thank you
#help-36
flint perch
tulip coyote
Anyways, it's "easy" to integrate something like these, though, hence the reason for the absolute value break-up
flint perch
oh yup
I see
my prof didnt specify but do you think they crossed this question out because the solutions are wrong?
if the solutions are not wrong and they crossed it out, prob means its not tested..
oh
I think the answers are wrong
tulip coyote
Mind you, an example along their lines shouldn't be hard to construct I guess 
flint perch
for this question, I got a diff answer
my diagonal matrix is different
I used i switched the -2 and 1
yea
cause it should match the order of the qi vectors in Q
tulip coyote
does the one you get work at least, though? 
final saddleBOT
@flint perch Has your question been resolved?
daring mantle
how do i know a physics problem involves torque unless its very obvious like a wrench?
final saddleBOT
how do i know a physics problem involves torque unless its very obvious like a w...
daring mantle
for instance, what in this problem is creating torque
robust mulch
well its about rotational motion
daring mantle
the entire unit im doing is based on rotational motion, but only about a third of the problems involve torque. So i was just wondering what specific parts of systems create torque
proud plover
ig the rotational inertia
daring mantle
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whole skiff
hey!
I have a math problem
two actually
would give nitro to anyone who can solve it
it's 3d integrals; calc III
ping me if ur down!
final saddleBOT
hey!
I have a math problem
two actually
would give nitro to anyone who can solve...
runic needle
hey!
I have a math problem
two actually
would give nitro to anyone who can solve...
sup?
whole skiff
yyyo
runic needle
im down
runic needle
$\int_M \dd{\omega} = \int_{\partial M} \omega$
soft zealotBOT
xd
whole skiff
0 0
-4 (-16/3)*pi\*(a^3)
was incorrect
runic needle
you're incorrect
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primal sierra
Solve $4 + 3\sqrt{2} \cdot \cos{(5x)} = 2\cos{(4x)} + 2\cos{(6x)} + 3\sqrt{2} \cdot \cos{(x)}$
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Solve $4 + 3\sqrt{2} \cdot \cos{(5x)} = 2\cos{(4x)} + 2\cos{(6x)} + 3\sqrt{2} \c...
soft zealotBOT
Dork9399
primal sierra
ofc i could just get the 6th degree polynomial
and try to grind out the roots
but
the chances of that working are relatively low
whole skiff
:(
primal sierra
scroll up
primal sierra
you cant reopen it
primal sierra
bcuz i opened this channel
whole skiff
.ban @primal sierra
whole skiff
.kick @primal sierra
strong herald
💀
whole skiff
.nuke @primal sierra's house
warm wraith
The hell is happening here
primal sierra
Solve $4 + 3\sqrt{2} \cdot \cos{(5x)} = 2\cos{(4x)} + 2\cos{(6x)} + 3\sqrt{2} \c...
this
warm wraith
First off what‘s up with redJ? Did he just come in your channel to troll?
primal sierra
his old channel closed
whole skiff
no my channel is missing
primal sierra
hes trying to reopen it
primal sierra
hey!
I have a math problem
two actually
would give nitro to anyone who can solve...
this is his old channel
warm wraith
If no messages get sent for a while the bot closes them yeah. You have to get another one
warm wraith
I‘m looking at it. And it looks like a mess lol hold on
Maybe you can use double angle identities and sum identities to bring everything into just plain cosines and sines
primal sierra
cos(6x) = -1 + 2 (9 cos^2(x) - 24 cos^4(x) + 16 cos^6(x))
which is 6th degree
eh idk
ill just bash it
who cares
.close
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craggy citrus
whats this method/type of equation called?
final saddleBOT
whats this method/type of equation called?
obtuse flame
it is a polynomial
obtuse flame
you can solve it as the question says, by factorisation
craggy citrus
how tho
obtuse flame
what do you mean how, what have you tried so far?
obtuse flame
first you need to find out the greatest common factor in the coefficients and variables
the coefficients here are 21, 15, and 21
can you tell me what the gcf of that is?
