That’s pi/6 or 30° that gives that value in 0-90° domain
#help-10
timid silo
long hedge
That’s pi/6 or 30° that gives that value in 0-90° domain
how did you find that
timid silo
You do have to memorise a few standard trig values 
I think those are one of the first things to learn after elementary definitions
long hedge
i got it
timid silo
This table
limber quartz
Yeah so @long hedge the hypotenuse should have been 2sqrt(3)
And if you divide through by that so the hypotenuse is 1, you see the trig ratio for a 30 degree angle
Or really, I see the triangle legs for it
sqrt(3)/2 > 1/2
:. theta = 30 degrees and not 60
obtuse pebbleBOT
@long hedge Has your question been resolved?
pure dragon
how do you call this symbol outside of a2 - b2 in english?
obtuse pebbleBOT
how do you call this symbol outside of a2 - b2 in english?
pure dragon
asking because im brazilian and it has a different name
tardy epoch
Absolute value
long hedge
wtf is this range
obtuse pebbleBOT
wtf is this range
dull rune
it's just typed poorly; [-7-pi/2, -7+pi/2]. i havent read it all over, but it seems plausible
tardy epoch
wtf is this range
The range of the inverse function is the domain of the function. You're given the domain in the problem
obtuse pebbleBOT
@long hedge Has your question been resolved?
next lantern
obtuse pebbleBOT
next lantern
could someone find the mistake in my algebra, ive looked over it so many times and im still wrong
warm canopy
check 2nd blue line
warm canopy
how
next lantern
no idea
warm canopy
no i mean how is it wrong, what have you done to decide its wrong
warm canopy
why
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
whole zephyr
Bezout’s identity
Why can’t I just say that since gcd(a,b)|a,b by definition, then it must divide a(x)+b(y)
obtuse pebbleBOT
Bezout’s identity
Why can’t I just say that since gcd(a,b)|a,b by definition, t...
warm canopy
That's just telling you that the gcd divides linear combinations of a and b, not that there are x and y such that ax + by = gcb(a,b)
whole zephyr
That's just telling you that the gcd divides linear combinations of a and b, not...
Ohh true
I’m reading a book that gave this statement
Would what I said work to show that?
warm canopy
Well no because now n doesn't necessarily divide a and b
whole zephyr
Well no because now n doesn't necessarily divide a and b
Huh?
warm canopy
?
warm canopy
n is bigger than the gcd, the greatest common divisor
warm canopy
What does n not dividing a and b show?
Well your whole argument was relying on the fact that gcb divides a and b
whole zephyr
Well your whole argument was relying on the fact that gcb divides a and b
Yeah that the gcd of a and b divides a and b
warm canopy
But n need not
whole zephyr
But n need not
Yeah I don’t think I need n to divide a and b for it to work?
I mean gcd(a,b) divides a and b
So if ax+by=n then we can factor it out on the left hand side and therefore it must divide n?
Conversely, if gcd(a,b)|n then n=gcd*N so we can have px+qy=N where gcd*p=a and gcd*q=b
That’s what I’m thinking though
tardy epoch
Yeah I don’t think I need n to divide a and b for it to work?
For what to work
whole zephyr
For what to work
By the fact the gcd divides both a and b, it must divide any linear combination of a and b
tardy epoch
Uh huh what are you trying to show though
whole zephyr
Uh huh what are you trying to show though
That the gcd must divide a linear combination of a and b
And if the gcd(a,b) divides a number n, then there exists a linear combination of a and b that represents n
haughty venture
obtuse pebbleBOT
haughty venture
just making sure this is what the problem is asking for
nocturne minnow
What do you think it's asking?
haughty venture
average rate of change
nocturne minnow
What does average rate of change, basically mean?
nocturne minnow
Yes that's what I was getting at
It's the slope
The question is asking, what is the most reasonable slope between 100 and 200
nocturne minnow
Yes
haughty venture
.close
obtuse pebbleBOT
haughty venture
.reopen
obtuse pebbleBOT
✅
haughty venture
how do you make a channel avaliable again
hybrid gull
.close
obtuse pebbleBOT
hybrid gull
That's how lol
haughty venture
ok
obtuse pebbleBOT
Available help channel!
naive fable
obtuse pebbleBOT
naive fable
sorry for asking so many questions, but how would i graph this?
bold bane
What does the question show for the vector component values?
