your mother
#help-10
sharp pecan
atomic tendon
ugh
sharp pecan
as in, her statement is correct
obtuse pebbleBOT
obtuse pebbleBOT
@dark bay Has your question been resolved?
brave bramble
You have a proof of the fact you are trying to prove in front of you?
obtuse pebbleBOT
@dark bay Has your question been resolved?
solemn wharf
Help me with this
obtuse pebbleBOT
Help me with this
solemn wharf
<@&286206848099549185>
timid silo
think about the divisibility test for 11, and extend it to 101
obtuse pebbleBOT
@solemn wharf Has your question been resolved?
shy bone
how to prove this by Induction $\prod_{k=2n}^{3n}1-\frac{1}{k}=\frac{2n-1}{3n}$ should I prove it for $\prod_{k=2(n+1)}^{3(n+1)}1-\frac{1}{k}$ or \prod_{k=2n}^{3n+1}1-\frac{1}{k}$?
obtuse pebbleBOT
how to prove this by Induction $\prod_{k=2n}^{3n}1-\frac{1}{k}=\frac{2n-1}{3n}$ ...
warm shaleBOT
Kedi
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
timid silo
the first one
shy bone
what does it mean to start from $k=2n+2=2(n+1)$?
warm shaleBOT
Kedi
timid silo
what does it mean to start from $k=2n+2=2(n+1)$?
it means the first time in that product is that you sub in is 2(n+1)
if you write out
what terms go into each product
shy bone
it means the first time in that product is that you sub in is 2(n+1)
so first term will be $1\frac{1}{2n+2}$ then $1\frac{1}{2n+2+1}$ ... $1\frac{1}{3n+3}$
warm shaleBOT
Kedi
shy bone
then all multiplied
timid silo
you will see that you can replace some fo the terms in the k+1th product with the kth product
timid silo
then all multiplied
1 - 1/(2(n+1))
and so on
all multiplied
note that for the kth product
you sub in:
2n
2n + 1
2n + 2 = 2(n+1)
2n + 3 ....
and in the k+1th product
you start at 2n+2 = 2(n+1)
2n + 3 ...
see how you can sub in the kth term product?
shy bone
note that for the kth product
you sub in:
2n
2n + 1
2n + 2 = 2(n+1)
2n + 3 .....
so we start with $2n+2$ and I wanna separate the product into $\prod_{k=2(n)}^{3(n)}1-\frac{1}{k}$ and sth. else
warm shaleBOT
Kedi
shy bone
And then sub in your result for the kth product
I am really confused we don't start from $2n$ but $2n+2$ so how can I seperate?
warm shaleBOT
Kedi
obtuse pebbleBOT
@shy bone Has your question been resolved?
shy bone
<@&286206848099549185>
timid silo
wdym separate
id advise you write out the sums
for the first few terms and last terms
for the kth step and the k+1th step
and youll see some similarities in the sum
obtuse pebbleBOT
@shy bone Has your question been resolved?
undone summit
Hello, how would I mirror x^3 along the line y = -x + 1?
obtuse pebbleBOT
Hello, how would I mirror x^3 along the line y = -x + 1?
undone summit
ionic egret
Try it translated first
Then move it back up
It'll be the same graph, and it's going to be a lot easier to reflect over y=x type things
undone summit
I suppose I could
I just forget my linear algebra
Im trying to generalize something for code
i got it
obtuse pebbleBOT
@undone summit Has your question been resolved?
Available help channel!
Available help channel!
late rose
Could someone help/teach me how to evaluate this log? I honestly don't know how to even start.
obtuse pebbleBOT
Could someone help/teach me how to evaluate this log? I honestly don't know how ...
late rose
Ok
timid silo
But it has no base
A log written without a base written is usually meant to refer to log with base 10
late rose
So like an unspoken rule like when x has a power of 1
timid silo
Yeah well, except that it is not a "rule" nor is it uniform
Some people mean it as base e, some people mean it as base 2
Depends on the context of your class
But most usually base 10 yes
late rose
Depends on the context of your class
Ok
timid silo
Could someone help/teach me how to evaluate this log? I honestly don't know how ...
Anyhow, this is just $log_{10}4 -log_{10}10$
warm shaleBOT
♡LexQa♡
warm shaleBOT
♡LexQa♡
late rose
Log 1?
timid silo
Not quite
think of it this way
It can be rewritten in exponential form to be
$\log_{10}10 = x \iff 10^x = 10$
What number x do you think suits this equality
late rose
1
timid silo
Yeah
warm shaleBOT
♡LexQa♡
timid silo
So the answer is just 1
For $\log_{10}4$ you can't do much except simplify it by rewriting $4 = 2^2$
warm shaleBOT
♡LexQa♡
timid silo
And taking the exponent down, like you said
late rose
So using rules of exponents kinda
warm shaleBOT
♡LexQa♡
timid silo
Can someone please help me?
