Do lots of them
#help-28
wide sundial
fiery valve
what are some good resources you reccomend
fiery valve
nah
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dire flame
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dire flame
anyone know where i went wrong?
keen spruce
did u do partial fractions right
dire flame
did u do partial fractions right
wait was i supposed to?
im confused why i would need that
dire flame
goodnight
junior willow
Can u circle the original question
dire flame
uh it was a physics problem but i can circle the original integral
junior willow
Ok
dire flame
thorny horizon
it looks correct upto here
$-k\alpha\left(\left[L-d\ln\left(L+\alpha\right)\right]-\left[0-\ln\left(\alpha\right)\right]\right)$
dire flame
hmm i think i accidentally had a negative i wasn't supposed to
glossy valveBOT
š¾ilverš¾oldier
junior willow
The d dissapeara
dire flame
i subbed it out of the integral
junior willow
it looks correct upto here
$-k\alpha\left(\left[L-d\ln\left(L+\alpha\right)\righ...
What all these left and rights for
junior willow
i subbed it out of the integral
Oh didnt see that
dire flame
left and rights?
dire flame
ohh
thorny horizon
What all these left and rights for
well i thought maybe the brackets might not look good coz theres a lot of nesting
but idt it matters a lot š
dire flame
wait i redid it without the negative one sec
i just remove a negative that was there since the brgining
the answer has ka(l-dln(1+l/d))
im going to cry
thorny horizon
you forget a d in front of the second ln
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torn jolt
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torn jolt
can someone see where i went wrong with this?
worthy tree
$V = \arctan(\sqrt{x-1})$
torn jolt
yep
glossy valveBOT
Mehdi_Moulati
torn jolt
okay thank u!
torn jolt
and multiply it with 1/x
yepp
worthy tree
okay thank u!
anytime
torn jolt
alright thanks
worthy tree
alright thanks
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@torn jolt Has your question been resolved?
dense edge
Who discovered the logarithm change of base formula?
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Who discovered the logarithm change of base formula?
dense edge
It seems rather amazing to me that log5(x-y) is equivalent ln(x-y) / ln(5)
Where ln can be any log base
log69, log6969, log696969, you name itā¦
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@dense edge Has your question been resolved?
viral jasper
Probably the person who described logs in the first place
@dense edge pretty easy to prove
naive bison
who works faster
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who works faster
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torn jolt
hello
torn jolt
i found this formula in the internet but have no idea how it work
it is a formula to calculate circumcenter coordinates of a triangle with given vertices's coordinates
can you help me?
sharp flame
You're better off not using a formula that you haven't been taught
Instead, recall the definition of the cirumcenter and try using that
torn jolt
You're better off not using a formula that you haven't been taught
can you explain to me where it come from?
sharp flame
I don't know I haven't seen that either
torn jolt
i tried to use the origin formula but this one, man, it is like magic
much faster to program
sharp flame
They probably assumed general points and applied the condition for the circumcenter
torn jolt
hmm ok let me try that
sharp flame
Are you writing a computer program or are you solving for the circumcenter in a math question?
torn jolt
i am writing a program
this do it in 3 lines of code while mine did in 300
i could use it but i really want to understand where it come from
sharp flame
Then I think you should look online for a better representation of the formula and perhaps a derivation
I understand why you'd use this for a computer program
torn jolt
And a proof apparently wonderful
can you share it ?
sharp flame
He just did^
torn jolt
sharp flame
Mad textbook
Do they encourage you to use this?
Because I'd rather just find it using the condition
torn jolt
Do they encourage you to use this?
No lol
but my origin formula do not use any sin cos
torn jolt
but my origin formula do not use any sin cos
Hm
i founded a lot of those in the internet
can sin cos formula be converted to non sin cos?
They are just ratios lol
Ratios of sides
So ofc yes
sin cos is not ratio
they are functions
sharp flame
Bro pulled out the big guns for trig
torn jolt
sin cos is not ratio
torn jolt
Feel free to use these results
sharp flame
they are functions
They are both
torn jolt
yeah i didnt learned math in english so im not sure
let me try to convert those into my origin see if it worked
Good luck
i mean there could be ratio but you need to be in a right triangle
that would be a lot of drawing
Ofc yes
That is why solution of triangles exist
Feel free to use them too
yeah i learned all of them. Just new to english math
thanks bro
Oh not a problem
ill put the formula here in case someone know it
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@torn jolt Has your question been resolved?
