and the hint on the hw was to use kinetic energy
#help-49
old sapphire
dull yoke
ye u can use WE theorem
i was just abt to type that lol
but kinematics is enough
if u wanna use WE go ahead ig
old sapphire
but kinematics is enough
ok how to do it with kinemtaics?
i thought i was doing correct
above
either is fine with me
dull yoke
W+ K_i = K_F, then (1150-625)(40) + 0.5(90)(0^2) = 0.5(90)(v_f)^2
thats how u do it with WE thm
with kinematics you can do
(1150-625) = 90 * a, v_f ^ 2 = v_i^2 + 2ad
you should get the same answer for both
just 2 different approaches
old sapphire
you should get the same answer for both
ok i will get back to u in a sec
dull yoke
if ur using WE, u dont need to calc acceleration
old sapphire
if ur using WE, u dont need to calc acceleration
i see so i think my kinematics thing was correct just was using a wrong value
for the net force
anways
ty 🙏
close
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random wharf
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wraith aurora
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trail stone
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bitter tide
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coarse quartz
This question confuses me. Is it asking me to find the lim or derivative?
midnight plankBOT
This question confuses me. Is it asking me to find the lim or derivative?
keen herald
The limit is part of the definition of the derivative
By finding the limit of that equation, you get the derivative of the function sin(pi/3)
coarse quartz
limit = derivative?
last slate
midnight plankBOT
last slate
correct?
balmy brook
yes
wary thorn
what about this one
!show
midnight plankBOT
what about this one
Show your work, and if possible, explain where you are stuck.
solar fractal
Correct, also cool name
midnight plankBOT
Correct, also cool name
As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.
wary thorn
so to get the same denomotar i made it 2/8 then minused
good, that's right
last slate
Correct, also cool name
Thanks
simple acorn
midnight plankBOT
simple acorn
Did i miss something over here?
I need both 20 and 3 to be negative to add up to -23 but I also need to multiply to -60
<@&286206848099549185>
.close
last slate
midnight plankBOT
last slate
I cant visualize this question
if that makes sense
i dont understand the wording
<@&286206848099549185>
what are the 3 focal points ?
midnight plankBOT
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coarse quartz
@last slate find the compound interest for year 11 and year 19
last slate
what abt the 2 equal payments ??
do i only need to solve for 1 of them
bcs theyre equal anyways
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silent sorrel
midnight plankBOT
silent sorrel
Is this the right setup
grand pondBOT
silent sorrel
<@&286206848099549185> pls help me sorry for the ping
rose kayak
seems reasonable. What did you get for x?
bronze wigeon
Should mention that technically it’s reciprocated, but if t1=t2 then 1/t1=1/t2 so
silent sorrel
What
silent sorrel
Should mention that technically it’s reciprocated, but if t1=t2 then 1/t1=1/t2 s...
which is t1 and which is t2
rose kayak
What
they're saying that it makes more sense for you have them "flipped", i, e, 400/(x + 5) = 360/(x)
but it doesnt' technically matter in this specific example
silent sorrel
Oh ok
rose kayak
which is t1 and which is t2
t1 and t2 are just other words for variables. The key here is that it's the same amount of time taken for both trips
grand pondBOT
A brief description and guide on how to use me was sent to your DMs!
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rose kayak
,rccw
grand pondBOT
rose kayak
yep that seems reasonable! Let's see if they come out to the same amount of time
,calc 400/50
grand pondBOT
Result:
8
,calc 360/45
grand pondBOT
Result:
8
How do you tell which is numerator and which is in denominator
silent sorrel
I actually just took that trip this weekend
cool
silent sorrel
How do you tell which is numerator and which is in denominator
In the context of the rational word problems
rose kayak
How do you tell which is numerator and which is in denominator
This is where units are helpful. You'll learn about something called "dimensional analysis" at some point
silent sorrel
the only problem is that I have a test on this tomorrow
rose kayak
ah ok
so let's take this example
speed is usually calculated as "miles per hour" aka "miles/hour" aka "mph" etc, right?
silent sorrel
yes
rose kayak
ok
silent sorrel
wouldn’t speed be equal to the ratio and not in the ratio
rose kayak
can you clarify what you mean by that?
rose kayak
they mean the same thing. "per" in this case would be "divided by"
colloquially
ok
so let's take your example
give me some time to set this up please
silent sorrel
Wait
silent sorrel
The ratios are equal to time, so it’s just h/mph?
