its just how they are called
#help-17
north kestrel
woeful stream
its just how they are called
like what's the definition for automatic/non-automatic?
vast shale
<@&286206848099549185>
Hello
Hello asian boy
Plz help me
No
Ok thanks
Are you yr 7?
Your about me
Now what do I do
Ok
Ok
Yes
Acc thanks for the help
I can do it myself now
Yes
haughty monolith
Daniel randomly chooses two of the soccer jerseys and puts them in a bag.
How many different combinations of soccer jerseys can be found in Daniel's bag?
summer spade
I think 6
vocal sleetBOT
@haughty monolith Has your question been resolved?
vocal sleetBOT
vocal sleetBOT
Available help channel!
fallow cloak
can somebody please explain teh solution for question b
vocal sleetBOT
can somebody please explain teh solution for question b
fallow cloak
.close
unborn condor
What am i supposed to do?
Set the expression equal to an unknown value x and then solve for it??
vocal sleetBOT
What am i supposed to do?
Set the expression equal to an unknown value x and the...
unborn condor
Or try to simplify the expression?
Or use some concept knowledge to disect it just with words and logic?
Ping me when anyone answers pls.
brittle girder
What am i supposed to do?
Set the expression equal to an unknown value x and the...
Do you know the triangle inequality
unborn condor
I believe i do
brittle girder
see if you can get an inequality with |a-b|
Its a slight variation of thr usual triangle inequality
brittle girder
see if you can get an inequality with |a-b|
And apply it to |z-1|
unborn condor
I'll try, however i am not fully aware of its application on this situation
brittle girder
see if you can get an inequality with |a-b|
This will give a lower bound for $|z-1|$ and combined with thr fact that $|z| \geq 0$ you get a lower bound for thr whole expression
twin meteorBOT
catGPT
unborn condor
What's lower bound
brittle girder
You'll get $|Z-1| \geq $ stuff
If you're having trouble with it, start with $|a|=|(a-b)+b| \leq |a-b| + |b|$
twin meteorBOT
catGPT
brittle girder
And rearrange
vocal sleetBOT
@unborn condor Has your question been resolved?
vocal sleetBOT
@unborn condor Has your question been resolved?
north kestrel
wdym closed by someone else
wtf
i had question and someone else closed my ticket
polar summit
Can I help?
unborn condor
And rearrange
How do u even resolve this? Work it out?
I got 4 values, -1≥-1
Z≤1
Z≤0
Z≤0
brittle girder
How do u even resolve this? Work it out?
$|z-1|=|1-z| \geq |1|-|z|$
twin meteorBOT
catGPT
unborn condor
If i treat 1-z as the a and b then yeah
brittle girder
So $|z|+|z-1| \geq$...
twin meteorBOT
catGPT
unborn condor
That would be what i would write it as
brittle girder
Can you finish now?
unborn condor
We are treating z and 1 as a and b?
And then carrying it over to the bigger expression?
brittle girder
Yes
I used thr inequality $|a-b| \geq |a|-|b|$
Then plug into thr original expression
twin meteorBOT
catGPT
unborn condor
**catGPT**
Why are you swapping z-1 to 1-z
brittle girder
So originally I did z-1 then I noticed that if I swapped the sign, things cancel out
unborn condor
Okay hold on... Lemme try to see why would that even be allowed to happen
brittle girder
Okay hold on... Lemme try to see why would that even be allowed to happen
|z|=|-z|
Multiplying by -1 doesn't change thr magnitude
unborn condor
I see
unborn condor
|z|=|-z|
Ended up with this,
Simplifying gives me 2z-1
Applied the identity for |z-1|
And got that into the original expression
Okay wait, i guess ill have to apply the appropriate identity on the original expression and also on the
|z-1| and merge them
<@&286206848099549185> yeah i am not sure how to go about this.
Cat has given me clues, when i apply what he is saying in any type of way i end up with weird inequalities that give 4 different values, or weird values like x≥x
Like how do i even go about this???
@brittle girder my man, i got the values from the the identity of |z-1| and then applied them in the original inequality, still nothing
.close
hushed cosmos
vocal sleetBOT
hushed cosmos
how do you do d?
hushed cosmos
N! * (N+1)=(N+1)!
wait what
could you elaborate please
can u just multiply bottom by n+1
nocturne cloak
can u just multiply bottom by n+1
First represnt n! and (n+1)! using a series of multiplications
hushed cosmos
First represnt n! and (n+1)! using a series of multiplications
can you just turn n! into n+1!?
nocturne cloak
can you just turn n! into n+1!?
No, but (n+1)! is a very simple progression from n!
Take n = 3 and n+1 = 4
3! = 1×2×3
4! = 1×2×3×4
So really (n+1)! is just n!*(n+1)
nocturne cloak
Exactly the same as what?
hushed cosmos
say if i had n! and (n+3)!
nocturne cloak
Anyways, to add two fractions together, you want to make the denominators the same
nocturne cloak
You also have to time all the numbers smaller than n.
That is, n!(n+1)(n+2)(n+3) = (n+3)!
nocturne cloak
i did that here right
You did n×, not n!×
hushed cosmos
oh crap
ohh okay
that makes sense then
oh and could i get some help on this
for b)
the solution is this
but i thought it should be 4x4x3x2
since it says without repetition
nocturne cloak
but i thought it should be 4x4x3x2
So which digits can each position choose from, according to your solution?
hushed cosmos
this is thje solution
hushed cosmos
So which digits can each position choose from, according to your solution?
