thats what theyre askign for all 3
#help-27
pastel veldt
misty escarp
okay so any x less than 0 should be undefined
pastel veldt
so would it be > 0 ?
misty escarp
it would be < 0
misty escarp
lol I'm sorry are you tired
pastel veldt
ahaha
all good
i got a test on friday and im geekin out lol...
i really dont wanna fail
misty escarp
yeah that's pretty stressful
misty escarp
what grade are you in?
misty escarp
lol show me
pastel veldt
misty escarp
so how am i finding the F() ?
what do you mean?
pastel veldt
F ( )
misty escarp
wait can you not drag the same thing for the f( ) too?
pastel veldt
oh i can
misty escarp
that's a relief
misty escarp
oh no really?!?
pastel veldt
yeah
misty escarp
that was one of my huge worries since I didn't see any other way you could do it lol
misty escarp
who made this test 😭 I feel like it's flawed
pastel veldt
who made this test 😭 I feel like it's flawed
this is just hw
the test is on paper...
misty escarp
doesn't really make sense
pastel veldt
yeah idk lol
misty escarp
you should be entering the same x into the f(x) function
I guess they just messed up the website lol
pastel veldt
ah
misty escarp
unless I'm missing something still
misty escarp
yeah I wonder
pastel veldt
would it be x = +- 24?
misty escarp
the sqrt one?
pastel veldt
no the new 1
pastel veldt
this 1
misty escarp
the sqrt one?
did you mean x = +-sqrt(-24)
misty escarp
yeah
misty escarp
yeah that's correct
misty escarp
I don't know why lmao
misty escarp
yeah that's a good substitute
misty escarp
it shouldn't be too hard
pastel veldt
so that means like x1 = x2?
misty escarp
ok hm
f(n) = n+17 would be one to one and onto since you can find its inverse n-17 same with the f(n) = n-17
misty escarp
I wish I could explain this better
misty escarp
I don't think I'm good enough lol
pastel veldt
lmao ur doing great
misty escarp
I should have studied more lmao I haven't done enough questions like this
misty escarp
I've kind of just accelerated to advanced topics without slowly absorbing all the stuff I should be learning in that journey
pastel veldt
ah
misty escarp
I'm familiar with this I just haven't ever done it enough to just answer quickly
pastel veldt
ahah ur good lol
misty escarp
I'm pretty sure f(n)=17 would be surjective since you're taking all N and putting that onto this single number 17
so that's onto but not one-to-one
misty escarp
okay
misty escarp
I believe n/2 would be onto and one-to-one aswell
pastel veldt
misty escarp
lmao I didn't see the +- on the function some how
misty escarp
I was pretty much as clueless as you lmao
misty escarp
lmao
misty escarp
yeah
I really got to study this more basic stuff some more
I've forgotten all of it
pastel veldt
ah
misty escarp
damn I don't understand why this is like that lmao
misty escarp
brb
misty escarp
unless I'm missing something still
foreshadowing
misty escarp
this would have been when x<0 f(x) is undefined then lol
it's embarrassing that I didn't notice that
pastel veldt
ahahh its ok
misty escarp
lol well obviously I have some studying to do
I think we should close this help channel now
good luck on the test lol maybe by then I could help you with the material on it
teal island
Hello I need help with a few things I've never seen before
devout snowBOT
Hello I need help with a few things I've never seen before
restive river
just post the question(s)
teal island
Okay so I'm grade 9 and I've never seen this stuff before
I'm doing exam prep but I can't go to the next algebra level without finishing these questions
zinc veldt
you need to understand how the graph is affected by changing the coefficient of x^2
teal island
Yes please!
Understanding would be better than just getting the answer tho its not necessary, I just need to get everytime right to go to the next stage
What's h(x)?
zinc veldt
What's h(x)?
I’m not sure what you’re asking
teal island
I'm asking for the answers because I can't get to the part I actually have to practice without getting past these questions
zinc veldt
xd
well idk the full questions
post a screenshot with the full question
not multiple bc it’s confusing for me
zinc veldt
bruh the graph isn’t even to scale
teal island
😰😭
zinc veldt
I was gonna say try plugging in x=1
teal island
The first 2 questions are about this graph
teal island
I was gonna say try plugging in x=1
Into the function?
zinc veldt
anyway f(x) is 2x^2 and h(x) = -1/2 x^2
zinc veldt
it’s the middle one
zinc veldt
the x intercept is always (some number, 0)
because the y coordinate is always 0
vice versa for y intercept
teal island
So there's 2 axis on a graph
teal island
And x and y occupy both lines where the meeting point is 0 the graph functions cross the sectors?
