealBOT
Ann
wintry gazelle
Think about it like this 2x4x6x8x10 = 2^8)x3x5 = 8^(5)x15
Owhhhhhh i understand this already, i forgot to account about multiples of 2^x which will multiplies to 8
Okay now i have to resolve this issue
Can i just count all multiples of 2^x and sum the numbers?
Okay im doing it rn
lone heartBOT
@wintry gazelle Has your question been resolved?
wintry gazelle
Is it correct?
vale wigeon
that... looks a little odd to me?
wintry gazelle
I do the same, except i find all multiples of 2^x instead of 8^x
Then since three 2 makes 8, i divide the sum of numbers by 3 and get the integer part
wintry gazelle
Heres example for smaller number, 2x4x6x8x10x12x14x16x18x20:
Multiple of 2: 10 (come from 20/2)
Multiple of 4: 5 (come from 20/4)
Multiple of 8: 2 (come from 20/8, take only integer part)
Multiple of 16: 1 (come from 20/16, take only integer part)
Sum of numbers = 10 + 5 + 2 + 1 = 18
k = 18/3 = 6 (take only integer part if the answer contains decimal)
Looks correct tho
Anyway thanks a lot for helping me!!!!
.close
umbral hatch
lone heartBOT
umbral hatch
It says that he makes deposits quarterly and its compounded annually
so how come the mark scheme made it so it compounds quarterly
or maybe Im just misunderstanding the compound interest formula
so can u help me understand it
lone heartBOT
@umbral hatch Has your question been resolved?
umbral hatch
<@&286206848099549185>
quaint furnace
for part a it is annually but in part b it says he makes deposits quarterly
fast lichen
ye so annual is 1+(3.2/100) but quarterly its 1+(3.2/(100*4))
umbral hatch
ye so annual is 1+(3.2/100) but quarterly its 1+(3.2/(100*4))
in the question he adds deposits quarterly
but its compounded anually
how do u represent that
fast lichen
nominal annual interest rates can be compounded quarterly if it is specified or even monthly
so in this case it is a nominal annual interest of 3.2% compounding quarterly with 0.8% per quarter
i do think it should be more clear though in the question that it compounds quarterly but its not a crazy assumption to make when they tell you he deposits quarterly
lone heartBOT
@umbral hatch Has your question been resolved?
cold leaf
math help
cold leaf
hello
modern sedge
Post question
cold leaf
Factor the expressions and write an equivalent expression using the distributive property
the question is 30b+60y
modern sedge
So what can you factor out?
cold leaf
uh 15
cold leaf
30
modern sedge
So what will be the full factored expression?
ocean sealBOT
MathIsAlwaysRight
modern sedge
What will be inside the parenthesis?
cold leaf
30(1b+0.5y)
modern sedge
If you expanded this, you would get 30b+30*0.5y. Which is 30b+15y
But you need it to be 30b+60y
cold leaf
but how 30 divided by 60 is 0.5
modern sedge
Yep, but you have to divide 60 by 30
cold leaf
so 30(1b+2y)
modern sedge
yep
ocean sealBOT
MathIsAlwaysRight
modern sedge
1b can be written as b
cold leaf
yeah in my class it is shown as wrong when you add a 1 next to a number
i also can barly speak
or think today
I woke up and bashed my head on brick
anyway i got more math problems
18x+24y
@modern sedge IS the facotr 6
modern sedge
yep
cold leaf
ok so 6 divded by 18 and 24 right
cold leaf
18(3x+4y)
modern sedge
yep
cold leaf
so 4(4n+3m)
modern sedge
correct
modern sedge
Yep
cold leaf
2(2x+5y)
modern sedge
correct
modern sedge
yep
cold leaf
12(2m+3n)
modern sedge
correct
modern sedge
yep
cold leaf
9(a+3b)
modern sedge
correct
cold leaf
says its wrong
modern sedge
Thats weird
cold leaf
what i put in was 9(a+3b)
modern sedge
ok so 9a+27b
Are you sure you typed the question correctly?
cold leaf
well that was wrong
modern sedge
3(3a+9b)
cold leaf
system shows wrong
modern sedge
bad system
cold leaf
its google sheet
modern sedge
Are you sure you have to factorize it?
cold leaf
yes its in the deractions
modern sedge
It must be wrong then
just skip that question and tell your teacher or whoever created it about it
modern sedge
yes
cold leaf
14(2x+3y)
oh crap
If i dont get this assignment done in 1 hour i will get a E
next problem is 45x+15y
15 is the facotor
modern sedge
yep
cold leaf
15(3x+y)
modern sedge
correct
modern sedge
If you want, you can save time by doing the easy tasks without verification. In last ~10 questions you didnt make any mistake
cold leaf
ok next one is 28x+35y
there facotor is 7
7(4x+5y)
ok next one is 8c+30d
there factor is 2
2(4c+15d)
@modern sedge Is this right
modern sedge
ye
cold leaf
ok next one is 16x+40y
the factor is 8
8(2x+5y)
ok next is 15v+6
there facotr is 3
3(5v+2)
ok next is 6f+4
there factor is 2
2(3f+2)
ok next one is 25n+55
there facotor is 5
5(5n+11)
ok 2an to last one
12g+18h
there factor is 2
modern sedge
there factor is 2
nope
cold leaf
is it 6
modern sedge
yep
cold leaf
6(2g+3h)
Alright last one
22a+55b
there factor is 11
11(2a+5b)
Hey @modern sedge thanks for the help
.close
summer stratus
lone heartBOT
quasi vector
!status
lone heartBOT
What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
1
quasi vector
do you know the laws of exponents?