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@torn jolt Has your question been resolved?
torn jolt
Oh not a problem
I solved it. It was not sin cos thing tho
torn jolt
I solved it. It was not sin cos thing tho
Ooh i wonder how tho
It turned out he was just solve normal equations like I did
but after solving, he shorten the result so it look nice
and also look confuse too
torn jolt
Well you probably don't want to look at the details
Oh dont worry that is far less worse than me doing trigonometry
lethal field
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lethal field
can someone please explain how to solve this questions
it would be nice if someone can send a pic of the steps
unborn rover
76th term
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76th term
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.
lethal field
can u explain the steps?
rose rain
if you are typing out the whole answer right now
unborn rover
can u explain the steps?
first and last 7 terms need to be same to cut ...
middle one needs to be zero
rose rain
you better not
unborn rover
As a helper, please do not give out answers that could be copied as a homework s...
sorry, but i solved in mind..
sly frigate
I'll give you an example
If the average of a_1, a_2, a_3 is 0 (a_n is A.P), what would a_2 be?
unborn rover
I'll give you an example
If the average of a_1, a_2, a_3 is 0 (a_n is A.P), what...
there are 151 terms
sly frigate
sorry, but i solved in mind..
Should I ping mods
onyx glen
sorry, but i solved in mind..
good for you, but this server isn't for showing off your mental math skills.
unborn rover
Should I ping mods
why?
sly frigate
there are 151 terms
Like I don't know that
onyx glen
and nobody here is a telepath.
unborn rover
what happen ?
unborn rover
good for you, but this server isn't for showing off your mental math skills.
bruh i am not
onyx glen
you're kind of breaking the rules and going against how this server works, jyot.
#āhow-to-get-help, #rules and #info. read those.
unborn rover
okay so i joined few hrs ago
lemme check that
if you feel i was flexing then i was not...
sly frigate
I thought it was common sense to read the rules as soon as you join a server
onyx glen
I thought it was common sense to read the rules as soon as you join a server
nah reading is for chumps
lethal field
so like can someone please help
sly frigate
I'll give you an example
If the average of a_1, a_2, a_3 is 0 (a_n is A.P), what...
Can you do this?
lethal field
I'll give you an example
If the average of a_1, a_2, a_3 is 0 (a_n is A.P), what...
a_1+a_2+a_3/3
0/3=0
lethal field
yes
sly frigate
What would you get as the average of a-d, a, a+d
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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.
unborn rover
what?
sly frigate
Bruh
lethal field
What would you get as the average of a-d, a, a+d
(3a)/(3)
sly frigate
Which is..?
lethal field
a
lethal field
yeah
sly frigate
Meaning a_2=0
lethal field
yes
unborn rover
@sly frigate we cant send any image as explanation ?
sly frigate
How about a_1, a_2, a_3, a_4, a_5 ?
What term would be 0?
unborn rover
Not with full work
bruh i said ans in beginning so some said steps ,so i send steps
sly frigate
Steps with an answer 
unborn rover
bruh i am out ...
good luck
lethal field
How about a_1, a_2, a_3, a_4, a_5 ?
What term would be 0?
sorry i didnt understand
im getting (4a+9d)/(5)
atomic blade
bruh i said ans in beginning so some said steps ,so i send steps
You guide them not give the work freely
unborn rover
You guide them not give the work freely
ok.. š
sly frigate
sorry i didnt understand
in an arithmic term, the sum of n terms (when n is odd) is n*middle term
sly frigate
$a_1+a_2+a_3+a_4+a_5=5a_3$
glossy valveBOT
jay.
lethal field
@sly frigate i understood
sly frigate
$a_1+a_2+a_3=3a_2$
glossy valveBOT
jay.
sly frigate
so if the average of 151 terms is 0, what would the sum of 151 terms be?
lethal field
so if the average of 151 terms is 0, what would the sum of 151 terms be?
u can just do
(151+1)/(2)
and find the required term
right?
sly frigate
yep
sly frigate
lethal field
how do i close this channel?
sly frigate
.close
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lethal field
ty
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storm bone
How do I solve this equation:
I have tried depressing the cubic, but still is no closer.