zinc veldt
but this specific function intersects the x axis twice
teal island
well there’s always 2 axes
So graphs in 3D can't exist
zinc veldt
And x and y occupy both lines where the meeting point is 0 the graph functions c...
yes basically I think
teal island
but this specific function intersects the x axis twice
Ohhhh
zinc veldt
So graphs in 3D can't exist
maybe in advanced math xD
teal island
Yeah I'd rather notbget into that when I can't even do this stuff😭😭😭
teal island
This app is so mean, you can't advance if you don't get 100
zinc veldt
it’s the intersecting one
zinc veldt
if you learn how to graph a quadratic function these will be pretty easy
teal island
SEE THERE'S PITCHFORKS
teal island
teal island
Oops
zinc veldt
is this related to the previous problem
teal island
Nope
zinc veldt
ok what do you see here
teal island
Its on 2, 2s
zinc veldt
one is just smaller
zinc veldt
well actually they didn’t show the full graph but they go on forever
teal island
Ohhhh
zinc veldt
It's on a 2 and 4
what is?
teal island
So there has to be an infinity somewhere
zinc veldt
if you look at f(x), what is the lowest point?
zinc veldt
oh lol
teal island
Everything else is based on this
teal island
The graph?
zinc veldt
yes
teal island
zinc veldt
this
teal island
Ohhh
zinc veldt
that’s the answer btw
zinc veldt
for the graphs of this
zinc veldt
lol
well you need practice
idk why they are making you do a quiz without practice
tbh I would go experiment on desmos if you have free time
teal island
Desmos?
zinc veldt
yeah it’s a cool graphing tool
teal island
yeah it’s a cool graphing tool
I'll check it out
So is it on app store
All of these are based on the same question 😎💀
teal island
I'll definitely check it out!!!
zinc veldt
All of these are based on the same question 😎💀
oof
teal island
Thanks for telling me about it btw
zinc veldt
np
zinc veldt
All of these are based on the same question 😎💀
are those all the questions lol
teal island
Yep
teal island
There's a 3 more
teal island
like question 3 💀
😭😭😭😭😭
zinc veldt
3 more parts or questions lol
teal island
This is why we need to protest against Swedish schools I stg
zinc veldt
I just don’t get why they’re making you do a quiz instead of practice
anyway it’s like 12:46am here and I think I need sleep 💀
sorryyy
teal island
I just don’t get why they’re making you do a quiz instead of practice
IKRRR
teal island
anyway it’s like 12:46am here and I think I need sleep 💀
Okkkk
Gnnn
Thanks for helping thoo
teal island
and good luck
Okiii
Thanks
✨╭━━┳╮╭┳━━┳━┳┳┳┳━━╮💖
✨╰╮╭┫╰╯┃╭╮┃┃┃┃╭┫━━┫💖
✨╱┃┃┃╭╮┃┣┫┃┃┃┃╰╋━━┃💖
✨╱╰╯╰╯╰┻╯╰┻┻━┻┻┻━━╯💖
. Close
. close
Hmmmm
💀
restive river
devout snowBOT
woven radishBOT
devout snowBOT
@restive river Has your question been resolved?
restive river
devout snowBOT
woven radishBOT
devout snowBOT
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
2 and 3
restive river
```
What step are you on?
1. I don't know where to begin.
2. I have begun but go...
I am on step 2
Or 3
devout snowBOT
@restive river Has your question been resolved?
restive river
<@&286206848099549185>
devout snowBOT
@restive river Has your question been resolved?
devout snowBOT
@restive river Has your question been resolved?
devout snowBOT
@restive river Has your question been resolved?
visual hazel
@restive river are you trying to convert nanograms to microliters?
restive river
<@456226577798135808> are you trying to convert nanograms to microliters?
Yes
charred zodiac
Hello. You should write ng as 10^(-9) first (n is nano)
Also remember that you can use the conversion factor
15.3336 g/cm³
or
1 cm³/(15.3336 g)
Which one is appropriate for this case in order to get the volume?
Then, you have to convert the resulting volume to liters
obsidian delta
devout snowBOT
obsidian delta
Pls help me
devout snowBOT
@obsidian delta Has your question been resolved?
devout snowBOT
@obsidian delta Has your question been resolved?
devout snowBOT
@obsidian delta Has your question been resolved?
devout snowBOT
@obsidian delta Has your question been resolved?
jaunty abyss
How did this
X + 4y = 1
Turn into this
X = 1 - 4y
devout snowBOT
How did this
X + 4y = 1
Turn into this
X = 1 - 4y
dapper tiger
by subtracting 4y from both sides
smoky nimbus
Wouldn’t - 4y come before the 1
It doesn't matter
jaunty abyss
Ok
smoky nimbus
X = -4y + 1 and X = 1 - 4y are the same
lime dome
devout snowBOT
lime dome
How do these look for A2 and A3
Theyre not like fully formatted proofs obviously but like the work is there, right? and this holds up?