Like they’re algebraicly swapped
like this one
,rccw
grand pondBOT
rose kayak
Say if you we know that the average speed is 45 miles per hour and we know that we traveled 360 miles. We want to know how long it took.
$\\$
So we can set up a ratio and orient our units based on our goal. We want to know how long it too.
$\\$
So we have: $\frac{45 \text{ miles}}{1 \text{ hours}} \cdot \frac{1}{360 \text{ miles}} = \frac{45 \text{ miles}}{360 \text{ hours} \cdot \text{ miles}} = \frac{1}{8 \text{ hours}}$. We can cancel out the miles since we have both units in the numerator and denominator.
$\\$
However, $\frac{1}{8 \text{ hours}}$ doesn't make a whole lot of sense for this context. If we flipped it at the beginning then we could have the miles be the correct unit.
$\\$
$\frac{1 \text{ hours}}{45 \text{ miles}} \cdot \frac{360 \text{ miles}}{1} = \frac{360 \text{ hours} \cdot \text{ miles}}{45 \text{ miles}} = \frac{8 \text{ hours}}{1} = 8$ hours.
ugh hold on
storm shore
Hey, can anyone help me with this... Kind of basic but I've been working on it for several hours and can't get it.. it's the last (bottom) problem
rose kayak
Hey, can anyone help me with this... Kind of basic but I've been working on it f...
#❓how-to-get-help this channel is occupied
rose kayak
Like they’re algebraicly swapped
Pretty much yeah.
In this example, it's simple enough (and what I assuming what you'll be working on for this section) where you can just probably flip it and get the proper answer.
But sometimes the orientation matters
hey I gotta head out for a bit but hopefully that example made sense
good luck with your test tomorrow
silent sorrel
@rose kayak is that 8mph
silent sorrel
good luck with your test tomorrow
Thanks
rose kayak
<@381633089891336192> is that 8mph
no in this case it'd just be 8 miles
NO WAIT
sorry
it'd be 8 hours
let me correc that real quic
grand pondBOT
MellowDramaLlama
rose kayak
just read through that part step by step
sage adder
can someone help me b and c?
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leaden mural
crystal sandal
can someone help me b and c?
no one helped 💀
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solid iris
can someone help me b and c?
try working out conditions to be in kerL then pick out a basis
midnight plankBOT
solid iris
.reopen
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✅
sick fossil
can someone help me b and c?
Try finding an element of ker L
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shy totem
For the top question how do I make an expression for area?
midnight plankBOT
For the top question how do I make an expression for area?
shy totem
2(6x + 2 + 3x) is right but your final answer is not.
I know how to fix and I will I’m just asking about area idk how to express it
18x + 4
verbal rain
A = LW
last slate
Greetings from laptop
I have a inquisition into a mater that involved number theory.
I know that a number n evenly divides a number a if $a = nk$ for some integer value k
midnight plankBOT
Greetings from laptop
I have a inquisition into a mater that involved number the...
grand pondBOT
<:F_button:1095679234497843251>
last slate
How would I use this knowledge to figure out if a number [a] is divisible by some number b who's digits are the number n
I'm asking this question because of this problem
https://codeforces.com/problemset/problem/122/A
Petya loves lucky numbers. Everybody knows that lucky numbers are positive integers whose decimal representation contains only the lucky digits 4 and 7. For example, numbers 47, 744, 4 are lucky and 5, 17, 467 are not.
Petya calls a number almost lucky if it could be evenly divided by some lucky number. Help him find out if the given number n is almost lucky.
4
7
47, 74, 77, 44
777, 774,744, 444, 447, 477, 474, 747
are lucky numbers
If the number I'm checking is less than 1000 I would have to check if my number is divisible by any of the above lucky numbers
next rover
that would make sense
you don't have to check the repeating ones
77,44,777 and 444
744 is also redundant
last slate
This was the trival solution i came up with
fn main() {
let mut scanner = Scanner::default();
//Gets number from standard input
let number:usize = scanner.next();
let almost_lucky:bool = Vec::from([
4usize,7usize,
47usize,74,44usize,77usize,
444usize,777usize,447usize,477usize,774usize,744usize,747usize,474usize
])
.iter()
.any(|lucky| number % lucky == 0);
println!("{}",
if almost_lucky { "YES" } else { "NO" }
);
}
But there has to be a way that doesn't involve enumerating all the possible lucky numbers
steep ledge
to generate them, you can notice that the lucky numbers are of the form sum a_k * 10^k where a_k is either 4 or 7
you can generate the list of lucky number with a simple list
a for loop that goes through all theses sums gives every lucky number
last slate
to generate them, you can notice that the lucky numbers are of the form sum a_k ...
