If x^2 = a
=> x = |√a|
#help-42
prime yacht
eternal shard
If x^2 = a
=> x = |√a|
I suppose you meant |x| = √a
prime yacht
Yea mb
calm coralBOT
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sick flame
pls help
sick flame
how do i find general formula i wasnt listening in class
😩😔
wait no its all g now
pls extension help
🙏🙏
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vestal tree
calm coralBOT
vestal tree
Is the change faktor not 1,66?
It says It’s wrong
I did 240/360=0,66 and that means it got bigger by 66% so basically 1,66 (166%)
But change faktors are written as 1,66 for example so I don’t understand why it’s wrong
leaden thunder
you rounded wrong
vestal tree
How
Ohhhhh wait will it be 1,70
Well that was wrong
Wait I got it
Thank u😭
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vestal tree
Ignore the translate app
How do I do this
I did the difference which was 42871/6423
Which was
6,674
I rounded it to
6,67
And im supposed to write it in %
So
667%
But that’s wrong
leaden thunder
can you crop
leaden thunder
,calc 42871/6423
potent lotusBOT
Result:
6.6746068815195
that doesn't look like 42871
leaden thunder
,calc (49294-6423)/6423 * 100
potent lotusBOT
Result:
667.46068815195
667 is right ¯_(ツ)_/¯
calm coralBOT
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remote mural
i no understand :'))
red badge
lol
remote mural
it just threw positive in my face, some other questions positive and negative
positive and negative waht.?
what am i looking for..?
remote mural
Exponential Functions, Graphing and Describing
red badge
ok that might give us a clue about what they want.
remote mural
:')
red badge
so what can you insert as an answer? numbers or symbols?
red badge
ah
red badge
ok
remote mural
show or explain how to do it
red badge
I got you. Give me a sec to work it out myself
remote mural
thank you so much !!
red badge
thank you so much !!
It looks like it is asking for the range of numbers. Split into its positives and its negatives. So, what I would attempt to do is graph the function. From there you should be able to tell where the function exists in the positive range and the negative range.
In this case I believe you only have a positive range
If you need help doing that I can explain it using the previous problem as an example
remote mural
the range to the problem would be (1,∞)
red badge
That's what I got yes
remote mural
but then im just completely thrown off after that
red badge
is that what you put originally
remote mural
i typed it in as an aswer, yes, and it was incorrect
i have 1 try left before the question is just marked off as incorrect
red badge
so I apologize if this is incorrect in advanced, but you got the right answer. So, I'm going to assume that you just have the range flipped around.
Because the way I'm looking at it you have to read where it's coming from in the (negative x axis) and where it is going (positive x axis)
if that makes any sense
remote mural
sorry, i really dont understand. I'm stressing for nothing because this isn't even MY homework.
he's got it atp, i give up :')
remote mural
you could try, I just wouldnt see a point in it. i'm horrible when it comes to math
red badge
No worries. Have you plotted the graph? If not we can do that first.
red badge
i have to find the positive and negative
alright do you want to post it
remote mural
red badge
ok have you tried graphing it
zenith bough
I think this is positive for all real numbers again.
zenith bough
That's a wrong graph, I think. The plus three should be part of the Exponent.
remote mural
i typed it as is in the problem :<
zenith bough
It doesn't look like it to me, but I trust you. Okay.
remote mural
sigh..
welp ! there goes that !!!
DNE it was !!
thanks for trying to help guys, i really appreciate it ^_^ <3
zenith bough
Okay, I was right that it was positive all real numbers, but that's all I thought you had to say. I didn't know you had to say specifically that DNE
For negative
calm coralBOT
zenith bough
It's very easy. Do you want me to explain it?
remote mural
sure !
zenith bough
Think about it this way In order for that value to be negative or 0. the first part would have to be Some negative number. The three to the power of the X plus 3. But just from knowing how, raising things to powers work you can't raise three to anything to make it negative. So therefore, whatever you do, it's always. going to be positive
And by the way, you did enter the graph wrong lol but its ok.