0, 1, 2, 3, 4 and 5
hushed cosmos
oh and could i get some help on this
this is the question
nocturne cloak
I mean what is the step-by-step reasoning you used to reach 4×3×3×2
You must consider what could be used for each of the four positions, one by one, so there is something that is different from the textbook solution that we should be able to pick out.
hushed cosmos
I mean what is the step-by-step reasoning you used to reach 4×3×3×2
ohh ok
first 4 cant be 0 since its a 4 digit number, second number can only be 4 numbers, excluding the one that was picked before and including 0 this time, third is just any number and fourth is the last two numbers remaining
nocturne cloak
How many choices are there for x if we have
240x
?
hushed cosmos
You must do the constraints first
wdym constraints
like the first digit not being able to be zero?
nocturne cloak
wdym constraints
The first and the last digit
nocturne cloak
Yes, but you did the last… well, last
That's what caused the problem, because the middle two digits depend on the last
(and the first)
hushed cosmos
so ishould always dothe constraints first?
hushed cosmos
but if i picked the first and last one wouldnt that mean theres only 2 left for the middle
3*
nocturne cloak
Isn't that the correct answer, 4×4×3×3
hushed cosmos
no i mean if u have 4x_x_3
if two are already taken doesnt that mean the second one can only have three options
since you cant repeat
nocturne cloak
if two are already taken doesnt that mean the second one can only have three opt...
We have six options
0
1, 2, 3, 4, 5
nocturne cloak
No worries, this is called fencepost problem
You can see it's such a common problem that it has a name
As a programmer I myself frequently gets confused by it, fortuantely it is not a hard one to spot.
hushed cosmos
can we use the same principal we did on the last question
like draw a box and multiply
or does that only work with permutations
nocturne cloak
or does that only work with permutations
This is also a permutation problem since you cannot have two same people
At least I think that's what the editor thinks
So yes, this should be solvable using the same principals and what we have learned from the last one:
- Do the constraints first
- Beware of the fencepost problem
hushed cosmos
apparently its a combination
hushed cosmos
This is also a permutation problem since you cannot have two same people
At leas...
do you have any idea how to do a?
nocturne cloak
apparently its a combination
Yup. Permutation is from everything and combinations is from some of them, often mess that up
nocturne cloak
do you have any idea how to do a?
Three vertices makes a triangle, so you just choose 3 from 6
hushed cosmos
howdo u even visualise thta
nocturne cloak
They say they lie on a circle it's just to make sure they they're not colinear, so three points are not on a straight line
Because then that three points don't make a triangle
hushed cosmos
ohh ok
nocturne cloak
(It's an interesting thing to prove that you cannot have three points on a circle that are colinear, maybe ask your teacher about that one
hushed cosmos
Three vertices makes a triangle, so you just choose 3 from 6
this is 6c3 right
nocturne cloak
this is 6c3 right
The expressions can be different and it gets confusing, so I'm just gonna say that you choose 3 from 6.
hushed cosmos
The expressions can be different and it gets confusing, so I'm just gonna say th...
how would you do the second one?
would it 19! ?
nocturne cloak
how would you do the second one?
Choose 2 from 20, because you're making pairs
Essentially the question is just how many pairs you can make from 20 people
hushed cosmos
ohh okay
do you know how to do d) on this question?
wait never mind i got it
thanks
nocturne cloak
Many of these problems are iterative in nature, so once you find a way to calculate a particular case, you can then manipulate the variables to find other cases, until everything is covered.
Factorial and choose function are also just shorthands for iterations
Just to give an insight
nocturne cloak
a or b, or both?
hushed cosmos
hvaent checked b yet
but a right now
wont all arrangements of the letters always have4
since its just rearranging
nocturne cloak
You can argue that it would be 0 if possible and if you think it is a risk worth taking
hushed cosmos
wait i figured it out
i dont understand the second question
both of the two under this question are badly explained imo
nocturne cloak
So for b we want to perform the single most important technique in mathematics: abstraction
Instead of saying we're choosing a president, a vice-p, a secretary and a treasurer
We just say that we're picking 4 people
nocturne cloak
Yes
hushed cosmos
is there anything else i need to do
nocturne cloak
Ah, I see the order matters
hushed cosmos
wait how do u know order matters
nocturne cloak
factorial because it has order?
Yes, though is subtle where to use the factorial
Can you figure it out?
hushed cosmos
yup
for pigeonhole theory do i hvae to show working
or can i just explain with words
is there even working for pigeonhole
nocturne cloak
is there even working for pigeonhole
In mathematics there is a proof technique called “proof by contrapositive”, used when proving the complimentary situation is easier
In this case, the contrapositive is “how many socks you can select without getting a pair”
hushed cosmos
what would be the working out for that?
nocturne cloak
So first we want to define what it means for two socks to be a matching pair
hushed cosmos
what would that bne
nocturne cloak
what would that bne
If two socks are the same color they form a matching pair
Not gonna lie. I think you're too tired to do math if you struggle to come up with this
hushed cosmos
should i go sleep
its 4am
but i wanna finish this
wait i can do the pigeonhole one
could i get some help on cc
before i go sleep
c)*
nocturne cloak
c)*
So these are all the possible configurations where
4 children sit together in 6 consecutive seats:
CCCCPP
PCCCCP
PPCCCC
Then we just see how many rearrangements are there for parents and children and times the number of possible configurations, listed above.
hushed cosmos
4!2!x3?
nocturne cloak
Yes
hushed cosmos
wait why is the 3 not factorial
nocturne cloak
So these are all the possible configurations where
4 children sit together in 6 ...