I'm stuck on f derivative differentiability
Is f' differentiable at 0? Prove or disprove.
F(x) = x^2 if x>=0 and 0 if x<0
So, for differentiability we have:
Lim x-> x_0 (f(x)-f(x_0))/(x-x_0)
But I'm not sure how to use this for f' and piecewise f(x)
obtuse pebbleBOT
Can someone please help me?
I'm stuck on f derivative differentiability
Is f' d...
brisk matrix
Can someone please help me?
I'm stuck on f derivative differentiability
Is f' d...
this is the definition of a derivative, not differentiability
for a function to be differentiable at a point x_0 it has to be:
continuous at x_0
it’s derivative at x_0 exists
so the derivative of a piecewise function can be found by deriving the function piecewise
so what would f’ be in your case?
timid silo
f'=2x
brisk matrix
that’s for x>=0
timid silo
for a function to be differentiable at a point x_0 it has to be:
continuous at x...
Oh yes
And 0 for x<0
timid silo
Yes
brisk matrix
do the derivatives from the left and right approach the same value?
obtuse pebbleBOT
@timid silo Has your question been resolved?
rain ice
I need to decide X
obtuse pebbleBOT
I need to decide X
topaz flume
SOH CAH TOA
obtuse pebbleBOT
eternal bolt
obtuse pebbleBOT
Available help channel!
warm shaleBOT
joyousbanana
vagrant compass
obtuse pebbleBOT
vagrant compass
i dont understand this step
unreal musk
Combining the coefficients of $\frac{dy}{dx}\frac{d^{2}y}{dx^{2}}$
warm shaleBOT
chartbit
earnest bear
What number gives a result of −3 when 8 is subtracted from the quotient of the number and 5?
Im not really good with these kinds of word problems if someone could help me that would be great!
obtuse pebbleBOT
What number gives a result of −3 when 8 is subtracted from the quotient of the n...
errant basin
(x/5)-8=-3
earnest bear
Wouldnt -3 be at the beginning?
Just trying to understand it
earnest bear
Oh alright
So whenever it asks "From the qoutient of the number and 5" will 5 be at the bottom of whatever unknown is there?
I mean will it always
obtuse pebbleBOT
@earnest bear Has your question been resolved?
grim herald
obtuse pebbleBOT
grim herald
I need help with part b
so i set up the equation as the following
factor out the 2
then it becomes
but dont those two just cancel out
its subtracting intself
when I check the answers it becomes
and I dont know if im forgetting a rule or something
This is the solution that the textbook gives me
but I dont follow how we go from step 1 to step 2
warm canopy
you have 4*(stuff) - (stuff) = 3*(stuff)
prime kraken
Consider the function fAgiven by y = a1 + ax° + ba? + ex + d, where a, b, c and d are constant numbers.
The graph of f is symmetric about the y-axis and its zeros are -1, 0 and 1. Determine the values of the constant numbers a, b, c and d.
obtuse pebbleBOT
Consider the function fAgiven by y = a1 + ax° + ba? + ex + d, where a, b, c and ...
prime kraken
.close
unborn brook
help??
warm canopy
have you tried using the algorithm
unborn brook
eh how do you use it?
warm canopy
look it up
unborn brook
I dont really understand this topic
warm canopy
so look up the algorithm and read
warm canopy
what about it dont you understand
warm canopy
whats the first step
unborn brook
If Euler’s Theorem indicates the existence of an Euler path or Euler circuit, one can be found using the following procedure:
If the graph has exactly two odd vertices choose one of these odd vertices as the starting point of an Euler path. If the graph has no odd vertices it has an Euler circuit. In this case, choose any vertex as the starting point.
warm canopy
okay so does the graph have any odd vertices
unborn brook
they all look the same too, idk how to tell
warm canopy
okay well you should go and look up the definition of an odd vertex
or the degree of a vertex
warm canopy
go and find the definition
i assure you that if you read the definition you will understand it
im not going to do things for you
warm canopy
what does it say
unborn brook
the points where two or more line segments or edges meet
unborn brook
thats what they gave me
warm canopy
but thats not what i asked you to find
unborn brook
highest point
warm canopy
?
what? are you just guessing words now?
scroll up and look at what i asked you to look up
and look that thing up
unborn brook
this is what came up y, a vertex is odd or even based on the number of edges touching it
warm canopy
right
there we go
so now you are you able to see if any of the vertices in your problem are odd
even if an even number of edges are touching it
odd if an odd number of edges are touching it
opal sun
obtuse pebbleBOT
warm canopy
opal sun
?
cedar lichen
Show your work
raven spire
Do you have to use epsilon delta definition for continuity?
because if it's the limit one, you can clearly state, lim_{x -> 0} f(x) = 0
(ヘ･_･)ヘ┳━┳
zenith raft
i'm not sure that's something you can say is 'clear' haha
plus limit definition and epsilon delta definition are basically the same
raven spire
why though (@_@;) f(x) = x for rationals as x tends to 0 is not 0?