craggy citrus
3
obtuse flame
it is not a number
obtuse flame
this is the final answer
craggy citrus
this is the final answer
am lowkey still very confused upon this
gusty furnace
basically for the exponents of x 2 is the lowest so you can pull that out and for y, 3 is the lowest so you can pull that out. Then you already said 3 is gcf of the coefficients so that goes on the outside of the parenthesis.
then you see what number multiplied by 3 makes the original coefficient and that becomes your new coefficients
and by rules of exponents you would just see what number adds to get the original exponents for the new exponents in the equation (for the first one 3x^2y^3 * 7y^4= 21x^2y^7)
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unique jay
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unique jay
I know to find the limit you need to use l'hopital's rule
but I dont know how to find derivative of tan(pi/4 + t)
oh i see my mistake, derivative of tan(pi/4) is 0
tough basin
oh i see my mistake, derivative of tan(pi/4) is 0
tan (pi/4+t) = (1+tant)/(1-tant)
unique jay
tan (pi/4+t) = (1+tant)/(1-tant)
whered the = (1+tant)/(1-tant) come from
i saw that on symbolab but didnt understand that
tough basin
whered the = (1+tant)/(1-tant) come from
Using the formula of tan(A+B)
Equals to tanA+tanB/1-tanAtanB
Since tan pi/4 =1
So ans is 1+tant/1-tant
unique jay
but isnt the derivative not sec^2(pi/4+t)?
tough basin
It is
unique jay
i mean it worked
tough basin
Yes
unique jay
thnaks man
tough basin
Np
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daring mantle
why does the 2m^2 length of the rod from moment of inertia get tacked on to the bullets weight?
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why does the 2m^2 length of the rod from moment of inertia get tacked on to the ...
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daring mantle
<@&286206848099549185>
daring mantle
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What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
What way did you find
Hi
I doubt there’s a second answer
Just a second method for the same answer
Oh maybe actually
Yea ok
Yes the other one should be the same but replace 197 with 360-197
Should work
Cause they don’t tell you which way it’s 197
So it could be in the other direction
Ykwim
If there’s a second answer this is it
197?
360-197?
Idk what you mean
Rip
I’m gonna sleep sorry
140 am
Gl
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smoky egret
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smoky egret
for part 8 i got $F'(x)=\int_0^x{f(t)}{\dd t}+xf(x)$
soft zealotBOT
pirateking0723
cosmic bolt
for part 8 i got $F'(x)=\int_0^x{f(t)}{\dd t}+xf(x)$
sure yea sounds good
smoky egret
now for 9
using same way as part 8 I arrived at $\int_0^x{f(u)}{\dd u}=\int_0^u{f(t)}{\dd t}$
soft zealotBOT
pirateking0723
smoky egret
is this correct
i did that by expanding f(u)(x-u) then separating the integral
then the integral of xf(u) wrt u is already done in part 8
and for uf(u) it will be xf(x)
bc of FTC
i am differentiating LHS first
smoky egret
**pirateking0723**
this leaves me with the integral on LHS here
cosmic bolt
that also sounds good
how do you prove that the original functions before differentiation are the same then?
smoky egret
x,u and t are dummy variables
so i can just change u with x and t with u on the RHS
but this sounds a bit illogical
smoky egret
because i already have u on the LHS
but doesnt this have the slightest effect
so doesnt it restrict this change of the name of the variable from t to u for example
also there is something i am finding a problem with
smoky egret
if we differentiate the RHS here
smoky egret
**pirateking0723**
how will it become this
i mean $\frac{\dd}{\dd x}\int_0^x{g(t)}{\dd t}=g(x)$
soft zealotBOT
pirateking0723
smoky egret
here $g(t)=\int_0^u{f(t)}{\dd t}\implies \frac{\dd}{\dd x}\int_0^x{g(t)}{\dd t}=\int_0^u{f(x)}{\dd x}$ right
soft zealotBOT
pirateking0723
cosmic bolt
yea
smoky egret
It is the same as above ik bc t and x are just dummy variables
cosmic bolt
i think you're having the right ideas, i'm not sure if you need much input lol
ur doing it fam
smoky egret
but my question here is : having some variables on the RHS doesnt affect the way we can change variables on LHS ?
so in another way
if i change x with u on the RHS
tired plume
[\int_0^xf(u)(x-u)du=\int_0^xf(u)\int_u^x 1 dt du]
soft zealotBOT
Max
smoky egret
should i change x with u on LHS too
cosmic bolt
the dummy variables on each sides don't matter
the only variable which needs to have the same name left and right is x
because that one is not bound by an integral
tired plume
I'm not sure why they want you to differentiate both sides though?