Nevermind. To find the resultant vector, move either of the red vectors to the tail of the other red vector.
obtuse pebbleBOT
@naive fable Has your question been resolved?
obtuse pebbleBOT
Available help channel!
gloomy comet
gloomy comet
how come it closed down in the first place
brisk grove
.close
nocturne minnow
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
merry cave
civic socket
This all you need
merry cave
thanks
one more thing
u think u can give me one more fact abt a triangle
and a not statement a not statement is like saying, Im NOT a square sum like that
civic socket
google it
prime reef
lmao people that need help normally have some higher level problems
merry cave
thats crazy
prime reef
i cant find anything else
u can put anything really... i am not a square (as you said) but i ll think of smth ig
obtuse pebbleBOT
prime reef
I am not a pyramid , My angles dont add up to 180 if i am not on a flat surface
obtuse pebbleBOT
Available help channel!
haughty venture
Hello
haughty venture
so for this problem I found the equation which is y=(x+2)(x-1)
and from what ive seen none of the answers are correct
tardy epoch
Is F(x)=f(x)?
high lily
you aren't told that the function is continuous
tardy epoch
so for this problem I found the equation which is y=(x+2)(x-1)
How do you know this is the function
haughty venture
How do you know this is the function
assuming because its what the unit is about
high lily
you can't assume how it behaves between those given values
haughty venture
my homework isn't worded well
high lily
that's all you know for certain
tardy epoch
assuming because its what the unit is about
Don't make that assumption
high lily
you can't just add additional things on top of that
high lily
nothing else, yes
haughty venture
oh I see because of that B is correct\
wait actually
f(x) stays consistent from x=1 to x=0
@high lily
so would B be correct
high lily
no
high lily
none of the options seem right
haughty venture
thats what I was saying from the start
high lily
glossed over that, focussed more on addressing the issue of assuming things
haughty venture
glossed over that, focussed more on addressing the issue of assuming things
all good
I learned a good lesson
obtuse pebbleBOT
Available help channel!
scarlet swan
cos2xsin4x=cos5xsinx
obtuse pebbleBOT
cos2xsin4x=cos5xsinx
prime reef
for the LHS cos2x (2sin2xcos2x) = cos2x (2 (2sinxcosx) cos2x) = 2cos^2(2x)sinxcosx and the sines cancel
obtuse pebbleBOT
@scarlet swan Has your question been resolved?
scarlet swan
ohh i see thank you
stable apex
obtuse pebbleBOT
solar trellis
You should try
solar trellis
Yes
warm canopy
soft tiger
have you done integration by parts?
stable apex
have you done integration by parts?
yah
stable apex
soft tiger
k
stable apex
This has to be integration by substitution?
soft tiger
integration by parts
soft tiger
∫udu is not 1
stable apex
what is it then?
soft tiger
basically
errant gulch
reverse power rule?
power rule for integration
stable apex
stable apex
power rule for integration
ok great
soft tiger
yes
stable apex
ok got it
soft tiger
after you replace it, that's your answer. don't forget the + C though since it's an indefinite integral
timid silo
obtuse pebbleBOT
urban patrol
when the upper bound is less than the lower bound you need to flip them and multiply the integral by a negative
other than that it looks good
obtuse pebbleBOT
Available help channel!
novel crater
can someone explain how the hell did we get to the conclusion and what is "c" here
obtuse pebbleBOT
can someone explain how the hell did we get to the conclusion and what is "c" he...
novel crater
if anyone is wondering this about linear dependence of two vectors
kind hawk
they tell you what c is
obtuse pebbleBOT
@novel crater Has your question been resolved?
tulip steeple
what is the derivative of
obtuse pebbleBOT
what is the derivative of
tulip steeple
^ of this
Can you apply the quotent rule when a fraction is not fully simplified is the bigger question?
tulip steeple
what is the derivative of
since uses quotent
tulip steeple
but than can also be (x+5) if you simplify quadratic anc cancel both x-3
tulip steeple
factor x^2+2x-15
(x+5)(x-3)
urban patrol
so whats the derivative of x+5?
tulip steeple
x+5 is the derivative from simplifying quadratic and cancelling x-3
tulip steeple
from ^
timid silo
x + 5 is not the derivative
tulip steeple
what is the derivative of
but then i get ^ with quotent rule
tulip steeple
x + 5 is not the derivative
ohh, just 1 then
timid silo
Yes
tulip steeple
but thats scuffed as well?
tulip steeple
what is the derivative of
how cna i get this also
timid silo
,w derivative of (x^2 + 2x - 15)/(x-3)
warm shaleBOT
timid silo
you probably took the derivative wrong
tulip steeple
what is the derivative of
would you be able to check if i did somehting wrong here, using quotent rule
tulip steeple
what do you mean?
tulip steeple
what is the derivative of
im just wondering why/how i did this wrong
tulip steeple
since should work here?>
timid silo
please don't ghost ping
tulip steeple
sorry.
u badicly ditched me so nice but eh
figured it out with other peeps
.close
gleaming rose
obtuse pebbleBOT
polar fossil
so we have 1 impulse = 1/1000 second
and we want to figure out X impulses = 1 second?
gleaming rose
yes so we multiply it by 1 second?
so one second would be 1000/1000
and since this is only 1 thousandth of a second it can pulse 1000 times a second?
