#help-27
magic rapids
yeah i didnt learn that
tawdry trellis
Idek if there’s some crazy inductive step here or something but I feel like you kinda need that knowledge
magic rapids
maybe
magic rapids
anyways is it too long to write that this way?
tawdry trellis
No that’s more or less how you’d write it
But that’s just a special case
I showed the general formula
(for integer powers)
magic rapids
supple trench
This is a better representation
Sorry to be picky but any experienced LaTeX user would prefer that the ellipsis to be vertically aligned with the horizontal stroke of the addition sign.
tawdry trellis
Sorry to be picky but any experienced LaTeX user would prefer that the ellipsis ...
Lmao that’s beyond picky but I didn’t write that
tawdry trellis
is this good?
I guess I mean sub in 1/x for y
tawdry trellis
Right
Look I’ll explain to you the method and you can decide if you can be bothered
So if you spot the matching coefficients of the terms (the numbers) we can factor each of those
Basically to get x^13 + 1/x^13 + 13(x^11 + 1/x^11) + 78(x^9 + 1/x^9) and so on
And we know the right hand side
So we can work out x^13 + 1/x^13 if we know the other terms
So basically
We can work out x^11 + 1/x^11 etc in the same way
It would take forever
But it would work
magic rapids
think i got it
tawdry trellis
Personally I’d try to spot some sort of pattern starting from x^3 + 1/x^3 but do what you will
rustic bramble
Isn't this connotation wrong? Since multiplying the matrix m times with itself is different from multiplying each element m times with itself?
devout snowBOT
Isn't this connotation wrong? Since multiplying the matrix m times with itself i...
supple trench
Idek if there’s some crazy inductive step here or something but I feel like you ...
my textbook's author also hided the combinatorical meaning of the theorem with induction. it's sad that many students get stuck reading the inductive proof
tawdry trellis
my textbook's author also hided the combinatorical meaning of the theorem with i...
Yeah the choose function especially should be taught before. It’s so incredibly useful I can’t believe it’s not completely standard material to learn, since it’s the perfect moment
supple trench
i confess that i needa take a moment to revise nHr
supple trench
Isn't this connotation wrong? Since multiplying the matrix m times with itself i...
it seems to me that the superscript m doesn't refer to index here
rustic bramble
should be (m) not m then, shouldn't it?
since (m) refers to the mth step in the rest of the book
supple trench
it would be better if you can provide the source, or the whole page/theorem/question/whatever.
it's like reading part of a sentence without knowing the context
rustic bramble
its from a German book unfortunately
the chapter is about markov chains
it basically says:
"the m-step transitionmatrix W^(m) is a transitionmatrix to the power of m, meaning:"
so while W^(m) = W^m is true i don't think the element notation is right
supple trench
should be (m) not m then, shouldn't it?
you mean the matrix elements?
rustic bramble
yeah for the matrix elements
supple trench
supple trench
yeah for the matrix elements
i agree that $w_{ij}^{(m)}$ is better than $w_{ij}^m$, but IMHO, that's question of style
woven radishBOT
vin100
rustic bramble
yeah i think for my thesis ill go with (m) since that just follows the rest of the style
thanks a bunch
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vast eagle
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winter patrol
what have you tried?
vast eagle
i have no idea what to do honestly i tried sqrt(m^91+2m^90) and tested answer choices
runic moth
you can do like m^90(m+2) m^90 is square of m^45 so (m+2) also must be sqaure of smth. 34+2=6^2. so answer should be E
vast eagle
you can do like m^90(m+2) m^90 is square of m^45 so (m+2) also must be sqaure of...
i see tysm!
.close
hybrid violet
This is a sat math question with no calculator
devout snowBOT
This is a sat math question with no calculator
hybrid violet
How can I solve this quickly? the officail explenation took me like 10 minutes to write everything out and the entire section you get 25 minutes for 20 questions
devout snowBOT
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@hybrid violet Has your question been resolved?
runic charm
Hey guys, how would I do this?
devout snowBOT
Hey guys, how would I do this?
devout snowBOT
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warped spire
You could try to show that the function is always decreasing, that it goes to -infinity as x goes to infinity and that it goes to infinity as x goes to -infinity
runic charm
You could try to show that the function is always decreasing, that it goes to -i...
hmm, did it like this
warped spire
shouldn't you also show that f'(x)=0 doesn't have any solutions?
devout snowBOT
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runic charm
shouldn't you also show that f'(x)=0 doesn't have any solutions?
Shall I?