If you show the derivatives are always the same you still need a fixed point
smoky egret
because that one is not bound by an integral
so i cant just change u with x on RHS for example ?
cosmic bolt
no if you change a dummy variable into a free variable you change the meaning
smoky egret
If you show the derivatives are always the same you still need a fixed point
to avoid the constant resulting from integrating again
tired plume
So when $x=0$ both sides the same.
Then show that their derivative is the same.
Or alternatively you just derive it using what I put above
cosmic bolt
If you show the derivatives are always the same you still need a fixed point
they're building up to something! in exercise 10
soft zealotBOT
Max
cosmic bolt
sure of course
smoky egret
they're building up to something! in exercise 10
actually this has a follow up question later with a generalization by replacing x-u with (x-u)^n later
cosmic bolt
but the textbook wants you to do another method and maybe that's also interesting
cosmic bolt
yeah i mean there's also multiple ways to do this, you can also do more explicit calculations
tired plume
when x=0 both integrals will be 0 am i right
Yes
If you want them to be the same, just because you differentiate them and they get the same result doesn't mean they are equal.
For instance
[f(x)=x]
[g(x)=x+2]
Have the same derivative but are different expressions
soft zealotBOT
Max
tired plume
So you evaluate the integral at a point, show they are the same.
Then differentiate and show they are the same.
tired plume
**Max**
Alternatively do the much easier method
Which extends easily for the induction
cosmic bolt
why are you hating so much on the instructions from the textbook
let them do the silly way it's cute
smoky egret
Alternatively do the much easier method
but after i differentiate both sides i am off a constant
so integrating again i can do what you said and plug x=0
this will give c=0
and both integrals will be equal no ?
cosmic bolt
exactly, you have it exactly right
tired plume
why are you hating so much on the instructions from the textbook
I'm not hating on it... I'm saying if they differentiate to show they are the same expression they haven't shown they are the same, which the textbook probably intends. Hence the missing gap is to create a fixed point at $x=0$ then the proof is concluded
soft zealotBOT
Max
tired plume
and both integrals will be equal no ?
Yes
smoky egret
so the textbook just gave the first step
i needed to pay attention to the resulting constant and plug x=0 to find that the constant is 0
is that what you were telling me
tired plume
Yea
smoky egret
**pirateking0723**
ok then how should i make these equal
tired plume
Because if two functions have the same derivative it doesn't mean they are equal functuons
smoky egret
sure i slipped on that fact
smoky egret
ok then how should i make these equal
i mean i cant change u with x on the RHS
tired plume
**pirateking0723**
I mean these are not equal in general
smoky egret
ah wait differentiating must give$\int_0^x{f(u)}{\dd u}=\int_0^u{f(x)}{\dd x}$
soft zealotBOT
pirateking0723
tired plume
[F(x)=\int_0^x xf(t)dt =x\int_0^x f(t)dt]
[F'(x)=\int_0^x f(t)dt +xf(x)]
soft zealotBOT
Max
soft zealotBOT
pirateking0723
smoky egret
so $\int_0^x{f(u)(x-u)}{\dd u}=\int_0^x{f(u)}{\dd u}$
soft zealotBOT
pirateking0723
tired plume
[F_1(x)=\int_0^x f(u)(x-u)du=\int_0^x f(u)(x)du-\int_0^x f(u)(u)du]
soft zealotBOT
Max
smoky egret
for part 8 i got $F'(x)=\int_0^x{f(t)}{\dd t}+xf(x)$
yes and from part 8 this was the answer for the first integral
tired plume
Yea
smoky egret
**pirateking0723**
so this will be the result
tired plume
Now differente the RHS
[H(x)=\int_0^x\left(\int_0^uf(t)dt\right)du=\int_0^x G(u)du,]
where $G(u)=\int_0^uf(t)dt$
soft zealotBOT
Max
tired plume
Hope that helps 🙂
tired plume
We are after H'(x)
soft zealotBOT
pirateking0723
smoky egret
i realized where my mistake was
when i differentiated this i replaced t with x not u with x
tired plume
Yea 🙂 everything else was really good
smoky egret
thats why
tired plume
**Max**
Good luck with the induction, I recommend doing it this way and then repeating the same using this and compare the efficiency.