I do not want to generate them either
if the number im checking is extremely large then generating them might not work
steep ledge
you can't predict every single lucky number tho, bc of Dirichlet theorem
the further you go, you'll eventually get prime lucky numbers again and again
and if you could predict their pattern, you would be solving some part of millenium problems
last slate
That is surprising
I have not learnt enough about number theory to know Dirichlet theorem
I am saddened to know there is no O(1) solution to this
TY for help
.close
blissful trench
A group of friends decides to share a cake. If it takes Alice $2$ hours to eat the entire cake, Bob $3$ hours, and Carol $4$ hours, how long will it take them to eat the cake together?
midnight plankBOT
A group of friends decides to share a cake. If it takes Alice $2$ hours to eat t...
grand pondBOT
Akira 🍇
blissful trench
!status
midnight plankBOT
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 was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
1
vale zephyr
i dont remember why we do this, i learned this like 2 years ago, but we take thier least common mulitple iirc
blissful trench
how
main current
Think in terms of rates.
Alice eats 1/2 of a cake in an hour
Bob eats 1/3 of a cake
Carol eats 1/4 of a cake
How much do they eat in an hour combined
grand pondBOT
Akira 🍇
blissful trench
solve for t now?
main current
That's exactly it
cedar coral
i would put it as t, not 1/t. It's gonna be easier to work with
midnight plankBOT
main current
You can sum them for a rate, but then you have to flip that for the time taken
slow moon
main current
Take an open channel
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Available help channel!
cedar vortex
quick notational question @steep ledge
midnight plankBOT
quick notational question <@249632691564183553>
obtuse flame
Sorryyyy
cedar vortex
so I got the basis
and everything but the last one is skew symmetric
so it should be something like [0 0 0 2]
cedar vortex
what's f ?
f(A) = A - A^T
cedar vortex
also, show your basis
basis is {[1 0 | 0 0], [0 0 | 0 1], [ 0 1 | 1 0], [0 1 | -1 0]}
steep ledge
f(A) = null matrix if A is symmetric, and 2A if skew
steep ledge
is [f]b a notation to say image of the basis in the basis ?
if yes, I guess so
but that seems weird use of notation
cedar vortex
is [f]b a notation to say image of the basis in the basis ?
uh yeah
the notation is so confusing
I know how this works
steep ledge
the problem is that the definition of the notation isn't in this theorem
cedar vortex
the problem is that the definition of the notation isn't in this theorem
yeah
steep ledge
but I guess [0, 0, 0, 2] makes sense if it means image of something expressed in basis B
cedar vortex
but I guess [0, 0, 0, 2] makes sense if it means image of something expressed in...
so it's good?
I'm so confused lmao
but like shouldn't it be a constant
like$[0, 0, 0, 2x_4]$
grand pondBOT
nosqldb
steep ledge
again, I simply don't know this notation
waxen silo
could someone explain why theres a 3 here?
midnight plankBOT
could someone explain why theres a 3 here?
waxen silo
could you care to highlight that? I cannot see it in the answer
btw I have a slight understanding on how this stuff works
so I may falter under some explaination, I apologise in advance
grand pondBOT
Afi
waxen silo
wait... what??
rose cobalt
Ok lemme ask you what is P’(Alpha)
waxen silo
oh, if I were to put all the roots in like (x+a)(x+b)(x+y)
and expand it
I would get 3 b's
is that what your saying?
rose cobalt
Not rly
rose cobalt
$P’(x)= 3x^2 + 2ax + b$
grand pondBOT
Afi
waxen silo
mhm I understand that
rose cobalt
Just plug in x=alpha
rose cobalt
Write down what you get after plug in x=beta and x=gamma
waxen silo
oh you do get 3b's
rose cobalt
Add all of them together and what will you get
waxen silo
WOW THIS MAKES MORE SENSE NOW
3a^2+ 3B^2+ 3y^2 + 2aA +2aB +2ay + 3b
facortise 3 and 2 out respectively
rose cobalt
Yes and a can be factorised out too
waxen silo
goode gawd
it all makes sense now
I get it now
thank you for the help
could I quickly ask just one more related to this?