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How do I solve this equation:
I have tried depressing the cubic, but still is n...
@storm bone Has your question been resolved?
storm bone
<@&286206848099549185>
storm bone
How do I solve this equation:
I have tried depressing the cubic, but still is n...
I want to solve this by hand without computer
undone kettle
Ig you should take sum of roots, product of roots and do some algebraic manipulations ig youāll get it
storm bone
Ig you should take sum of roots, product of roots and do some algebraic manipula...
How do I find the roots without solving it?
undone kettle
How do I find the roots without solving it?
What is the sum of the roots for a cubic?
storm bone
What is the sum of the roots for a cubic?
16-20+4+1
undone kettle
No no
Letās for now say alpha beta and gamma are the roots of this cubic.
The the sum of these roots is 20/16 = 5/4
And product of roots is -1/16
And the sum of products of roots taken 2 at a time is 4/16 = 1/4
undone kettle
This is applicable for quadratic equations too
undone kettle
Can you show me a site where I can read about this technique?
Iāll have to search wait
I have a book
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cursive void
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cursive void
I know we need to use this equation
But what would my bounds be for P(B) integration?
vocal coral
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vast fossil
Generally a quadratic expression $an^2 + bn + c$ reaches its maximum at $n = -b/2a$
glossy valveBOT
A Lonely Bean
vast fossil
So, in this case, the answer to a is supposed to be 120/4
Same as 30
To calculate the number to b, you need to plug in n = 30 and evaluate P(30)
vast fossil
Yup
vast fossil
Post your question in an available help channel
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@vocal coral Has your question been resolved?
median cedar
Where did the 1/2 come from
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Where did the 1/2 come from
median cedar
this is integral
robust slate
Differentiating $(2x-1)^4$ yields a factor of $2$ using the chain rule, so multiplying by $1/2$ cancels out this factor of $2$.
glossy valveBOT
Civil Service Pigeon
robust slate
but like, how am i supposed to know
You could integrate by substitution if you need to make it more explicit
median cedar
how do i know that i have to multiple by 1/2
median cedar
idk what is this
i will read online i think
is it ok to keep this channel open? i might have other questions
robust slate
Sure
median cedar
i don't get how's integral by substitution related, mine is not multiplied by anything
robust slate
$t=2x-1$?
glossy valveBOT
Civil Service Pigeon
robust slate
$dt=2 \boxed{dx} \implies dx=\frac{1}{2} dt$. Thereās your factor of $1/2$.
glossy valveBOT
Civil Service Pigeon
robust slate
Sure ā¦ I guess?
median cedar
is this correct?
robust slate
,w integrate (3x-4)^5
glossy valveBOT
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wanton mesa
can anyone explain how they went from the first line to the second line?
calm osprey
they start by expanding 1 to 4/4 then they bring the squareroot of three into the big squareroot
stiff wagon
These are the notes from my professorā¦just to clarify, Iād have to find antiderivative if the function right?
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These are the notes from my professorā¦just to clarify, Iād have to find antideri...
stiff wagon
Like, Iād find antiderivative of 3+2x ^2
quaint prawn
if you want to know the area, those integrals will give you it. But to find the exact value, yes you would have to find the antiderivatives and evaluate them
you would find the antiderivative of (3+2x-x^2)
and evaluate it from 2 to 3
and you would add to that the antiderivative of x^2-3-2x evaluated from 3 to 4
stiff wagon
you would find the antiderivative of (3+2x-x^2)
Why do we have 2 sets of bounds? Is it because the function becomes negative when evaluated from a certain set of bounds and positive when evaluated with another?
quaint prawn
Because in order to find the area between two curves, as you know we take the integral of the upper function minus the lower function. But for this case, do you see how the two functions swap which is higher and which is lower? so we have to setup two different integrals for each of the sides
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@stiff wagon Has your question been resolved?
rustic hamlet
Can anyone point me in the direction to get started on this? I've had about 5 false starts on the proof so far, and I'm getting really frustrated with myself.
rustic hamlet
I've tried multiplying out the RHS side, using the property of conjugate multiplication on the left hand side, and I'm just stuck now.