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ancient coral
You should take the derivatives of boths cases, and check when are they equal in the transition point, like you did in a
west horizon
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ancient coral
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Not exactly but close
west horizon
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west horizon
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ancient coral
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Ha ok lol😅
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ancient coral
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Try doing this derivative with the power law too
Because although the value of the function is 2, the derivative isnt
west horizon
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ancient coral
3 could be written as 3x⁰
west horizon
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ancient coral
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Times 0
west horizon
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ancient coral
Exactly
west horizon
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ancient coral
You just found the derivative function of f, f'= -1 (x<1), 2ax+b (1≤x)
west horizon
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ancient coral
And checking whether f is differentiable is the same as checking whether f' is continous
west horizon
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ancient coral
At the transition point, just like you did in a
west horizon
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ancient coral
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The important part is them being equal at x=1
west horizon
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ancient coral
The important part is them being equal at x=1
We don't care about all of the other places
ancient coral
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Yes
west horizon
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minor gust
Lock in Kenzo
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ancient coral
Is the last section you got another equation for a and b right?
west horizon
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minor gust
You’re gonna use system of equations
west horizon
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minor gust
For continuous
2=a+b
For diffirent able
-1=2a+b
west horizon
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minor gust
Do you see how I got that
west horizon
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minor gust
Ok now use sub
west horizon
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minor gust
Either 2-a=b
Or
2-b=a
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minor gust
And plug that value into the section equation
west horizon
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minor gust
Oh nvm what you did is right
west horizon
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ancient coral
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Nicee!! I wasn't sure you would see this shortcut👏
west horizon
Nicee!! I wasn't sure you would see this shortcut👏
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minor gust
Ye it’s negative
minor gust
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.
west horizon
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ancient coral
You just confused the sides of the subtraction
west horizon
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ancient coral
2a+b=-1
a+b=2
2a+b-a-b=-1-2
a=-3
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zealous badger
aren't you missing an answer
frosty olive
Horizontal is when the derivative equals 0 right
So solve for when the derivative equals 0
west horizon
aren't you missing an answer
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remote mural
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horizontal tangents occur when the derivative at that point is 0
frosty olive
You found 1, find the other
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frosty olive
You found one try factoring
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zealous badger
or that too. many ways
frosty olive
Since x = 1 is a root of your quadratic then factor out (x - 1)
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frosty olive
You got this
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frosty olive
Find the other factor
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frosty olive
Hmm no
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frosty olive
Wait why
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frosty olive
Yes
west horizon
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frosty olive
Indeed
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frosty olive
Oh is it that do the odd ones
Lol
Like do the odd numbered problems
That’s what my teacher is always doing
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frosty olive
Np
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supple glade
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supple glade
can anyone help me with this? I got to that A is positive but idk how to approach the second part
cedar kernel
can anyone help me with this? I got to that A is positive but idk how to approac...
Its same thing
How did you get A
By the symmetry of y?
supple glade
yup
cedar kernel
Then you know B ;p
y - odd * cosy - even -> odd
supple glade
is there a general approach to find this ?
like what's the best way to / strategy to apprach?
supple glade
Then you know B ;p
y - odd * cosy - even -> odd
so the result would be zero correct?
cedar kernel
Check the function is even or odd on a symmetry area…I think this is the only way
cedar kernel
so the result would be zero correct?
yepp
supple glade
Check the function is even or odd on a symmetry area…I think this is the only wa...
ahh alright
well thank you so much apprecite it!
cedar kernel
np ;p
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past dune
If A, B and C are all different digits and they're not 0,
-> 3 figure ABC is divisible by 9
-> 2 figure AB is divisible by 4
-> 2 figure BC is divisible by 5
Then what's A+B-C equal to?