rose cobalt
Sure
waxen silo
I just want to understand the correlation of this
the top part
I know its to do when you add all the roots together and they correlate to the P(x) becuase math laws
rose cobalt
Those two parts are independent
The first part is the given info
The second part is what you write down
rose cobalt
You have $\alpha, \beta, \gamma$ as the roots of $P(x)$
waxen silo
and so and so
grand pondBOT
Afi
waxen silo
mhm I get that
rose cobalt
From here
Well it’s called Vieta formula
Or more intuitively
Think of $P(x)=a(x-\alpha)(x-\beta)(x-\gamma)$
grand pondBOT
Afi
waxen silo
ok know what Vieta's formula are
waxen silo
**Afi**
I assume if we were to expand this, every coefficient of x would line up to something right?
waxen silo
oh boy time to expand a cubic 
last slate
bit new to recipirocal functions, i got the top part (local max=local min for reciprocal functions), but the bottom two I don't understand why they have a point there and cross through the parabola
midnight plankBOT
bit new to recipirocal functions, i got the top part (local max=local min for re...
last slate
what is the equation of the function and what is the equation of its reciprocal
main current
Any time the function crosses through y = 1 or y = -1, you could put one of those points
last slate
so reciprocal is constant if there are 1's
main current
Because those are the numbers that aren't changed when you take a reciprocal
1/(1) = (1)
1/(-1) = (-1)
main current
Yeah you could say that too
midnight plankBOT
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Available help channel!
last slate
How to prove this using proof by exhaustion?
For every n ∈ N, n(n+1) is even
midnight plankBOT
How to prove this using proof by exhaustion?
**For every n ∈ N, n(n+1) is even*...
last slate
do you know what a proof by exhaustion is?
I understand the concept but I don't know how to use it in practice
last slate
I understand the concept but I don't know how to use it in practice
So, for any natural number, it can be one of two things
what are those two things?
odd and even?
lyric charm
in proofs involving parity, it is sometimes (but not always) to split into two cases based on parity of one thing or another
last slate
yes
so you can consider both cases individually
i.e. consider when n is even and also consider when n is odd
last slate
in proofs involving parity, it is sometimes (but not always) to split into two c...
writing this down
last slate
i.e. consider when n is even and also consider when n is odd
once you are done writing that, do you know how to represent an even number, to start with the even case?
last slate
once you are done writing that, do you know how to represent an even number, to ...
2k for an even number and 2k+1 for an odd number ?
yeah
so start with n = 2k
substitute that into your expression
observe what your resultant expression would be
I'm sorry I don't understand why we assume that n is even, we're supposed to prove that n(n+1) is even
Its a proof by exhaustion
So what we are doing is this
dawn hazel
suppose n is odd
last slate
we know that n can be any natural number
dawn hazel
then n+1 = even
even * odd = even
suppose n= even
well then it's even easier
since even*anything is even
lyric charm
I'm sorry I don't understand why we assume that n is even, we're supposed to pro...
we break into two cases
one case in which n is even
dawn hazel
thus we have exhausted the two cases
lyric charm
the other case in which n is odd
last slate
we know that n can be any **natural number**
odd numbers + even numbers = the entirety of the natural numbers
so if you can verify that both the even and odd n's give you an even expression, then you thus verify it for the entirety of the natural numbers as well
ok i will leave 3 helpers will just confuse
last slate
ok i will leave 3 helpers will just confuse
thanks for your time!
so suppose that n is even so n=2k and then from that we build to n(n+1)?