opal sun
Do you have to use epsilon delta definition for continuity?
i think so but not 100% sure
raven spire
in- in- intuitively??? Alright, let's write f(x) = p/q in simplest form, for x = rationals... then as q -> +infty, x -> 0, f(x) -> 0 is that fine now?
zenith raft
no
raven spire
🤕
raven spire
(╯°□°）╯︵ ┻━┻ da heck, It's 0 for irrational numbers
zenith raft
(which you can kinda do but that also requires explanation)
raven spire
ohhh you mean I'm not explaining why it's 0 not at any other place except for 0?
that wasn't my motive though >_< I was only explaining the part why f(x) is continuous at 0
warm canopy
if you're trying to use sequential continuity, you need to prove the limit is 0 for any sequence, not just a sequence of all rational or all irrational numbers
raven spire
Hmm . how'd you suggest to start?
zenith raft
you can skimp out on working from a definition of continuous for showing it's continuous at 0 with squeeze theorem
but it's not hard to do from definition either
warm canopy
take an arbitrary sequence a_n --> 0 in R, and then consider limsup and liminf of f(a_n)
oh that probably doesnt work bc negatives
squeeze doesnt sound like a bad idea
zenith raft
i would not really recommend anything other than epsilon-delta definition lol
opal sun
yeah thats the definition i probably understand the most
zenith raft
but squeezing between $x\mapsto 0$ and $x\mapsto x$ for showing it's continuous at 0 is ok
warm shaleBOT
💜𝓁𝒶𝓎𝓁𝒶💜
opal sun
i would not really recommend anything other than epsilon-delta definition lol
how would you suggest starting off this way?
zenith raft
pick a point x other than 0
then think about a neighborhood around x
the function will evaluate to 0 in some places and something very close to x at others
soooo
choose epsilon = |x|/2 or something
raven spire
how'd you get epsilon = |x|/2?
zenith raft
i didn't say that but i got it from the intuition just before it lol
and actually that's only good for rational numbers
i do want |x|/2
raven spire
(ヘ･_･)ヘ┳━┳
wild swallow
hmmmm density
raven spire
because if it's the limit one, you can clearly state, lim_{x -> 0} f(x) = 0
anyways,
here's what you can do for x -> 0
|f(x) - f(0)| ≤ |x - 0| ≤ |x|,
so, for all epsilon > 0, there exists delta = epsilon such that if |x| < delta, |f(x) - f(0)| < epsilon
therefore f is continuous at x = 0
if you were supposed to use ep-delta definition
obtuse pebbleBOT
@opal sun Has your question been resolved?
opal sun
ok yeah i think i can get it now thank you
mellow compass
obtuse pebbleBOT
mellow compass
what happened to the ln(n) and ln(n+1)?
cedar lichen
As n -> ∞, ln(n + 1) ≈ ln(n)
dusk siren
how does the u substition work. how does x become 2u in this case. I understand how u substition works i just dont understand how its been applied here
obtuse pebbleBOT
how does the u substition work. how does x become 2u in this case. I understand ...
cedar lichen
When you do the substitution, you get a constant * ∫ 1/(u² + 1) du, which is a standard integral
However, if you're like me and don't like remembering inverse trig integrals, you can also do a trig sub
dusk siren
but where does the 2 come from
wild swallow
you're probably expected to know that the integral of 1/(1 + x^2) is arctan(x)
this is why you want to put it into that form
dusk siren
yeah i understand that
but i just dont understand where the 2u came from
because in u substition dont u have to take the derivative of what ur substituting
wild swallow
to put the denominator into the form of (1 + something^2)
dusk siren
u = x
du = 1 dx
dx = du
cedar lichen
x = 2u
dx = 2 du
cedar lichen
Yes
dusk siren
so if i wanted to i could do x = 23492384u
cedar lichen
Wouldn't do much good, but yes
cedar lichen
You could do sin(x) = e^(u²)
small fern
obtuse pebbleBOT
small fern
<@&286206848099549185>
timber fox
partial fraction decomp
earnest knot
I need to prove that the area of σ is this using the Stoke's theorem.
obtuse pebbleBOT
I need to prove that the area of σ is this using the Stoke's theorem.
earnest knot
I don't know how to start. 😦
obtuse pebbleBOT
@earnest knot Has your question been resolved?
earnest knot
<@&286206848099549185>
obtuse pebbleBOT
@earnest knot Has your question been resolved?
clear leaf
magic portal
Determine the image distance and image height for a 5.0cm tall object placed 48.0 cm from a converging lens having a focal length of 24.0cm
Would I use the maginification formula to solve this??
obtuse pebbleBOT
Determine the image distance and image height for a 5.0cm tall object placed 48....
magic portal
wait nvm I got it
obtuse pebbleBOT
@magic portal Has your question been resolved?
obtuse pebbleBOT
@magic portal Has your question been resolved?
nova quarry
obtuse pebbleBOT
nova quarry
i’m confused on how to set it up
grizzled shore
You have some vibration / seconds
And you have some seconds
Multiply the 2 to get vibrations / seconds * seconds = vibrations
nova quarry
thanks
obtuse pebbleBOT
Available help channel!
cursive citrus
Can you only make phase portraits for autonomous ODE's and not non-autonomous?
obtuse pebbleBOT
Can you only make phase portraits for autonomous ODE's and not non-autonomous?