Just make sure if you lay out your proof formally show they have the same constant of integration c or in more formal terms, the same fixed point.
smoky egret
about this , is it faster to expand (x-u)^2
tired plume
Nah use the chain rule
Hmm actually
Yeah use the chain rule, it's not super rigorous but it works
smoky egret
tbh i am not sure how to do that
but i will give it a shot
if necessary i will expand everything and do it that way after trying chain rule to check my answer
tysm if i need further help i will open a new channel
tysm both of you
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smoky egret
it seems that $\frac{\dd}{\dd x}\int_0^x f(u)(x-u)^2\dd u=2\frac{\dd}{\dd x}\int_0^x f(u)(x-u)\dd u=2\int_0^x f(u)\dd u$ am i right
soft zealotBOT
pirateking0723
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smoky egret
<@&286206848099549185>
tranquil pine
?
smoky egret
**pirateking0723**
is this correct or no
final saddleBOT
@smoky egret Has your question been resolved?
smoky egret
<@&286206848099549185>
wild wigeon
<@&286206848099549185>
tired plume
@smoky egret I have a better way than using the chain rule
Wait nvm
It doesn't work
smoky egret
i expanded and it worked too
tired plume
Expanding it will get there
However
When we do this inductively we can't just expand it
smoky egret
<@769420534537912331> I have a better way than using the chain rule
but when i am using the chain rule it worked if i took the derivative of (x-u)^2
smoky egret
Exactly but I don't know how to justify it lol
you mean why not take derivative of f too
tired plume
Hmmm
tired plume
you mean why not take derivative of f too
Yeah but we can't just differentiate it
And we can just bring x outside
Hmmm I mean it works
And it's how you need to do it because otherwise you can't do the induction
If you expand then the induction will be too tricky
If you don't expand u need to use the chain rule but its kinda sus that this works
smoky egret
yes but what do you mean by chain rule
because here we are differentiating wrt x
and we have the factor (x-u)^n
so using the chain rule will always give 1*n(x-u)^(n-1) right
so i mean the composite functions here do not new terms when differentiating
@tired plume
ah wait i maybe found out why this works
tired plume
I mean essentially if [F(x)=\int_0^xf(u)(x-u)^n du,]
then
[F'(x)=f(x)(x-x)^n+\int_0^xf(u)n(x-n)^{n-1}du\
=n\int_0^xf(u)(x-n)^{n-1}du]]
smoky egret
$\frac{\dd}{\dd x}\int_0^x (x-u)^2f(u)\dd u=\int_0^x \frac{\partial}{\partial x}(x-u)^2f(u)\dd u=\int_0^x 2(x-u)f(u)\dd u$
soft zealotBOT
pirateking0723
tired plume
Yeah but we can't bring the partial inside because of the x on the integral sign
smoky egret
ahh i figured out this may be the case
smoky egret
shouldnt the integral in F' have n^2 term instead of n
smoky egret
shouldnt the integral in F' have n^2 term instead of n
because you will be multiplying n from F by n from the derivative of (x-u)^n
tired plume
In the first equality we have used the fundamental theorem of calc and product rule
And chain rule
tired plume
because you will be multiplying n from F by n from the derivative of (x-u)^n
There is only one n coming down tho?
smoky egret
you probably didnt mean to include an n in F
soft zealotBOT
Max
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
smoky egret
sorry i shouldnt have to point out this because it is obvious that it was included by mistake
tired plume
**Max**
Compile Error! Click the <:errors:504266556054962196> reaction for more ...
