Quick question, what's the derivative of 1/y' with respect to x?
#help-26
unreal zealot
odd pagoda
google doesnt know what y is itself a function of x
(which is what I assume you have)
topaz sinewBOT
@unreal zealot Has your question been resolved?
unreal zealot
Ok wolfram alpha gave me this.
fair thorn
you could have done it manually using the chain rule
unreal zealot
~~you could have done it manually using the chain rule~~
Yeah now i can see. I was just unsure as hell.
unreal zealot
google doesnt know what y is itself a function of x
Not sure if this legit.
I also tried on symbolab, but it seems like it's having a stroke.
unreal zealot
Yeah now i can see. I was just unsure as hell.
So i guess it's - y'' / (y')^2
golden blade
How can you say I guess when you just got the answer lol
unreal zealot
I have anxiety. :(
I have to triple check.
golden blade
epic
thorny flameBOT
bacc the sigma😔🤞
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unreal zealot
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spark meteor
Can someone help with this?
topaz sinewBOT
Can someone help with this?
craggy haven
could you show the contrapositive instead? might be easier
spark meteor
could you show the contrapositive instead? might be easier
Nope didn't work
unreal bronze
,rccw
thorny flameBOT
craggy haven
Nope didn't work
I think it should
spark meteor
I think it should
It would only for one part of the inequation
In the other it would be superior to (1/4)³+1/2-1
Which is negative
craggy haven
well, yes, that's negative
craggy haven
so if x < 1/4 then it'll be even more negative
mortal steeple
You should put 1/4 then 1/2
You will see that it is once neg and the pos therefore it must have been zero in between
spark meteor
And we need to demonstrate that it is different from 0
spark meteor
You should put 1/4 then 1/2
You will see that it is once neg and the pos therefo...
Yes but we are trying to use contrapositive
spark meteor
It's a logical reasoning
spark meteor
Oh
So no one got the answer?
If only we studied the quadratic formula for equations of 3rd degree
unreal bronze
What is contrapositive?
The contrapositive of a statement "if p, then q" is "if not q, then not p". The two statements are logically equivalent. For example
If x is prime, then x = 2 or x is odd
means the same thing as
if x is not 2 and not odd, then x is not prime
craggy haven
contrapositive...
to prove P -> Q,
we prove ~Q -> ~P
mortal steeple
Ohh
unreal bronze
so in this case, we want to show: if x <= 1/4 or x >= 1/2, then x^3 + 2 x - 1 can't be 0
spark meteor
do you know either derivatives or discriminants?
Discriminants
spark meteor
what grade/class is this for?
11th
unreal bronze
so can you show the cubic has only one root?
mortal steeple
So I was thinking
Can we say that on putting 1/4 we get a negative number
And for numbers less than 1/4 it gets more negative
Similarly for 1/2
Therefore 0 can only like in between
spark meteor
so can you show the cubic has only one root?
We studied the discriminate of only 2nd degree formulas
unreal bronze
So I was thinking
Can we say that on putting 1/4 we get a negative number
And f...
yeah that's the calculus approach (the derivative is always positive so the function is always increasing)
spark meteor
Nah dawg gotta be sth else
unreal bronze
We studied the discriminate of only 2nd degree formulas
ah ok
unreal bronze
So I was thinking
Can we say that on putting 1/4 we get a negative number
And f...
I think this approch is still the way to go
show if x <= 1/4 then f(x) <= f(1/4)
and if x >= 1/2 then f(x) >= f(1/2)
spark meteor
That's what I tried to do
neon iron
f(1/4) * f(1/2) < 0
spark meteor
Sadly it didn't work
spark meteor
f(1/4) * f(1/2) < 0
What for?
neon iron
what are yall doing bruh
spark meteor
Oh I see
unreal bronze
so the root is between 1/4 and 1/2
there is a root between 1/4 and 1/2
how do you know it's the only root?
neon iron
why do i gotta prove that
unreal bronze
that's what the question asks for
essentially "show all roots of this cubic are between 1/4 and 1/2"
neon iron
cuz its always increasing
unreal bronze
cuz its always increasing
and how do you show that (derivatives are not allowed because this is grade 11)
neon iron
f(b)-f(a) > 0 if b>a ig
spark meteor
Depends on whether the equation is increasing or decreasing
neon iron
check it den
spark meteor
I can't lol
neon iron
?
neon iron
f(b)-f(a) > 0 if b>a ig
put a,b
neon iron
that doesnt make sense
unreal bronze
It's increasing
if you've shown the function is increasing, you've got it
because an increasing function can only have one root
and f(1/4) is negative while f(1/2) is positive, so there's a root between 1/4 and 1/2...
unreal bronze
how did they do it?
spark meteor
@unreal bronze @neon iron @
It's countrapositive
My dumbass
Forgot 1 thing
Wanna see the whole exercises?