@cursive citrus Has your question been resolved?
cursive citrus
<@&286206848099549185>
obtuse pebbleBOT
@cursive citrus Has your question been resolved?
cursive citrus
<@&286206848099549185>
obtuse pebbleBOT
@cursive citrus Has your question been resolved?
steady flint
Can someone able to help me to answer this question?
obtuse pebbleBOT
Can someone able to help me to answer this question?
@steady flint Has your question been resolved?
steady flint
Anyone there :((
drowsy nest
obtuse pebbleBOT
@steady flint Has your question been resolved?
obtuse pebbleBOT
@steady flint Has your question been resolved?
steady flint
Tell me if you need more clarification my work is a bit messy <@6298682512869949...
Omg thank you
I love the little face
quick hazel
lol hope it helped 👍
timid silo
obtuse pebbleBOT
https://i.imgur.com/xqmfJ8g.png
timid silo
so which one is it?
shy vigil
what do you think
timid silo
im stuck
shy vigil
where
timid silo
whole thing
timid silo
ah so its c
shy vigil
it should be, yes
shy vigil
i think it'll be a
b*
see, you take out the constant, i.e., 1/3
then take log of 1/y
final thunder
obtuse pebbleBOT
@timid silo Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
vital frost
vital frost
can someone help me understand the quadratic eq line
timid silo
what do you not understand
vital frost
how to bracket it
i know it will be (w^2 -8) (w^2 + 1)
dont know how to include rest
<@&286206848099549185>
obtuse pebbleBOT
@vital frost Has your question been resolved?
vital frost
what do you not understand
what are my a,b,c values
obtuse pebbleBOT
@vital frost Has your question been resolved?
pulsar heron
obtuse pebbleBOT
pulsar heron
can someone help me with this problem
i have solved all the equations but now i am stucked on how to get values of x
warm shaleBOT
Vaibhav
$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$
bronze imp
Sry I typed something here
vital frost
Yes
obtuse pebbleBOT
@pulsar heron Has your question been resolved?
tropic bronze
Hi, What is the multiplicative inverse of x=17 modulo 231?
obtuse pebbleBOT
Hi, What is the multiplicative inverse of x=17 modulo 231?
timid silo
hello can someone help out?
tropic bronze
how do I calculate it
Ive found a google calculator but do not understand the concept behind it
warm canopy
Euclids algorithm to get bezouts identity
tropic bronze
I'll look into it, I got 68 do you think thats right
warm canopy
,w 17*68 mod 231
warm shaleBOT
tropic bronze
thanks
obtuse pebbleBOT
@tropic bronze Has your question been resolved?
jade harbor
$\sum_{n=1}^{\infty} \sin(\frac{n\pi}{2})$
obtuse pebbleBOT
$\sum_{n=1}^{\infty} \sin(\frac{n\pi}{2})$
warm shaleBOT
sumduck
timid silo
figure out what all the terms are by looking at the first four
kind hawk
next look at the partial sums
jade harbor
i kidna forgot what those are
is it like what it adds to as you go on?
1, 1, 0, 0, 1...?
timid silo
yeah
kind hawk
remember that the value of the series is defined to be the limit of the partial sums
jade harbor
but the partial sums just alternate between 0 and 1 right
kind hawk
if the partial sums diverge then the series diverges
jade harbor
wait so the limit is infinity?
kind hawk
diverge = limit does not exist
jade harbor
there is no limit??
wait so i was right here?
kind hawk
yes
jade harbor
oh okay lol ty
is there an easier way
like a test
i can do?
or should i just check the partial sums for any series
kind hawk
isnt this already pretty easy? at least for this series?
jade harbor
yes it was
kind hawk
well there are tests for other series, sure
jade harbor
is there one for this one
kind hawk
comparison test, integral test, stuff like that
jade harbor
bc on my sample exam it asks for test used
kind hawk
I guess the integral test would also work here. kinda. but why overcomplicate it
I mean you use tests for series where the partial sums are too hard
jade harbor
doesnt the integral test need decreasing
kind hawk
does it? ok nvm then. it's been some time since I've used it
jade harbor
I mean you use tests for series where the partial sums are too hard
oh okay
kind hawk
write "test used: direct application of definition"
celest gorge
obtuse pebbleBOT
obtuse pebbleBOT
@celest gorge Has your question been resolved?
celest gorge
<@&286206848099549185>
obtuse pebbleBOT
@celest gorge Has your question been resolved?
neon wyvern
Is 3.141414 to the infinite a rational number?
languid iris
what is 0^0
obtuse pebbleBOT
Is 3.141414 to the infinite a rational number?
sharp pecan
what is 0^0
1
actually, just dont 0^0
fickle turret
Is 3.141414 to the infinite a rational number?