dawn hazel
no
N= even, then we have that n(n+1)= even
that is because even* anything is even
and for n= odd we have that n+1=even
so we again have even*anything=even
last slate
that is because even* anything is even
okay got this
so we got the first case, the when n is even
now we check for when n is odd
dawn hazel
Yes
Or even easier to visualise
n and n+1 are two consecutive numbers
so one must be even and one must be odd
and since we're multiplying them, it doesn't matter which one is odd or even
since odd*even=eventimesodd
and that is also equal to even
since 2k(2n+1)=4kn+2k=2(2kn+k)
last slate
okayokay that makes sense
dawn hazel
ok
dawn hazel
try plugging n=2k=1
last slate
but why
dawn hazel
wait sorry
2k+1
forgor to hold shift
and that is because 2k is even and when we add 1 to an even we get an odd
dawn hazel
to n(n+1)
when n is even, n=2k
when n is odd, n=2k+1
plug each value into the equation
and see how it works out
dawn hazel
what can you say about the number 4k^2 + 2k
last slate
I can write it as 2(2k^2+1) which means it's an even number times an odd number which means it's even?
last slate
that makes sense
last slate
no way
last slate
where did the 2 come from
dawn hazel
plug in 2k+1 for n
last slate
oh wait I got it i got it
dawn hazel
n+1=2k+1 +1
last slate
I forgot about the n
last slate
yes so we get 4k^2 + 6k +2 right?
dawn hazel
yeah
last slate
and it's a multiple of 2 so it's even
dawn hazel
yeah
So you've exhausted both cases
When n=even and where n=odd
and you've shown that n(n+1) is even for both of them
last slate
okay thanks a lot for the help!!
last slate
first year computer science
dawn hazel
wait so like university
last slate
yep
midnight plankBOT
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last slate
.close
midnight plankBOT
last slate
there you go
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Available help channel!
gentle fossil
what would be a domain for this?
midnight plankBOT
what would be a domain for this?
gentle fossil
0 through 5?
dawn hazel
idk what domain really means in english lmao
domain of V is like values of V?
or values of x?
gentle fossil
or values of x?
x
dawn hazel
Volume has to be >0 right
dawn hazel
infinity
gentle fossil
what about this
The reasonable domain for V is x ∈ [0,9].
dawn hazel
did you write v(x) correctly?
gentle fossil
did you write v(x) correctly?
the function?
gentle fossil
it's correct
my equation?
dawn hazel
Yes
I forgot to read the first part
now it's obvious
x>0
9-2x>0
=>9>2x
=>x<4.5
so 4,5>x>0
so we have x=(0;4.5)
gentle fossil
so 4,5>x>0
so 0≤x≤4.5
gentle fossil
you'd be cutting the whole paper
thats fine tho, no?
midnight plankBOT
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last slate
in a poker hand consisting of 5 cards, find the probability of holding 2 aces and 3 jacks
midnight plankBOT
in a poker hand consisting of 5 cards, find the probability of holding 2 aces an...
last slate
so uh, im not quite familiar with how poker is played usually
wind current
poker has 52 cards
last slate
yeah
wind current
4 of them are aces (ace of hearts/spades/clubs/diamonds)
4 of them are jacks (jack of hearts/spades/clubs/diamonds)
hard shard
Do you remember the full house question?
last slate
no sadly its been a bit, but i do remember our discussion
last slate
aces are not distinguisable from each other right
wind current
the problem is not asking for specific types of aces in your hand
so they are not distinguishable
next rover
a hand is uniformly one of 52c5 hands
last slate
okay so
next rover
it's just counting combinations, you can phrase it with people
last slate
lets find the sample space first i suppose
so our sample space is
any set of hands
which is $\ds \binom{52}5$
grand pondBOT
next rover
absolutely
last slate
so,
we are trying to find the possibility of being dealt 2 aces and 3 jacks
there are 4 cards of each
so
Assuming that $A$ is the event that you get 2 aces and 3 jacks: [
\map P A = \f{\binom 4 2 \binom 4 3}{\binom{52}5}
]
grand pondBOT
last slate
right?
next rover
yes
last slate
okay this might sound really weird but im like in the middle of like distingushing between when to be considering permutations and combinations.