normal tree
idk maybe Cauchy-Schwarz?
nova basin
Isn't it asking to prove C.S. though ?
rustic hamlet
It's about the Cauchy-Schwarz theorem?
normal tree
yes you basically have to prove the cauchy-schwarz inequality for complex numbers
I guess if you're feeling particularly lazy, you can show that C^2 with the standard dot product is an inner product space
and then regurgitate the proof LOL
rustic hamlet
Ah - the Cauchy-Schwarz inequality....I see that now! I'll dig into that, I just found it in my notes. Thank you so much for pointing me in the right direction!
nova basin
and then regurgitate the proof LOL
The one that says <u+tv, u+tv> >= 0 for all t and rearrange that into a quadratic with negative discriminant ?
Asking because we didn't study hermitian spaces yet
rustic hamlet
I think it's the one that says the modulus of (z1w1 + z2w2)^2 less than or equal to the moduluses added together
normal tree
oh wait there's a little wrinkle where I think the standard inner product involves conjugation
since you need that for positive definiteness
nova basin
Yes
normal tree
but this should be okay because you can replace w with the conjugated stuff and it will be ok
nova basin
Hermitian spaces are just euclidian spaces with half of things being the conjugate of what they were
normal tree
I've forgotten what all of the spaces mean at this point
they all have these weird names
it better be complete and have an inner product or into the garbage it goes
nova basin
Euclidian -> real
Hermitian -> complex
And of finite dimension for both
Prehilbertian -> real with possibly infinite dimension
Hibert space -> complete prehilbertian space
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timber ginkgo
help
timber ginkgo
i donāt know what to do for this problem at all
atomic blade
Replace the x
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Please read #āhow-to-get-help
atomic blade
Yeah
timber ginkgo
so y=1
timber ginkgo
help
so if x is 2y we can do
2x+5(1)=9
get rid of the 5 so it becomes
2x=4
divide that by 2
x=2?
atomic blade
Yes
timber ginkgo
okay
short siren
Wait
timber ginkgo
i know
atomic blade
Yeah that is easier
timber ginkgo
i thought of that but i thought it may be wrong so i did it how i would usually
short siren
Well you can check your answer using the second equation
2(2) + 5(1) = 9
4 + 5 = 9
9 = 9
True
So your solution is correct
short siren
Sure
timber ginkgo
short siren
,rccw
glossy valveBOT
timber ginkgo
yes
short siren
What would you do with it?
short siren
Hmm
You'd want to use substitution and the question asks you to do that
Btw is this a multiple-choice or can it be written?
timber ginkgo
itās multiple choice
short siren
Okay
timber ginkgo
short siren
Yeppo you'd wanna use the second equation to make it part of the first
timber ginkgo
how would we do that though because theyāre not equal
timber ginkgo
yes is think so
short siren
How would the second equation look like when you isolate x?
short siren
What did we do with the x = 2y in the last example?
timber ginkgo
used it to substitute the x
short siren
Yep
short siren
You got the idea right but the substitution is wrong
timber ginkgo
hmm
short siren
Mhm
But I think that this step is unnecessary since they ask for the equation after substitution and the choices aren't simplified
timber ginkgo
But I think that this step is unnecessary since they ask for the equation after ...
true
thank you so much
short siren
proper arch
Did I do something wrong here?
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Did I do something wrong here?
proper arch
But for some reason the teacher marked that I did something wrong or Iām missing something
steel jewel
What the full question?
proper arch
Apparently, the orange arrows means I got something wrong
midnight dew
It looks right to me
steel jewel
Might be stupid but if sqrt(-1)=i shouldnāt it just be 2i not +or-2i
proper arch
Hmm, maybe
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tiny terrace
I know that the following statement is false, but I'm not sure why.
Let f be a real-valued function on the set of integers such that sum of all values of f is 1. Then f is the PMF of some random variable.
simple totem
can you think of a function of that type that couldnt be a PMF?
tiny terrace
oh, if there are negative values?
simple totem
yes
median wigeon
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median wigeon
is the equation correct?
100=8.3v + 1/2(v/4)(12.3)^2
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@median wigeon Has your question been resolved?
median wigeon
<@&286206848099549185>
gritty rose
is the equation correct?