polar fossil
👍🏻
gleaming rose
thats right way of thinking of it?
warm shaleBOT
zephyrperegrine
gleaming rose
👍🏻
thank you
i dunno what happened to your message b4'
and also @static pasture thank you for putting that in aswell
static pasture
dw :D
polar fossil
i dunno what happened to your message b4'
I realized it was wrong so I deleted it
gleaming rose
I realized it was wrong so I deleted it
thank you regardless
tulip steeple
how do you do 'c'
obtuse pebbleBOT
how do you do 'c'
obtuse pebbleBOT
@tulip steeple Has your question been resolved?
pseudo swift
mainly, how did worked answer find that y=2
typo they mean y=-2 in both cases
tulip steeple
typo they mean y=-2 in both cases
would you just asuume if there is no gradient at x=0
thus it must be a linear horizontal line
and if i sub x=0 into normal f(x) pointis y=-2
thus y = -2 no gradient
pseudo swift
well yeah, if the gradient is 0, your tangent is a horizontal line
tulip steeple
and what about were its stationary
ik its when deriv = 0
but like
how do u get the answers
tulip steeple
just solve the equation
but like, i get to $x^4 - 2x^2 + 1 = 0$ idk what to do after
warm shaleBOT
vladthelad69
pseudo swift
(x^2-1)^2 = 0
hmm
you're sure that's the correct derivative ?
seems wrong to me
tulip steeple
you're sure that's the correct derivative ?
$12x(x^2-1)^2$?
warm shaleBOT
vladthelad69
tulip steeple
how do u use the w, bot
pseudo swift
alright alright
tulip steeple
i forgot
warm shaleBOT
tulip steeple
,w derivative y=2(x^2-1)^3
warm shaleBOT
pseudo swift
nah alright sure
tulip steeple
how would you solve for x then - correctly
pseudo swift
x(x^2-1)^2 = 0
you have a product of 2 numbers which equals 0
so either one of them is 0
either x = 0 or (x^2-1)^2 = 0
tulip steeple
yep
pseudo swift
what are all our solutions then ?
tulip steeple
-1, 0 1
pseudo swift
yea ^^
timid silo
i was curious and so looked up the derivative of $\Gamma(x)$ and found $\Gamma(x)\varphi^{(0)}(x)$ and am confused by what $\varphi^{(0)}$ represents? I thought it might be just a weird way of writing the totient function $\varphi(x)$ but (i think) $\varphi(0) = 0$ so..
obtuse pebbleBOT
i was curious and so looked up the derivative of $\Gamma(x)$ and found $\Gamma(x...
warm shaleBOT
cinnabasil
timid silo
what is it 
wolfram alpha (where i got the derivative from)'s representation:
and if it were $\varphi^0$, I would also be confused because why put it there at all, since $\varphi^0 = 1$ (presumably)
warm shaleBOT
cinnabasil
timid silo
It's not 1
It's probably the first order expansion of a function
Ohh I see - as in the taylor series of it or?
pseudo swift
timid silo
I.. did not see that
pseudo swift
some even weirder function then the gamma function your psi(x)
timid silo
Wait I'm now a little confused, since the definition of the digamma function is the logarithmic derivative of $\Gamma(x)$, which itself contains the digamma function
warm shaleBOT
cinnabasil
timid silo
https://proofwiki.org/wiki/Derivative_of_Gamma_Function <@456226577798135808>
Oh! Okay, that makes a lot more sense tyty
Right, $\Gamma(x)' = \ln(t)\Gamma(x)$
warm shaleBOT
kenfps
timid silo
(I think so)
That's what it looks like, yeah
Thanks for all the help!
no worries, hope it cleared something up
there's also this video that I haven't watched
timid silo
Right, $\Gamma(x)' = \ln(t)\Gamma(x)$
Wait, shouldn't it be $\Gamma'(x) = \int_{0}^{\infty} ln(t)\Gamma(x) \dd t$
warm shaleBOT
cinnabasil
timid silo
Since otherwise having t doesn't make much sense
timid silo
https://www.youtube.com/watch?v=cIRiyoPAmoY
Ah, I'll give it a watch! Ty!
timid silo
**cinnabasil**
Gamma itself is defined as an integral
so no
Oh, so where do we get the value for $t$ in $ln(t)$?
warm shaleBOT
cinnabasil
timid silo
hmm, could you be more specific?