It's in french tho
unreal bronze
sure
topaz sinewBOT
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rare gull
IDK how to derivate this $f(x)=\sqrt{x+\sqrt{x^2+1}}$
topaz sinewBOT
IDK how to derivate this $f(x)=\sqrt{x+\sqrt{x^2+1}}$
thorny flameBOT
Silicium
topaz sinewBOT
vivid stone
Use chain rule
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shut obsidian
topaz sinewBOT
shut obsidian
I want to ask if there is generally a systematic way to do these or if you just try to visualize it in your head
I.e. think of more complex figures, not a cuboid
topaz sinewBOT
@shut obsidian Has your question been resolved?
topaz sinewBOT
@shut obsidian Has your question been resolved?
topaz sinewBOT
@shut obsidian Has your question been resolved?
crystal goblet
I want to ask if there is generally a systematic way to do these or if you just ...
Keep increasing d till the plane goes from being under the cuboid to being above it?
maiden coyote
neon iron
you want your work to be checked/
maiden coyote
It’s wrong
neon iron
It’s wrong
yeah
maiden coyote
What did I do wrong
neon iron
should be 1/2 = c_1 = c_2
maiden coyote
Ahh
neon iron
What did I do wrong
probably messed up the second equation in your 2x2 system
it's c_1 + c_2 = 1 and c_1 = c_2
maiden coyote
-1=2c2
neon iron
yeah
maiden coyote
It’s suppose to be 1
topaz sinewBOT
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mystic siren
can i just give the zero matrix of 3x3 as a solution?
topaz sinewBOT
can i just give the zero matrix of 3x3 as a solution?
mystic siren
official solution
prisma mesa
seems like they specifically chose a non-zero matrix B
mystic siren
i mean i dont really get what hes saying too much, but i mean the zero matrix is very obvious
prisma mesa
0 matrix works
mystic siren
seems like they specifically chose a non-zero matrix B
but they didnt require it right?
prisma mesa
yeah, they didn't, probably by accident
mystic siren
i mean clearly they didnt
mystic siren
yeah, they didn't, probably by accident
can you help me understand his solution as well?
i know all the concepts, but not really understanding what he did
prisma mesa
i gtg for few mins...
mystic siren
i think he forgot to say there are NON-TRIVIAL a1,a2,a3 \in R
alright
i think i get it now, ty mate
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toxic otter
topaz sinewBOT
toxic otter
Am i going good for now?
smoky sparrow
yep, you have a good understanding of log rules!
toxic otter
yep, you have a good understanding of log rules!
Okay
smoky sparrow
lol it happens to all of us
smoky sparrow
okok
toxic otter
Wait if i want to put it
And i have y^2
I mean
Change the root to
^1/3
But if i have y^2
Should then i have
(x^1/3) * (y^2/3)
toxic otter
why would you want to do that
Cause how else do i do that
smoky sparrow
note that $\log (xy^2)^{1/2} = \frac{1}{2} \log (xy^2)$ by the way
toxic otter
I always was changing root in logs to
thorny flameBOT
higher's secret twin brother
toxic otter
**higher's secret twin brother**
No but i have root
smoky sparrow
yeah
smoky sparrow
you mean 1/2 but yes
smoky sparrow
Log (3sqrt(xy^2))
ohhhhh wait you mean cube root
smoky sparrow
yeah not $3 \sqrt{xy^2}$ but $\sqrt[3] {xy^2}$ got you
thorny flameBOT
higher's secret twin brother
toxic otter
Oh so at the hour of writing
smoky sparrow
next time just write log ((xy^2)^(1/3))
toxic otter
Its okay
Good to know
And I should have
1/3log x + 2/3log y
Wait no
7/3
Becayuse
2* 1/3
Is
6/3*1/3
Wait
Is that right
Its
6/3+6/3
No
Wait
Or is it
rustic silo
yea so 2/3 would be quialent
toxic otter
Wait
Guys
Why did
In my textbook
So there are answers right
Its is said that c) should be 15
But where the duck did they got 15
Oh wait
I have 15
Im
Nvm
Im just schizo
Guys
This means
Log(xy) * log(y) which is (log(x)+log(y)) * log(y)?
smoky sparrow
Log(xy) * log(y) which is (log(x)+log(y)) * log(y)?
yep
toxic otter
Ok thats the end of my exercise
smoky sparrow
I mean it depends on the brackets
smoky sparrow
there's a big difference between $(\log y)^{\log xy}$ and $\log(y^{\log xy})$
I think they mean the second one cause they want you to use the log exponent property
thorny flameBOT
higher's secret twin brother
smoky sparrow
but you should check if you copied the question correctly
toxic otter
Huh
smoky sparrow
**higher's secret twin brother**
they mean the 2nd one
topaz sinewBOT
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tropic notch
Help
tropic notch
discrete math problem with contradiction proof
inner crow
Since it's proof by contradiction, you need to say what will happen if n isn't prime
topaz sinewBOT
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inner crow
!occupied'
They're the owners of the channel
frail reef
!occupied'
This looks like his channel to me
inner crow
lmao dw
tropic notch
Since it's proof by contradiction, you need to say what will happen if n isn't p...
Right so, n would not be prime. So it would be composite
I end up solving by contrapositive
inner crow
Isn't that contradiction? Wouldn't contrapositive be saying that if n isn't prime then 2^n -1 isn't prime, then proving that, and hence the opposite is also true?