I dont know honestly
warped spire
Well if I understand correctly you say to assume that f(a)=f(b) and show that this implies that f'(x) =0 for some x between a and b. What I assume is the point that you are trying to make is that this would contradict the fact (which you would have to show) that f'(x) is never equal to zero, so f(a) is not equal to f(b) for a not equal to b so you can only have at most one solution to f(x)=0
carmine eagle
I am trying to do this problem:
devout snowBOT
I am trying to do this problem:
carmine eagle
which looks like this on a graph
and revolve it around the x axis and then find the volume
so I did this in my calc
and it gives me this error
was wondering if someone knows a solution or if i did something wrong to get this etc.
devout snowBOT
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carmine eagle
<@&286206848099549185>
just tried another problem with pi in the boundaries and gave me same error
devout snowBOT
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devout snowBOT
@carmine eagle Has your question been resolved?
devout snowBOT
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Available help channel!
unborn leaf
If < 1 is 2x + 8 degrees and < 8 is x - 5 degrees, what is the value of x?
manic juniper
ok
let y=2x+8
what is the size of angle 4
let's do it an easier way
Angle 1 + Angle 4 = [1]º ([2])
(2x+8)+ Angle 4 = [1]º
Angle 4 = [3]º-[4]
Angle 4 = Angle 8 ([5], [6] // [7])
[3]º-[4]=x-5
[4]-x=-5-[3]
[6]=[7]
[8]=[9]
x=[10]
fill in all those
unborn leaf
ok
manic juniper
think
What is [1]? (Tip: Think of [2] first)
How would you prove the angle sum?
Angle 1 + Angle 4 = [1]º (adj. angles on st. line)
(2x+8)+ Angle 4 = [1]º
Angle 4 = [3]º-[4]
Angle 4 = Angle 8 ([5] angles, AB // CD)
[3]º-[4]=x-5
[4]-x=-5-[3]
[6]=[7]
[8]=[9]
x=[10]
wait a min
did it say AB is parallel to CD?
leaden aurora
hey
leaden aurora
How do I show that this function crosses the $\theta$ axis infinitely often $f(\theta)= 2\sin{\theta} + 4\sin{2\theta} + 8\sin{3\theta} + ... + 2^{n-1}\sin{(n-1)\theta}$
woven radishBOT
azeem321
leaden aurora
If we could get it in terms of one trig function and then find stationary points of that trig function i think that would be enough to prove that it cross the $\theta$ axis infinitely often. as trig functions periodic
woven radishBOT
azeem321
leaden aurora
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devout snowBOT
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wind sail
for this question i get X=-1 but if u dont cancel out the As and Bs if u dividing and have them as a inverses thats confusing
devout snowBOT
for this question i get X=-1 but if u dont cancel out the As and Bs if u dividin...
wind sail
sick marsh
I assume you can just do A(BX+I)=B which gives BX+I=A^-1B, BX= A^-1B-I which finally gives X=B^-1(A^-1B-I)
Only possible cuz determinant is non zero
Oh wait I think it's incorrect
Should be (BX+I)A I think
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Available help channel!
tight badger
i cant seem to find an integral to compare to for part c
devout snowBOT
i cant seem to find an integral to compare to for part c
tight badger
a lot of functions i've tried isnt entirely larger on the whole range 0 to infinity
nvm
.close
vague valve
devout snowBOT
vague valve
That the problem and my answer I would like to know if it correct
<@&286206848099549185>
devout snowBOT
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crystal rune
@vague valve Why subtract from 1?
vague valve
That the formula that I learn from my professor to solve that problem
vague valve
Yea
crystal rune
Yeah so that is already the probability of z < 0.9
if you subtract the value from 1, you get P(Z > 0.9) which you dont want
vague valve
Does the graph look correct?
crystal rune
Graph is right but the shaded area isn't what u need
you need the area to the left of z=0.9
which is just the value you get by reading 0.9 from the normal table
vague valve
Is there a way that you could demostrate it
crystal rune
You need P(Z < 0.9) which is the area to the left of the dotted line you made at 0.9
vague valve
Words could be so hard to understand
crystal rune
vague valve
So that the way the graph supposed to look
crystal rune
Yes
vague valve
So I need to shade to the left?
crystal rune
If you do 1 - ...., you get the other area which is P(Z>0.9)
Yes
so answer is just 0.8159 because reading the value from a normal table already gives area to the left
For the right area we subtract the value from 1
crystal rune
Yes for >
We first find value if 1.23 from normal table
Then subtract that value from 1
For <, you don't need to subtract, just put the value from the normal table
devout snowBOT
crystal rune
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✅
vague valve
don't close the section
let me do it and send it trying to get the assigment correct lo
How about now @crystal rune
devout snowBOT
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vague valve
devout snowBOT
vague valve
Would like to confirms if my answers is correct
otherwise help me to correct it
<@&286206848099549185>
<@&286206848099549185>
ANyone please helpppp
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tardy vessel
Hey I don't really need help with a question but does anyone have a Google drive link with past papers for methods.