100=8.3v + 1/2(v/4)(12.3)^2
!show
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is the equation correct?
100=8.3v + 1/2(v/4)(12.3)^2
Show your work, and if possible, explain where you are stuck.
@median wigeon Has your question been resolved?
median wigeon
I'm stuck as to how to find velocity via equation. Since there are 2 unknowns I don't know how to set up the equations.
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@median wigeon Has your question been resolved?
late rain
how can you tell how many no non real zeros there are
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how can you tell how many no non real zeros there are
midnight dew
it tells you its fourth degree
but you can only see 2 zeroes
but the fundamental theory of algebra says there must be 4 zeroes
late rain
and each time it crosses the x axis do i subtract or add a zero
and how do i see there is 2 zeros
sorry i didnt get taught this
midnight dew
oh woops
so you see how it does not cross the x axis
when polynomial of degree $a$ does not cross the x-axis, it has zero real zeroes and $a$ imaginary zeroes
glossy valveBOT
CrEpasPmkinPie
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when polynomial of degree $a$ does not cross the x-axis, it has zero real zeroes...
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.
midnight dew
i could give you the long answer instead
late rain
ok, so when it does cross the x axis and is a fourth degree polynomial each time it goes up or down do you add or subtract a zero
midnight dew
not quite
because its degree is four
theres a theorem that says it must have 4 zeroes
but it does not cross the x a xis
so they must all be imaginary
thick minnow
The main point is that - The graph of polynomial cuts x-axis at preciously the roots
ie $\alpha$ is a root if and only if $f(\alpha) = 0$
glossy valveBOT
numbpy
thick minnow
Now, since the graph of the polynomial doesn't cut the x-axis anywhere what does it mean?
glossy valveBOT
thick minnow
as you can see, the graph cuts x-axis at 2 and 3 which are exactly its roots
late rain
its not
torn jolt
than what?
thick minnow
oh yeah, it's all 3 roots are real
cause 2 roots are same
for example - consider (x-2)(x-3)(x-3)
,w plot (x-2)(x-3)(x-3)
glossy valveBOT
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hot herald
a lot of them are wrong
i can point out the issues with your functions
3 doesn't satisfy conditions a,c
5 doesn't satisfy condition c
etc, many satisfy one property but not all
severe spear
how comfortable are you with finding limits?
for instance, a limit of a constant is always itself
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ocean elk
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ocean elk
Is this answer right?
gritty rose
,w int pi/4 to pi/2 csc^2(x) cot^5(x) dx
glossy valveBOT
gritty rose
nice
zinc jungle
Need help pls and can you explain to me how to do this
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Need help pls and can you explain to me how to do this
@zinc jungle Has your question been resolved?
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@zinc jungle Has your question been resolved?
tulip beacon
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https://gyazo.com/476c3e555c251c8a9aa529c6769ca828
gritty rose
Word sucks
glossy valveBOT
~Martin
scenic wren
LaTeX is cool
lusty hearth
if in latex, you can try the bigint package
limber flicker
tulip beacon
i wish the teacher just gave us perms to copy and paste images of equations instead of writing them out
lusty hearth
if in latex, you can try the bigint package
I use it for all my electrodynamics problem sets when dealing with integrals with greens functions
sharp vine
Word sucks <:catthumbsup:614540188747563008>
Word is pro, you have to know how to use it š
also, some commands from LaTeX actually work in Word
so you don't have to search for basic symbols/operators
best version
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lunar ermine
This is the problem I am confused about
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This is the problem I am confused about
lunar ermine
This is what I have tried. When I googled $\int{\frac{1}{x^4e^{-2x}}}$ they were not able to give me an answer.
glossy valveBOT
MattTheAsian
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@lunar ermine Has your question been resolved?