Yes, it's 311/99
fickle turret
1
actually, just dont 0^0
Yeah, it is defined as 1
neon wyvern
how did you know its not?
sharp pecan
how did you know its not?
is not what
neon wyvern
rational
sharp pecan
its a fraction
languid iris
1
actually, just dont 0^0
ight cool but what is -1-1
sharp pecan
ight cool but what is -1-1
get your own help channel my son
neon wyvern
ah I think I see how you did it
fickle turret
ah I think I see how you did it
Then explain it to me 🙂
neon wyvern
excuse me because I'm not a native english speaker so its gonna be hard
but theres 3.14
which goes on forever
but we select the 14 which is the one thats repeating
and put this into an equation
x=3.1414
fickle turret
If you know german you can speak it, too
fickle turret
im not german lol but close
Well, I thought because of your name
fickle turret
Yes, that's the idea
fickle turret
A more rigorous way of doing this is geometric series, but that works, too (That's how I got to the answer)
neon wyvern
x=311/99
but I still dont understand what those Z and N were
we dont use those
or at least I didnt hear it lol
fickle turret
Z is the symbol for integers and N the symbol for the natural numbers (actually the symbol is slightly different but I don't know command by heart)
fickle turret
It's still down or down again?
kind hawk
dunno
fickle turret
Because I've tried it some days before and it didn't work then
neon wyvern
I think I understand everything now
kind hawk
nah it worked earlier today. it's not down for that long
neon wyvern
and if one of the division numbers were irrational then the fraction would also be irrationay correct?
fickle turret
A fraction a/b with a in Z and b in N is a rational number
Then you couldn't write it like that
The proof that something is irrational is more work
neon wyvern
well I mean you just prove its rational
if you can
all right thank you guys
.close
rose bluff
obtuse pebbleBOT
obtuse pebbleBOT
@rose bluff Has your question been resolved?
rose bluff
.close
timid silo
hello can you help out with a question
obtuse pebbleBOT
hello can you help out with a question
timid silo
.close
hazy cape
we have 7 items (lets say squares, does not matter)
3 are red, 2 are blue, 2 are green
we are choosing 4
what are the odds of choosing at least one green and one blue
I feel like I am on the right track, since I got the result somehow, but I dont get the logic. If given a different problem I'd be lost
obtuse pebbleBOT
we have 7 items (lets say squares, does not matter)
3 are red, 2 are blue, 2 ar...
hazy cape
So far my ideas were to either get the complemetary odds somehow, which I did by complete randomness or just get the "real odds", but there I am lost too
the at least one in both Green and Blue keep messing me over
I am starting to doubt the result I got
yea no I have no clue
<@&286206848099549185> save my dumbass please
drifting wraith
so the complement is (no green ∪ no blue)
drifting wraith
or correct
hazy cape
right makes sense
drifting wraith
you get no green if you do 5 choose 4
and you get no blue if you do 5 choose 4
and they don't intersect, (no green no blue) is 3 choose 4 which is 0
drifting wraith
we're counting the complement, A ∪ B = A + B − A&B
if your choice has no blue, it's some combination of green and red, and you find it immediately as (3+2) choose 4
hazy cape
ohh right makes sense
drifting wraith
i didn't know it would work until it did, was just trying random stuff
hazy cape
or wait maybe I am still lost
drifting wraith
sure
hazy cape
ahhh
I can so clearly see the logic but I cant apply it for some reason
Do you think its maybe possible to use this somehow?
It feels similar
hazy cape
we're counting the complement, A ∪ B = A + B − A&B
wait, that this, but less "developed", no?
drifting wraith
that's not good at all
it's when the "shape" is fixed, you don;t just have Cola and Pepsi but specifically 2+2
drifting wraith
we have 3+1 and 2+2 as two options to get e.g. red+blue
hazy cape
cuz technically right
2 green + 2 blue is also good
or like 2 green 1 blue 1 red
cuz it's at least
but that favorable, not complementary
mb
somehow slipped into favorable
drifting wraith
there's not really any alternative to what i did
R
G
B
RG
RB
GB +
GRB +
these are all possible compositions
the first three are all 0
there's not enough balls to have single color pick
we want to add GB + RGB
we don't know how, we look for the rest of it instead, RG+RB
no blue R no green
no blue G
B no green
no blue RG
RB no green
GB
GRB
and the formula you showed doesn't help
we don;t know how many of each composes RG or RB
but we can simply choose 4 from the sum (3+2)
like i don't have a feeling that this is very clear, but also there's probably not a better way
like it's very helpful that there's no way to get single color, we'd have to just deal with those too otherwise
obtuse pebbleBOT
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timid silo
Hello?