Would really appreciate it if anyone had all saints college papers. Thanks :)
devout snowBOT
Hey I don't really need help with a question but does anyone have a Google drive...
@tardy vessel Has your question been resolved?
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@tardy vessel Has your question been resolved?
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@tardy vessel Has your question been resolved?
shy fossil
can someone dumb down the middle one (between the two equal signs) for me?
devout snowBOT
can someone dumb down the middle one (between the two equal signs) for me?
@shy fossil Has your question been resolved?
celest tide
devout snowBOT
celest tide
how do I evaluate this?
hmm so wolf says it's 2(√3 - 1)... so how did it arrive at that? I am assuming there is some method or algo involved?
I thought maybe it just substituted and evaluated to get a decimal answer .....
but it also gave an answer in the form of radicals.... was that just by simplifying ?
<@&286206848099549185>
halcyon night
<@&286206848099549185>
supple knot
hmm so wolf says it's 2(√3 - 1)... so how did it arrive at that? I am assuming t...
Yes just simplify
supple knot
13 times over wtf?
The values in the summand are periodic
Find a pattern by evaluating the first few
supple knot
You didn't learn that sines and cosines are periodic?
devout snowBOT
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celest tide
@supple knot how many periodic terms should i be getting?
2 or 3?
4 makes the most sense 
devout snowBOT
@celest tide Has your question been resolved?
supple knot
<@261933205387477002> how many periodic terms should i be getting?
Just evaluate them until you find a repeated term. It's not that hard
4 sounds right. Show your work if you want
deep flower
how do we get prime factorization of 24!
devout snowBOT
how do we get prime factorization of 24!
prisma ibex
product of primes (from 1 to 24) x the product of the non-primes i guess?
deep flower
the answer is $24! = 2^{22} × 3^{10} × 5^{4} × 7^{3} × 11^{2} × 13 × 17 × 19 × 23$ but dont know how to get it
woven radishBOT
2022 squared
merry seal
the answer is $24! = 2^{22} × 3^{10} × 5^{4} × 7^{3} × 11^{2} × 13 × 17 × 19 × 2...
write 24 as 1 * 2 * 3 * ... * 24 then factor each number
prisma ibex
write 24 as `1 * 2 * 3 * ... * 24` then factor each number
yeah i was about to say that
PS: you can write 2 as 2^1 , 4 as 2^2 etc and then when you multiply
the powers add up
do the same with stuff like 3 and 9
deep flower
write 24 as `1 * 2 * 3 * ... * 24` then factor each number
factor each number?
like 8 = 2^3?
merry seal
yeah
pseudo basin
there is a trick to it that can help somewhat
if you don't want to compute factorization after factorization
there's this formula called legendre's formula
which gives you the exponent of a prime p in the factorization of n!
what?
devout snowBOT
pseudo basin
oh, yes.
devout snowBOT
Available help channel!
left trench
$$
(3\Bbb N + 1) \cap (5\Bbb N + 3) = 15\Bbb N+13
$$
devout snowBOT
$$
(3\Bbb N + 1) \cap (5\Bbb N + 3) = 15\Bbb N+13
$$
woven radishBOT
0xj4yZ
left trench
Could you guys prove this ?
I tried a lot of things in 1 hour, but none of them are makes sense..
But I know that, 3N + 1 Set is includes number that remainder 1 when divided by 3, same thing for 5N + 3 remainder 3 when divided by 5
distant harbor
Does N include 0
left trench
Yes/no
Is it changes the answer though?
I just included it, $$6\Bbb N + 1 = {1, 7, 13, 19, ...} \ 5\Bbb N + 3 = {5, 14, 23, 32, 41, 50, ...}$$
whoops
weak tundra
**0xj4yZ**
To prove set equality, show that one is contained in the other.
Take n in (3N +1) n (5N +3). Then n is in 3N +1, so n = 1 mod 3, and similarly n is in 5N + 3, so n = 3 mod 5.
Use the CRT to conclude n = 13 mod 15.