Btw the configurations can only be found by exhaustion, there is no shortcut
nocturne cloak
wait why is the 3 not factorial
You're truly tired.
Because it's the number of configurations
hushed cosmos
Btw the configurations can only be found by exhaustion, there is no shortcut
so i would have to write it out?
nocturne cloak
so i would have to write it out?
You can, just to add authenticity
nocturne cloak
Ur welcome, gn
hushed cosmos
goodnight
nocturne cloak
thanks for the help
remember to type .close
kind wadi
i just saw this mod identity used: if a = b mod m then ac = bc mod m with a note that the proof is obvious
vocal sleetBOT
i just saw this mod identity used: if a = b mod m then ac = bc mod m with a note...
kind wadi
i need a proof for it, couldnt find it online
also by = i meant is congruent to dont have that symbol on my keyboard
hard atlas
you know that a=km+b for some integer k
and you want to show that ac = sm + bc for some integer s
kind wadi
b = remainder ?
hard atlas
where are you pulling that first equality from?
kind wadi
yeah
thanks
i have another thing to proof
proof that if ac = bc (mod m) then a = b (mod m) only and only if HCF(c, m) = 1
hard atlas
do you know bezouts lemma
kind wadi
what is it? i might know it by another name
hard atlas
if x,y are integers then there are integers s,t with sx+ty=gcd(x,y)
kind wadi
no sorry never heard of it
hard atlas
I suppose we dont need it here
we want to show that m divides a-b
we know that m divides ac-bc
kind wadi
ac - bc = mk
a - b = m(k/c)
a - b = mk_1 where k_1 = k/c
a = b mod m
why do we need the hcf condition then?
oh wait, k/c isnt always a integer
warm mesa
Hello! I have a big exam coming up, and I am trying to solve some tasks with the same "level" difficulty as the ones on the exam. The question is **"use the figure to prove that 68 x 27 = 1836." **I have done this before, but I completely forgot how.
vocal sleetBOT
Hello! I have a big exam coming up, and I am trying to solve some tasks with the...
vast shale
such a weird question why do you need a rectangle to prove multiplication
does it tell you anything else
warm mesa
such a weird question why do you need a rectangle to prove multiplication
that's what im thinking. but, it will definitely be a question D:
warm mesa
does it tell you anything else
nope, thats it
vast shale
it doesnt tell you any side lengths
warm mesa
but, each one of the squares will be a part of the answer. (1836)
warm mesa
it doesnt tell you any side lengths
nope
vast shale
ok... have you learned algebra yet
warm mesa
yes
vast shale
do you know that area of a rectangle is base * height
warm mesa
yes
vast shale
ok so im guessing, that what you have to do is, if we take just the short side of the large rectangle, set the side length of the green to be "x", and then the blue one to be "27-x"
warm mesa
ok so im guessing, that what you have to do is, if we take just the short side o...
to solve 27-x, i need x? or no?
vast shale
what you can do is add up the areas of the small rectangles and it should give you 27*68
vast shale
to solve 27-x, i need x? or no?
yeah but in the end it doesnt matter because everything cancels out
warm mesa
im sorry, i dont really understand D:
vast shale
it doesnt matter what x is its just a dummy variable becuase its true for any x value
like it doesnt matter how large x is, it doesnt matter where you cut the line between the rectangles because if you add their areas you will always get 1836
warm mesa
Ohh, wait, in this picture you're only finding the area of blue square? yes?
i remember one thing, and that is that i have to use all squares. they all should get an answer, that will result in 1836 once i add them together
cuz, the 68 and 27 arent measurements.
.close
warm mesa
If 2 chocolate bars and 1 waterbottle costs $40, and 4 chocolate bars + 3 water bottles cost $98, how much does 1 chocolate bar cost?
vocal sleetBOT
If 2 chocolate bars and 1 waterbottle costs $40, and 4 chocolate bars + 3 water ...
hasty pulsar
write the equations
hasty pulsar
good now solve it
hasty pulsar
solve for one variable in one equation then sub that variable in another equation
warm mesa
ok, ive tried to solve it and i dont get it
hasty pulsar
show work
vocal sleetBOT
@warm mesa Has your question been resolved?
dapper blaze
Chocolate: x
water: y
1) 2x + y = $40
2) 4x + 3y = $98
hint: cancel something, you must try cancelling x or y by multiplying by minus
warm mesa
hint: cancel something, you must try cancelling x or y by multiplying by minus
I'm sorry, i dont understand D:
dapper blaze
okay you dont need to do that if you cant
x=20-y/2 right
and you know that 4x+3y=98
you've expressed x in terms of y and now place it in
4x+3y=98
we dont want x here so we can solve for y
can you do it?
warm mesa
solve it for y now
do you mean i solve 4(20-y/2)+3y=98 or y = 40 - 2x
warm mesa
i can try the first one
dapper blaze
exactly
warm mesa
can i show you what i did? i have another question
Here, I wanna move the 80 to the other side?
i move 80 to the other side before do the equation
warm mesa
-2y?
dapper blaze
yes
warm mesa
that was a mistake, i see now. i added 4 + 3
dapper blaze
what did you find for y
warm mesa
y = 18
dapper blaze
yes
warm mesa
SO WATERBOTTLE is 18! now i can find chocolate bar
warm mesa
yeah! :D
dapper blaze
Chocolate: x
water: y
1) 2x + y = $40
2) 4x + 3y = $98
here
warm mesa
thank you
warm mesa
wait, x = 40 - 18 ?
warm mesa
oh yes, two chocolate
dapper blaze
yes
warm mesa
x = 11
dapper blaze
exactly
dapper blaze
you are welcome
warm mesa
it was a really frustrating task, it feels good to be done!
warm mesa
.close
vocal sleetBOT
vocal sleetBOT
Available help channel!
normal vessel
which function do i use to create this shape left in the G?
vocal sleetBOT
which function do i use to create this shape left in the G?
normal vessel
algebra 2^
rugged vortex
which function do i use to create this shape left in the G?