Sure sure, given say $\Gamma'(3) = ln(t)\Gamma(3)$ right?
warm shaleBOT
cinnabasil
timid silo
Using your definition earlier
So,, how do we evaluate it since we don't know the value of $ln(t)$
warm shaleBOT
cinnabasil
timid silo
I actually think the definition I gave was false, because we define $\Gamma(z)$ to be $\int_{0}^\infty t^{z-1} e^{-t} \dd{t}$, right? Which means we are integrating with respect to $t$
warm shaleBOT
kenfps
timid silo
So the input depends on $z$ (the exponent of $t$)
warm shaleBOT
kenfps
timid silo
Or, wait, is it: $\Gamma(x) = \int_{0}^{\infty} t^{x-1}e^{-t} \dd t \implies \Gamma'(x) = \int_{0}^{\infty} t^{x-1} ln(t) e^{-t} \dd t$
Yeah, that's what I was writing (slowly)
use { } when taking exponents in latex
uhh
warm shaleBOT
cinnabasil
timid silo
i promise i'm good at latex i just forgot
Ah, I just found an answer to your initial question
Look into the polygamma function $\phi^{(0)}(z)$
warm shaleBOT
kenfps
timid silo
Indeed, $\Gamma ' (z) = \Gamma(z)\psi^{(0)}(z)$
warm shaleBOT
kenfps
timid silo
Ah okay! I'll have a look into it :>
That makes a lot more sense (that it's an actual function I mean)
Although I feel like this is a bit circular: it says $\psi^{(0)}(z) = \frac{d}{dz}ln\Gamma(z)$, and that requires the derivative of $\Gamma(z)$, which includes the polygamma function? Although, I guess you can use that other definition of the derivative of $\Gamma'(z)$
warm shaleBOT
cinnabasil
timid silo
I feel like I'm doing an XY problem here though since this is part of a bigger question which might be easier to solve some other way fdhsjkg
lethal sand
Well it indeed is circular. Though you can define digamma witth many integral interpretation as well
timid silo
Well it indeed is circular. Though you can define digamma witth many integral in...
Ah I see I see
lethal sand
I think there are also recurrence definition for it
Either way though, you are going to have to use some infinite series to compute it.
timid silo
I feel like I'm doing an XY problem here though since this is part of a bigger q...
Just to make it clear, I'm trying to solve: Find the value of $n$ that maximizes the function $f(n) = \frac{k^n}{n!}, k\in R^+, n \ge 0$
warm shaleBOT
cinnabasil
timid silo
Either way though, you are going to have to use some infinite series to compute ...
Yeah I imagine so
rocky goblet
**cinnabasil**
is n supposed to be an integer or a real number?
timid silo
**cinnabasil**
which led me to finding the derivative $f'(n) = \frac{k^n ln(n)}{n!} + k^n ln(n!) \cdot \frac{d}{dn}\left( \Gamma(n-1) \right)$
warm shaleBOT
cinnabasil
timid silo
is n supposed to be an integer or a real number?
real number as well
rocky goblet
using n for a real number is weird
timid silo
My bad, I made the question 
I just am used to seeing $n!$ so I used $n$ but I guess $f(x)$ makes more sense
warm shaleBOT
cinnabasil
lethal sand
You are misremembering. Gamma(x)=(x-1)!
timid silo
Ohh, so it should be $f'(n) = \frac{k^n ln(n)}{n!} + k^n ln(n!) \cdot \frac{d}{dn}\left( \Gamma(n+1) \right)$?
warm shaleBOT
cinnabasil
lethal sand
Yes
timid silo
And I guess I can factor out $k^n ln(n)$ but I'll do that later probably anyway
warm shaleBOT
cinnabasil
lethal sand
Hmm though I'm not sure if this road is just gonna get much worse. I'm trying to see if there's anything we can do to avoid this
Also, your derivative is wrong, can't believe i didn't notice that
timid silo
Wait it is?
lethal sand
You are having p(n)/q(n), the derivative of 1/q(n) wrt n is not ln(q(n))*q'(n)
That's integrating you are thinking of
timid silo
Oh you're right 
Soooo it should be
$f'(n) = \frac{k^n ln(k)}{n!} - \frac{k^n}{(n!)^2} \cdot \frac{d}{dn}\left( \Gamma(n+1) \right)$
lethal sand
Yes, that's it
timid silo
Gotcha gotcha
lethal sand
Ln(k) btw
warm shaleBOT
cinnabasil
timid silo
One day I will not mix up integration and differentiation but it's not today
So, $\frac{d}{dn}(\Gamma(n + 1)) = \int_{0}^{\infty} t^n ln(t) e^{-t} dt$ which I guess I can try evaluate?
warm shaleBOT
cinnabasil
timid silo
IBP time I guess 
lethal sand
Actually, using the digamma definition is better here
timid silo
Oh really?