What would you modify in the original scenario to turn that 52c5 to like 52p5
just for my own understanding
next rover
you don't have to modify it, it would give the same answer if you do permutations
next rover
okay no
like your sample space becomes 52p5
but then 4p2 × 4p3 undercounts hands
it makes you only consider hands that look like AAJJJ, but it could be JAJAJ
sudden needle
okay this might sound really weird but im like in the middle of like distingushi...
if the question said something like first 2 cards you pick need to be aces and next 3 should be jacks, then you'd do permutations
basically if its asking that something needs to be in a specific order
you do permutations
next rover
(4p2 × 4p3 × 5c2) / 52p5 would work
sudden needle
you do permutations
and if order doesnt matter you do combinations
last slate
ok the "ordeR" becomes a bit vague in some situations
but i get your idea yes
okay as another exercise
lets calculate the chance of getting the royal flush
next rover
combination is essentially amounts
a multiset
"3 of something and 6 of something"
to visualize it, you put the elements in some sort of fixed order like alphabetically
sudden needle
for number of royal flushes you dont need anything you can just count them, spade, clubs hearts and diamond = 4 possible royal flushes
and for probability just divide by 52C5 (total no of cases)
slate talon
can anyone explain how n was solved and got to that answer
midnight plankBOT
can anyone explain how n was solved and got to that answer
slate talon
of 150.5
wooden dock
midnight plankBOT
@slate talon Has your question been resolved?
vale zephyr
midnight plankBOT
vale zephyr
Is this right $\mathrm{T_n = \frac{3n\sum_{r=1}^{n}(r^2)}{2n+1}}$?
grand pondBOT
!Yajat!
vale zephyr
this is the general term i have made of thos sequence
the only problem is i think im abusing any summation notation, any help would be appreciable, thanks
midnight plankBOT
@vale zephyr Has your question been resolved?
mighty sleet
@vale zephyr Looks right to me.
I don't think you are abusing summation notation, but you may be able to express the whole sum without nesting summations, and that might be more convenient in some cases
vale zephyr
like to show the summation in expanded form?
vale zephyr
**!Yajat!**
in this?
mighty sleet
No, I mean if you express the sum as a sum over Tn, you will have a sum inside a sum
You might be able to avoid that, but I would not bother until you need to
vale zephyr
no i will open this summation likes sum of squares of first n term = n (n+1) (2n+1) / 6, and then simplify a bit and then apply the final Sum of this sequence summation
so it wont be a summation inside summation
mighty sleet
Yes, that simplification is what I am talking about
grand falcon
Is a rectangle a rhombus always, sometimes, or never
midnight plankBOT
Is a rectangle a rhombus always, sometimes, or never
grand falcon
I had this question on my homework and I’m not sure
If i were to make a guess though
sometimes if the rectangle has all congruent sides?
heady lark
Is a rectangle a rhombus always, sometimes, or never
only if rectangle is a square
grand falcon
only if rectangle is a square
Huh
heady lark
then it's rhombus also
grand falcon
So the answer is never
heady lark
So the answer is never
no, answer is when it is square
grand falcon
I mean
Ok look
A rectangle with all equal sides is a square
So my answer is right?
heady lark
A rectangle with all equal sides is a square
yes
grand falcon
So my answer is right?
?
slim valve
if i have a number x which is divisible by 7 and 2 how do i prove that x has to be divisible by 14 as well?
i guess you can say x = 7a and x = 2b, but how does knowing that imply x = 14 c??
midnight plankBOT
if i have a number x which is divisible by 7 and 2 how do i prove that x has to ...
floral apex
more or less i think
just argue that both 7 and 2 exist in the factorization
so x = 7 2 b where b is some natural
slim valve
so you can substitue a for 2b?
wouldnt u have to then prove a is divisible by 2
i dont think its always true tho?
for example 4 * 6 = 24 by 36 which is divisble by 4 and 6 is not divisible by 24
i think perhaps it has to do with even and odd integers
steep ledge
Gauss lemma, if a divides bc and gcd(a, b) = 1, then a divides c
you can prove it from Bezout's identity
slim valve
i cant use things not covered in the class :(
steep ledge
since x = 7k for some integer k, 2 divides x = 7k, and 2 is coprime with 7, 2 divides k, and k = 2q
then x = 14q
slim valve
how do you know 2 divides k because they are coprime?