A1 and A4 I am more or less completely lost on
I know A4 is strong induction but I lowkey barely know how to do that
trail eagle
Hum I think you might need to review induction or something. Your base cases aren't what they should be and your induction steps don't show that n implies n+1 at all.
For A2, your base case is n=1, so you must show that F_3 is even.
Then the induction step is done by assuming that is holds for some k (so that means that F_(3k) is even) and showing that this implies the k+1 case (F_(3(k+1)) is even).
lime dome
Okay, so base case is n=1 which is f_3(1) which is just f_3
ok
i move frmo here
heres this
i keep going
trail eagle
Yes that works for your base case
trail eagle
Yes.
trail eagle
First off the second term is F_(3k+1) not F_(3k-1)
trail eagle
Second off, remember that what you would like is to have F_(3k) to appear there because the only assumption you made is that F_(3k) is even.
Maybe expand F_(3k+2)?
lime dome
Second off, remember that what you would like is to have F_(3k) to appear there ...
this is what I was trying to do but I dont see how u can do that
i think theres some algebra im missing
trail eagle
Again, just expand F_(3k+2).
trail eagle
No just do the same thing you just did with F_(3k+3).
lime dome
No just do the same thing you just did with F_(3k+3).
subtract it by 1..?
trail eagle
Use the definition of the sequence : F_n = F_(n-1) + F_(n-2)
lime dome
i seriously dont know what im missing and I feel so dumb
where do I apply that definition
like
do I replace k with k-1?
trail eagle
Right, so you went from F_(3k+3) to F_(3k+2) + F_(3k+1). Just do the same thing with the F_(3k+2) term.
lime dome
do u get f_3k+1 + f_3k
trail eagle
Yes.
trail eagle
What do you have in total now?
trail eagle
Yes,
lime dome
the sum of two even integers is even so we can conclude it seven
trail eagle
Indeed.
lime dome
ok so lets move on to a3 if thats ok
trail eagle
Yes.
lime dome
so we proved f_3 is even
and f2 is odd since f_2 is 1
so its an even + odd integer
which is odd
right?
lime dome
Yes.
can we use the theorem before like this or is that not allowed?
heres what I have so far
trail eagle
That works, but you would need to explain a bit more when you actually type everything out. It's not clear without your explanation why F_3 and F_2 sum up to an odd number.
lime dome
That works, but you would need to explain a bit more when you actually type ever...
hm
do I necesarily need induction for this?
trail eagle
No. It just seems out of the blue, especially when a student writes it. Just explain in your words what you conclude
Because as far as a correcter is concerned, you just wrote that F_{4} = F_{3} + F_{2} and F_{5} = F_{4} + F_{3}.
It's not really insightful, you need to explain your thought process. Why do you stop there? What makes this a base case to the theorem you're trying to prove?
trail eagle
I don't get how you came to the conclusion that F_{3n+1} is odd.
trail eagle
That works yes.
But here you know this because you know F_2 is odd. How can you now say that F_{3n+1} is even without any form of induction?
lime dome
I guess so
so the base case holds i guess but I dont see what more induction we need to do
trail eagle
Well you showed F_4 and F_5 are odd. And for some reason you just conclude that it works for any number that isn't a multiple of 3?
lime dome
right
so lets move back
so now we know the base case for f_3n+1 holds
so we move to induction hypothesis
Suppose there exists k such that f_3k+1 is odd
this right?
trail eagle
Yes. I would do both at the same time though, just like you did both F_4 and F_5 together.
trail eagle
Yeah that 's good for the hypothesis.
lime dome
Yeah that 's good for the hypothesis.
unsure what to do for the inductive step
I have f_3(k+1)+1
=f_3k+3+1 = f_3k+4
trail eagle
Again, you have to use what you know from the premises of your problem. You know the definition of the fibonacci sequence and you know from that induction hypothesis that f_{3k+1} and f_{3k+2} are odd. Use those.
lime dome
Again, you have to use what you know from the premises of your problem. You know...
idrk if this is exactly how the definition applies or not
trail eagle
f_3k+4 = f_3k+3 + f_3k+1
No.