Take n in 15N + 13. Then n = 13 mod 15. So n = 13 + 15k for some k in Z. Then n = 1 mod 3 and n = 3 mod 5.
left trench
To prove set equality, show that one is contained in the other.
Take n in (3N +1...
Wow! Thanks sir.
.close
green wagon
(r, theta) are the usual polar coordinates, I need to calculate the divergence and the curl of the following vector field
devout snowBOT
(r, theta) are the usual polar coordinates, I need to calculate the divergence a...
green wagon
I'm getting confused by the change of variables
wise sonnet
If you want to calculate the divergence in polar coordinates, you have to use your nabla operator in polar coordinates too. Either you just google, what it is and apply it or you calculate it by yourself
same for the curl
devout snowBOT
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green wagon
I didn't know the nabla operator was different for polar coordinates, that's probably where my confusion came from
thank you, I'll take a look and come back if I need more help
fading wedge
Can someone Tell me if I am right
devout snowBOT
Can someone Tell me if I am right
devout snowBOT
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devout snowBOT
@fading wedge Has your question been resolved?
blissful elk
If you want a nice bit of software to check your answer, Desmos - Graphing Calculator is pretty useful. Sub in your numbers and see how the desmos graph compares to the figure you've been given
worldly chasm
hi
worldly chasm
can someone please explain to me this notation?
sorry if its a stupid question
please someone help this is my first internship with a professor and im still in high school so a bit stupid but i really dont want to disappoint him tomorrow in a meeting
i know ∧ means "and"
prisma ibex
... means continuation
worldly chasm
but im a bit confused by the arrow and the "..."
prisma ibex
the arrow on the right, i think it means bm tends to the value 't'
worldly chasm
... means continuation
yeah i understand but continuation for what? Like, is it going to go like this fi1=b1 and fi2 and b2 ...?
prisma ibex
i think its the sum of b1 + ..... bm (which is f(im) ?)
is there anything before this
worldly chasm
Yes
prisma ibex
okay yeah sorry i have no idea what a rule is, if you could explain what it is maybe i could figure it out idk
btw, fi1 and b1 are not like equivalent to each other
thats what i understood by the second part
like fi1 ≠ b1 i think
worldly chasm
Oh alright but one question strictly regarding notation if you can help
when does a statement conclude to value "t" or i assume means truth
like when does value and value lead to true
how does it work
prisma ibex
when the limit of the expression goes towards a certain value, and gets very close to it you can consider it to be that value
like lim 1/x as x -> infinity for the domain of [0,infinity] you can say it tends to 0
(by graphical interpretation)
devout snowBOT
How do I do this question with the half life formula
prisma ibex
https://media.discordapp.net/attachments/903430333888884736/963292339865010216/u...
so you know the time taken for it to reduce to 1/16 of its original value
and you know half life means the time taken for it to reduce to half of its value
right?
mighty acorn
ye
prisma ibex
yeah thats right but find n lol
(1/2)^n = 1^n/2^n
1^n will just be 1 so you need to just solve
2^n = 16
prisma ibex
mighty acorn
how would u find value of n
prisma ibex
do you know what power means in the first place? @mighty acorn
mighty acorn
the answer is 4 tho
prisma ibex
yeah n = 4
then
you know its gone through 4 HALF lifes in 14 minutes
so how long is 1 HALF life ?
mighty acorn
3.5 minutes
prisma ibex
exactly
mighty acorn
IOHHH
prisma ibex
thats your answer
prisma ibex
yep
mighty acorn
I kinda get it, is it okay if i ask a question to calirfy my thinking
prisma ibex
sure
prisma ibex
ah alright
so when you do that
try using both values
and see what works
because if you choose n =1
then 2^1 = 16
thats not correct is it?
so 1 is not the solution
the other solution is 4
mighty acorn
also i understand this but my teacher told us to use the formula f(x)=ab^x with a being intial value and b being half life time and x being time over half time
if u used this formula do u know why there is no a value
prisma ibex
if u used this formula do u know why there is no a value
oh there is
just consider the initial value as a
and the final value as a/16
mighty acorn
what would be the intial value tho
1?
oh that would make sense beacuse that would mean u start off with 100 percent plutonium
if im wrong please correct me
prisma ibex
yeah
prisma ibex
id prefer to use a variable tho it just works better for me but 1 will work
mighty acorn
the equation would also work if its this as well right
c ause i get 3.5
with this
prisma ibex
yep
prisma ibex
no worries
mighty acorn
ye
prisma ibex
in these questions
if its not half life then b is different
but i mean
cmon when will that ever happen
XD
prisma ibex
np
elder parcel
Suppose there are 4 coins. You throw them. Heads will give a value of 1 and tales a value of zero. However, the coins are weighted. They have chances of throwing heads of 1/2, 1/3, 1/4 and 1/5. X will be the total value of the 4 coins. How can I calculate E(X)?
devout snowBOT
Suppose there are 4 coins. You throw them. Heads will give a value of 1 and tale...
weak tundra
Suppose there are 4 coins. You throw them. Heads will give a value of 1 and tale...