summer stratus
most of it, but it still confuses me
quasi vector
well what are the laws that you know?
summer stratus
summer stratus
the denominator is 4xâ¸yâś?
quasi vector
yes
quasi vector
$\frac{9\cdot x^4}{4\cdot x^8} = \frac{9}{4\cdot x^4}$
ocean sealBOT
kheerii
summer stratus
oh sorry
ocean sealBOT
kheerii
summer stratus
which is?
quasi vector
what
quasi vector
yes but you can take the y^-1 to the denominator as well
summer stratus
9/4x^4 y^1?
quasi vector
$\frac{9}{4\cdot x^4\cdot y}$
ocean sealBOT
kheerii
summer stratus
9/4x^4 y^1?
is this the same?
alpine sable
how do i solve this
i know answer is 1/16 but like i have to simplify and answer
any1 can help?
steady basin
lone heartBOT
steady basin
need a bit of help plz
firstly, i don think i can find the intersection using these two equations since theres 3 unknowns and 2 equations
do i need to make each cart. equation into its parametric form first?
lemme have another go
lone heartBOT
@steady basin Has your question been resolved?
steady basin
will the equation be an equation of a line?
raven haven
pseudo ice
Well thereâs one way to find out⌠
pseudo ice
,w 2x+3y-z=4, x-5y+2z=7
ocean sealBOT
pseudo ice
You wanted that being -13 right?
pseudo ice
Yep looks all good to me!
One thing I will say though
Is that youâre basically solving the equations $2x+3y-z=4, x-5y+2z=7$
ocean sealBOT
@pseudo ice
steady basin
ye
pseudo ice
It might be easier to do that e.g. by the matrix method you learned earlier?
Where you reduce the corresponding matrix
pseudo ice
You could do it like that, you might like that more but itâs up to you(!)
Also another point too
Is that from this point, you could have taken those and set them to be some parameter and then just rearranged to get x, y, z to be in terms of said parameter, then write (x, y, z) in terms of that parameter (think that method youâve seen before?)
At least to me doing the cross product seems to be extra pain imo and itâs easier to do it without(?)
pseudo ice
Hmmm is there more steps they have after that?
steady basin
yh i was gonna do that
but our teacher never taught it like that
she taught us the cross product way
so i wasnt sure if i would be allowed to do that
but yh thats WAY easier
pseudo ice
Be better than your teacher 
pseudo ice
But yea, assumedly she might have assumed that it was obvious that you could do it like that, or maybe she just thought to teach it that way 
At the end of the day, whatever works and makes sense really(!)
steady basin
true
also chartbit
do u know how to derive this formula
its to find shortest distance from a point
steady basin
cuz i have a question thats asking me to use it, but derive it first đ
i can use it
easy
idk how to derive it tho
pseudo ice
Aha, found it 
steady basin
kl
pseudo ice
Check your DMs, that one is basically equivalent
lone heartBOT
@steady basin Has your question been resolved?
steady basin
.close
hot jewel
Hello! May I ask on how to get the value of X? I know the steps on getting the angle but I dont seem to get how you can get the value of x.. Property Of Parallelograms is the lesson thank you
hot jewel
vague mirage
Step one make a ||gm
Then apply the property : sum of angle in same side of two parallel lines are 180°
vague mirage
I like that name of second ||gm cause she never does that about me
hot jewel
Then apply the property : sum of angle in same side of two parallel lines are 18...
what i did was (x-5)(2x+20)=180
is that correct?
vague mirage
what i did was (x-5)(2x+20)=180
Why multiply
hot jewel
addition?
vague mirage
Yes sum means addition
hot jewel
Why multiply
i am new to the lesson and im having a hard time
hot jewel
Yes sum means addition
ohhh
vague mirage
i am new to the lesson and im having a hard time
Class 9?
vague mirage
Ha bhai thik h abhi add kr do
vague mirage
You have to add but you have to take care of signs
hot jewel
oh okk
vague mirage
Yupp
hot jewel
3x + 15 = 180
vague mirage
Yes
vague mirage
Yes you substitute it to x values of the angles then you will get the exact magnitude of the angles
And you have to find angle S and D don't forget
vague mirage
Divide by 1/3 in both sides
vague mirage
,w 3x+15=180
ocean sealBOT
vague mirage
Yes you're right
hot jewel
yay
vague mirage
Now put the value of x in
hot jewel
okok
vague mirage
And remember opposite angles in a ||gm are equal
vague mirage
opposite interior angles
Alternate interior angles
hot jewel
Alternate interior angles
o yes
vague mirage
And remember opposite angles in a ||gm are equal
Just use this concept
vague mirage
but i do know the theorems
You know all then theorems then why don't you use it?
Have confidence
Math requires confidential skills
hot jewel
yes
hot jewel
Just use this concept
like i add the two angles?
vague mirage
like i add the two angles?
Nope you have all the angles
hot jewel
You know all then theorems then why don't you use it?
idk how to solve, thats the part im confused
hot jewel
Nope you have all the angles
oh
hot jewel
Oh you have to make diagonals here
o
the one with like split into two
a parallelogram split into two triangles
vague mirage
the one with like split into two
Yes but you have to do it precisely
hot jewel
okok
vague mirage
Means you can't make a random cut you have to split according to the question
You can Join C and R though
hot jewel
o
hot jewel
C A
R E
Or
E R
C A
you said what i said on the second one
vague mirage
Sorry a lil mistake
vague mirage
I have edited that
hot jewel
after that
vague mirage
Btw
vague mirage
E R
C A
hot jewel
okok
vague mirage
Hm
hot jewel
done
hot jewel
caer