It's the sum of the last two terms, not the last one and the third to last one.
lime dome
It's the sum of the last two terms, not the last one and the third to last one.
ah so
f_3k+3 + f_3k+2
right?
trail eagle
Yes.
lime dome
this reduces to f_3k+3 + F_3k+2
do I expand it again?
i think so, right?
then I get it to (f_3k+2 +f_3k+1 )+(f_3k+1+f_3k)
we know f_3k is even and f_3k+1 is odd so thats odd
do we know the parity of f_3k+2?
i guess so because we can change it to f_3k+1 + f_3k + f_3k+1
which is odd + even which is odd
then odd + odd which is eve
so we get odd + even
which is odd
trail eagle
this reduces to f_3k+3 + F_3k+2
This is far too much work. Using the theorem from the last problem, F_3k+3 is even and from the hypothesis F_3k+2 is odd...
lime dome
This is far too much work. Using the theorem from the last problem, F\_3k+3 is e...
ok, got it
Could we work on A4 ?
trail eagle
that finishes the entire proof right?
I mean you should still show that F_3n+5 is odd but it should be the same essentially.
lime dome
I mean you should still show that F_3n+5 is odd but it should be the same essent...
why do we need to show this?
lime dome
To show that F_{3n+2} is always odd
would we start out showing this by doing f_3(k+1)+2 then just do the smae?
trail eagle
Well in your hypothesis you have F_{3n+1} and F_{3n+2} odd. Now you proved that F_{3n+4} is odd and you have yet to show that F_{3n+5} is odd.
trail eagle
Yes that seems alright. Do note though that since you've just proven that F_{3k+4} is odd, you don't need to split it further.
lime dome
nice
lime dome
Yes that seems alright. Do note though that since you've just proven that F_{3k+...
think we can move to a4?
trail eagle
Yes.
lime dome
Yes.
my brain cannot even comprehend this
a2 and a3 i at least had an idea of what I needed to show and do
but a1 and a4 are just
not it
trail eagle
Start with base cases.
You want to show that a_n = (n+1)2^n for all n, so what about those easy cases (a_0, a_1)? Do they satisfy it?
lime dome
You want to show that a_n = (n+1)2^n for all n, so what about those easy cases (...
how do u know thats what we want to show
i dont understand that
wait
nvm lol
lime dome
You want to show that a_n = (n+1)2^n for all n, so what about those easy cases (...
heres what I have now
moving on to induction hypothesis
Suppose there exists k such that e_k = ((k+1)+1)2^(k+1)
how does that look
trail eagle
Hum for your base case I guess it's just a typo but 2*2 is not 2.
lime dome
Hum for your base case I guess it's just a typo but 2*2 is not 2.
is the inductive hypothesis good?
trail eagle
In this specific case, I think it's better using either the assumption that the last two cases hold, or some stronger assumption like that any case less than k+1 hold
lime dome
In this specific case, I think it's better using either the assumption that the ...
wdym by this?
trail eagle
So you prove using a specific formula for e_n. However, the recursive definition of the sequence uses the previous two terms. When you try to do the inductive step by proving the formula holds for e_{k+1}, you will eventually have to deal with e_k AND e_{k-1}
So if you only assume that the formula holds for e_k, you're kind of stuck
lime dome
So this is strong induction then
trail eagle
Some form of it
It is your choice how strong you want your assumption to be. Ensuring that the last two terms hold works fine here. You can also assume that all the previous terms hold, which is what you usually would call "strong" induction.
lime dome
wouldnt assuming all the previous terms hold be easier?
trail eagle
It would be the exact same argument tbh, since you would really only use the last two.
But strong induction works here so you can go with that
lime dome
how do inductive hypothesis change when doing strongi nduction?
how exactly are all cases denoted?
trail eagle
Hum you could say suppose e_n = (1+n)2^n for all n <= k. Then you show that is must hold for e_{k+1}.
lime dome
So moving into the start of the inductive step we get e_k+1=(1+(k+1)2^(k+1)
trail eagle
Well this is what you want to show, you can't really start with that.
trail eagle
Btw, this whole thing about induction is really just about the way we construct natural numbers. The set N is defined as the set that contains 1 AND such that for any n in N, n+1 is in N as well. (so 1 in N, then 2 in N, 3 in N, so on.)
What you're doing when using this for proving is that you're given some proposition and you let S be the set of natural numbers that satisfy this proposition.