But we're saying that if n isn't prime then 2^n -1 is still prime, then attempting to show that, but in turn contradicting ourselves, hence proving it's true.
So I'm pretty sure proof by contradiction would be you trying to show that if 2^n -1 is prime, then n is not prime, I got the order wrong way around originally
tropic notch
Sorry for the long wait, I got caught up in something
With my course, they say that contradiction is the negation of the statement
so in this case ~(p->q)
which is then p ^ ~q
and then you are supposed to prove it by discovering some sort of contradiction that appears?
Sorry, I'm still not great at this part of proofs
inner crow
Okay, so, the original statement is that n is prime IF 2^n -1 is prime
Therefore, the contradiction of that would be that n is NOT prime IF 2^n -1 is prime
inner crow
So you're saying that 2^(not prime) -1 = prime
So 2^(not prime) = prime + 1
Prime + 1 is always not prime, with the exception of prime = 2, and I don't see how you can get 2^(not prime) -1 = 2, because then you're saying 2^(not prime) = 3, and that's not possible with integers, since I don't believe decimals count as primes?
inner crow
So therefore you're saying that 2^(not prime) = not prime
...which is correct, so I think I've somehow ended up with contrapositive
tropic notch
oh
hearty turret
So therefore you're saying that 2^(not prime) = not prime
...which is correct, s...
yeah this is a case of a question where really u're just proving the contrapositive
tropic notch
okay, it probably is
my instructor is using AI to generate our homework and class quizzes 😭
inner crow
So basically I was right originally 😭
inner crow
my instructor is using AI to generate our homework and class quizzes 😭
Is that, like, fr, or a joke
inner crow
Okay, your teacher should be fired, that is peak laziness
tropic notch
ikr
inner crow
The question made me sure I did it right originally, but then you said that it wasn't contradiction so I was like "huh?", your teacher is so confusing
tropic notch
yeahhhhhh 😭
inner crow
Tell your teacher to do his job! Ig that the question's sorted now though
tropic notch
mhm, thank you for your help!
hearty turret
i mean you can still do a proof by contradiction
it's just a "fake" proof by contradiction
(cus it doesn't need to be phrased as a proof by contradiction)
topaz sinewBOT
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vapid seal
how can we tell if it's right or left coordinate space?
topaz sinewBOT
how can we tell if it's right or left coordinate space?
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amber ember
Hello!
amber ember
I was wondering how I could solve for x in equations that look like this
Rationals I think they’re called
I’ve evidently finished some them, but for those ones it was clean, relatively simple values I received
I keep getting 2x^2+5x+5=0 and I don’t know how to extract X with that
It has been introduced to us in class, but I’m not sure if that’s what he wants us to do
And what do you mean by completing the square
Is that not what I have on the left?
three terms right
Ohhh
What does a square trionomial look like
Yeah for those series of questions I dont think we’re using quadratic formula
it was like basic algebra
amber ember
What does a square trionomial look like
would look something like 2x^2+4x+2?
thorny flameBOT
faiyrose
amber ember
This is the equation for square trinomials?
I can’t I’m not gonna see him until Monday 😭
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patent anvil
im so confused
topaz sinewBOT
im so confused
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white spindle
Is there a more convenient method for converting 0.1240234375 to hexadecimal?
The way I've been doing problems like these with a decimal is to take the integer 1240234375, convert it to base 16, then divide by A^(# of digits). For the problems with less digits after the decimal point, this method was fine. But for this number with many digits beyond, it is very tedious doing two decimal to hexadecimal conversions before doing a long division
topaz sinewBOT
Is there a more convenient method for converting 0.1240234375 to hexadecimal?
...
@white spindle Has your question been resolved?
white spindle
<@&286206848099549185>
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granite rune
Hey, im doing some analysis stuff and im working on this open-set proof problem and I think while I have the forward direction ($\Rightarrow$) correct, I am less sure I did the reverse side correct. I just am not as sure if I approached it correctly? Note we havent introduced topologies yet [note: this is for an indepndent study course where my work isnt graded, it matters most i understand what im doing]
topaz sinewBOT
Hey, im doing some analysis stuff and im working on this open-set proof problem ...
thorny flameBOT
something funny
granite rune
proof in latex ^ ?
topaz sinewBOT
@granite rune Has your question been resolved?
topaz sinewBOT
@granite rune Has your question been resolved?
granite rune
I think to clarify those containment steps, I think we are saying,
essentially we are saying that for any D_1 - p - neighborhood. If there is D_2 - p_1 - neighborhood that is a subset of the first, we can find some arbitrary subset of that first neighborhood such that it encapsulates the same points as the D_2 - p_1 neighborhood, essentially almost creating a mapping between the D_1 and D_2 metrics?
idk if that is a step to "formalizing" that second part of the proof?
topaz sinewBOT
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tight carbon
topaz sinewBOT
tight carbon
i know that independent events are p(E1 intersection E2)=p(E1).p(E2)
radiant torrent
this is a bit of a trick question, note that
tight carbon
Okay noted ..lol
tight carbon
What??