$X = X_1 + X_2 + X_3 + X_4$.
Then $$\mathbb{E}(X) = \mathbb{E}X_1 + \mathbb{E}X_2 + \mathbb{E}X_3 + \mathbb{E}X_4.$$
woven radishBOT
1345631
tame bridge
.open
is the parametric formula, \left(\left(t-1\right)x_{1}+t\cdot x_{2},\ \left(t-1\right)y_{1}+t\cdot y_{2}\right)
devout snowBOT
is the parametric formula, \left(\left(t-1\right)x_{1}+t\cdot x_{2},\ \left(t-1\...
tame bridge
sorry let me write in the proper way
please take this as an example
so this is not my grade, neither I am solving anything related to this
but I was curious what does the t variable mean?
<@&286206848099549185>
devout snowBOT
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tame bridge
<@&286206848099549185>
<@&286206848099549185> where are you
<@&286206848099549185>
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glossy atlas
devout snowBOT
glossy atlas
i understand how the equation for the rate of change is
paint in - paint out
but i dont understand how to get the "out" part
devout snowBOT
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glossy atlas
<@&286206848099549185>
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timber pebble
i understand how the equation for the rate of change is
paint in - paint out
bu...
the "out" part?
I feel like these can be weird since you have to just trust that this r/a is capturing what we are losing
does it make sense that the amount you are losing per dt is a function of how much is already in the tank?
glossy atlas
wdym
graceful cosmos
The concentration of red is r/30
And, that is indeed the "out" part
Or wait, maybe 3 times that
mild mist
How would I do 26 a b and c?
mild mist
<@&286206848099549185>
mild mist
<@&286206848099549185>
devout snowBOT
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mild mist
<@&286206848099549185>
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indigo hull
do you know what volume and capacity are
devout snowBOT
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mild mist
The problem is idk how to convert into kiloliteres
ok but what does that have to do with kl
Wait
Is 1000ml = 1 kl?
I was looking at the wrong question
WHOOPS
@fickle warren okay so starting with a) what process would I do to find the capacity
(Redoing it cause I was confusing myself)
Alright
I think I got A
Now how about B and C
So just the height and the extra depth of 6?
Or would it be the diameter
supple knot
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small willow
devout snowBOT
small willow
Howdo i determine weather rows are linearly independent
main gull
By looking at the row reduced matrix
small willow
Alright:
main gull
You realize it gave you that, right?
small willow
You mean part c?
small willow
wherre was it given?
main gull
If you read, matrix B is the row reduced equivalent
small willow
OH MY GOOD I AM STUPID
I am assuming its linearly dependednt
@main gull Is this right;
main gull
Please do not ping me
small willow
my bad g
main gull
But yes, that's right
small willow
3 and 5 are linearly dependendt ight?
main gull
Sure
small willow
It is only independent when the number that leads the row is a 1?
main gull
I believe so, I don't recall that
devout snowBOT
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rare snow
hello
rare snow
can anyone help me?
The ratio of the sides of a right tringle is 3:4:5. If the triangle has an area of 96 sq. meters find the perimeter of the triangle
devout snowBOT
@rare snow Has your question been resolved?
rare snow
Area = (1/2) (base)(height)
so it should be 3x+4x+5x=96 right?
how do i find the value of x?
pseudo basin
no
rare snow
whatt?
novel goblet
so it should be 3x+4x+5x=96 right?
wrong
rare snow
oh
pseudo basin
sure, the sides of your triangle are 3x, 4x and 5x
the area of a right triangle is half of the product of its legs
write this down as an equation
pseudo basin
96= (1/2) (3x)(4x)
yes, this is the correct equation
clean up the right-hand side and you might have an easier time solving for x from there.
novel goblet
96= (1/2) (3x)(4x)
express x as the subject
rare snow
idk how
novel goblet
move all the numbers to one side and leave x only in another side
pseudo basin
do you know how to simplify $\frac{1}{2} \cdot 3x \cdot 4x$?
woven radishBOT
Ann
rare snow
move all the numbers to one side and leave x only in another side
x^2= (3)(4)
then square root?
pseudo basin
no, this is very wrong.
rare snow
x^2?
pseudo basin
yes
pseudo basin
and what is 1/2 * 3 * 4?
rare snow
6
novel goblet
actually (1/2)(3x)(4x) = (1/2)(3)(4)(x)(x)
novel goblet
actually (1/2)(3x)(4x) = (1/2)(3)(4)(x)(x)
i hope you know this
pseudo basin
okay, so what does 1/2 * 3x * 4x simplify to?
in light of anonymous user's comment too
rare snow
okay, so what does 1/2 * 3x * 4x simplify to?