Then you show that 1 is in S (this is your base case) and you show that if n is in S (inductive hypothesis) then n+1 is in S (induction step). Then you can conclude from the construction that S = N (all natural numbers satisfy the proposition)
Strong induction is just an alternative way of saying it. Here, you show that 1 is in S (base case(s), can be more that 1) and you show that if 1, 2, 3 ,... n is in S (induction hypothesis) , then n+1 is in S (inductive step).
lime dome
im gonna be honest
i think im just gonna go to sleep
im seriously too tired to do this anymore
I seriously appreciate your help
lime dome
Btw, this whole thing about induction is really just about the way we construct ...
like this is so amazing, thank you
lime dome
Btw, this whole thing about induction is really just about the way we construct ...
i'll continue working tomorrow.
.close
devout snowBOT
trail eagle
That's ok!
devout snowBOT
Available help channel!
jaunty robin
devout snowBOT
jaunty robin
managed to do part a) but I don't have half a clue as to what part b) is asking me to do
any ideas on how to approach this?
<@&286206848099549185>
.close
carmine hill
can anyone help explain how to solve this
devout snowBOT
can anyone help explain how to solve this
@carmine hill Has your question been resolved?
languid sorrel
How can I assume concavity from this graph? I thought the inflection point was C, but I guess it isn't
devout snowBOT
How can I assume concavity from this graph? I thought the inflection point was C...
hybrid snow
Omori also blew my brains out
languid sorrel
HAHA
hybrid snow
Okay so you can kinda think of concavity as like cups
hybrid snow
So like where would the function be cupping down versus cupping up
And where it switches cupping is the inflection point
Depressed cubics tend to inflect at the origin
Or somewhere on the x axis if they're not shifted upwards
Oh but that graph is f'(x)
Okay so you gotta use sign analysis instead
Mb I thought it was f(x)
languid sorrel
ohhh
hybrid snow
If that's the graph of f'(x), then you're just looking where f'(x) is increasing and decreasing
Where f''(x) > 0 => f'(x) is increasing, you have a concave up region
hybrid snow
Ye
languid sorrel
so it's concave up, down, up?
hybrid snow
Seems to be so
languid sorrel
If that's the graph of f'(x), then you're just looking where f'(x) is increasing...
that makes so much sense thanks so much
hybrid snow
Unless I'm just dumb
languid sorrel
it worked!! thanks so much
hybrid snow
Np
languid sorrel
.close
vital halo
devout snowBOT
vital halo
l=8 and f=7
am i supposed to use an integration table to solve this and if i am what equation?
finite briar
am i supposed to use an integration table to solve this and if i am what equatio...
its possible it might be some form of substitution 
vital halo
where would I start
finite briar
perhaps sin^2 x = u
vital halo
ill give it a try rn
finite briar
aight
vital halo
i got (U^2 cos^2(7x))/8cos(8x) du
i cant remember how to cancel out trig functions if the inside of the parenthesis are difernt
finite briar
nah it wont work afaik
devout snowBOT
@vital halo Has your question been resolved?
deep wing
im working on finding the mclaurin series for this function
devout snowBOT
im working on finding the mclaurin series for this function
deep wing
i got this
is this correcT? it made the derivatives and created a formula but it seems that formula is just the definition of a mclaurin series
acoustic leaf
you should come up with a formula for $f^{(n)}(0)$ and use that in your expression
woven radishBOT
cloud
deep wing
hmm
deep wing
you should come up with a formula for $f^{(n)}(0)$ and use that in your expressi...
i think it would just be n!
cause f^(n)(0) is
1
1
2
6
24
120
so it be $\frac{n! \cdot x^n}{n!}$
woven radishBOT
Arm
acoustic leaf
notice that we've essentially derived the geometric series formula from the opposite direction
acoustic leaf
we know that a geometric series is in the form $\sum r^n$, and by the geometric sum formula $\sum_{n=0}^{\infty} ar^n = \frac{a}{1-r}$.
On the other hand, we find that if we take the expression $\frac{1}{1-x}$, the maclaurin series for it is $\frac{1}{1-x} = \sum_{n=0}^{\infty} x^n $.
If we take $a=1$ and $x=r$, we find that they are identical. The only difference is that in one case we started with a series and got a function, and in the other case we started with a function and ended with a series.
woven radishBOT
cloud
deep wing
ahhh i see what you mean
thats interesting, thanks for the detailed explanation
i had a final question
if im testing for the interval of convergence
for this one its (-1,1) but i must check at the end points
at -1 i have
sum (-1)^n
whic would just be 0 since -1 would oscilate and cancel its self
no since it equals 0 as n approaches infinity i can say that it converges correcT?
or did i mix up the definition
acoustic leaf
the sequence doesn't converge since it just switches between -1 and 1 forever, never settling on one or the other. Similarly, the series just flips between 0 and 1 (or -1 and 0, depending on your starting point) forever, so it also doesn't converge. It's a little counterintuitive since we're used to diverging series shooting off to infinity but there are also other ways to diverge
acoustic leaf
no since it equals 0 as n approaches infinity i can say that it converges correc...