lethal sand
Since after that, you can factor out gamma(n+1) and k^n
After you do common denominator of course
timid silo
Ahhh I see
sooooo:
$f'(n) = k^n \Gamma(n+1) \left( \frac{ln(k) - \psi^{(0)}(n+1)}{(n!)^2} \right)$
warm shaleBOT
cinnabasil
timid silo
I think
Now I gotta solve that equal to 0 
Although doesn’t that mean I need the inverse functions of $\Gamma(x)$ and $\psi^{(0)}(x)$ hmm
warm shaleBOT
cinnabasil
lethal sand
You dont have an inverse here, that's the problem I was talking about earlier. The road only leads to hell
timid silo
I've got $\psi^{(0)}(n+1) = ln k$ but then I'm stuck :<
warm shaleBOT
cinnabasil
lethal sand
A way to solve it is to just use a series approximation and solve it, or have a really beefy computer
warm shaleBOT
cinnabasil
timid silo
Or $-\zeta(1, z)$
warm shaleBOT
cinnabasil
timid silo
(I think, I'm just plugging m = 0 into these)
lethal sand
Don't really see a way to do tthis nicely here
timid silo
Yeah, me neither - Maybe it would've been easier with the integral derivative since there's no non-invertable functions in there, and the gamma function factors out and disappears when = 0 anyway
Not sure 
lethal sand
From what i can see, digamma is unbounded and increasing on R^(+) this implies there will always exist a root for our first derivative. And also, since digamma is increasing, that means ln(k)-digamma(x+1) will changes sign from positive to negative. Which implies f(x) is increasing then decreasing. So this just ensure us that we always have a maxima
There is no nice form to express that maxima though, but if given a particular k, there is a way to approximate it by using a graphing calculator, or some coded algorithm
timid silo
Yeah I see what you mean 
It might not really be possible to get it as a function of n in terms of k
I tried with the integral and the issue is that you then have an n! in there, which is the gamma function, which gives the same issues as with polygamma really
I think my whole question relied on the fact that n! had an inverse function, which I'm now finding out it doesn't
lethal sand
Well technically there exists one, but no one has ever found the need to name it yet
Or maybe im just finding out about that now
timid silo
I don't think there does - there's an approximation for it but from my quick google, no actual formula
lethal sand
Yes of course there is no way for us to express it in elementary functions, what im trying to say is, with correct restrictions, there will always be an inverse to a nicely defined functions
timid silo
Ohh right right, yeah I get what you mean
Well, even if there is no nice solution, still was good practice 
Ty for all the help :>
.close
frosty brook
on my reference sheet for maths it's say $y = e^{f(x)} -> \frac{dy}{dx} = f'(x)e^{f(x)}$ what has happened here
obtuse pebbleBOT
on my reference sheet for maths it's say $y = e^{f(x)} -> \frac{dy}{dx} = f'(x)e...
warm shaleBOT
chromium
timid silo
Do you know the chain rule?
timid silo
Oh my bad
frosty brook
$e^{(x^2)}$
warm shaleBOT
chromium
frosty brook
it results in some imaginary result?
timid silo
It shouldn't?
frosty brook
oh shit
timid silo
$f(x) = e^{(x^2)}, f'(x) = 2e^{(x^2)}x$, no?
frosty brook
what the fuck is wrong with me
warm shaleBOT
cinnabasil
timid silo
Ahhh
I guess it's similar to the gaussian integral, although I'm trying to figure this out myself
The solution to your question is that bprp has apparently done a video on it so: https://www.youtube.com/watch?v=zorcLisjRUI and https://www.youtube.com/watch?v=jkytxdedxhU&t=0s
slate kayak
obtuse pebbleBOT
slate kayak
z = 1/3 + 2x^2
is this right?
I don't understand how to structure the z from the given question
obtuse pebbleBOT
@slate kayak Has your question been resolved?
obtuse pebbleBOT
@slate kayak Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
timid silo
not a problem but a lack of understanding
obtuse pebbleBOT
not a problem but a lack of understanding
timid silo
i dont understand why the log of something is 1/x
for example
f(x) 7ln(x)
f'(x) 7/x
burnt viper
In this case, you can always look for the proof!
https://www.khanacademy.org/math/ap-calculus-ab/ab-differentiation-1-new/ab-2-7/a/proof-the-derivative-of-lnx-is-1x
little cedar
do u know the limit methos to find a derivative
little cedar
yeah lim h->0 f(a+h)-f(a)/h
timid silo
yeah
little cedar
try doing it by it you will also need to know the basic properties in limits
to find it
forest dawn
(a+b)^2
rich plume
what is your question?
rich plume
Okay so what is your question?
mystic jetty
Slight spelling mistake
warm shaleBOT
almas
fiery nacelle
Slight spelling mistake
Stop bullying
tardy epoch
Stop bullying
correcting* not bullying
fiery nacelle
correcting* not bullying
Hardcore bullying
forest dawn
(x+y-z)(x^2+y^2+z^2-xy+yz+zx)
mystic jetty
What
forest dawn
(x+y-z)(x^2+y^2+z^2-xy+yz+zx)
Find The product
mystic jetty
Ah
forest dawn
(x+y-z)(x^2+y^2+z^2-xy+yz+zx)
factorisation
fiery nacelle
Find The product
$x^3+y^3+z^3+3xyz$
warm shaleBOT
almas
fiery nacelle
Distribute and simplify
bold bane
What is the equation for the area of a circle?
pi r^2 ring a bell?