tardy epoch
timid silo
Hello, what is y < - 15x + 3000
y < 5x?
tardy epoch
y < -15x + 3000 is already as simplified as possible
i guess you can factor out 15 or something, but that's not any better
solar trellis
He's riemann after all
tardy epoch
who's riemann
drifting wraith
me?
obtuse pebbleBOT
@zealous ivy Has your question been resolved?
dusk mauve
I want to ask about logarithms, how to find a characteristic, and mantissa
dusk mauve
<@&286206848099549185>
obtuse pebbleBOT
<@&286206848099549185>
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.
tardy epoch
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
dusk mauve
If i were to say common log 232.92 what is the characteristic and mantissa and how to find it?
characteristic and mantissa which are used to find the answer on the logarithm table
warm canopy
well find the two closest powers of 10 to 232.92
dusk mauve
the characteristic part is easy but then the mantissa part
warm canopy
okay well you could've said you already knew the characteristic
dusk mauve
ok the mantissa is hard do you know how to find it?
warm canopy
use a calculator
dusk mauve
the book is asking to find the mantissa specifically, how do i find it on the calculator
warm canopy
well if you can use a calculator then literally just compute log(232.92)
dusk mauve
ok that part is understood but if using the logarithm table how can i find it using that?
warm canopy
write 232.92 as x*1O^n
obtuse pebbleBOT
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brave trail
I need help with a fourier transform
obtuse pebbleBOT
I need help with a fourier transform
brave trail
These are the properties I'm working with, but my workings aren't matching the solution that my teacher posted
Posted solution:
gilded needle
my suggestion would be to try to put your g(t) into the form 2a / (a^2 + w^2)
and use the inverse transform property
brave trail
and use the inverse transform property
So I've written the numerator as 2(3) + 4
and I can use the third identity there
but then what do I do about the second term
gilded needle
btw, does the instructor's checkmarks and 4 mean that you got full credit?
brave trail
This is another students work, I did not get this correct on the test
but even in this students solution, which the teacher took and uploaded as the solution, the +4 just seems to disappear
gilded needle
ah i see thx
lemme do a quick read over the student's solution, one moment
i think the $2(3) + 4$ is a bit of a red herring, but i do agree that setting $2a = 10$ and $a^2 = 9$ are inconsistent, so this isn't quite right. i would simply do:
$$\frac{10}{t^2 + 9} = \frac{10}{6} \frac{6}{t^2 + 9}$$
warm shaleBOT
Bungo
brave trail
Yeah that makes much more sense to do
gilded needle
which would then lead to the student's solution, except the right solution would have a 10/6 scale factor in front
brave trail
which would then lead to the student's solution, except the right solution would...
exactly
I changed the numerator to 6 already and am getting the same answer as the student
Ok, so there is an error in the solution
brave trail
Ok, i'll do out some workings and send them here, I have another question
gilded needle
ok
brave trail
@gilded needle are there any flaws in the steps that I took to get to this solution, or is there a more logical or more legible process?
gilded needle
<@761155030513352705> are there any flaws in the steps that I took to get to thi...
everything looks all right, the only suggestion i have is that it's a bit confusing that you're using g and G to denote more than one pair of functions, maybe on the second line, call that function something like F(t) instead of G(t)?
brave trail
everything looks all right, the only suggestion i have is that it's a bit confus...
You mean like where I'm just declaring some identities I'm using, might as well just change the letters for clarity
?
gilded needle
You mean like where I'm just declaring some identities I'm using, might as well ...
yeah, maybe use different letters there, and just reserve g and G for the original function and its Fourier transform
it'll just make things a bit clearer
brave trail
Yeah I do like that better
The question and the table are both G's but they don't necessarily have to be
gilded needle
yea i know it's common to reuse letters like that, but there are plenty of letters to choose from 😀
brave trail
Thanks for your help ❤️ ❤️ ❤️ ❤️ I've been going crazy over this because the solution seemed clearly wrong, and nobody in my class would respond to me
So now I'm convinced they're just more lost than me
gilded needle
no problem, and you were absolutely correct
brave trail
How do I close the channel
gilded needle
.close
brave trail
.close
verbal comet
obtuse pebbleBOT
verbal comet
im confused as to how the above matrix is the form that a skew symmetric matrix comes in
isnt it ( a b| -b c)?
gilded needle
isnt it ( a b| -b c)?
A^T = -A, right?
verbal comet
ye
gilded needle
that forces the diagonal elements to satisfy a_ii = -a_ii, which is only true if a_ii = 0
gilded needle
haha no worries
verbal comet
.close
rocky plank
Can someone explain to me this extension of the arc length Calc 3 formula?
obtuse pebbleBOT
Can someone explain to me this extension of the arc length Calc 3 formula?