ruby cosmos
Okay noted ..lol
have they given any other information? (options?)
tight carbon
Yes options available
ruby cosmos
they havent provided probability of E1 and E2
tight carbon
tight carbon
they havent provided probability of E1 and E2
No
ruby cosmos
whats the answer given.
ruby cosmos
no like
ruby cosmos
okay one second
ruby cosmos
I guess you are on right track
have u learnt de morgan's theorem
ruby cosmos
But only in sets<@712806945580384376>
its also applicable in probability
because the event E1 and E2 can be considered two sets
you see E1* intersection E2* right in the second term
it is just (E1 union E2)*
tight carbon
Okay so?
ruby cosmos
we know for any set A
A intersection A* is a null set
so (E1 union E2) intersection (E1 union E2)* is a null set
that means this event does not exist or is improbable
hence i concluded probability is 0
topaz sinewBOT
@tight carbon Has your question been resolved?
tight carbon
hence i concluded probability is 0
I got no information
ruby cosmos
I got no information
?
ruby cosmos
yeah i have the same doubt as 0 is less than 1/4 equal to sign cannot hold
topaz sinewBOT
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tight carbon
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topaz sinewBOT
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young lagoon
Could someone please explain why dividing a polynomial of n degree by a polynimial of <n degree provides the equation of the oblique asymtote of the function
topaz sinewBOT
Could someone please explain why dividing a polynomial of n degree by a polynimi...
loud oasis
you can write the division as
numerator/denominator = quotient + remainder/denominator
since the remainder has a degree less than the deniminator, the (remainder/denominator) term will go to 0 as x goes to infinity, leaving only the quotient, which is the oblique asymptote
young lagoon
does the limit not apply to the quotiont?
So lets say I had
$$\lim_{x \to \infty} \left( x^2 - 2x + 6 - \frac{11}{x + 2} \right)$$
thorny flameBOT
Nyxzore
young lagoon
why the quotient?
finite storm
Because when u divide to get the quotient
U can eliminate it
Because it will not majorly contribute to the behavior of f(x) at very large x
The oblique asymptote just tell u which way the function will follow if it goes to infinity
Consider ur example for instance
young lagoon
oh, so as x gets larger the fraction becomes smaller and eventually insignificant to the output of the function
finite storm
Yes
topaz sinewBOT
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languid marsh
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languid marsh
Find the area of the triangle and write it as a square root expression in simplest fork
Form
I asked the teacher we'll use pythagorean theorem to find out the hypotenuse of one of the triangles and then we will do the area of triangle formula etc she said no? 😭
spring wolf
where are you having trouble?
yes because you don't need to. recall the formula for the area of a triangle
spring wolf
yeah
languid marsh
also is the thijg in the middle equal to the sides tho?
smoky sparrow
also is the thijg in the middle equal to the sides tho?
no
smoky sparrow
an isosceles triangle means that the two diagonal sides are the same length
the question didn't even say it was isosceles
languid marsh
So if they gave us side and base we would use pythagorean to find out height??
smoky sparrow
So if they gave us side and base we would use pythagorean to find out height??
yeah that's a good point, yes
languid marsh
okay thank u
smoky sparrow
you're onto something actually
if you're interested look up "cosine rule proof using Pythagoras"
npnp
languid marsh
you're onto something actually
if you're interested look up "cosine rule proof u...
i havent leadnt about cosine
learnt
smoky sparrow
oh wait, Heron's formula proof
languid marsh
hmm ill check it out
jolly agate
Say i have my inflection points, how do i decide the intervals where they are concave or convex?
topaz sinewBOT
Say i have my inflection points, how do i decide the intervals where they are co...
smoky sparrow
Say i have my inflection points, how do i decide the intervals where they are co...
concave up means $f''(x) > 0$
thorny flameBOT
higher's secret twin brother
smoky sparrow
similarly concave down means f''(x) < 0
jolly agate
I have my inflection points at x= 0, x= 3+(3)^(1/2) and x= 3-(3)^(1/2)
Well what do I do with the 0 then?
thorny flameBOT
jolly agate
I’m doing c)
smoky sparrow
that means you test the derivative at say, x = -1, x = 1, x = 3, and x = 5
because 3 - sqrt(3) < 3 < 3 + sqrt(3)
0 < 1 < 3 - sqrt(3) and so on
jolly agate
Ok gimme a sec u will send a pic
smoky sparrow
smoky sparrow
Do I also test my inflection points ?
no need
you already have the inflection points
so if you can find the gradients and draw the arrows like so
you know the shape of the graph
smoky sparrow
,rccw
thorny flameBOT
smoky sparrow
wait actually sorry, test the sign of the second derivative
also 3 - sqrt(3) is not in between -2 and -1
x = -1, x = 1, x = 3, and x = 5 works
smoky sparrow
yep, that's correct from what I did on Desmos
jolly agate
And this tells me that?
smoky sparrow
so concave, convex, concave, convex
jolly agate
No convex?
smoky sparrow
in other words, f(x) is concave down before x = 0
smoky sparrow
No convex?
oh, concave down = concave and concave up = convex
just different terminology
jolly agate
So (-inf, 0) Concave?
smoky sparrow
So (-inf, 0) Concave?
yes
jolly agate
Ahh okey
And from (0, 3-sqrt(3)) its concave?