past dune
I know it's a basic question and i think so too, but i think the question itself is wrong here? Or maybe i am just dumb
İt's a multiple choice question so A)4 B)5 C)6 D)7 E)8
amber bolt
C is maybe 0
past dune
I started from the last one, figured C would be 5
past dune
C is maybe 0
Not possible, question clearly states they're inequal to 0
nimble harbor
A + B + C is divisible by 9
AB is divisible by 4
C is either 0 or 5
nimble harbor
C is 5
past dune
But questions says c can't be 0 so it's 5
amber bolt
then A+B must be 4 or 13
past dune
But if 5 is five, then the answer isn't on the answer key
past dune
Wait
nimble harbor
not A + B
amber bolt
so it's 8 assuming it's all true
past dune
13? Oh i didn't think of that 😭
Lemme check
Yeah it is 8
Thank you I'm so sorry for wasting time😭
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blazing coyote
calm coralBOT
blazing coyote
Have to verify if these are vector spaces, or not
$c$ is a vector space. It's closed under addition and scalar multiplication and satisfies all the vector space axioms
potent lotusBOT
Veni, vidi, perii is not f(wai)
blazing coyote
d) isn't a vector space. 1-1=0, which isn't in $\mathbf{P}$
potent lotusBOT
Veni, vidi, perii is not f(wai)
vagrant oak
looks right 
operations of P are addition of polynoms and multiplication by reals i suppose
vagrant oak
I think (e) is. a VS too
Yep
blazing coyote
(f) isn't a vector space
Say the column sum is 1
There doesn't exsit a multiplicative identity >
vagrant oak
what do you mean by multiplicative identity
the only multiplication vector spaces have is scalar multiplication
vagrant oak
I think you misunderstood it
[a b]
[c d]
It's the VS of all such matrices, with a + c = b + d
or that's how I undestood it
they are not equal to anything specific, the column sums are just equal to each other
so
[1 1]
[1 1]
is there, as is
[3, 0]
[0, 3]
blazing coyote
Fair. Okay
I'll stop here for now. too ill to continue
Thanks for the help
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exotic kite
Did I do this correctly?
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Did I do this correctly?
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hard iris
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hard iris
HELP
junior fern
Does the thermostat give the actual temp or the temp inputted
hard iris
i dont know
junior fern
I don't thinkbit matters actually
hard iris
ok so how do u write an equation out of this
this is my question
i know how to solve but i dont know how to write it
junior fern
Well if it's plus or minus 15 then you would agree it's withing plus or minus 14 or 13
Or 14.9 14.8
hard iris
what
junior fern
Like if it tells you it's within 400 plus or minus 15
Then its within 400 plus or minus 14 too
Basically the values can be a range of numbers between 400-15 and 400+15
junior fern
Which is what will help you construct an equation I thjnk
I believe the equation would be 400+x where |x|<=15
hard iris
so the maximum temperature inside the oven will be 415 and the minimum temperature will be 385
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tough star
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tough star
how do i approach this problem
slender oar
looks like you need to just count how many times you get to selina without going backwards
is this discrete math?
i would start with the easiest ones first... ex: start from cora's palce then just go up then right. that is 1 path
another path would to be just start going right immediately then go up
(the outer rectangle)
so that is 2 paths
it looks like there aare a ton of paths
tough star
right but how would i do it without manually counting all of them
slender oar
prob need to form an equation with how many dots there are
your teacher didnt give you an equation for that?
tough star
gr 12 data management
tough star
no 💀
slender oar
the lines are called vectors i believe
slender oar
and the dots are vertices i think., hold on
ok the paths are vertex
and the dots are vertices
tough star
okay
tough star
what abt the dots?
so whats the first step in solving a problem like this
slender oar
that is a great question this needs an algorithm im pretty sure
honestly i am not sure
this is weird question since i am not sure what 'defined path' means
what did you teacher tell you that means
and what would they consider backtracking? going over the same line?
i am not a helper, maybe you should ping a helper
tough star
and what would they consider backtracking? going over the same line?
i think its going south or west
slender oar
if you think it means not going south or west then you should just count
because it is easy that way
tough star
if you think it means not going south or west then you should just count
well the answer key says the answer is 63
but thats still a lot doing manually lol
amber bolt
it should take a minute or so
i'll time it
ok, i see the problem
you can weird loopy paths in this one
you don't go backwards and that one node without a blue dot is a mistake
then it's 63
i didn;t time it, but i think it was under a minute
slender oar
lol
would u mind helping me i am 1 down from here
how did you go about solving this btw what are the numbers
amber bolt
no i don't know calc
slender oar
o geez
amber bolt
you add the left neighbor and the down neighbor
slender oar
so how did you get 5 for that one?
amber bolt
there was a 4 to the left of it
amber bolt
yeah
amber bolt
what do you mean
i just saw this problem at some point, maybe 8 years ago, and someone solved it
juis like you know now
tough star
ohhh
makes sense
thx
how would u do this one?
its the same concept but diff cuz they both are walking
tough star
ohh
so we can repeat what we did for the previous question?
but only getting to the center
tough star
and then square that number
why square it?