slim valve
i dont think i can use that assumption tho
maybe there is another way without that lemma
steep ledge
then justify that both 2 and 7 needs to appear in the prime factorization
and factor 2 and 7 ig
slim valve
🤔
steep ledge
2 and 7 are prime numbers, so if your number is divisible by 2 and 7, in the prime factorisation, 2 and 7 appear with some exponent >= 1
and your number is written as a product
factor a 14 out of it since it's possible bc of 2 and 7 being in the prime decomposition
slim valve
i dont think i can use prime factorization since that isnt covered and not defined in the class im in
steep ledge
did you see something in that class lmao
slim valve
my prof said one way is to use the lemma even * odd = even
steep ledge
well, you can reformulate Gauss like that ig
since x is divisible by 7, it's a multiple of 7, that has to be even since x is divisible by 2, and the even multiples of 7 are the multiples of 14
but then to prove it you would still need some arithmetic results, we're running in circles
slim valve
ok i think i got it :/
so 7b = 2a = x so since 7b is even since x is even. b must be even since 7 is odd and the only way to get an even number is for b to be even so sub in b for 2c and you get 14c
steep ledge
you're saying 2 divides 7b, but 2 is coprime with 7, so 2 divides b
you're just formulating it by saying 7 is odd, but being odd is the same as being coprime with 2
slim valve
hmm yea my prof wants to use only definitions that we have gone over
thanks for ur help
👍
.close
spiral iron
midnight plankBOT
shell pendant
Well what does colinear mean and what does rank less than 3 mean?
midnight plankBOT
@spiral iron Has your question been resolved?
spiral iron
Collinear means they lie on the same line, right?
But I don't know how to show that their rank is less than 3.
wary thorn
But I don't know how to show that their rank is less than 3.
if the matrix's RREF has less than 3 pivots
spiral iron
<@&286206848099549185>
midnight plankBOT
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midnight plankBOT
@spiral iron Has your question been resolved?
midnight plankBOT
@spiral iron Has your question been resolved?
midnight plankBOT
@spiral iron Has your question been resolved?
storm spindle
I’d probably assume that x3 stands in some relation to x1 and x2 and write y as mx+b
But thats just intuition, it might not lead to anything
livid bramble
=> they are a line so write (xi,yi)'s as (x1,y1),(x1+a,x1+b),(x1+La,y2+Lb) as they have the same slope
then find a way to eliminate a column or something
<= rank<3 <-> dim(column space)<3 so the column vectors are linearly dependent, then do what you have to do
rare shuttle
What’s the name of combinatoric problems similar to this How many ways are there for a checker to travel from the bottom left corner to the top right corner of a 5x5 board if it can only move right or up by one square each time, but it cannot pass through the center square?
midnight plankBOT
What’s the name of combinatoric problems similar to this `How many ways are ther...
narrow jungle
i think its called grid path problem
midnight plankBOT
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frank pecan
this is formula for findin area of triangle using matrices
u just have to prove that determinent of this is equal to zero
we know are of a line is zero
so these points are collinear
midnight plankBOT
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hallow mauve
Hi
steep hinge
mh..
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hallow mauve
<@&286206848099549185>
midnight plankBOT
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cedar olive
Question 3G
midnight plankBOT
Question 3G
cedar olive
The goal is to remove the radical from the denominator
Textbook ans is below
I dont know where to begin
If i could get the first step it would be nice
crystal rivet
Well first I would try to remove the fraction from the denominator
cedar olive
How to do that?
crystal rivet
By multiplying top and bottom by 3
cedar olive
Perfect my answer matches
I was stuck on what to multiply by
Thank you mate
Good night
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midnight plankBOT
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Available help channel!
last slate
hey just a general question
midnight plankBOT
hey just a general question
last slate
for domains, how would you include multiple segments of it
in set notation
for example i have (-3,-2)U(3,inf)
how would I write that in set notation
${xeR|-3<x<-2, x>3}$
grand pondBOT
RecRio
last slate
seperated by a comma?
dense chasm
What are the next two numbers 4,9,61,52,63,94,46
midnight plankBOT
What are the next two numbers 4,9,61,52,63,94,46
wary thorn
!original
midnight plankBOT
Please show the original problem, exactly as it was stated to you. A picture or screenshot is best.
If the original problem is not in English, then post it anyway! The additional context might still help helpers help you. Do your best to translate.
dense chasm
last slate
I assume it wants you to spot the pattern
wary thorn
Is this a test?
tall copper
2x2= 4
3x3 = 9
4x4 = 16 reverse 61
5x5 = 25 reverse 52
midnight plankBOT
2x2= 4
3x3 = 9
4x4 = 16 reverse 61
5x5 = 25 reverse 52
As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.
dense chasm
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naive flint
midnight plankBOT
naive flint
hi
This seems tough to graph
THere is also no HA
So do i just use a calculator or something
small ore
THere is also no HA
HA?