In i want to write it in interval form
If*
smoky sparrow
And from (0, 3-sqrt(3)) its concave?
no, convex
smoky sparrow
so concave, convex, concave, convex
.
jolly agate
Because ut goes from - to +?
smoky sparrow
Because ut goes from - to +?
you can't say that
for example, consider y = x^4 which has f'(x) = 0 at x = 0
but x = 0 is not a point of inflection!
the concavity of x^4 is always convex
jolly agate
Hmm but what
smoky sparrow
cause you tested the concavity in that region
smoky sparrow
And from (0, 3-sqrt(3)) its concave?
and you found it's concave there
jolly agate
jolly agate
,rcct
smoky sparrow
,rccw
thorny flameBOT
jolly agate
Look at the 3) c
jolly agate
It says that aswell
jolly agate
How do i tell that !!
smoky sparrow
How do i tell that !!
you tested one value in each region!
you can just test the concavity at x = 1
jolly agate
Yes but say example at the inflection point 0
smoky sparrow
to know it for all values in (0, 3 - sqrt3)
smoky sparrow
Yes but say example at the inflection point 0
yeah so (-infinity, 0) is one of the regions
you tested x = -1
jolly agate
Yes
smoky sparrow
what's the issue then
jolly agate
I got tjat tre values Will be negative
But i rene vener in order to know that a point is convex or concave, the signs has to change
Remember *
smoky sparrow
But i rene vener in order to know that a point is convex or concave, the signs h...
the sign of the second derivative changes at the inflection points
so at x = 0 it changes sign
jolly agate
Really
smoky sparrow
yeah that's the definition of an inflection point
thorny flameBOT
smoky sparrow
you only need one line
jolly agate
Well I know it’s not formally correct but could you look at it like that?
smoky sparrow
Well I know it’s not formally correct but could you look at it like that?
oh wait, so if the second derivative is increasing
yeah then you're talking about the third derivative
that would be correct but we never use the third derivative to analyse a graph
smoky sparrow
well that's what you just did
smoky sparrow
from that information, the second row is the sign of 3rd derivative
that's correct yes
jolly agate
Ok well that was not what I ment to do
smoky sparrow
yeah so I found it weird that you did that
jolly agate
So I look at the -1 and 0 first
smoky sparrow
here just watch this
smoky sparrow
So I look at the -1 and 0 first
no, you look at x = -1
cause that represents the region (-infinity, 0)
jolly agate
Yes
But how does a (-) tekk me that it was concave or convex or whatever it was ??
Then I have to look at the inflection point right !
Which is 0
And then it tells me that it will switch sign from - to +, and then I know it’s a concave
smoky sparrow
But how does a (-) tekk me that it was concave or convex or whatever it was ??
if the second derivative is less than zero, it's concave
more than zero means convex
you don't have to look at the inflection points
jolly agate
ok so since second deriative with x = - , er knep its concave
We know
X= -1 we get that the y value is something negative, it’s concave
smoky sparrow
X= -1 we get that the y value is something negative, it’s concave
yes, so if you choose regions between the points of inflection
then if you know the second derivative's sign at one point
you know it for the whole region
(by definition, the point of inflection is where the second derivative changes)
jolly agate
So for (0, 3-sqrt(3)) we have a posetive value for y, we know it’s convex
And for (3-sqrt(3), 3+sqrt(3)) we have a negative value of y, we get that f’’(3) = - something. We know it’s concave
That’s how we think?
smoky sparrow
So for (0, 3-sqrt(3)) we have a posetive value for y, we know it’s convex
yes
smoky sparrow
And for (3-sqrt(3), 3+sqrt(3)) we have a negative value of y, we get that f’’(3)...
and yes
jolly agate
Awesome!!
Thank you I know how to look at it
Another question, are you good with geometric series?
smoky sparrow
please ask someone else
jolly agate
Hahaha okey sorry..
jolly agate
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urban barn
Of the people in a debating club, 42 percent are more than 55 years old and 68 percent are married.
topaz sinewBOT
Of the people in a debating club, 42 percent are more than 55 years old and 68 p...
urban barn
Does this mean that there are people in the debating club that are not 55 and not married?
my question is how does inclusion exclusion look on this
topaz sinewBOT
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thick oyster
2sintheta = 2sin(theta)cos(theta) but i cant substitute 1 in for cos(theta) because that makes the numerator 0
topaz sinewBOT
2sintheta = 2sin(theta)cos(theta) but i cant substitute 1 in for cos(theta) beca...
thick oyster
so what do i do with the numerator to not make it 0/0
restive inlet
consider double angle identity for numerator
thick oyster
1-sin^2(x)?