6x?
pseudo basin
why?
didn't you just say x * x was x^2?
so why does 1/2 * 3 * x * 4 * x now become 6x and not 6x^2?
pseudo basin
i encourage you to pay attention to the things you say and do
and maybe review basic algebra, which at the moment you seem to be struggling with
okay, so now you have 6x^2 = 96
does this equation look like something you're able to solve?
rare snow
4?
pseudo basin
does that mean "yes, i think i can solve it and i think the answer is 4 but i doubt my own answer"?
rare snow
uh, i have a habit of putting a ? whenever i'm asking for help
pseudo basin
well you should know how it makes you sound
it makes you sound like you're constantly uncertain of your own answers
are you actually uncertain of your own answers?
rare snow
sometimes
pseudo basin
...
okay let me be even more clear
are you uncertain of your own answer to this particular equation: 6x^2 = 96
rare snow
nope
pseudo basin
okay...
so why were you so evasive about it
it felt like you were trying to dodge my questions without good reason
rare snow
i'm not, it actually makes sense
pseudo basin
alright
well ok
you are correct anyway
x = 4 is indeed the solution to 6x^2 = 96
so now that you know the value of x, and you know that the sides of your triangle are 3x, 4x and 5x
are you able to calculate the perimeter?
rare snow
oh yup
you multiply x to 3,4,5
=48
there's this question, i have anwer but i'm still gonna ask you if my answer's correct just to be sure
Consider two similar right triangles, triangle ABC and triangle PQR. The measures of the sides of triangle ABC are 6ft, 8ft and 10ft. If the measure of the shortest side of triangle PQR is 21ft, Find the measure of its 2 other sides.
ans: QR= 28 ft, PR= 35 ft
pseudo basin
yes
rare snow
A 15-meters high building casts a 6-meters shadow on level ground. A person 1.7-meters tall wants to stand in the shade as far away from the building as possible. What is this distance from the building?
does anyone know how to visualize this?
pseudo basin
make a picture...
rare snow
it doesn't have any.. it's just a word problem and i dunno how to visualize it
rare snow
i have an idea but i'm not really sure... it's similar triangles cut by a transversal
pseudo basin
already overthinking it
rare snow
it's just an idea since my teacher made some examples of these
craggy prairie
devout snowBOT
craggy prairie
Justification for the equation
devout snowBOT
@craggy prairie Has your question been resolved?
hazy totem
Try to bring everything to one side of the equation and try to look for a notable formula
ashen tendon
X = ln(x) + 1, how do you solve for x ?
pseudo basin
@ashen tendon please read #❓how-to-get-help and get your own help channel.
sand field
dumb question maybe
devout snowBOT
dumb question maybe
sand field
lets say i need to eat 160 apples on the first day.
and 40 apples on the 23rd day.
and there are total of 1755 apples i need to complete by the 23rd day.
how do i find the rate so that the number of apples to be eaten is decreasing gradually in a constant rate.
i swear i read something like this on grade 12 but forgot. and dont know what to type for google to show answers
devout snowBOT
@sand field Has your question been resolved?
icy marsh
there were 4 real coins weighing 1 gramm each, and 1 fake coin, and 1 gramm of weight. Weigh the coins 3 times and detect the fake coin. /theres no way that fake coin is lighter or heavier than real coin/ (year 2005 1st school entrance exam)
devout snowBOT
there were 4 real coins weighing 1 gramm each, and 1 fake coin, and 1 gramm of w...
tall linden
What happens if you weigh and it turns out that one of them is fake?
polar bolt
Start with weighing 3 of the 5 coins?
(Also broken English - not clear what the fake coins weigh compared to real coin.)
icy marsh
fake coin is not lighter nor heavier than real coin
icy marsh
it is not known*
that fake coin is lighter or heavier than real coin
i mean
not exactly not lighter nor heavier
polar bolt
Either lighter or heavier?
polar bolt
Start with weighing 3 of the 5 coins?