Can you like draw on the screen what you mean
The left curve of the G?
Do you know parametrics?
normal vessel
rugged vortex
They look like logarithmic curves
normal vessel
alright im going to try and work around logarithmic and see if i can find a solution
rugged vortex
I mean worse case scenario, parameterizations work really nice if you can figure them out
normal vessel
ive tried to tweak things so that it lines up properly but it doesnt seem to work
is there any other functions that could work beside whatever paratremeitcs is
vocal sleetBOT
@normal vessel Has your question been resolved?
vocal sleetBOT
@normal vessel Has your question been resolved?
vocal sleetBOT
@normal vessel Has your question been resolved?
vocal sleetBOT
@normal vessel Has your question been resolved?
vocal sleetBOT
vocal sleetBOT
Available help channel!
hushed tree
What's the probability that:
a) if i roll a dice 4 times, to get exactly 2 times "6"
b) if i roll a dice 4 times, to get maximum 2 times "6"
c) if i roll a dice 5 times, to get exactly 3 times "6"
vocal sleetBOT
What's the probability that:
a) if i roll a dice 4 times, to get exactly 2 time...
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
waxen portal
Read notes.
regal bane
You'll want to look into the binomial distribution
dark kiln
there are 6 cases in a)
e.g. you get 6, then don;t get 6, then get 6, then don't get 6
giving (1/6)(5/6)(1/6)(5/6)
they are mutually exclusive, so you add them together
vocal sleetBOT
@hushed tree Has your question been resolved?
hushed tree
there are 6 cases in a)
e.g. you get 6, then don;t get 6, then get 6, then don't...
and the oder doesnt matter
right?
quaint silo
and the oder doesnt matter
no
hushed tree
and at b)?
vocal sleetBOT
@hushed tree Has your question been resolved?
hushed tree
.close
elfin moon
How to find out the last question limit?
vocal sleetBOT
How to find out the last question limit?
elfin moon
It says 0 to 1/2
vocal sleetBOT
@elfin moon Has your question been resolved?
viscid ore
oh uh
wait
yeah
got it
the term actually is
$\displaystyle \prod_{i = 1}^{n} \left( 1 - \frac{1}{2i}\right)$
twin meteorBOT
rikusp2002
viscid ore
nth term of the sequence
it's because of the (2n - 1)/2n thing
that's precisely 1 - 1/2n
so you just multiply them upto n to get the nth term
viscid ore
**rikusp2002**
if you don't know what this means
it is this
$(1 - \frac{1}{2 \cdot 1})(1 - \frac{1}{2 \cdot 2})(1 - \frac{1}{2 \cdot 3})........(1 - \frac{1}{2 \cdot n})$
twin meteorBOT
rikusp2002
viscid ore
now see than nth term is this, and to get the n+1 th term, you multiply with
$(1 - \frac{1}{2 \cdot (n + 1)}$
twin meteorBOT
rikusp2002
viscid ore
which is precisely less than 1
so
n+1th term is less than nth term, and is bounded below by 0
so the sequence is monotonically decreasing and bounded below
must be convergent
similarly do the sequence
$\displaystyle \prod_{i = 1}^{n}\left(1 - \frac{1}{2i + 1}\right)$
twin meteorBOT
rikusp2002
viscid ore
this is a similar sequence, also converging (bounded below and monotonically decreasing)
Consider the product of the two sequences
it's precisely $\left(\frac{1}{2n + 1}\right)_n$
twin meteorBOT
rikusp2002
viscid ore
this converges to 0
so either our original sequence converges to 0, or the other one.
now as (1 - 1/2n) is less than (1 - 1/(2n + 1)) for all n
the new sequence is greater than our original sequence
Now, 0 < 1 - 1/n
1 < 2 - 1/n
1 < 2(1 - 1/2n)
So nth term of the new sequence is less than double the n+1th term of the original sequence
By squeeze theorem (sandwich theorem) if even one of them converges to 0, both of them will.
So our original sequence must converge to 0
@elfin moon
vocal sleetBOT
@elfin moon Has your question been resolved?
elfin moon
n+1th term is less than nth term, and is bounded below by 0
By comparing n+1 and n term
1- 1/2(n+1) is greater than 1- 1/2n so function is increasing how decreasing
elfin moon
@viscid ore
viscid ore
By comparing n+1 and n term
1- 1/2(n+1) is greater than 1- 1/2n so function is i...
No, that's between two different sequences. And yes you are right about that.
If you consider terms of the same sequences, both the original and the new sequences are strictly decreasing
viscid ore
**rikusp2002**
This is b_n, the new sequence
viscid ore
**rikusp2002**
This is a_n, the original sequence given in question
Check three factors - $a_{n+1} < a_n$
$b_{n+1} < b_n$
$a_n < b_n$ (that's what you just proved)
twin meteorBOT
rikusp2002
elfin moon
How to find out the last question limit?