small ore
factor theorem
small ore
x=2? are you sure
small ore
yh
ok so you have root
Find what the graph does as x approaches negative infinity, positive infinity, x=3 from positive direction and x=3 from negative direction
then find where the graph crosses the y-axis (x=0)
then u should have enough info to do rough sketch
naive flint
what is confusing me is how zoomed out these are
I sketch it but the coordinates r so hard to locate idek
they tell me to use graphing device
i guess i will do the same coordinates as them
up to -150
and 150
i got a question
isnt the VA the dotted Line
and nothing crosses it
midnight plankBOT
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midnight plankBOT
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magic magnet
magic magnet
bitter vine
midnight plankBOT
Available help channel!
last slate
midnight plankBOT
sick fossil
can you state the definition of “increasing from the right to the left”, because usually that’s called “decreasing”
last slate
I Sent the wrong one
last slate
midnight plankBOT
last slate
what went wrong?
<@&286206848099549185>
<@&286206848099549185>
<@&286206848099549185>
midnight plankBOT
@last slate Has your question been resolved?
last slate
<@&286206848099549185>
wet rune
Damn man this helpers ain't do nun to the poor guy
midnight plankBOT
@last slate Has your question been resolved?
last slate
<@&286206848099549185>
fallen galleon
@last slate do you have the answer to this?
last slate
<@456226577798135808> do you have the answer to this?
unfortunately no, but the website says my answer is wrong
fallen galleon
didnt really find anything wrong in your steps
fallen galleon
unfortunately no, but the website says my answer is wrong
did it specify anything about significant numbers or decimal points
last slate
did it specify anything about significant numbers or decimal points
3 significant digits
last slate
didnt really find anything wrong in your steps
maybe it's a calculation error
fallen galleon
yeah maybe some accuracy is lost during the middle but nothing is wrong really in your steps
midnight plankBOT
naive flint
How would i find the vertical asymptote here again
Like it is weird for me as
i have to set x^2+x=0 xd
Idk how to do anything
barren blade
.
fallen galleon
i have to set x^2+x=0 xd
Set x^2 + x = 0, factor it to find your vertical asymptotes
midnight plankBOT
@naive flint Has your question been resolved?
magic field
What's the definition of an nth power residue? Also, is it only defined for prime powers? Why so? I see no reason why not to define it for any modulus m.
midnight plankBOT
What's the definition of an nth power residue? Also, is it only defined for prim...
magic field
I have seen a textbook define it for a general modulus m.
But most of the internet seems to suggest it being defined only for prime moduli.
For (a,m)=1, if x^n congruent to a (mod m) has a solution, then we say that a is an n-th power residue mod m.
Also, why do most people seem to drop the co-prime condition of 'a' with m when defining so? Is that another variant of the definition..?
Or is it like understood that a has to be coprime with m?
midnight plankBOT
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@magic field Has your question been resolved?
midnight plankBOT
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Available help channel!
bronze helm
midnight plankBOT
bronze helm
In the sheded region can we not do
Int 0 to 9 √x-x dx
midnight plankBOT
@bronze helm Has your question been resolved?
warm veldt
it's a extrema point
one notable thing about it that the derivative of the curve at that point is zero
raw grove
midnight plankBOT
lyric charm
ok so you have 4 math books, 3 science books, 2 geo books and 4 history books
for 4 subjects in total
to arrange them in a way that groups them by subject, you need to first decide which order the subjects go in (4! ways), then decide within each subject which order that subject's books go in (4! * 3! * 2! * 4! ways)
last slate
hi, i was wonderinng how long would it take approximately to learn calculus from michael spivak's book? and also what other resources complement it?
midnight plankBOT
hi, i was wonderinng how long would it take approximately to learn calculus from...
@last slate Has your question been resolved?
midnight plankBOT
@last slate Has your question been resolved?
lavish cairn
Write three rational numbers (as a fraction) between the following rational numbers.
9. -1/4 and 1/2
midnight plankBOT
Write three rational numbers (as a fraction) between the following rational numb...
lavish cairn
Help
midnight plankBOT
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lavish cairn
<@&286206848099549185>
magic stone
3/10
balmy brook
there's an infinity if number that verify those conditions
magic stone
Yeah you can pick anything in between .25 and .5
And find it's fraction and your done
balmy brook
-0.25
lavish cairn
Why