This isn't necessarily true. Any series that converges must have its sequence converge to 0, but not all sequences that converge to 0 have their series converge (e.g., the harmonic series)
deep wing
This isn't necessarily true. Any series that converges must have its sequence co...
ah i see
so when testing endpoints
i should plug in the end point for x
then evaluate the limit
and in this one it happend to be (-1)^n which dosent diverge since it osiclates
it dosent approach anything as n goes to infinity
acoustic leaf
plug in the end point for x, then evaluate the convergence of that particular series. If it diverges by the limit of the sequence not approaching 0, then stop there. if it doesn't, try other methods (usually the ratio test, sometimes alternating series test)
deep wing
yup thats what i did
at one end point we had the above
and the other it went to infinity
so diverging at both ends
converges for (-1,1)
thanks for the help!
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obsidian socket
is there where i can ask for help?
devout snowBOT
is there where i can ask for help?
dull forum
How do I solve for a b c d using simultaneous equations
devout snowBOT
How do I solve for a b c d using simultaneous equations
restive river
How do I solve for a b c d using simultaneous equations
are those the 4 eq
dull forum
yes
restive river
How do I solve for a b c d using simultaneous equations
evaluate each then, and do you know how to solve simultaneous eq
lets start with eq 4
dull forum
yeah so I just do it through elimination no?
restive river
yh thats one way
another long one is getting each in terms of the other, like c= -3a(270)^2 + ....
dull forum
i did eq 3 - eq 1
which = eq 5
then eq 5 - eq 4= eq 6
eq 4 - eq 2 =eq 7
eq 7 - eq 6 = eq 8 to make just a
but i think it doesnt work
restive river
can i see all those
restive river
when i do the elimination method, i usually do it with a matrix
not sure if its too early for you
dull forum
but i have to do it with simultaneous equations
its just cuz its for an assignmetn and i have to show algebraic working
my course didnt teach matrices
restive river
but i have to do it with simultaneous equations
yh its def early for you
okay one moment
dull forum
could you show me how to do it thru simultaneous equations?
restive river
How do I solve for a b c d using simultaneous equations
what i had in mind was
on eq 4 get c = ?? (make c the subject of the formula)
then sub that c into eq 3
to get d in terms of (a and b)
then the last c into eq 2,
to get either a or b,
now sub all of those into eq 1 to get a/b
then just back subsitution and you're done
Eq 4
$$0 = 3a(270)^2 + 2b(270) + c$$
woven radishBOT
restive river
c=?
restive river
c=-3a(270)^2 -2b(270)
yh sub that into eq 3 to get d
dull forum
wait lemme try
restive river
i hope these equations are correct to begin with, what was the original question
dull forum
wait idk what u mean
restive river
How do I solve for a b c d using simultaneous equations
look at eq 3
dull forum
i hope these equations are correct to begin with, what was the original question
trying to find a, b, c, d with the 4 eq
restive river
nvm you did fine
restive river
now make d the subject of the formula
restive river
trying to find a, b, c, d with the 4 eq
i mean how you got those 4 eq
restive river
yh but my god that is messy couldnt you have found lower values for x and y so we didnt have to deal with 270^3 etc
restive river
lets first try to evaluate those bit by bit
restive river
270^3 = 19.6m
dull forum
so just simplify the numbers
restive river
nah its cuz im trynna plug points into a polynomialk
what was the original original question
dull forum
its an assignmetn
but im trynna plug in the points (200,10) into this polymial
and make it have the same gradient as the previous function i had which is an exponential
so it looks like this
dull forum
the purple line is this function im working out
ive done it on calculator
but i have to show how to do it algebraically
restive river
and dude can you respectfully change your pfp
clearly against the rules, im giving a warning before i ping moderators
dull forum
dull forum
clearly against the rules, im giving a warning before i ping moderators
oh i didnt know
its a rlly rare pic man
u cant find it anymore
i dont even know where it is anymore
wait so do I sub d into eq 1 or eq 3
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sonic sluice
Anyone help pls? The thing I did was this only
100x+80y=1560
4x+3y=61
sonic sluice
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tall trellis
Aftab tells his daughter, "Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be
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Aftab tells his daughter, "Seven years ago, I was seven times as old as you were...
tall trellis
Aftab tells his daughter, "Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be
devout snowBOT
Aftab tells his daughter, "Seven years ago, I was seven times as old as you were...