Mera question tha ki answer m 1/2 aaya hain vo samajh ni aaya h
@viscid ore
viscid ore
A66a main likh ke bheju?
elfin moon
A66a main likh ke bheju?
Ha zaroor
viscid ore
elfin moon
Hmm aage kya karna h isme
elfin moon
Acha isme first term 1/2 hain toh aage ye decrease ho rha h...so 0- 1/2 k bich bound rahega ye 1/2 function se hi le lia h
elfin moon
Maine first dekha 1/2 hain fer agla term 3/8 which is less than 1/2 so it's decreasing 😁
vocal sleetBOT
@elfin moon Has your question been resolved?
elfin moon
My answer is D but they says B why?
My answer is 4 but they says A why?
<@&286206848099549185>
My answer is B but they says D
proper fox
My answer is 4 but they says A why?
the n-th derivative of sin at 0 alternates between 0, 1, 0 and -1
there seems to be something seriously wrong with these
where do these questions come from
elfin moon
Are bhai ho gya
elfin moon
How to solve this? I tried but the answer is not infinity
high hare
?
elfin moon
Chor do, so jao
Kal karna
Ye
high hare
You're muslim?
high hare
You're the one who mentioned hindu
vocal sleetBOT
@elfin moon Has your question been resolved?
vocal sleetBOT
@elfin moon Has your question been resolved?
elfin moon
.close
short bridge
I need help to solve the first problem with Am gm
The question is proof that …
where abcd is positive integer
short bridge
$\frac{ad^{b-c} + bd^{c-a} + cd^{a-b}}{3} \ge \sqrt[3]{abc}$
twin meteorBOT
mc768
short bridge
$\frac{x+y+z}{3} \ge \sqrt[3]{xyz}$
twin meteorBOT
mc768
vocal sleetBOT
@short bridge Has your question been resolved?
raven bough
can we conclude that ([a] + {x}) where x tends to infinity would always be an irrational number ?
vocal sleetBOT
can we conclude that ([a] + {x}) where x tends to infinity would always be an ir...
raven bough
And what's an irrational function
whose value can't be expressed in p/q ?
flat whale
whose value can't be expressed in p/q ?
That's an irrational number
If p and q are integers
raven bough
ah yes sorry , edited my ques
flat whale
Is a constant?
raven bough
Is a constant?
yea , and sorry i meant to write [a] , where [.] is the greatest integer function
vocal sleetBOT
@raven bough Has your question been resolved?
flat whale
yea , and sorry i meant to write [a] , where [.] is the greatest integer functi...
You should be able to find your answer just by testing a few different a and x values
dreamy kite
I don't know if anyone would be interested <@&286206848099549185> but most likely I would expect you to not. I need help learning basic mutliplcation- It's hard for me to come out like this but I surely would've wished that when I was younger I paid attention during class but I didn't.
vocal sleetBOT
I don't know if anyone would be interested <@&286206848099549185> but most likel...
ornate ember
!15m
vocal sleetBOT
Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
ornate ember
but normally the way the help channels work is you post a problem youre stuck on and we help guide through it
did you have a particular problem in mind?
dreamy kite
no
paper depot
do you know your way around addition and subtraction?
dreamy kite
yeah
strange oak
Like what’s hard with multiplying?
paper depot
right, in that case you might do well to start off learning the multiplication table
strange oak
Like 32•54? Or 2•12
dreamy kite
Like what’s hard with multiplying?
¯_(ツ)_/¯
modern ledge
dawg named de outhere asking whats hard with multiplicatiion 💀
dreamy kite
right, in that case you might do well to start off learning the multiplication t...
How'd you suggest I'd do that?
modern ledge
youtube vids probably
paper depot
well, you know that the multiplication table is made of rows right
modern ledge
here is what ann was referring to
paper depot
the 2 row (2, 4, 6, 8, 10, 12, 14, 16, 18, 20) the 3 row (3, 6, 9, 12, 15, 18, 21, 24, 27, 30), etc.
try to practice
- reciting these rows
- solving multiplication problems by recalling the right place in a row
strange oak
I recommend the mental math app on iOS it helped me a lot
paper depot
also practice doing repeated addition to get the same results, e.g. you should be able to get the value of 3*8 both by adding 3 copies of 8 (or 8 copies of 3...) and by recalling the eighth number in the 3-row
learn the rows one by one, so first start off with just the 2s, then add in the 3s, then the 4s and so on
@dreamy kite that's approx how you would start with learning multiplication
could also go for some visuals like rectangular arrays of dots to make some of those basic multiplication facts stick better
dreamy kite
Ohhh okay thanks
paper depot
then once you're comfortable with the multiplication table, you can move on to long multiplication -- first multi-digit by single-digit, then multi-digit by multi-digit
vocal sleetBOT
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lean cairn
Theory:
∀x ( superhero(x) ↔ ∀y ( ∀z enemy(y, z) → beat(x, y) ) )
∀x ∀y ( hero_for(x, y) ↔ beat(x, main_enemy(y)) )
∃x superhero(x) ∧ ∃x ∀y enemy(x, y)
∀x enemy(main_enemy(x), x)
I need to prove that:
∀x (∀y hero_for(x, y) → superhero(x))
all are predicates, just main_enemy is function symbol
vocal sleetBOT
Theory:
∀x ( superhero(x) ↔ ∀y ( ∀z enemy(y, z) → beat(x, y) ) )
∀x ∀y ( hero_fo...