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@lunar ermine Has your question been resolved?
quaint prawn
@lunar ermine still need help?
lunar ermine
Yeah. Good to see you again
quaint prawn
hello
lunar ermine
I thought I had it made, then I was told otherwise lol
lunar ermine
I know I forgot the negative on the e^-2 at the end, but it said it was still wrong
quaint prawn
Here is your issue
(I am not good with latex so this will take me a moment to type out, but bear with me)
lunar ermine
No problem
glossy valveBOT
AustinU
lunar ermine
I still see what you were saying
quaint prawn
for our equation
glossy valveBOT
AustinU
lunar ermine
Right
quaint prawn
what is p then?
glossy valveBOT
AustinU
lunar ermine
The instructor had me do this whole derivation of the equation so I thought P was the P of the y_1
Dang that makes a lot more sense.
Cheers.
quaint prawn
yeah np
lunar ermine
.close
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lunar ermine
P of the original, not P of the y_1
glossy valveBOT
AustinU
lunar ermine
Yee
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willow wasp
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willow wasp
I just got stuck at the part where is asks me to find the lengths, does it want me to find the length between the previous point and the final?
and how would i find the angle of the final vector when its just one line??
i thought of using trig for this but it doesnt look like a right angled triangle
willow wasp
I just got stuck at the part where is asks me to find the lengths, does it want ...
realised i can use the gradient formula, y2-y1/x2-x1
but i still could use an explanation for the angle part please i am totally lost at that part
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@willow wasp Has your question been resolved?
regal forge
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regal forge
stark hinge
What is the question? (it isn't clear in the image)
regal forge
What is the question? (it isn't clear in the image)
case:2
I'm not sure what I did weong
stark hinge
what that is pretty smart
Dude, I have no idea what you did wrong..
broken orchid
lolllll
regal forge
Dude, I have no idea what you did wrong..
that was correct lol
how did you do it?
!close
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dense edge
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rose rain
Well okay
Are you familiar with functions and inverses
The best way to think about this is logarithms undo exponentiation so
Normally what you'll do is what is the result of 10^x. Say that's y
Now logs basically are undoing that
So given a y, what x makes it such that 10^x = y
So if we raise y to something say p
y^p = 10^(xp) right?
So our result is xp
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lunar sky
1+1=?
dense goblet
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torn jolt
I forgot how to do it
oooh so
dense goblet
yes?
torn jolt
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torn jolt
nws
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trail kindle
Hey, on the last step of solving this separable differential equation (the line in the rectangle) am I right in putting +/- at the end? The video I was watching on it didnāt include it, but I thought this would be a correct step when undoing the square on the y. Thanks in advance
(Please ping me if answering)
lyric cargo
you should be, but it depends on your initial conditions @trail kindle
lyric cargo
then yes, it seems to be correct
trail kindle
alright tyvm
lyric cargo
np
trail kindle
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real glade
I have an equation A*f(x)^(5/2) = B/x^2
with A and B constants, and I need to find f(x) but I'm not sure where to start, any hints?
real glade
sorry for the messy notation I'm no mobile
kind jay
Taking log first I think
flat hornet
Take dx on the R.H.S and integrate it with B/xĀ² and on L.H.S integrate f^5/2 with df
kind jay
Is df/dx also on the exponent?
real glade
no
flat hornet
No its in multiplication
real glade
Take dx on the R.H.S and integrate it with B/xĀ² and on L.H.S integrate f^5/2 wit...
I'm allowed to integrate each side with different variables?
flat hornet
f with df and x with dx thats not different variables
crystal glen
Hello hello, Calculus work right now
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Hello hello, Calculus work right now
crystal glen
I know it's French but I can translate, just wanted to show the functions
I am stuck at c) find at which moment de object goes forward and backwards
I'm looking for intervals right?
When V is + or -?
glacial pasture
When V is + or -?
sounds about right
crystal glen
I found the derivative for that function
So do I just
Make a interval table
?
Wait hold on
Lemme try it
Out
Yep I got it
Ignore my question.
glacial pasture
brisk valve
ok guys
plush egret
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@brisk valve Has your question been resolved?
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@brisk valve Has your question been resolved?
velvet marlin
y=mx+b
It is indeed that. It just looks a bit different from what you might expect.
Simplify this and you'll get y = mx +b
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elfin lynx
could anyone help me out with this problem?