amber bolt
because you would find the spider's path
you multiply by the fly's paths to get "ways"
tough star
wouldnt that be times by 2
amber bolt
because it has every segment we can do 6c3 instead of manual counting
times two doesn't make sense, i don't know how to explain why
so it should be 400
tough star
so it should be 400
hmm yeah thats what i think too
this is what the back of the textbook says tho
amber bolt
interesting
maybe the idea is that it's more like 5×5
and then there's two meeting points
tough star
maybe, ill confirm with my teacher tmrw
amber bolt
ok i'm wrong about "1 or 2"
i always mess this up
yeah 252
we could also figure out that each complete path, corner to corner, defines the meeting point, so it's just 10×9×8×7×6 / 120 = 252
calm coralBOT
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twilit bramble
Need to find the area enclosed by these 2 graphs but I’m not sure how to do it
noble crane
you need to find the bounds first
after that you need to determine which function is on top and the one at the bottom to set up your integral
u their?
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twilit bramble
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tough star
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tough star
can someone help with this?
what would be the first attempt in approachin this problem
calm coralBOT
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teal hazel
I guess we are gonna make the net force or what ever it's called to be 0
oh there;s acceleration, net force isn't0
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terse swan
Can someone help me with this question please?
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dusky crescent
Can anyone help me understand how I can get from the first image to the second image?
dusky crescent
with simplification
calm cradle
you can first move things around using the commutativity law to get
(~Q v T) ^ (~Q v T v ~S) ^ (~Q v ~S) ^ (~Q v ~S v ~T)
We will now group things together and focus on the two pairs, namely we will try and simplify
[(~Q v T) ^ (~Q v T v ~S)] ^ [(~Q v ~S) ^ (~Q v ~S v ~T)]
you can write (~Q v T) as (~Q v T v false); then notice that (~Q v T) ^ (~Q v T v ~S) is just (~Q v T v false) ^ (~Q v T v ~S). The nice thing about this is that both of these clauses contain (~Q v T), so to simplify things, we will just label it as R. But then we get
(R v false) ^ (R v ~S)
Does this now look familiar? Is there a rule you can use here?
dusky crescent
you can first move things around using the commutativity law to get
```
(~Q v T)...
I think I may have messed up the last line. I put ~QvT when I believe that is wrong. Since in the line before there was ~TvT
which is lem so can't I just eliminate that by lem
and that leaves me with ~Q
Like this?
there are still more steps that need to be done though
calm cradle
~T v T is just true so the term (~Q v ~T v T) vanishes
calm cradle
yeah so you get (~Q v ~T v ~S) ^ (Q v ~S) ^ (~Q v ~S v T)
we get the first expression which is good
so all that's left is simplify the last two
calm cradle
you can write `(~Q v T)` as `(~Q v T v false)`; then notice that `(~Q v T) ^ (~Q...
that also leads back to here
but with different terms
you can write (Q v ~S) as (Q v ~S v false) so the last two terms is just (Q v ~S v false) ^ (~Q v ~S v T)
then observe that Q v ~S appears in both terms so we can make things a bit easier and just write it as R to get
(R v false) ^ (R v T)
but does this look familiar to you? Is there perhaps a rule that you've seen which deals with this?
dusky crescent
but does this look familiar to you? Is there perhaps a rule that you've seen whi...
I can't think of it at the moment
calm cradle
let p, q, r be propositions. what does p v (q ^ r) look like? what does p ^ (q v r) look like?
dusky crescent
first one looks like something that can be used with the distribution law
i am not sure about the second one though
calm cradle
well they are both the distributive laws
p v (q ^ r) = (p v q) ^ (p v r)
p ^ (q v r) = (p ^ q) v (p ^ r)
one of these seems like the one we want!
dusky crescent
The second one
calm cradle
what would your p, q, r be
calm cradle
then observe that `Q v ~S` appears in both terms so we can make things a bit eas...
it might help to look at the last expression in this msg
namely, (R v false) ^ (R v T)
calm coralBOT
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@dusky crescent Has your question been resolved?
orchid ridge
calm coralBOT
orchid ridge
am trying to use shell method to do part b (learning so pls help)
$2\pi \int_{0}^{1} (3x - 3x^3) , dx$
potent lotusBOT
Sho
orchid ridge
at first i though the signed area would be from -1 to 1
but it works for 0 to 1
is it because of the symmetry of the graph?