lean cairn
does anybody have an idea how to solve that? I have tried to prove it using tableau but unsuccessfully, i could not close all branches
I have also tried to find a counter example structure, but unsuccessfully too
.close
pearl crest
vocal sleetBOT
pearl crest
how to solve this for x axis?
for z there are no force components in z direction so the length just changes
wb x
vocal sleetBOT
@pearl crest Has your question been resolved?
mossy belfry
is every subspace kernel of a linear transformation? if so, how do i write (a) and (b) as a kernel of a linear transformation?
vocal sleetBOT
is every subspace kernel of a linear transformation? if so, how do i write (a) a...
mossy belfry
all the linear transformations that map (1,2) to (0,0)?
worthy citrus
That would be the kernel, but what's the map
mossy belfry
not sure
mossy belfry
A(1,2)?
mossy belfry
wait so i would write S is a subspace of V because S=ker(T:M2,2 ---> R^2, T(A) = A[1,2])? @worthy citrus sorry for the ping, just wanted to make sure
vocal sleetBOT
wait so i would write S is a subspace of V because S=ker(T:M2,2 ---> R^2, T(A) =...
worthy citrus
Yes
mossy belfry
okie 🙂
vocal sleetBOT
@mossy belfry Has your question been resolved?
vocal sleetBOT
vocal sleetBOT
Available help channel!
pliant coyote
I don't understand this type of excersices
vocal sleetBOT
I don't understand this type of excersices
patent nymph
does sen mean sin?
muted folio
It's just asking what happens when it approaches 0 from the positive sign
patent nymph
one way to guess the answer is to try evaluating the expression for x = 0.00001
on your calculator
muted folio
It means that equation might be undefined if it's asking that
pliant coyote
It means that equation might be undefined if it's asking that
Yeah
muted folio
one way to guess the answer is to try evaluating the expression for x = 0.00001
Yeah this is how I do it
muted folio
I mean the only way to do that equation is to actually graph it and see where it goes
Then it might be going to positive infinity or negative infinity
pliant coyote
The correct answer is e^4
pliant coyote
I mean the only way to do that equation is to actually graph it and see where it...
The thing is I can't do that
muted folio
Ah then you might use trigonometric identities
pliant coyote
Such as?
muted folio
Ah sorry wait a minute my valorant match is about to start
Define cot first
as sin/cos
pliant coyote
Ah sorry wait a minute my valorant match is about to start
Don't worry don't worry
muted folio
this is (1 + something), make that something to 1/n and turn the exponent by equating it to that something
pliant coyote
Huh
muted folio
Ah ok so make sin(4x) = 1/n
pliant coyote
1/sin(4x) = sin/cos?
patent nymph
Ah sorry wait a minute my valorant match is about to start
out of curiosity are you helping people because you’re bored
muted folio
Just lemme finish
pliant coyote
Ah ok so make sin(4x) = 1/n
Oooh
muted folio
yeah
then do limit x-> 0 at than
that
see where that goes
cause the law of limits says, the limit of a function is a function of the limit
pliant coyote
What happened to the sin/cos
muted folio
But it basically means you can just apply limits to certain variables
We don't care at that first
Let's deal with the parenthesis first
pliant coyote
Oh okok
muted folio
then it solves itself later on
pliant coyote
So I'd need to solve lim sen(4x)
vocal sleetBOT
@pliant coyote Has your question been resolved?
muted folio
@pliant coyote
Sry about that
so we have n= 1/sin(4x0)
or n = 1/0
Since it's asking for 0+ then positive infinity
so we have now lim n-> +infinity (1 + 1/n)
then just equate x
vocal sleetBOT
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Available help channel!
somber valley
Hi guys, really need help with the following problem. I don't understand it at all. For a given production function Q(K,L)=(2L^(1/4)*K^(1/3)) where Q is the volume of output, K is the volume of funds (capital), L is the volume of labor at K0=108 , L0=157 , find the marginal yield of funds and marginal productivity of labor, the marginal rate of substitution of labor for capital, the elasticity of output by funds and by labor.
vocal sleetBOT
Hi guys, really need help with the following problem. I don't understand it at a...
@somber valley Has your question been resolved?
vocal sleetBOT
@somber valley Has your question been resolved?
vocal sleetBOT
@somber valley Has your question been resolved?
mystic wraith
I need to figure out if the sequence and the series {a_n} converges
mystic wraith
I'm not sure how to find the general term of the sequence
hybrid fossil
you dont need to find the general term
just take the limit of n to infinity on both sides
mystic wraith
Im not sure what you mean could you rephrase it
upbeat chasm
does a_n converge as n goes to infinity?
hybrid fossil
yes
mystic wraith
The question says a_n>1
twin meteorBOT
upbeat chasm
sqrt(x) is an increasing function yeah
mystic wraith
yes
upbeat chasm
and diverges as x goes to infinity
hybrid fossil
this sequence does not diverge
hybrid fossil
anyways
the sequence is decreasing
and bounded from below by 1
now from that you can conclude that the sequence converges
but you should prove that the sequence is decreasing
and then you can take the limit of n to infinity on both sides of the equation
peak matrix
||is it enough? cant it smh alternate between 1.1 and 1.2 or sth? I know that it's not this case, but how would you prove it?||
upbeat chasm
given that the sequence converges, it would be appropriate to say as n tends to infinity, a_(n+1) = a_n
worthy citrus
||is it enough? cant it smh alternate between 1.1 and 1.2 or sth? I know that it...
you prove its decreasing a bounded below
this is monotone convergence
peak matrix
Oh ic
hybrid fossil
given that the sequence converges, it would be appropriate to say as n tends to ...
its probably better to write $\lim_{n \to \infty} a_n = \lim_{n \to \infty} a_{n+1} = a$
twin meteorBOT
heavy
mystic wraith
Would it be a good way to prove its decreasing by doing a_(n+2)/ a_(n+1)
hybrid fossil
as far as i remember thats not the standard way but it should still work i think
just try it
the easy is way is induction
mystic wraith
What would be the standard way?