And how many degrees are in a circle?
How many degrees are in angle BAC?
timid silo
Ok
timid silo
Since cos^2(theta) + sin^2(theta) = 1
does that mean that given 3(cos^2(theta)-sin^2(theta))
we can re-arrange it and create 3(-1(sin^2(theta)+cos^2(theta))
and then substitute 1
for the identiity
and get -3
wooden cipher
_>
wooden cipher
does that mean that given 3(cos^2(theta)-sin^2(theta))
This step
wooden cipher
we can re-arrange it and create 3(-1(sin^2(theta)+cos^2(theta))
And this step
Are not equal
timid silo
if we have x-y is that not = -y + x
wooden cipher
Yes
soft tiger
cos^2(theta) - sin^2(theta) is not equal to cos^2(theta) + sin^2(theta)
wooden cipher
But -y+x is not -(y+x)
bronze adder
I need help
obtuse pebbleBOT
I need help
bronze adder
robust sleet
What ave you yrtied
bronze adder
What ave you yrtied
(2/9b^3)^2'
warm shaleBOT
methisalwaysright
trim portal
can you compute the square root?
obtuse pebbleBOT
bronze adder
.close
obtuse pebbleBOT
Available help channel!
timid silo
can i have some help on this question
obtuse pebbleBOT
can i have some help on this question
timid silo
.ask
obtuse pebbleBOT
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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
sorry im just confused
royal basin
what's your current progress
timid silo
timid silo
that top bit was what my teacher sent me for the first question
so i used that to lay out my working out
royal basin
ok well it is gonna be confusing for both you and whoever else has to read it
timid silo
they dont need to read it, its for online work
royal basin
AB = 49/tan(28°) is correct
royal basin
they dont need to read it, its for online work
so it is rough work that is ungraded and unread?
timid silo
im just too stuck and i cant ask my teacher for help because its late and over dues
due
royal basin
doesn't answer my question either way.
timid silo
im confused on the question
royal basin
ok not gonna get that from you any time soon
let's get back on topic
AB = 49/tan(28°) is correct
do you see how to proceed from here Y/N
royal basin
you know angle BAD and you know edge AB
timid silo
yeah
royal basin
and you know ABD is a right triangle as it is explicitly marked as such
whatever angle you might be viewing it at
it is going to happen that you view some shapes at weird angles. it's 3D.
if you want you can draw a copy of ABD face-on.
royal basin
you know angle BAD and you know edge AB
and you want edge AD
what trig ratio connects AB and AD
royal basin
you haven't done what exactly?
timid silo
trig ratios
royal basin
what are sin, cos and tan if not trig ratios
timid silo
i have no idea, im sorry im just dyslexic so im confused
royal basin
anyway
again
your angle is BAD
the sides you care about are AB and AD, one because it's known and the other because it's sought
which of sin, cos and tan would you use here to involve both of those
timid silo
cos
royal basin
great, so write that out in full
timid silo
would it be cos56
royal basin
in full!
timid silo
cos56=BD?
royal basin
no
cos(56°) is equal to a ratio of sides and not to one single side
cos(56°) = ??/??
fill in the question marks with your sides in the proper order
timid silo
ohh so cos56=AB/AD
royal basin
AB is already known!
it is AD that you don't know! i told you to rearrange that equation for it.
timid silo
oh yeah! 49/tan28
So i need to find out how to get AD
ill try but im not sure ill get it
timid silo
alright but quick question, do i lay it out like thisCos56=49/tan28/AD ?
royal basin
bad
a/b/c is ambiguous as (a/b)/c means a different thing from a/(b/c) and you are guaranteed to forget which way it was and confuse yourself
don't need to bother w the value of AB at all just keep it as AB
only replace it with 49/tan(28°) at the end
timid silo
okay im just confused on how to work AD out
royal basin
5/x = 3, how would you work x out
timid silo
devide it by 5?
royal basin
"it"?
timid silo
5/x
royal basin
divide only that by 5, while doing nothing on the right?
timid silo
is x 5/3
royal basin
why are you tampering exclusively with the left hand side of the equation while not doing the same thing on the right?
royal basin
ok well you're gonna have to revise basic algebra and the concept of applying the same operation to both sides
im off for zzz
timid silo
times the left side with three then times 15/x by x to move it on the othe side?
<@&286206848099549185> can anyone give me a hand with this question
.close
shell ether
I understand how to use the simple formula for calculating percentages is / of but I am a bit confused about a particular scenario.
I have a range of numbers which is -80 to 24 and I am trying to take a random value, say -23 and find what percentage it is between those two numbers.
If it isn't clear, I am wanting a formula that makes the lowest value -80 be 0 and the highest value 24 be 1.