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could anyone help me out with this problem?
elfin lynx
after rearranging the equation I got sin(theta) = -cos(theta)
then after dividing both sides by cos(theta) I get
tan(theta) = -1
real relic
nice
then you can use the fact that tan(-theta) = -tan(theta)
(if you visualise the tan graph)
elfin lynx
then you can use the fact that tan(-theta) = -tan(theta)
I don't understand
don't I have to find the principle angle?
real relic
the graph is an odd function (if you know what that is)
elfin lynx
like this tan^-1(1)
real relic
don't I have to find the principle angle?
yes but you can find the negative angle and then add 180 degrees
because tan repeats every 180
elfin lynx
oh ok, but I was taught to just ignore the negative
real relic
oh that's not quite correct for tan
elfin lynx
so it is correct for sine and cosine but not tan?
real relic
it's only correct for cosine
elfin lynx
ok so do I acknowledge that it is negative before or after finding the principle angle?
for example tan(x) = -1.3
when I take the inverse I get 52.4 so do I use this as my reference on which quadrants to use or do I use -1.3?
real relic
sorry I'm not sure what you mean?
real relic
when I take the inverse I get 52.4 so do I use this as my reference on which qua...
the inverse of 1.3?
elfin lynx
so -1.3 is negative so I have to use the quadrants where tan is negative which are quadrants 2 and 4
whereas if it was positive 1.3 I would use the quadrants where tan is positive which are quadrants 1 and 3
real relic
okay I see what you mean
but you don't have to worry about that
you can take inverses of negatives
elfin lynx
oh
real relic
the principle angle is just the smallest one that's positive right?
elfin lynx
I thought it is the angle you get when you take the inverse
real relic
yeah it might be that then
your principle angle (the one shown on your calculator) is the solution between -180 and 180
if your principle angle is negative you want to add 180 because the question specifies 0 to 360
elfin lynx
so then the first solution I get by adding 180 to -52.4 is 127.6
real relic
that's fine
elfin lynx
I just want to know when to determine which quadrants to use, is it before or after taking the inverse?
real relic
either one
real relic
right exactly
elfin lynx
so Q2 and Q4
real relic
so you already know the quadrants
elfin lynx
although after I take the inverse I get positive 52.4 which is Q1 and Q3
which one do I use in order to determine the quadrants -1.3 or 52.4?
do you see what I mean?
real relic
although after I take the inverse I get positive 52.4 which is Q1 and Q3
the inverse of what though?
like explicitly arctan of what
elfin lynx
tan^-1(-1.3)
real relic
that isn't 52.4 I'm pretty sure
real relic
yes so you're making it positive
so you'll get a different value
be explicit when you taking the inverse
because the inverse of -1.3 is -52.4
elfin lynx
oh I see
so the negative just indicates that I use Q2 and Q4
in my calculations I can just use 52.4
real relic
yes
elfin lynx
alright thanks I get it
elfin lynx
yeah and 360 - 52.4 = 307.6
real relic
yeah
elfin lynx
okay so going back to the original question
real relic
yes
real relic
yes
elfin lynx
so my solutions would be theta = 180 - 45
elfin lynx
theta = 360 - 45
real relic
yes
real relic
No problem
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loud hull
Find derivative of y=(3x-5)^5 * (1-x^5)^4
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Find derivative of y=(3x-5)^5 * (1-x^5)^4
loud hull
[\frac{d}{dx}(3x-5)^5 (1-x^5)^4]
[((3x-5)^5 * 4(1-x^5)^3 * -1) + (5(3x-5)^4 * 3(1-x^5)^4]
[(3x-5) * -4(1-x^5)^3 + 15(3x-5)^4 (1-x^5)^4]
[(3x-5)^4(1-x^5)^3 [-4(3x-5)+15(1-x^5)]]
[(3x-5)^4(1-x^5)^3 [-15x^5-12x+35]]
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dopediscorduser
loud hull
What am I doing wrong? I don't see how they were able to factor a 5 out of the -4 and 15 coefficients?
fleet briar
i dont think youre doing the chain rule correctly
loud hull
why are you multiplying by -1
Because the x coefficient in (1-x^5) is -1
loud hull
i dont think youre doing the chain rule correctly
What am I dong incorrectly?
hot herald
there is no x term there
fleet briar
but, thats not how you differentiate 1 - x^5
hot herald
the coefficient of x^5 is -1,
the derivative of (1-x^5) is not -1
loud hull
The derivative of (1-x^5) would be (0 - 5x^4) or 5x^4?