restive inlet
no
thick oyster
which one theres like 3
restive inlet
the one that'll result in having a single term in the numerator would be most efficient
restive inlet
no
thick oyster
wat
restive inlet
you should still have 0/0 up until cancelling the factor/component responsible
so something is off with your work
thick oyster
lim x->0 2(cos^2(x)) - 1 = 2(cos^2(0)) - 1 = 2(1^(2)) - 1 = 2(1) - 1 = 2 - 1 = 1
oak salmon
S
restive inlet
theta = double what?
thick oyster
double x
oak salmon
theta state
tame pine
flow state
oak salmon
💪
restive inlet
not the answer i'm looking for
tame pine
🥶
oak salmon
thick oyster
theta / 2?
restive inlet
If you aren't going to contribute anything meaningful please leave.
that sort of stuff is more suited for #chill
and apply the double angle identity using that
(and use the form that'll result in a single expression when simplifying)
don't worry about doing anything with limits at this stage
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burnt swift
Let $B = {(1, 0, 0), (1, 1, 0), (1, 1, 1)}$ and $B' = {(1, 0, 1), (0, 1, 1), (0, 0, 1)}$ be bases of $\mathbb{R}^3$.
Find $\mathbf{v}$ and $\mathbf{w} \in \mathbb{R}^3$ such that $\mathbf{v} + \mathbf{w}$ has coordinates $(1, 1, 2)$ in the basis $B$ and $2\mathbf{v} + 3\mathbf{w}$ has coordinates $(2, 1, 1)$ in the basis $B'$.
topaz sinewBOT
Let $B = \{(1, 0, 0), (1, 1, 0), (1, 1, 1)\}$ and $B' = \{(1, 0, 1), (0, 1, 1), ...
thorny flameBOT
938c2cc0dcc05f2b68c4287040cfcf71
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burnt swift
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neon iron
@burnt swift still need help ?
fallow heart
Well, you can find v+w and 2v + 3w, can't you?
topaz sinewBOT
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@burnt swift Has your question been resolved?
burnt swift
Well, you can find v+w and 2v + 3w, can't you?
how?
burnt swift
v+ w = (1,0,0) + (1,1,0) + 2(1,1,1)
fallow heart
Yep that's it
So v+w = (4, 3, 2)
And in the same way you can find the vector 2v + 3w
Which gives 2v + 3w = (2, 1, 4)
So now you have 2 equations in 2 unknowns. Therefore you can solve this system and find v and w
burnt swift
So now you have 2 equations in 2 unknowns. Therefore you can solve this system a...
how
burnt swift
topaz sinewBOT
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quiet kite
fallow heart
how
Subtract double of the first equation from the second equation, and you can find w
Now that you've found w, you can replace it in the first equation and find v as well
burnt swift
burnt swift
(10,8,2)=v
fallow heart
Therefore v = ||(10, 8, 2)||
fallow heart
(10,8,2)=v
Exactly
burnt swift
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strange kindle
Someone finally helped bro
torpid nimbus
Hey guys!
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onyx vector
A Stone is dropped from a very high location. It takes the Stone 2.00 seconds to fall the second half of the drop (in terms of distance). To the nearest tenth of a second, how long did it take the Stone to fall the entire distance? The stone fell for seconds.
I tried using displacement equation and some others, plugging in and stuff and can't find the right answer. Please help me, thanks!
viral fulcrum
do you know the formula: time = root ( 2y / g )?
wait
assuming no air resistance right?
onyx vector
I don’t think we’ve learned it yet (sorry for late reply)
onyx vector
assuming no air resistance right?
Yeah
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keen vessel
guys istg i clcualted htis right
topaz sinewBOT
guys istg i clcualted htis right
keen vessel
i used sum of squares (n(n+1)(2n+1)/6
wait i didnt read
i didnt know it was a greaatest integre funtion nvm umm
.close
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manic sparrow
in factorization case 7 sum or difference of perfect cubes, exponents get factorized or divided
topaz sinewBOT
in factorization case 7 sum or difference of perfect cubes, exponents get factor...
@manic sparrow Has your question been resolved?
sweet shard
in factorization case 7 sum or difference of perfect cubes, exponents get factor...
This isn't coherent
manic sparrow
what do you mean?
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teal dagger
Yo i'll help anybody
topaz sinewBOT
Yo i'll help anybody
smoky sinew
Uh
rapid wyvern
Yo i'll help anybody
usually what youd do is wait for somebody to post a question, go to their channel, see if you can help and if you can you help
smoky sinew
Just go into a help channel and help someone
opening a help channel asking for someone to help is diabolical
mortal steeple
!done
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mortal steeple
@teal dagger
plucky patio
Im confused and stuck. Where did that -6 come from?
topaz sinewBOT
Im confused and stuck. Where did that -6 come from?