Thank you!
obtuse pebbleBOT
I understand how to use the simple formula for calculating percentages `is / of`...
lone dirge
Hi, let's take a simpler example
Say numbers 1,2,3,4
What would you want to get ?
You said for 1, p(1) = 0, and for 4 you wanted p(4)=1
What about p(2) and p(3)
One option for numbers in the interval $[a,b]$ is to take $p(x)=\frac{x-a}{b-a}$
warm shaleBOT
cain0196
lone dirge
For our example it would give p(2)=1/3 and p(3) = 2/3
somber swift
hi
tardy epoch
.close
gleaming glade
I know this question is a little bit silly (also I'm not 100% sure this is the right spot to be asking this) but the conjugate of 2sqrt(9+h) is just 2sqrt(9+h) right?
obtuse pebbleBOT
I know this question is a little bit silly (also I'm not 100% sure this is the r...
polar fossil
$\overline{a + \sqrt{b}} = a - \sqrt{b}$
warm shaleBOT
Hayley
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
lucid marsh
Hi, I was just curious about how I need to solve this? is it just simplifying?
lucid marsh
.close
obtuse pebbleBOT
lucid marsh
.reopen
obtuse pebbleBOT
✅
obtuse pebbleBOT
@lucid marsh Has your question been resolved?
obtuse pebbleBOT
@lucid marsh Has your question been resolved?
obtuse pebbleBOT
@lucid marsh Has your question been resolved?
timid silo
question?
lucid marsh
question?
I wanted to know how do I solve it because there are a lot of variables going into the problem
timid silo
This?
timid silo
k let me look
vital patio
On a frictionless inclined plane, if an object moves at a constant speed v, does that mean the total work done is 0? How would that make sense when it is known that gravity does some work in this scenario?
obtuse pebbleBOT
On a frictionless inclined plane, if an object moves at a constant speed v, does...
shy summit
am stuck on this
teal turret
@shy summit #❓how-to-get-help
shy summit
oh sorry
so i basically have no idea how to begin, the only thing i noticedis that the 1/5 corresponds to the 5th root that the question wants. other than that im pretty lost. also probably know it has something to do with the (1+x)^n formula but no idea how its being applied
teal turret
Bruh get ur own channel lol
shy summit
OHHH okay my bad i was confused
shy summit
it says to pick a channel thats available tho
so this was under the available section
so i was confused
teal turret
Yea this channel was taken right before u put ur message
shy summit
ahh damn mb
teal turret
It was taken by the guy above u Jin Mu Won
shy summit
Set (1+x)^(1/5) = (31)^1/5 then solve for x
oh ok thats a clue
shy summit
It was taken by the guy above u Jin Mu Won
ahh so should i post on another available channel again?
teal turret
On a frictionless inclined plane, if an object moves at a constant speed v, does...
Is it moving up or down
teal turret
Ok well if it’s moving down at a constant speed, doesn’t that mean there’s a constant retardant force opposite the gravity that’s pulling the object down?
And if it’s going up at a constant speed, there’s a constant force that’s pulling the object up opposite the gravity that’s pulling it down
Bc if constant speed, then F_net = ma = 0
Hmmm or am I screwing something up
Is the normal force enough
And if it’s moving at a constant speed, won’t the net work done on the object equal 0?
Gravity does work, but there must be another force to counteract the gravity in order for the object to move at a constant speed with 0 accel
So the work done by gravity gets canceled out
At least I believe so
Perhaps some can give you a more definite answer mr mu won
obtuse pebbleBOT
@vital patio Has your question been resolved?
vital patio
Perhaps some can give you a more definite answer mr mu won
3 month break 😔
Thanks for your answer
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
scenic patrol
hello
glossy basalt
!15m
obtuse pebbleBOT
Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
prime reef
also use google/wolframalpha for trivial problems it s both quicker and doesnt take up our time
timid silo
2x + 7 is both + 9 and -9
proven zephyr
i am getting 1 and - 1
how are you getting those numbers?
obtuse pebbleBOT
Show your work, and if possible, explain where you are stuck.
kind hawk
also use google/wolframalpha for trivial problems it s both quicker and doesnt t...
their question is not what the solutions are, their question is why the solutions are what they are. WA does not help with that
proven zephyr
and-2x+7=9
this is where you went wrong
scenic patrol
their question is not what the solutions are, their question is why the solution...
yes
scenic patrol
so either 2x+7=9 or -(2x+7)=9
how did you get to second one
because if we assume x to be negative then why is the whole lhs gone negative?
scenic patrol
so either 2x+7=9 or -(2x+7)=9
the answers are correct with this one but why?
kind hawk
its not about x being positive or negative
its about the whole thing inside the abs to be positive or negative
either 2x+7=9 or 2x+7=-9
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
fervent tusk
obtuse pebbleBOT
fervent tusk
i found the min and max values for the mod
how do I find the values for z
btw: max = 3root(2)
min = root(2)
fervent tusk
geometrically
lethal sand
hmm, then I'm not quite sure how to figure out the z's at which the modulus attain the extremas geometrically. Probably can use some trigonometry.