I think that's what we are trying to do but why we can do that idk, it seems right lol
Perhaps ask in #real-complex-analysis
smoky egret
bro spivak is super
i learned calculus from stewart
bc i didnt know about spivak at the time
but now when i looked into some problems of spivak it is just much better than stewart
i mean the problems are on a whole another level from those in stewart
tired plume
Not sure what spivak and Stewart 😂
Yeah this is interesting but very inefficient
You can prove these identities much quicker using $(x-u)=\int_u^x 1dt$
soft zealotBOT
Max
smoky egret
Not sure what spivak and Stewart 😂
authors of 2 different calculus books
tired plume
Ah nice
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smoky egret
I will wait here too maybe someone has a way to prove that
smoky egret
<@&286206848099549185>
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smoky egret
@tired plume
$\lim_{h\to 0}\frac{\int_0^{x+h}f(u)(x+h-u)^2\dd u-\int_0^x f(u)(x-u)^2\dd u}{h}=\lim_{h\to 0}\frac{\int_0^x f(u)(x+h-u+x-u)(x+h-u-x+u)\dd u+\int_x^{x+h} f(u)(x+h-u)^2\dd u}{h}=2\int_0^x f(u)(x-u)+\lim_{h\to 0}\frac{\int_x^{x+h} f(u)(x+h-u)^2}{h}=2\int_0^x f(u)(x-u)\dd u+\lim_{h\to 0} f(c)(x-c)=2\int_0^x f(u)(x-u)\dd u, c\in [x,x+h]$ so $h\to 0\implies [x,x+h]\to {x}\implies c\to x\implies f(c)(x-c)\to 0$
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pirateking0723
smoky egret
sorry for the ping but I thought that maybe you would like to know the proof of why the thing you told me to do worked nicely
tired plume
Yeah but can you repeat it for general $n$
soft zealotBOT
Max
tired plume
It's good though, good job
smoky egret
**Max**
for general n it will probably be wild
but maybe induction will do the job easily
smoky egret
It's good though, good job
i got tons of help in #real-complex-analysis without that help i wouldnt have solved it
tired plume
That's good bro 🔥
smoky egret
tysm
now i will give the general case a shot
btw it turns out that there is something similar to what we did in differentiating for functions in general
it has to do with leibniz rule
smoky egret
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tranquil pine
can someone explain why 16 - t^2 = 31 - 8t??? <@&286206848099549185>
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neon fern
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neon fern
So am i supposed to be doing all to the power of 1 or power of 1/15
1/15 makes more sense to me and its decaying by .2 every hour or i do 1 and it decaying by 2.87 which is an 87% decay or 13%
nvm its just to the power of 1 right
and decreased 13% every hour
shell tide
to the power of t/h t being the total amount of time and h being the half life so 1/15 to the power of 1/15 would make sense
i think
neon fern
Yea but it says 8.2% every hour over a period of 15 hours
Not 8.2% in 15 hours
Thats why im confused
Maybe
Ehh no nvm
That would only make sense if it was 1.87 not 2
Any ideas anyone? lol
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thorny trench
Hi I just need help understanding this.
For example we have this figure, can the value of a variable in one pair of corresponding sides be the value of a variable in another pair of corresponding sides?
final saddleBOT
Hi I just need help understanding this.
For example we have this figure, can th...
@thorny trench Has your question been resolved?
thorny trench
<@&286206848099549185>
jolly ivy
I…
Dont think so
Unless its stated that OL=LE
If thats what ur asking
@thorny trench
digital steeple
Hi I just need help understanding this.
For example we have this figure, can th...
what should "the value of a variable in one paier of corresponding sides be the value of a variable in another pair ..." mean? there is only one variable, and typically has a variable the same value in all appearing terms.
If I understand the figure right then you have two definitions for LV. 5x-1 and 2x+8, so you can calculate x, and if you know x you can calculate all sides.
@thorny trench
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cerulean jackal
no idea where to start here
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cobalt eagle
lmo
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cerulean jackal
no idea where to even start here
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no idea where to even start here
zenith sierra
Do you know the formula for the area of a sector of a circle?
& the formula for arc length.
Wait, before that...
!status
final saddleBOT
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
1
cerulean jackal
Do you know the formula for the area of a sector of a circle?
not entirely sure, 360 * pir^2 and 2pir(theta/360)?
there's also radian formulae but idk those
cerulean jackal
Wait, before that...
you there?