woeful drift
they plugged in x=-2
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graceful leaf
sry its addition of vectors so kind of math
topaz sinewBOT
sry its addition of vectors so kind of math
graceful leaf
i got exam in 15 days so im starting from lecture 1
How come the Green vector Result one
Stops at the tip of B
neon iron
direction
neon iron
they are anti parallel vectors
graceful leaf
yes
neon iron
that is they are parallel but opposite in direction
you can think of this particular example as a number line, you walk till A and then start walking to B
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golden sky
how is it not 1
topaz sinewBOT
how is it not 1
teal meadow
-2.5 + 2.5 = 0
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cunning torrent
I'm struggling to understand how the space of linear maps (specifically L(R2,R2)) has a basis and how to go about understanding the way to construct bases for vector spaces of linear maps. The way I see it is that to define basis vectors for the space of linear maps doesn't make sense because my linear map could have dimension 2 or 1. So if I choose two basis vectors then for the case where I have a 1 -dimensional vector space this wouldnt work. My class is using Axler for context
topaz sinewBOT
I'm struggling to understand how the space of linear maps (specifically L(R2,R2)...
cunning torrent
Just moreso what would the basis of L(R2,R2) would be
loud oasis
it's easiest to use a matrix representation here. so if we choose a basis for R^2 then each linear map can be represented as a 2x2 matrix
cunning torrent
so rather than thinking of linearly independent vectors i should think about linearly indepedent 2x2 matrices?
loud oasis
yes. remember that dimension is a property of a vector space rather than a vector. so a linear map can have a certain dimension associated with its range or kernel, but when we consider it as part of the vector space of linear maps, it's just one vector and doesn't have a dimension on its own
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thorny sorrel
Find the rank of the following matrices, where k is a real number (The answer depends on the values of k.)
topaz sinewBOT
Find the rank of the following matrices, where k is a real number (The answer de...
thorny sorrel
i dont realy know how to start
i tried plugging in when k = 0, then put the matrix into rref and the rank was 3
but where im confused is, theres no way thats how to solve the problem. since technically wouldnt i have to check infinity numbers?
so how exactly do i solve this problem?
<@&286206848099549185>
topaz sinewBOT
@thorny sorrel Has your question been resolved?
pure estuary
You should first try putting the matrix in rref without plugging in anything for k
thorny sorrel
well how would i do that if i dont know the value of k?
pure estuary
You don't need to know its value to perform rref. You can just work with k like you would do in algebra. For example, the first step I would do is change row 3 into row 2 + row 3. This makes the matrix
\begin{matrix}
k & 1 & 2 \
1 & 1 & 1 \
0 & 2 & 2-k
\end{matrix}
Then I would change row 2 into (row 1) - k* (row 2), making the matrix
\begin{matrix}
k & 1 & 2 \
0 & 1-k & 2-k \
0 & 2 & 2-k
\end{matrix}
and so on
thorny flameBOT
pash
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
thorny sorrel
well i tried, and it seemed likethe k's cancelled out and im just left with the identity matrix
but i mightve done something wrong, this doesnt really seem right
pure estuary
Yah that doesn't sound right. Do you understand the first two row operations I described above?
thorny sorrel
let me try again
pure estuary
Okay I see why you got the identity matrix. But you can only get to that if k is not equal to 0
or k is not eqaul to 1
thorny sorrel
wait so does that mean its still wrong?
because then k is restricted to something
and i cant put it into rref, idk if im missing something or like what
im new at this
pure estuary
I think so. Might have to bring someone else in here - it's been a while since I touched this. What I ended up getting is the matrix
\begin{matrix}
2k & 0 & 4 \
0 & 1-k & 2-k \
0 & 2 & 0
\end{matrix}
The rank of the matrix is the number of non-zero columns. We see that if k = 0, then the first column is all zero and the last two are non-zero. Thus, when k = 0, the rank is 2. If k is not equal to 0, then all the columns are non zero, so when k is not equal to 0, the rank is 3. This covers all the cases for k.
thorny flameBOT
pash
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thorny sorrel
i thought the rank was the number of non zero rows, but other than that i think i understand the solution
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neon copper
.close
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rugged adder
hey, (x+4)^2/0.25+ (y-6)/4=1
is my answer correct? this is about ellipse :))
c = -4,6
f = -4,6 +- 1.936
neon iron
so if I'm not wrong, the question is
$$\frac{(x + 4)^2}{0.25} + \frac{y - 6}{4} = 1$$
thorny flameBOT
Edmund Cloudsley
rugged adder
Yesyesyes
neon iron
yes?
rugged adder
correct
neon iron
awesome
and what are the values of a, b, c and f you have mentioned?
do we need to represent this in the equation of an elipse?
rugged adder
a-0.5, b = 2, c=1.936
my foci is -4,6 +-1.936
rugged adder
do we need to represent this in the equation of an elipse?
nooo noo just need the values thank youu
rugged adder
Yes and a,b,c if mine are correct :'))
i also have to look for more but at the moment i wanna know if its correct or wrongg
neon iron
the foci is definitely correct
rugged adder
OKAYY thank you so much!
cloud sage
k == -1 || k == 2 && rank(A) = 2 else rank(A) = 3
neon iron
$$
\frac{(x + 4)^2}{0.25} + \frac{(y - 6)^2}{4} = 1
$$
$$
a = 0.5, \quad b = 2
$$
$$
\frac{(x + 4)^2}{(0.5)^2} + \frac{(y - 6)^2}{2^2} = 1
$$
$$
c = \sqrt{b^2 - a^2} = \sqrt{2^2 - (0.5)^2} = \sqrt{4 - 0.25} = \sqrt{3.75} \approx 1.936
$$
$$
\text{Foci:} \quad (-4, 6 \pm 1.936)
$$
$$
\text{Foci coordinates:} \quad (-4, 7.936) \quad \text{and} \quad (-4, 4.064)
$$
thorny flameBOT
Edmund Cloudsley
rugged adder
THANK U SM
rugged adder
why don't you respond?