@rocky plank Has your question been resolved?
verbal comet
obtuse pebbleBOT
verbal comet
shouldnt C be d?
its b but i thought the dimension of the VS would be the dimension of R4
im also confused for E
i think the reason its d is because a,b,c all are closed under addition and multiplication and are non empty
but i cant understand why d isnt asubspace of V
unreal musk
but i cant understand why d isnt asubspace of V
Is 0 in U\V?
verbal comet
ah
okay
just to check, is it closed under addition and multiplication , U\V that is
unreal musk
No - assuming that U has an element u which isn't in W, then -u is also not in W (otherwise closure of W would give you that u was in W), but their sum u + (-u) is zero, which is in W
In other words, u, (-u) are in U\W, but 0 = u + (-u) is not in U\W
verbal comet
okay and what about this one
i thought the R4 is one of the ways to indicate the dimension of V
narrow vault
it's at most dimension 4 but can be lower
unreal musk
okay and what about this one
For this one, I believe (if my steps are correct) you can express $a = c + 2d$ and $b = -2c - 3d$
warm shaleBOT
chartbit
narrow vault
by observation note that 1+4 = 2+3
so (a,b,c,d) = (1,-1,-1,1) satisfies both restrictions
then you have 2 vectors forming your basis so it's at most dimension 2
but they're lin.independent so it is dimension 2
narrow vault
oh yeah chart's the rigorous way :p
i got lazy and just wanted to plug 1/-1 to get a solution
narrow vault
so if 2 of (a,b,c,d) are +1 and the other two -1 you get a+b+c+d=0
and you work a little bit harder to make that suit a+2b+3c+4d=0
but no if you isolate a in the first equality and b in the second you get chartbit's sol and that's the sound way to do it
verbal comet
is r4 the field
unreal musk
is r4 the field
$\mathbb{R}$ is the field, but $\mathbb{R}^{4}$ is the vector space
warm shaleBOT
chartbit
verbal comet
so what does Fn mean
unreal musk
so what does Fn mean
Is there context behind that? I'm assuming the finite field of n elements
verbal comet
well when i see it written its F^n
unreal musk
Ohh I see - basically if $F$ is the field, then $F^{n}$ is a vector space of "coordinates" $(a_1, \ldots, a_n)$, where each of the $a_i$ are in the original field $F$
warm shaleBOT
chartbit
unreal musk
I'm guessing that there may be some cases where you're considering real vector spaces and complex vector spaces in particular
verbal comet
okay i am just sturggling to understand the rules about size of basis and dimension specifically
i thought the dimension 5 means that the basis has to be of 5 elementrs
then b would be correct right?
unreal musk
Remember the definition/requirements of a basis - you need to be both linearly independent and span the vector space
One direction of this is true: if you're a basis, then you have 5 elements
But the other isn't necessarily: you can have a set of 5 vectors that aren't linearly independent, and therefore don't form a basis
verbal comet
ah okay
so a spanning set must also have 5 or more elements rihgt?
and c would be knocked out, cause a set with 6 elements no longer can be LI for a VS
unreal musk
so a spanning set must also have 5 or more elements rihgt?
Yeah - a spanning set must have (at least) 5 elements
quiet drum
obtuse pebbleBOT
quiet drum
so for d i got 9.4608x10^12 and for c i got 7.56x10^9
however the answers say its wrong can someone tell me where i messed up
drifting wraith
maybe just try again?
quiet drum
i tried that
i dont think im doing anything wrong
i just want to know if im wrong or if theres a typo in the book
drifting wraith
i think d is correct but not c
polar roost
clue for c: if one day has 24 hours, how many hours does a week have? ans should be 1.81e11
d seems right though
quiet drum
1.8144*10^11?
polar roost
yeah
timid silo
A set of 36 people are standing in a room on positions defined by an 6x6 grid. Each person decides to turn to exactly one of their neighbors and other to shake their hand. A handshake only takes place if two people turn and face each other. What is the the probability that two specfic neighbors end up shaking hands? What is the expected number of handshakes? (A person can see front, back, left, right)
obtuse pebbleBOT
A set of 36 people are standing in a room on positions defined by an 6x6 grid. E...
@timid silo Has your question been resolved?
obtuse pebbleBOT
@timid silo Has your question been resolved?
obtuse pebbleBOT
@timid silo Has your question been resolved?
dark stirrup
What have you tried
timid silo
Number of people in the room: 36
Probability of two neighbors shaking hands: 1/4
Expected number of handshakes:
36 x 1/4 = 9 handshakes
For two specific neighbors to end up shaking hands, both of them must turn towards each other. The probability that this happens is 1/4, since each person has four possible directions to turn in.
The expected number of handshakes is the number of people in the room (36) multiplied by the probability of two neighbors shaking hands (1/4). This gives 36/4 = 9 handshakes?