fleet briar
The derivative of (1-x^5) would be (0 - 5x^4) or 5x^4?
first one
loud hull
[\frac{d}{dx}(3x-5)^5 (1-x^5)^4]
[((3x-5)^5 * 4(1-x^5)^3 * -5x^4) + (5(3x-5)^4 * 3(1-x^5)^4]
glossy valveBOT
dopediscorduser
loud hull
So would this be a correct first step in the chain rule then?
fleet briar
So would this be a correct first step in the chain rule then?
yes that checks out so far
torn jolt
hello, I have a quick question about semantics. There is this function in MATLAB called linspace it allows you to 'partition' a sequence of numbers into equally sized partitions.
Take linspace(1,10,5) this is similar to saying linspace(first,last,number of elements)
which will partition the set of numbers similar to
x --- x --- x --- x --- x
now compare that to a right endpoint riemann sum which would partition similar to
o --- x --- x --- x --- x --- x
instead
My question is, is there any specific name for the case that linspace has?
torn jolt
the length of a partition for the first case would be equivalent to [
p = \f{b-a}{n-1}
]
while the second it would be
[
p = \f{b-a}{n}
]
where $b$ and $a$ are the ending and starting points respectively. And $n$ is the number of elements
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@torn jolt Has your question been resolved?
thin flint
i don't understand your question
torn jolt
i don't understand your question
i just want to find out the name of the b-a/(n-1) partitioning similar to how the riemann sum case you can call it a right endpoint partitioning
well i guess its an odd question
thin flint
well when you take a riemann sum you can have a left side riemann sum and a right side
and middle
and some others i don't remember
so you could call it left side(d) partitioning
left side(d) or preferred linear partitioning
i don't think it specifically has a name
on wikipedia it gives it the name 'left rule'
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alpine chasm
Any reason why we choose the mean E(X) specifically? Why not use the variance V(X) instead.
fast peak
well if you know E(X^2) then you can just calculate V(X) and vice versa
and this way the expression is a bit simpler
oh whoops I slightly misread. well to get variance you need the mean anyway
alpine chasm
oh whoops I slightly misread. well to get variance you need the mean anyway
Oh okay also another question: If we have one unknown parameter than it is enough to use E(X). But can we not use E(X^2) and get the same estimation?
fast peak
why should that get the same result
but well it depends on whether you can express the moments from the parameters
alpine chasm
Because if the true population mean is approx equal to the sample mean. Then the square of true population mean should be approx equal to the sample mean squared
fast peak
no
the mean just tells you something about the center of the dataset, it doesnt tell you anything about how spread it is
imagine two datasets symmetric around 0, one with very big entries and one with very small ones
their mean is the same but the sum of squares are very different
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tepid valve
can anybody help? cant get derivative right using quotient rule
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maximo
simple totem
so v is just 1-6x
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brazen prairie
what is the value of a?
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what is the value of a?
sonic sparrow
the equations probably represent a line, and a curve
and the question says that the line is a tangent
so what u gotta do is simplify the given equations to the standard form so that u can identify which is which
brazen prairie
why its obviuos that is the curve and the otherone is the line
one is x to the power of two and the other is to the power of 1
i just dont understand how to find a
sonic sparrow
why its obviuos that is the curve and the otherone is the line
bcuz the first one has x^1; and is in the form of y=mx+c
and the second one has x^2, so ur gonna have to remove the sqrt by squaring
sonic sparrow
i just dont understand how to find a
youll have to use the given condition; the line is a tangent at the poi with the y acis
axis
sonic sparrow
hmm wait imma try
brazen prairie
i got a= - the sqrt of 2
oh i get it now
the incline of both functions are equal at the point of contact and because its on the y axis we know that x=0
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sonic sparrow
oh i got the answer
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oh i got the answer
sonic sparrow
theyll have the same intersection coordinate at x=0
so just sub that
and compare the equations
a=-1
sonic sparrow
i got a=-1
yup
brazen prairie
what do you mean the same intersection coordinate
can you send how you calculated it
a photo
sonic sparrow
oh yes alright
instead of substituting x=0 and zeroing a, just compare both equations when theyre equal
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fathom cairn