Oh helloo :))
neon iron
the vertices and the covertices as well right?
rugged adder
the vertices and the covertices as well right?
Yesyes if thats okay
and also how to get them so i can do it myself for the other questions :))
topaz sinewBOT
$$
\frac{(x + 4)^2}{0.25} + \frac{(y - 6)^2}{4} = 1
$$
$$
a = 0.5, \quad b = 2
$...
As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.
cloud sage
what is this?
neon iron
As a helper, please do not give out answers that could be copied as a homework s...
noted my apologies
rugged adder
Ohhh i see i see u subtracted with A?
rugged adder
Oooooo
neon iron
and for the co-vertices, you have to add and subtract b from the y-coord
sorry if my explanation is a bit confusing 
but yeah I think that's how you do it
rugged adder
would vertices be: (-4, 8) and (-4,4)?
rugged adder
sorry if my explanation is a bit confusing <:cat_happycry:636407813144576010>
Nonono its good dwdw
rugged adder
Thank you so much ! :))
neon iron
also what grade math is this is you don't mind me asking?
rugged adder
also what grade math is this is you don't mind me asking?
im in eleventh gradee
rugged adder
yesyes thank you so much againnnn
neon iron
I've seen 2 courses drop circle equations and elipses
neon iron
yesyes thank you so much againnnn
my pleaseure goood luck
rugged adder
I've seen 2 courses drop circle equations and elipses
ouu im in stem T_T
rugged adder
the math in a levels is usually harder
hmm we dont have that (or im just not sure)
😭
i revently transferred schools so idrk their levels HAHAH
topaz sinewBOT
@rugged adder Has your question been resolved?
neon iron
sin ø = 1/4
I have sin(ø/2)
so cos ø = √15/4
and sin(ø/2) = √(4 - √15)/8
neon iron
How can I get it into any of those forms?
smoky sparrow
sin ø = 1/4
I have sin(ø/2)
so cos ø = √15/4
and sin(ø/2) = √(4 - √15)/8
use the formula cos(a - b) = cos a cos b + sin a sin b
then if x = arcsin 1/4
sin x = 1/4 = opposite/hypotenuse
so find the adjacent side of the right triangle you draw
neon iron
but why not cos(π/2 - x) = sin(x)
smoky sparrow
oh wait cos(1/2 arcsin 1/4) then you need the half angle formula arghhh
flint stump
you have cos^2() = (4 - √15)/8
So you have to somehow complete the square on numerator on RHS
(4 - √15)/8 = (5+3 - 2√15)/16
neon iron
mm why cos^2() = (4 - √15)/8
flint stump
but why not cos(π/2 - x) = sin(x)
coz this
and I stayed one step behind so I left the expression as sin^2(phi/2)
neon iron
yeah just sin^2(phi/2), well, ig that is irrelevant
flint stump
(4 - √15)/8 = (5+3 - 2√15)/16
Anyways, rewriting the value in this format is the key to select your correct answer from amongst the options
flint stump
yes
topaz sinewBOT
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plucky patio
I need help with the non-real solutions
topaz sinewBOT
I need help with the non-real solutions
night imp
I need help with the non-real solutions
(-4±√-36)/2
You have done it already, what's the doubt?
plucky patio
You have done it already, what's the doubt?
i put it in as 1i,-5i
it got marked wrong
Got tired of waiting, asked bing to check my work so I can see where I made my mistake at.
wait no mb i wrote that wrong
nvm.
bing came through for me.
shoulda have asked it rather than wait for a whole hour
.close
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idle helm
Good day, may be an odd question but well, looking for any resource whether it be a book, a video, etc. related to Numerical Methods with this specific kind of format/solving in terms of factorial polynomials, Forward, Central, and Backward difference, that contains numerous examples with solutions. For resources online appear to be in differing formats, and most I've seen do not appear to use the same methodology to arrive at the "final" answer (marked in those that are boxed)
topaz sinewBOT
Good day, may be an odd question but well, looking for **any** resource whether ...
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idle helm
<@&286206848099549185>
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torpid nimbus
Oh my gosh.... I'm now just looking through the chats send recently. What kind of math are you guys in? I'm only in pre-algebra.
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misty valley
topaz sinewBOT
misty valley
how to solve this limit using wondrful limit
unique quarry
try l'hopital
unique quarry
l'hopital
lim x->a (cos(x)/1)
u use l'hopital when u get 0/0 or +-infinity/+-infinity from the substitution
misty valley
but how to solve this using wonderful limits
unique quarry
sry i have no idea what wonderful limits are
topaz sinewBOT
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