Well i have tried by induction, ive shown that it does decrease for the first few terms but im not sure how to show it does for all n>=1
hybrid fossil
suppose that a_n+1 <= a_n
then a_n+2 = sqrt(2a_n+1 - 1)
now since f(x) = sqrt(2x - 1) is an increasing function and since a_n+1 <= a_n you can say that sqrt(2a_n+1 - 1) <= sqrt(2a_n - 1)
all these exercise basically follow the same path, its not wrong to just memorise it
mystic wraith
And that would be enough to show that it's decreasing right
But i dont quite understand that part sorry "since f(x) = sqrt(2x - 1) is an increasing function and since a_n+1 <= a_n you can say that sqrt(2a_n+1 - 1) <= sqrt(2a_n - 1)"
vocal sleetBOT
@mystic wraith Has your question been resolved?
hazy sparrow
vocal sleetBOT
hazy sparrow
why isnt the red correct?
proper fox
that would work if there was an extra 1/2sqrt(t) factor
hazy sparrow
huh?
hazy sparrow
man im sooooo blind so i was making this on a paper and i didnt get the exercise fully right
i scraped something in the exercise
like this it would be right
ok nvm i understand
proper fox
all good ?
hazy sparrow
but now i dont understand the first first step
proper fox
which one
hazy sparrow
How the-
twin meteorBOT
Labyrinth
hushed pewter
Looks like you took log of different bases on each side
You should show more steps between lines 1 and 2
vast shale
First, 
Second, this isn't of the form a^b, this is of the form a(b^c)
You should use another property of logs, one regarding multiplication inside the log
No, log(ab)
There is no property regarding log(a+b) that I know of
hushed pewter
I would keep it separate
vast shale
hushed pewter
You're trying to solve for x
vast shale
log(6^(x^2-x))=(x^2-x)log(6)
vast shale
I'll reiterate, you're missing parentheses around x^2-x
hushed pewter
You need parentheses in your life
expand what?
Also, you don't need to calculate the log values
You can just leave them as log5 and log2 and log6.
You get a more exact answer that way, but whatever you're more comfortable with imo
expanding what?
This?
I see an x² term, so it looks like you have a quadratic equation on your hands
The way you wrote it, no
vocal sleetBOT
@pine swan Has your question been resolved?
vast shale
Looks alright to me
vocal sleetBOT
hollow bear
.close
civic oracle
There's no way this is true
vocal sleetBOT
There's no way this is true
civic oracle
This identity cannot be proven
Right?
I've spent so long on this, it's not possible but I need to make sure
dark field
Hint: What is cot in terms of sin and cos?
crimson jetty
plot in desmos.
civic oracle
Hint: What is cot in terms of sin and cos?
I know it's cos/sin and it doesn't help
civic oracle
plot in desmos.
I need to prove the identity plotting it won't help
I need to make left side = right side
crimson jetty
There's no way this is true
well since you seem convinced theres a mistake in the question
perhaps a plot would at least convince you otherwise.
civic oracle
Ohhhhhh
Bruh I thought someone like accidentally put their pen there
Still some kind of mistake
crimson jetty
you plot them each separately
.
civic oracle
ok
crimson jetty
I seem to agree there is a mistake in the question
crimson jetty
There's no way this is true
unless you add that penned in blue -, in which case it would be correct
vocal sleetBOT
@civic oracle Has your question been resolved?
vocal sleetBOT
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Available help channel!
tropic glade
Do I shade in like this or like this
vocal sleetBOT
Do I shade in like this or like this
@tropic glade Has your question been resolved?
flat whale
What's the question
tropic glade
@flat whale
mortal elbow
Yo.
lavish aurora
mortal elbow
Hold on tho. Can u lead me thru it? Cuz I have finals soon and I needa learn this part.
ornate ember
ooh this one looks fun 🙂
ornate ember
oh I think it is
ornate ember
so yeah first thing is first is to identify any identities
or just like simplify where you can
ornate ember
the first thing I would do would be to convert the fraction into this:
$\frac{\frac{a}{b}}{\frac{c}{d}} = \frac{a}{b} \cdot \frac{d}{c}$
twin meteorBOT
MellowDramaLlama
ornate ember
$a^2 - b^2 = (a + b)(a - b)$
twin meteorBOT
MellowDramaLlama
ornate ember
bingo 🙂
mortal elbow
Pk. thanks.
ornate ember
I see one in your problem
mortal elbow
Alright.
OHHHH
I SEE IT
Ok, i'll try.
Rhanks
Thanks
Oh my goodness that is so much easier.
Ok I found it, thanks.
.close
vocal sleetBOT
ornate ember
Oh my goodness that is so much easier.
🙂
vocal sleetBOT
Available help channel!
last sand
Brain Philippines (BP) offers expensive UPCAT training courses, claiming their graduates score better than those who have not taken any training courses. The average score of those who've not taken the training course is 50.