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tall trellis
Aftab tells his daughter, "Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be
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tall trellis
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fickle cedar
Need help with this question. verify: tanx * csc^2 - tanx = cotx
dry oxide
why not convert everything in sin and cos and simplify it a bit
fickle cedar
sinx/cosx * (1/sinx)^2 -sinx/cosx = cosx/sinx
fickle cedar
why not convert everything in sin and cos and simplify it a bit
?
dry oxide
now simplify your LHS
fickle cedar
LHS?
fickle cedar
ohhhh
dry oxide
the lefft part of this equality
fickle cedar
would it be (1/sinx)^2
dry oxide
ah no
fickle cedar
(1/sinx)^2 / sinx/cosx
dry oxide
show me your work
fickle cedar
tbh i don't really know how to do this
dry oxide
,, \frac{\sin x}{\cos x} \times \left(\frac{1}{\sin x}\right)^2-\frac{\sin x}{\cos x}= \frac{1}{\cos x \times \sin x} -\frac{\sin x}{\cos x}
woven radishBOT
!Yajat!
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hexed ocean
Can someone help me with this?
hexed ocean
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marble snow
can someone just double check if i did this correctly?
devout snowBOT
can someone just double check if i did this correctly?
pale bolt
what does "combine together" mean
its too informal
but yes, the idea is right
oh you also missed a set of parenthesis in the first line you wrote
the g(x) also needs to be negated
marble snow
the g(x) also needs to be negated
wdym
marble snow
its too informal
and you’re right thank u
pale bolt
pale bolt
you should actually add them together in another step, then take another step to "factor" it to be in the same form as the first line
also you are assuming you can always just add things that are within limits, but thats fine now
marble snow
you should actually add them together in another step, then take another step to...
gotcha
does that look better?
pale bolt
beautiful
tall prism
livid geyser
wot
slim mural
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slim mural
Idek what to make of this
pseudo basin
f(x) = min(2x+2, x/2+1, -3x/4+7)
slim mural
f(x) = min(2x+2, x/2+1, -3x/4+7)
Do we even calculate this?
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peak dagger
About calculus:
Given x and t are related by a function f such that x = f(t), we want to evaluate (d/dt)(dt/dx).
The normal way to do is to find dx/dt by differentiate x = f(t) and substitute it into equation. So in this case we do (d/dt)(1/f'(t)).
But I'm thinking something else. By refering to the chain rule dy/dx = dy/dt × dt/dx, the dt looks like can cancel each other out so this chain rule works. So I'm thinking of cancelling dt for (d/dt)(dt/dx) to get (d/dx)(1) which evaluates to 0. This is obviously wrong, but where goes wrong by doing this way?
devout snowBOT
About calculus:
Given x and t are related by a function f such that x = f(t), we...
feral agate
$\frac{d}{dt}\frac{dt}{dx}$ is essentially meaningless, I think you mistyped something
woven radishBOT
kheerii
feral agate
what are you trying to find here?
peak dagger
Basically expression of (d/dt)(dt/dx)
Lemme send the whole question but i think it is a bit irrelevant
Wait ah
The first equation is proven by chain rule, the second equation can be done by same thing
Like d²y/dx² = (d/dt)(dy/dx) × dt/dx
And since dy/dx = dy/dt × dt/dx,
(d/dt)(dy/dx) = (dt/dx) × (d/dt)(dy/dt) + (dy/dt) × (d/dt)(dt/dx)
The last term is (d/dt)(dt/dx)
Which is what i want to find
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brittle burrow
$\dv t \frac{dt}{dx}=\dv t(\frac{dx}{dt})^{-1}$
woven radishBOT
chlamydia
brittle burrow
power rule
devout snowBOT
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peak dagger
power rule
I just wonder why (d/dt)(dt/dx) = (d/dx)(1) wrong?
brittle burrow
an abuse of notation that doesn't work properly, i'd guess
peak dagger
an abuse of notation that doesn't work properly, i'd guess
🤔
Probably i guess
Anyway thanks a lot
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opal cloak
how do i prove that w^4=w
opal cloak
nope
scarlet sequoia
opal cloak
hmm yeah i have 8pi/3 as the angle
golden thorn
now you can convert it to the principle arguement by subtracting 2pi!
opal cloak
how would i show that
scarlet sequoia
sinx and cosx are 2pi periodic
golden thorn
$Arg(w^4)=\frac{8\pi}{3} - 2\pi$
woven radishBOT
SKELEROY
golden thorn
thus $w^4 = cis(\frac{2\pi}{3}) $ which means that $w^4 = w$
woven radishBOT
SKELEROY
devout snowBOT
worn geyser
whys perpendicular in negative
wont it turn to positive
because
x axis is positive
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visual hazel
whys perpendicular in negative
the perpendicular side is below the x-axis
so its negative
agile narwhal
In this task we want to evaluate if Jaccard similarity on a full set of k-mers is a
suitable measure of sequence similarity. To this end, we will use randomly mutated
genomes for different values of mutation probablity p. We will consider 1-p as the
true genome similarity (the percentage of bases that were conserved) and see if
the Jaccard similarity is in some way related to this value.