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tranquil pine
How do I know weather to use Sine or cosine
rancid prairie
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light violet
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light violet
<@&286206848099549185>
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gentle adder
can someone please explain how the 1st equation becomes the 2nd equation. not sure what is happening with the integral. for complex fourier series of f(x) = x^2 over [-1,1]
final saddleBOT
can someone please explain how the 1st equation becomes the 2nd equation. not su...
flint kettle
can someone please explain how the 1st equation becomes the 2nd equation. not su...
Its integration by parts
They just skipped a ton of steps
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cloud zealot
For Q7, why cant the answer be A?
final saddleBOT
For Q7, why cant the answer be A?
cloud zealot
I thought continuity interval was equal to domain
flint kettle
Its defined in -1
If you see the full dot at -1
Its discontinuous but has a defined value at -1
If both the dots were blank you would have A
cloud zealot
ohh
So for domain, limit is not important to exist or not exist?
we only check if the function is defined at that point?
flint kettle
For domain it has to have a defined value
flint kettle
So for domain, limit is not important to exist or not exist?
Exactly
It can approach 10 when moving from the left
5 when moving from the right
cloud zealot
Thanks
cloud zealot
I understand now
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gleaming gazelle
Hey, I just need a bit of help understanding something
final saddleBOT
Hey, I just need a bit of help understanding something
gleaming gazelle
I'm learning the proof for the standard limits and I was following up until this part, I went to a not so great high school so I'm lost on how the negative cos^2x becomes sin^2x
it's the one part I can't follow
gleaming gazelle
oh thank you, I don't know why I didn't think to do that
topaz plaza
there are so many trig identities, make sure to remember them
gleaming gazelle
I saw that in the literature but it just didn't register with me to move it around like that
ivory ingot
oh thank you, I don't know why I didn't think to do that
Time to time, happens to everyone 
Maybe revisiting algebra would help as well
Because this is a form of: when you have a + b = c, b = c - a.
gleaming gazelle
Trig identities are where the weakness is, I think i'm gonna have to take some time to properly familiarize myself
thanks for that
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ancient pulsar
a
ancient pulsar
hello
how do i do part 1 of this problem ? is it probability universe minus the other probabilities ?
exercise 5
help is appretiated
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versed crater
it says it's an exam?
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jolly ivy
Was bro in school)
tropic flax
can some one help me in trignometry idk when to use the formulas
pearl veldt
vale reef
Is this right
final saddleBOT
Is this right
vale reef
What happens when t tends to infinity?
silver maple
So it will depend on how s is defined. Dp youknow what e^x and e^-x look like
silver maple
yep
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wooden lion
How do u disjoin cycles of permutations? Like this one
final saddleBOT
How do u disjoin cycles of permutations? Like this one
@wooden lion Has your question been resolved?
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rose patrol
Hey. I am struggling with solving this equation for $y$. Maybe I have made a mistake before when trying to solve this ODE. Maybe someone can help 🙂 (Document is in German, sorry)
final saddleBOT
Hey. I am struggling with solving this equation for $y$. Maybe I have made a mis...
soft zealotBOT
Zue
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rose patrol
<@&286206848099549185>
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azure hazel
natural log of both sides?
bitter monolith
Hey. I am struggling with solving this equation for $y$. Maybe I have made a mis...
rose patrol
So you solved for x instead of y. Is that allowed?
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errant quartz
im struggling with 20, i get how log rules work im just confused how the numbers can make 21/2
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im struggling with 20, i get how log rules work im just confused how the numbers...
primal sierra
what is $\log_4{\frac{1}{4}}$
errant quartz
wdym
errant quartz
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Dork9399
primal sierra
you dont need a calculator for this one ^
solar glade
Rewrite 21 as 7 * 3
primal sierra
we can rewrite 21/2 as 42/4
or 42 * 1/4
we can evaluate log_4 1/4
and we are given log_4 6 and log_4 7
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mighty sundial
Help,
mighty sundial
What is an inscribed angle?
rare hare
What is an inscribed angle?
its when two lines that arent the radius (known as chords) intersect in a circle to make an angle
let me show a image
mighty sundial
Can the inscribed angle be bigger then 180 degrees?
rare hare
no it cant
rare hare
Can it be exactly 180 degrees?
yup
mighty sundial
Now how would I find JK here?
royal veldt
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<@&286206848099549185>
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mellow flicker
Now how would I find JK here?
length of JK?
mellow flicker
no other data is given any other lengths, just angles?
mighty sundial
Yes,
dusty orbit
Hi Vmoo
mighty sundial
Hi!
old iris
What gradE?