??
pls i dont want to have to start a new channel
tiny monolith
lol..
orchid ridge
im not that curious…
tiny monolith
<@&268886789983436800>
vivid ferry
hey shoe
vivid ferry
what do you need help on
orchid ridge
at first i though the signed area would be from -1 to 1
^
i feel like i should say smth more, but idk waht to say
uhh
is my integral alr?
marble pendant
Hey Pikachu
orchid ridge
yo wumpus
marble pendant
I don't know lol gl
calm coralBOT
@orchid ridge Has your question been resolved?
tiny monolith
but it works for 0 to 1
yea and yea
tiny monolith
when u rotate it 180deg u get the other half
so u just consider half or u divide your answer by 2
tiny monolith
oh
orchid ridge
why was it 0
tiny monolith
probably the other side gives negative area
orchid ridge
did I do smth wrong?
orchid ridge
probably the other side gives negative area
o
orchid ridge
o
ic
when I asked earlier about transitioning from q a) to b)
kokkiemon said this
is it jsut because using disc method with this is just way longer?
orchid ridge
.close
flint karma
calm coralBOT
teal drift
Why do you think it's 8?
teal drift
I'll give you a hint: perpendicular bisector of a segment
Do you know its definition?
(not talking about complex numbers for now, just think about euclidean geometry)
flint karma
would u find the slope of it?
ive done all the other imaginary numbers stuff so easilyt
this is the last stuff
I dont even know what its asking
teal drift
would u find the slope of it?
Nothing to do with slope
teal drift
(not talking about complex numbers for now, just think about euclidean geometry)
@flint karma
flint karma
I dont get it
what do u mean by that
because its only asking for z0
is it 4?
-8i?
teal drift
what do u mean by that
I mean exactly the definition (or property, if you prefer) of perpendicular bisector of a segment
I'm quite sure you've seen that in previous courses
jolly pilot
You might wanna start by returning to the most basic definition: |z-p| represeents the distance of a random point z from a known point p
if you understand this in context of your problem, it might be easier to see what is going on here
flint karma
is it asking for the exact value? or the definition
jolly pilot
its asking for the exact value of z0, not the definition
flint karma
will it include an imaginary number
teal drift
will it include an imaginary number
What's "it" in this question?
flint karma
z0
teal drift
Well, not necessarily
teal drift
But in this case, yes z0 is imaginary
teal drift
You might wanna start by returning to the most basic definition: |z-p| represeen...
Using this, and noticing that |z| = |z - 0|, can you tell something about the equation given?
flint karma
i get that |z| is the distance of the complex number from the origin
and the z-z0 is the distance from another number
but like
i got no clue how to get it
because it gives you barely anything
calm coralBOT
@flint karma Has your question been resolved?
flint karma
<@&286206848099549185>
calm coralBOT
@flint karma Has your question been resolved?
teal drift
i got no clue how to get it
Again, what property do the points belonging to the red line satisfy, in terms of distance from the origin and from the number z0? Those two distances have to be ...
lost wind
Solve $4z^4-8z^3+11z^2-8z+4=0$, where $z$ is a complex number, given that all the roots have modulus one.
potent lotusBOT
BOHO
lost wind
i found the roots to be alpha, beta and their conjugates
and since they have modulus one then alpha conjugate = 1/alpha and vice versa
so i thought you just use sum and product of roots for alpha, 1/alpha, beta and 1/beta but it gets really messy and idk how to solve for either one
is there a better way to do it?
compact lark
hollow lion
calm coralBOT
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maiden vigil
is there a better way to do it?
I am not sure if you'll consider it a better way or not
but you could proceed by dividing the whole equation by z^2
calm coralBOT
@lost wind Has your question been resolved?
lost wind
I am not sure if you'll consider it a better way or not
but you could proceed by...
do u use quadratic equation to solve for z after that??
maiden vigil
do u use quadratic equation to solve for z after that??
indeed
maiden vigil
cos ull have -8/z + 4/z^2
after that you'll rewrite the equation as 4(z^2+1/z^2) -8(z+1/z) + 11 = 0
do you get the idea?
then make a substitution z + 1/z = u
calm coralBOT
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hidden ferry
p,q prime numbers; Find all such p and q that: pq | 5^p + 5^q. What i got: p | 5^p + 5^q => 5^p+5^q=0 (mod p); from flt 5^p = 5 (mod p) => 5^q + 5 = 0 (mod p) => 5(5^(q-1) + 1) = 0 mod p
hidden ferry
Or 5^q-1 = -1 (mod p)
Maybe we can use orders here
5^2(q-1) = 1 (mod p)
5^d = 1 (mod p) (d - order) => d | 2(q-1)
calm coralBOT
@hidden ferry Has your question been resolved?