But do this
icy marsh
and
polar bolt
Try think for yourself then
devout snowBOT
@icy marsh Has your question been resolved?
devout snowBOT
@icy marsh Has your question been resolved?
restive river
can anyone help in finding the range pls
devout snowBOT
can anyone help in finding the range pls
restive river
<@&286206848099549185>
polar bolt
take derivative for example to figure out where it is increasing/decreasing
devout snowBOT
@restive river Has your question been resolved?
restive river
take derivative for example to figure out where it is increasing/decreasing
how would i know which point to take it?
restive river
Take derivative
yeah but after taking the derivative
arctic crystal
can anyone help in finding the range pls
i'll personally rewrite it as g(x)=11/(x-3) + 2
and from this u can see that there's an asym at y=2 (x -> inf)
hence the range will be all reals \ {2}
restive river
hence the range will be all reals \ {2}
i was thinking that too but the ms says its between 2 and 7.5
and idk why
arctic crystal
oops
there's a domain restriction lol
missed that one
f(5)=7.5
so ran(g) = (2, 7.5]
restive river
yeah so shouldn't it be greater than?
since x is greater than 5
why does it stop at 7.5?
arctic crystal
ye x is greater
do a quick sketch of the graph
this is a rectangular hyperbola
looks something like this
there's an asym at y = 2
and g(5) = 7.5
so ran(g) = (2, 7.5]
note that as x->inf, g(x)->2
i don't have a tablet rn so i can't really draw the graph
think of ur graph like this
the "top part" is 7.5 where x=5
and as x gets larger, g(x) approaches 2
restive river
ohhhh
polar bolt
yeah but after taking the derivative
If you took derivative you would see its always less than 0?
So decreasing
restive river
and as x gets larger, g(x) approaches 2
ok that makes sense
restive river
So all you had to do was evaluate at 5
ahh alr ty
polar bolt
take derivative for example to figure out where it is increasing/decreasing
Which I also said here
Was what you had to do
devout snowBOT
Available help channel!
river sentinel
I have a question
devout snowBOT
I have a question
winter patrol
have you tried drawing a diagram?
river sentinel
yeah
winter patrol
can you show what you drew
your diagram is incorrect
the bearing of A from B isn't represented properly
river sentinel
thanks
river sentinel
.close
restive river
devout snowBOT
restive river
I'm a little confused about this question
devout snowBOT
@restive river Has your question been resolved?
restive river
so he reached the bus stop at 7:43 since he was 23 minutes late
It took (7-3) = 4 minutes in the bus
thus 7:47
devout snowBOT
devout snowBOT
Available help channel!
fallow sparrow
I'm in the middle of a massive chi squared test and I've accidentally pressed the insert key on my casio fx-991EX calculator. Anyone know how to get rid of it? I've tried pressing insert again but it doesn't work
devout snowBOT
I'm in the middle of a massive chi squared test and I've accidentally pressed th...
solid lion
hey I would like to know if I got a correct answer here:
let (A = {x \in \mathbb{R} | (x > 0) \wedge (x^2 = 3)}). Give a simpler definition of set A
devout snowBOT
hey I would like to know if I got a correct answer here:
let \(A = \{x \in \math...
woven radishBOT
aru-hackZ
solid lion
this is my answer:
(A = {(x > 0) \wedge (x = \sqrt{3})})
woven radishBOT
aru-hackZ
solid lion
well the ((x = \sqrt{3})) can just be ((x^2 = 3))
woven radishBOT
aru-hackZ
woven radishBOT
aru-hackZ
solid lion
and by doing x > 0 you leave out the neg one
solid lion
yes
that's what I was thinking
so then it's this? ((A = {x | (x > 0) \wedge (x = \sqrt{3})}))
woven radishBOT
aru-hackZ
solid lion
how do I leave out the neg part then
restive river
what negative part
solid lion
restive river
Ohhhhh
okay
sure leave out the negative part
but even you have x >0 and x=+sqrt(3) its still redundant to have one of the statements
restive river
just x=sqrt(3)
solid lion
because you then assume you only want the + part
restive river
in fact you could just write A={sqrt(3)}
solid lion
yes
restive river
because you then assume you only want the + part
if theres only two options and one of them can't be satisfied you're left with only one option
x > 0 and x=+-sqrt(3) implies that x can only be +sqrt(3)
indigo abyss
how do i solve this
devout snowBOT
@indigo abyss Has your question been resolved?