But anyway, you could also just do this algebraically by just letting z=x+iy, for x,y in R
fervent tusk
ah that would give you a circle
which you could find the max and min points
for the z value right?
lethal sand
yes, you have a locus for all possible x, y. It then just turns into an optimisation problem.
I'll see if we can still do this geometrically though, There should be a way
lethal sand
yeah i know, just seeing if there is any other way
but if you have further question then you can close the channel
knotty wren
geometrically
How did you do it geometrically? If you found the points at which the maximum and minimum happen, then that's your z already.
knotty wren
But where is the geometry in that?
fervent tusk
well, i used the circle I guess
and the radii
anyways, the algebra solution sounds pretty good
knotty wren
What you're trying to optimize is the distance from a point (the origin) and the circumference of the circle.
You can easily see that the max/min distance between a point and a circle happens when the line segment is parallel to the diameter.
There's nothing much else to do.
obtuse pebbleBOT
@fervent tusk Has your question been resolved?
languid shuttle
Im just curious what does A\ mean?
obtuse pebbleBOT
Im just curious what does A\ mean?
civic zealot
A\B means "the set A without anything that is in B"
civic zealot
so A={1,2,3,4} and B = {2,4,6,8} then A\B = {1,3}
civic zealot
set minus
echo gazelle
obtuse pebbleBOT
echo gazelle
so i seperated ln(xy) to ln(x) + ln(y)
so for taking the derivative of that ik ln(x) is 1/x but for ln(y) idk how to do the derivative
robust sleet
you need to solve for y first
echo gazelle
ik i subtract ln(x) to have just ln(y) but idk how to do the derivative of ln(y)
robust sleet
whats your y=.. function
echo gazelle
wdym
robust sleet
what do u got for y
echo gazelle
idk yet
robust sleet
u dont know how to solve for y?
echo gazelle
i do but im stuck
robust sleet
show where
teal turret
Why not just do implicit diff?
echo gazelle
i made it ln(y) = 2x - ln(x)
i am but idk how to do the derivative of ln(y)
is it just 1/y?
teal turret
It’s same as ln(x), except every time u differentiate a term with a y, you have to multiply by dy/dx
teal turret
Yep differentiating ln(y) gives (1/y) * y’
echo gazelle
alr thank you
teal turret
U know how to go from there?
echo gazelle
yeah take the derivative of the right side so its y'=2- (1/x)
teal turret
$\frac 1y \cdot y’ = 2 - \frac 1x$
warm shaleBOT
northsteve
teal turret
How would u solve for y’
echo gazelle
ah okay so multiply right by y
teal turret
Yea mult both sides by y
echo gazelle
so its y' = 2y-y/x
teal turret
Ye
echo gazelle
cool ty
teal turret
Np
echo gazelle
.close
rough pecan
again because i was an idiot,
obtuse pebbleBOT
again because i was an idiot,
rough pecan
not sure how to approach this one
ive worked out the magnitude of OP as 5.92
jagged falcon
Do you know about dot product of vectors?
rough pecan
whats that
jagged falcon
How do you find the angle between two vectors?
rough pecan
pythagoras's theroeom no?
jagged falcon
dot product means scalar product (the one mentioned in part b)
Do you know scalar product?
jagged falcon
Yeah, so what's the scalar product of two perpendicular vectors?
rough pecan
its the products of the magnitude?
jagged falcon
are they the same thing
Yeah, dot product is another name
rough pecan
if the are perpendicular its zero
jagged falcon
its the products of the magnitude?
Not exactly
jagged falcon
if the are perpendicular its zero
But yes, that is correct
So if OP and OQ are perpendicular, their dot product should be zero
Can you work it out now?
rough pecan
so the magnitude of OP and OQ multiplied together it = zero
jagged falcon
Yes
jagged falcon
The scalar product of two vectors p and q is |p||q|cos(x), where x is the angle between the vectors
rough pecan
oh ok and if its perpendicular x is 90
jagged falcon
Yes, so cos x is 0
rough pecan
so one more question if you dont mind am i correct to use pythagoras to work the magnitude?
jagged falcon
Yeah, that works, if you're using it on pairs at a time.
rough pecan
Yeah, that works, if you're using it on pairs at a time.
is it possible that m=0? im stuck at 5.92 √(-m^2)=0
nevermind i think m does it equal 0 lol
jagged falcon
m should be 4
rough pecan
oh
jagged falcon
is it possible that m=0? im stuck at 5.92 √(-m^2)=0
How did you get only sqrt(m^2)? Can you show your calculations?
jagged falcon
so the magnitude of OP and OQ multiplied together it = zero
No