severe bobcat
Or 5^q-1 = -1 (mod p)
*only if p != 5
severe bobcat
5^d = 1 (mod p) (d - order) => d | 2(q-1)
Even better: the order must be even
hidden ferry
*only if p != 5
You can analyse the case of p=q (it will turn out p=q=5) and say p≠5
hidden ferry
Even better: the order must be even
Why?
severe bobcat
If the order is odd, then for any 0 < k < d we have 5^k != -1 mod p, because if 5^k = -1 mod p, then 5^(2k) = 1 (mod p), but 2k mod d is not zero, so if we let m = 2k (mod d) we found m such that 5^m = 1 (mod p) and m < d, but that can't be the case because d is the order
Now if we have some arbitrary K, we can reduce it to a k from [0, d) and apply the observation above
In our case we know that 5^(q-1) = -1 (mod p), so d has to be even
d can be larger than q-1, e.g. when d = 2(q-1)
hidden ferry
d can be larger than q-1, e.g. when d = 2(q-1)
Oh, yeah
severe bobcat
Alright, we know that the order d of 5 is even. Therefore the least integer m such that 5^m = -1 (mod p) must be d/2. Hence q - 1 = (2k + 1)d/2
If q != 2, it actually implies that d is divisible by 4
hidden ferry
If q != 2, it actually implies that d is divisible by 4
q=2 easy analysis (2,3), (2,5) only
severe bobcat
nice
severe bobcat
In conclusion, when p!=5 and q!=2, there're 2 cases.
- When ord(5) mod p is not divisible by 4, there're no solutions
- When ord(5) mod p is divisible by 4, we have infinitely many appropriate q
calm coralBOT
@hidden ferry Has your question been resolved?
hidden ferry
If the order is odd, then for any 0 < k < d we have 5^k != -1 mod p, because if ...
But if all 5^k != -1?
severe bobcat
But if all 5^k != -1?
That happens only if the order of 5 is odd
hidden ferry
That happens only if the order of 5 is odd
Why?
calm coralBOT
dull wraith
Can someone help to prove?
where c is a positvie
and lim n->inf (a_n) = 0
remote mural
!status
calm coralBOT
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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.
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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
- I don't know where to begin.
remote mural
I would try to do this using induction
dull wraith
i actually tried to write this as 1/sqrt(1) +..+1/sqrt(n) - 2sqrt(n) = -c + a_n
but idk what to do after
dull wraith
ik
dull wraith
are you aware of the concept of ibduction?
but i think that it doesnt work here
remote mural
hmmm oay
dull wraith
i mean it is not helpful
knotty lantern
c doesn't matter much
dull wraith
c doesn't matter much
yep
knotty lantern
i just want to see u prove an is convergent
dull wraith
i just want to see u prove an is convergent
it is diverges
how ever 1/sqrt(1) +..+1/sqrt(n) - 2sqrt(n) this one is converge
calm coralBOT
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fleet jungle
$\tan(\frac{1}{3}x) + \sec(\frac{1}{3}x) = 2 \newline\newline [0, 2\pi]$
potent lotusBOT
snooze
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remote mural
are the coordinates of the minimas of x pentation 2n (where n is a natural numenber) collinear?
jolly pilot
You need multiple minima for collinearity. Pentation, just like tetration, exponentiation, multiplication and addition yields a monotonic function
jolly pilot
I dont think so...
x pentation 2n should yield a similar behaviour to x^2n or x*2n or x+2n and so on. It must go on increasing as x increases
pentation in just repeated tetration, and tetration is just repeated exponentiation, and so on
remote mural
ah shit
jolly pilot
pentation for all natural numbers is increasing, and as such the minima is at 1
remote mural
they mean that for each n you have a different function
yes
glass heart
for each n you have a different function. like you would have different functions x^2, x^4, x^6. for each of those you have some minimum. and then you can ask where those minimums are in relation to each other
jolly pilot
2[4]2 < 2[4]3 < 2[4]4 < 2[4]5 < ...
remote mural
for each n you have a different function. like you would have different function...
zero for all
0^0 = 1?
nvm
I will ask this later
thanks guys
.close
calm coralBOT
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livid hound
What does it mean by
Centroid G and incenter I are collinearwith centroid B of the boundary of the triangle
silver tapir
What does it mean by
Centroid G and incenter I are collinearwith centroid B of t...