- Write a mathematical formula in your report giving the probability that a
k-mer at a fixed position in the original genome does not contain any mutation
in the mutated version for some value of p (the formula will use parameters k
and p).
devout snowBOT
In this task we want to evaluate if Jaccard similarity on a full set of k-mers i...
agile narwhal
$Pr(p,k) = (1-p)^k$
woven radishBOT
Michal
agile narwhal
is this correct?
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agile narwhal
k-mer is a sequence of length k
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opal cloak
let z = cosθ+isinθ. Determine z^2 in two different ways and hence show that:
(a) cos2θ = cos^2θ-sin^2θ
(b) sin2θ = 2sinθcosθ
devout snowBOT
let z = cosθ+isinθ. Determine z^2 in two different ways and hence show that:
(a)...
opal cloak
i dont get the 2 different ways
i know cos2θ and sin2θ are both double angle identities which appear when i solve for z^2
winter patrol
the two ways they're referring to are
binomial expansion
DeMoirvre's
then equate real / im parts for what they're asking
fluid flax
When we say that the absolute value decreases, does it mean that it goes from larger to smaller? I mean 5 4 3 2 1
devout snowBOT
When we say that the absolute value decreases, does it mean that it goes from la...
wooden veldt
e.g. 5 -4 3 -2 1 is a sequence where the absolute value of the terms decreases, but the numbers themself arent decreasing
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lucid pine
devout snowBOT
stable valley
AB and BC intersect at B right?
lucid pine
x=2
lucid pine
2,5
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✅
lucid pine
pseudo basin
you didn't need to post the exact same question 3 times.
what's troubling you with part (ii)?
@lucid pine
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devout snowBOT
i can't do this by pen and pencil on an exam.
untold crow
Given function: \ $f(x) = \sin(-10x^{2})$ \ Find the Taylor polynomial of f(x) of degree 8 and centered at x0 = 0.
woven radishBOT
HqppyFeet
untold crow
Wait- perhaps I found a technique
This is the formula for Taylor polynomials... knowing that a = x0
So the second derivative (then inserted to (f''(a)/2!)(x-a)^2) is \ $\frac{-20((\cos(10(x_0)^{2}))-20(x_0)^{2}(\sin(10(x_0)^{2})))}{2!}$
woven radishBOT
HqppyFeet
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
woven radishBOT
riemann
supple knot
Plug -10x^2 into the sine series, then evaluate the series at 0
untold crow
Plug -10x^2 into the sine series, then evaluate the series at 0
ahaa, so I would be substituting 10x^2 into x in the sigma notation, then... find the sum up of all values from k = 0 to k = 8?
supple knot
Degree is not the same as number of terms
Do you know what the degree of a polynomial is?
untold crow
Do you know what the degree of a polynomial is?
A straight line has a degree of 1, while a quadratic has a degree of 2-
untold crow
yup, got that idea
so if we are trying to find the taylor polynomial of f(x) of degree 8, would we find the answer through k = 8?
supple knot
Degree is not the same as number of terms
.
supple knot
Plug -10x^2 into the sine series, then evaluate the series at 0
Just write out a few and you'll start to see
untold crow
honestly I thought that the "degree 8" would mean that we would have to derive the expression eight times 😅
untold crow
Just write out a few and you'll start to see
I'll try
nevermind that doesn't make sense
when k = 2, I'm getting $\frac{(-10x^{2})^{5}}{5!}$
doesn't look pretty.
woven radishBOT
HqppyFeet
supple knot
Yea what degree is that
untold crow
10th xd
devout snowBOT
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untold crow
We are trying to find P_8 (x). And it looks like I just have to deal with it and find the eighth derivative.
We know that x_0 = a = 0, so the number behind the x_0 can just be simplified to 1.
untold crow
Yea what degree is that
but is there really a shortcut here?
wait a minute
to get the 8th degree...
when k = 1, \ $\frac{(-10x^{2})^{3}}{3!}$
woven radishBOT
HqppyFeet
untold crow
that gives us a degree of 6.