hybrid snow
how do i solve this
I'm assuming you just try out different LaGrange stuff
Using LaGrange error
Try first, second, third
And so on
But I'm not too sure since it doesn't specify a specific domain
devout snowBOT
@indigo abyss Has your question been resolved?
supple knot
.close
restive river
is the maclaurin series of $e^x$: $\sum_{n=0}^\infty \frac{x^n}{n!}$
woven radishBOT
Joseph Fourier
exotic stump
yeah
small willow
.reopen
violet lichen
How does one do polar cords.
devout snowBOT
How does one do polar cords.
lyric radish
polar coordinates are parameterized by x = rcos(theta) and y = rsin(theta), where r = sqrt(x^2 + y^2)
and theta = arctan(y/x)
lyric radish
yep :)
lyric radish
nah so since your converting from polar to rectangular, it should be simpler than that. You would have:
$(4, \frac{2\pi}{3}) \Rightarrow x = 4$cos$\frac{2\pi}{3} = -2$. \
and, \
$(4, \frac{2*\pi}{3}) \Rightarrow y = 4$sin$\frac{2\pi}{3} = 2\sqrt{3}$
woven radishBOT
Paulie
lyric radish
so your rectangular coordinates would be $(-2, 2\sqrt{3})$
woven radishBOT
Paulie
violet lichen
ahh ok thank you
restive river
I don't know how to do this question, I'm used to managing cosine and sine via TI-30Xa calculator and I have never learned this. Can I get help on where I'm supposed to start?
devout snowBOT
I don't know how to do this question, I'm used to managing cosine and sine via T...
autumn blaze
there is just a simple rule you can follow
main gull
I don't know how to do this question, I'm used to managing cosine and sine via T...
This might be helpful
restive river
what's the rule
autumn blaze
whatever angle you have in this case 70 just take it and subtact it by 90
20 in this case sine of 70 is equal to cosine of 20
you can do it on the claculator if you would like to confirm
devout snowBOT
devout snowBOT
Available help channel!
proven hamlet
How would you solve number 7 using the ratio test?
devout snowBOT
How would you solve number 7 using the ratio test?
proven hamlet
I'm not sure what to do since its alternating
proven hamlet
And you should notice smth
the only thing it says is about how the limit of the series is = rho
proven hamlet
What is |(-1)^n|?
oh
so it's basically insignificant to the equation
I did not think of that
thank you very much
devout snowBOT
@proven hamlet Has your question been resolved?
steel sage
You can compare it with n^4/9^n to show that it absolutely converges
proven hamlet
You can compare it with n^4/9^n to show that it absolutely converges
but that wouldn't be the ratio test then would it?
devout snowBOT
devout snowBOT
Available help channel!
jaunty vale
hey! i had a question regarding stokes theorem
devout snowBOT
hey! i had a question regarding stokes theorem
jaunty vale
I attempted to solve 2 b and c for this question and wanted to check my work -- am I going about this correctly?
<@&286206848099549185>
.close
odd elbow
Can someone pls help with with the integration
devout snowBOT
Can someone pls help with with the integration
supple knot
supple knot
,w integral 1/(1+cos(x))
woven radishBOT
shy quest
try multiplying n dividing by 1-costheta
crude warren
Do you remember any formula related to cos theta?@odd elbow
shy quest
yeah that too
odd elbow
Well trig??
crude warren
Yes
crude warren
Anything else you remember?
shy quest
specifically half-angle formulae?
crude warren
1+cos theta = something
crude warren
specifically half-angle formulae?
He won't be able to get this way
odd elbow
Sin²(t) = 1 - cos²(t)
shy quest
He won't be able to get this way
y not?
odd elbow
Now what
shy quest
works?
crude warren
You got to remember the formula's given in 11th class @odd elbow
crude warren
Damn
odd elbow
sin²(t) = [ 1 - cos(t) ][ 1+cos(t) ]
odd elbow
Ye
crude warren
Then how come you are solving integration
This is meant to be done after differentiation
crude warren
1+Cos2A=2cos²A this is a formula you need to remember which you will find in chapter trigonometry of 11th
crude warren
We're on with that
You are legit kid 
crude warren
Doesn't matter lol
crude warren
Ig you will be able to solve now
odd elbow
Hm
slow rampart
Hi! can someone help me with differential calculus
devout snowBOT
Hi! can someone help me with differential calculus
slow rampart
bold prism
do you remember your rules of differentiation?
bold prism
looks correct to me
slow rampart
I don't quite understand how to solve for this though
bold prism
you've identified the rules correctly but you don't remember what they are?
slow rampart
yeah
bold prism