what
livid hound
That's written in this book
silver tapir
What does it mean by
Centroid G and incenter I are collinearwith centroid B of t...
it means centroid G incentre and centroid B lies on the same line
livid hound
How are there two centroid
silver tapir
How are there two centroid
ye idk
there is only 1 centroid for a triangle
idk where's the second triangle at
livid hound
Bro no second triangle
silver tapir
Bro no second triangle
how can a single triangle have 2 centroids
i think they meant vertex B
and misprint as centroid B
calm coralBOT
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twin star
Hello just a quick question, can we prove that three vectors form a basis of the space simply by showing that they are orthogonal to each other without solving any systems?
twin star
I'm asking because I'd like a method to solve such exercises faster for my exams
primal bear
Hello just a quick question, can we prove that three vectors form a basis of the...
uhh yessss-?
That they are linearly independent yeah?
twin star
yes that's what I thought
but we never saw that method in class so I wondered
why we don't just do that
but thanks
primal bear
Well
they are orthogonal so lin independent
that's proof by sheer fucking obviousness
for spanning the vector space you can just take a random vector and show that in can be resolved in the 3 orthogonals yeah?
like we do that all the time with i cap j cap k cap
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broken dagger
|z-i| < 2 in the complex plane is open disk centered at 0+2i … remember graphing 2x+3y>6 and you’d make a dotted line and shade half the plane. Then |z-(i)|<2 would be a dotted circle (open disk/ neighborhood) centered at 0+1i aka (0,1) with radius two. So if z = x+iy any point (x,y) that would satisfy x²+(y-1)²<4 … Now imagine if δ>0 and x²+(y-1)²< δ² is the set of points closer and closer to (0,1) as δ → 0 (Sound like a limit to a point 😉)
Before I meet you, think what the set of points P =(x,y) [or complex numbers z = x+yi] that satisfy |z-(1-i)| = 3√2 would describe …. as well as the points that satisfy |z - 6i| = |z-8| look like. And the heck graph all the points where Im(z) = -4
calm coralBOT
@broken dagger Has your question been resolved?
calm coralBOT
@broken dagger Has your question been resolved?
distant stag
not sure how to solve for x here
calm coralBOT
not sure how to solve for x here
remote mural
not sure how to solve for x here
,,, do you know the two exponent properties
\e{itemize}{
\ii $a^n\2a^m = a^{n+m}$
\ii $a^n\divsymbol a^m = a^{n-m}$
}
glad parrot
put both sides as 2^(something)
potent lotusBOT
distant stag
yes
remote mural
try to use that to simplify the left part
glad parrot
write 4^14 as (2^2)^14
calm coralBOT
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viral scarab
why can't i use sin to calculate for beta in this scenario?
calm coralBOT
why can't i use sin to calculate for beta in this scenario?
cloud nexus
if you know its a right triangle, you can
urban relic
v is bigger than the hypoteneuse a?
something went wrong with your calculations beforehand
cloud nexus
i know it is but my calculator gives me an error
wym
just do arctan of
OH WAIT
Shit
viral scarab
yes i just figured it out i calculated v wrong
cloud nexus
Why is v bigger than a
rocky knot
i know it is but my calculator gives me an error
it gives you an error because the domain of arcsin is restricted
and you have gone outside of the domain
calm coralBOT
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remote mural
how do i simplify cosx/2 + sinx/2
calm coralBOT
how do i simplify cosx/2 + sinx/2
calm coralBOT
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atomic rune
calm coralBOT
atomic rune
wait i already tired to solv this and i got a wrong answer and i dont get how
potent smelt
!show
calm coralBOT
Show your work, and if possible, explain where you are stuck.
atomic rune
give me a sec
used this to solv for d
then used this to solv for x
first answer
second answer
potent smelt
Those are the points where the expression in the numerator equals 0. Not where the overall inequality is true
potent smelt
It doesn't
potent smelt
Instead, multiply both sides by (x-1)
And now you have 3 possible cases
Do you know what the cases are?
potent smelt
Yes, however this is just one of the three cases
atomic rune
what are the other 2?
atomic rune
doesnt x-1 have to give more than 0 cuz you cant divide by 0 mb for spilling mistakes btw
potent smelt
x-1 can be less than 0