@dark stirrup
zenith raft
do the ones on the border of the grid only have 2 or 3 options to turn to?
cus it seems like yes when i read the q but the first part would depend a lot on which specific neighbors it is
so no? they can face nothing?
timid silo
Honestly I am not too sure, I know just as much as you
About what the problem. asks for
I would imagine they can't face nothing as it states they turn to one of their neighbors
obtuse pebbleBOT
obtuse pebbleBOT
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timid silo
We know that $\log_3(2x+1)$ cannot be expanded any further. But any rigorous explanation?
obtuse pebbleBOT
We know that $\log_3(2x+1)$ cannot be expanded any further. But any rigorous exp...
warm shaleBOT
Genshin is Mid.
sage geode
Well I mean you could rewrite that as log_3(x + 1/2) + log_3(2) for the sake of expanding, why not?
timid silo
Well I mean you could rewrite that as log_3(x + 1/2) + log_3(2) for the sake of ...
lol obviously but not that
Now that I think about it
what even is expanding lol
obtuse pebbleBOT
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obtuse pebbleBOT
Available help channel!
zealous hornet
State the unknown (?) in these quadratic graphs:
obtuse pebbleBOT
State the unknown (?) in these quadratic graphs:
zealous hornet
how do u solve these types of questions?
cold thistle
It looks like it's symmetric about the y-axis which would mean that the second solution may be the same distance from the origin as the first
zealous hornet
so -3?
harsh basin
-3 i guess
timid silo
State the unknown (?) in these quadratic graphs:
Is that like
all that you were given?
timid silo
Then yeah I guess u can only really assume symmetry
cold thistle
With that given information I think just making the conjecture that it's -3 based on its symmetry is all you can do
timid silo
Not much else to do
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
tawny fog
$Log (\sqrt{ab}/c)=log (ab)^{1/2} - log (c) \newline \rightarrow \frac{1}{2}log(ab) - log (c) \rightarrow \frac{1}{2} log(ab/c)$
obtuse pebbleBOT
$Log (\sqrt{ab}/c)=log (ab)^{1/2} - log (c) \newline \rightarrow \frac{1}{2}log(...
tawny fog
All of this right?
warm shaleBOT
𝓐𝓡𝓝𝓐𝓑 𝓟𝓐𝓛
final thunder
No
tawny fog
What is the mistake here?
obtuse pebbleBOT
@tawny fog Has your question been resolved?
tawny fog
**𝓐𝓡𝓝𝓐𝓑 𝓟𝓐𝓛**
<@&286206848099549185> which concept is not right here
tawny fog
What's wrong in that?
warm shaleBOT
anand
buoyant dagger
Hi can I get some help
copper spade
Hi can I get some help
tawny fog
The end is wrong
Oh ok
tawny fog
And another thing there's a problem that I m having it says
Write log (40) in the terms of log (5) give the approx answer if log(5)=0.69
tawny fog
But you can't
Hm
tawny fog
Ohhhh got it
copper spade
And another thing there's a problem that I m having it says
Write log (40) in t...
Hmm lemme try
tawny fog
Ok
And the question dosen't says it is log_e or log_10
So yeah
So much less information for that
copper spade
I can just do 3log(2)+log(5)
That's what I did as well
But we don't know log2 naa
tawny fog
Yes
copper spade
@tawny fog here's one hint
We will use log base 10
Because log(base10)5 has the value of 0.69
Whereas log(baseE)5 has the value of 1.6
tawny fog
Yes
I also thought about that
And I get
2-log5² - log 10
= 2 - 2 log 5 - 1
= 1- 2×0.69
Right
Log 100=2
copper spade
Haa
tawny fog
,w 1-2×0.69
warm shaleBOT
obtuse pebbleBOT
tawny fog
I didn't even help
Still thanks
obtuse pebbleBOT
Available help channel!
copper spade
Oii @tawny fog
obtuse pebbleBOT
Oii <@518716603928543234>
copper spade
Ya did a bery smol mistake
Bery bery smollll
Ya here?
Broo 💀💀
Ping me when ya here @tawny fog
copper spade
Yeee
Previously ya forgot abt the brackets that's y ya got the wrong answer lul
.close
obtuse pebbleBOT
tawny fog
Yems thanks
copper spade
tawny fog
obtuse pebbleBOT
Available help channel!
glass tide
I need help
obtuse pebbleBOT
I need help
obtuse pebbleBOT
glass tide
X
copper spade
Exactly
glass tide
Ok i get it
copper spade
Bro this is a help channel 💀💀💀💀
obtuse pebbleBOT
Available help channel!
cursive tundra
Hey guys, i noticed some terminologies in lectures and textbooks when it comes to math operations and wanted to confirm what they meant.
For eg, weighted is used for multiplication
I dont understand why averaged with is used for addition though