As an independent statistician testing this claim, what should the null and alternative hypothesis?
vocal sleetBOT
Brain Philippines (BP) offers expensive UPCAT training courses, claiming their g...
last sand
<@&286206848099549185>
vocal sleetBOT
@last sand Has your question been resolved?
last sand
<@&286206848099549185>
pallid zenith
Brain Philippines (BP) offers expensive UPCAT training courses, claiming their g...
define a variable that somehow represents the score of people who take the expensive course first
what is a good choice
vocal sleetBOT
@last sand Has your question been resolved?
vocal sleetBOT
@last sand Has your question been resolved?
vocal sleetBOT
vocal sleetBOT
Available help channel!
winter raft
for part b, can i equate the two then square both sides?
and then do the discriminant is grearter than 0?
oblique rivet
Try it and what answer do u get
vocal sleetBOT
@winter raft Has your question been resolved?
winter raft
Try it and what answer do u get
im getting a really weird answer which does not match the answer scheme
my discriminant is 4a^2 + 29a + 16
oblique rivet
Here there’s actually a trick to this a
oblique rivet
Is the answer 3/2<a<2?
winter raft
let me check
winter raft
Is the answer 3/2<a<2?
2 is right but -4/3
oblique rivet
Wait sorry the 3/2 was the a) part
winter raft
ohk
oblique rivet
The trick here is visualise and drawing the ax+2
winter raft
yeah
oblique rivet
When we draw the ax+2 graph on this graph when do we roots of only 1?
winter raft
When we draw the ax+2 graph on this graph when do we roots of only 1?
uh when the gradient is higher than or equal to 2
oblique rivet
Exactly
So when a<2 we get 2 distinctive roots right?
Which means that is one part of the and
Answer*
winter raft
So when a<2 we get 2 distinctive roots right?
yea
that makes sense
what abt the other part
oblique rivet
Once again visualise it
When do we get only one root only
I hope this helps
My drawing is bad
winter raft
oh is that the x intercept
oblique rivet
Yes exactly
oblique rivet
Yes but it’s not over
oblique rivet
Now using the x intercept find the equation
winter raft
cool
winter raft
my discriminant is 4a^2 + 29a + 16
could you possibly check if this was wrong? out of curiosity
oblique rivet
The values are wrong
I acc don’t know if we can use this as there’s a mod
Which means the ax+2 graph intercepts at 2x-3 and -2x+3
subtle vessel
vocal sleetBOT
subtle vessel
how do i do part b)
midnight rapids
Okay horizontal velocity is V cos theta, vertical is v sin thera
Let’s start by calculating the time
Acceleration=-g, height= -h, initial velocity = vsin theta
-h = usin theta t -gt^2/2
Take the positive root of this equation to find t in terms of the given variables
Horizontal distance is v cos theta*t
Now you’ll get the horizontal distance as a function of theta, maximum value of sin theta= cos theta = 1 and max value of sin theta cos theta = 1/2 at pi/4 degrees. Depending on what you get as the horizontal distance, you can find theta and max distance accordingly
Also, find the final vertical velocity, root of ((vsintheta)^2 + 2gh)
Tan alpha = final vertical velocity/ initial horizontal velocity (and initial horizontal velocity = v cos theta)
crisp yoke
how to find a and then how to work the definition if it's in the form x/b and not bx
vocal sleetBOT
how to find a and then how to work the definition if it's in the form x/b and no...
@crisp yoke Has your question been resolved?
patent nymph
how to find a and then how to work the definition if it's in the form x/b and no...
it should be similar to when it is bx
scarlet mist
if anyone could show me how to get 16b here would be awesome
vocal sleetBOT
if anyone could show me how to get 16b here would be awesome
scarlet mist
this is the answer but i'm not sure how to get to it
vocal sleetBOT
@scarlet mist Has your question been resolved?
twin meteorBOT
rugged orchid
That’ll be the first step
vocal sleetBOT
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urban obsidian
Hi
urban obsidian
Normal fourier series is given as:
twin meteorBOT
hii_
twin meteorBOT
hii_
vocal sleetBOT
@urban obsidian Has your question been resolved?
brittle girder
Normal fourier series is given as:
Normal Fourier series is for a 2pi-periodic function. I think the one on wiki is for a function with any period P
urban obsidian
Normal Fourier series is for a 2pi-periodic function. I think the one on wiki ...
you're right
I don't understand why that mapping works though
for any period
I think it's a trigonmetry thing as well where asin(bx+c) + d and you have period = 2pi/b
don't really understand the logic behind it
brittle girder
The top answer here explains it better than I can https://math.stackexchange.com/questions/2984123/proof-that-frac-2-pi-k-is-the-period-of-y-sinkx
urban obsidian
The top answer here explains it better than I can https://math.stackexchange.com...
and i assume this answers my fourier question as well, right?
brittle girder
No that's the explanation of why the 2pi/P in sine and cos makes them have period of P
urban obsidian
No that's the explanation of why the 2pi/P in sine and cos makes them have perio...
which explains the mapping for the fourier too?
the first fourier definition is for 2pi-period
the other one is generalized for any period because of the 2pi/period = frequency
brittle girder
The Fourier series MUST have the same period as the function
urban obsidian
The Fourier series MUST have the same period as the function
right
urban obsidian
the first fourier definition is for 2pi-period
the other one is generalized for ...
is this the explanation?
@brittle girder
or is it based on something totally different
and it's not reltaed
also sorry if i sound woke or something lol
brittle girder
Sorry I got distracted. Yes that's correct
brittle girder
Yes
vocal sleetBOT