10th
old iris
Please bro imma cry someone was about to help me left and never came back
dusty orbit
Tell him what it is
old iris
Like what subject, trigonometry,
Geometry
dusty orbit
What is it?
Geometry
mighty sundial
DM me, let's not use up this channel,
old iris
Plesse say yes before i have a sttroke
mighty sundial
Yes,
mighty sundial
Got it!
old iris
Bro one time i had a homework and someome dmed me answers thrns out they was wrong i failed i even asked for explanation
dusty orbit
Bro one time i had a homework and someome dmed me answers thrns out they was wro...
He started texting in ur server
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steep temple
can someone help me with part ii, the w has really thrown me off😭
final saddleBOT
can someone help me with part ii, the w has really thrown me off😭
honest carbon
!status
final saddleBOT
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
i don’t know where to begin
honest carbon
What is arg function?
honest carbon
Assume x +yi = w
steep temple
yeah
my teacher tries to denote the points as |z-(x-iy)| but wouldn’t know how to plot it
honest carbon
That's gonna be very difficult to plot, since z is a complex number.
steep temple
i can’t really visualise it
honest carbon
Don't
steep temple
okok
honest carbon
Use tan(arg(x+iy)) = y/x
steep temple
okok
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tawny wigeon
Hi, so for a research project I’m trying to estimate irrational number using a geometric montecarlo method. Eg the square to circle area to calculate pi. I’ve gone one step further and used ellipses whose mathematical equation is n(x^2) + y^2= 0 to calculate any square root as one of the radii will be equal to( sqrt n )/n. I’m now trying to use a similar ratio of areas to find e. But I can’t find any shape whose area contains e but I don’t need e to graph cause that would defeat the estimations purpose. Any ideas?
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Hi, so for a research project I’m trying to estimate irrational number using a g...
@tawny wigeon Has your question been resolved?
silver maple
Hi, so for a research project I’m trying to estimate irrational number using a g...
You can consider a taylor's series expansion of e^x. However you will need to cut off the terms of the taylor's series at some point
tawny wigeon
So I haven’t really done anything on Taylor series and I only have like a vague understanding of them. But ye I see the expanded form. But I technically need an area for my method and I’m not sure how I would do that
I can cut of the terms at like some number of iterations so I don’t think that will be too much of a problem
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restive copper
ii
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restive copper
<@&286206848099549185>
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restive copper
🫵
pine forge
<@&286206848099549185>
if one large trophy has volume 27 times the other then the dimensions are 3 times longer. If the height of the longer is 42cm the height of the shorter is 14cm
restive copper
if one large trophy has volume 27 times the other then the dimensions are 3 time...
ii
I've done i already
I'm confused on how the length 42cm is larger than the surface area
pine forge
cm and cm^2 are not the same
pine forge
side length is 3 times bigger therefore surface area is 9 times bigger
restive copper
side length is 3 times bigger therefore surface area is 9 times bigger
ohh got it thx
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tranquil pine
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tranquil pine
can i get a small hint on this
i've tried observing some patterns like a_ij = a_ji
i tried to get the (ax+by+cz) factors in common
but none of that seems to work
forest ember
I don't think there is a whole lot you can do to simplify this unless you know some of the entries are zero
tranquil pine
can i get a small hint on this
i've been given this question to help improve critical thinking, so i just want a small hint
forest ember
but you can probably find some shortcuts while you expand it
tranquil pine
I don't think there is a whole lot you can do to simplify this unless you know s...
this is all the info in the question
tranquil pine
but you can probably find some shortcuts while you expand it
i dont think i'm expected to expand it
think there is some clever way around it
please tag me
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tranquil pine
<@&286206848099549185>
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sick agate
Hello, I need some help with a quadratic function, I got the equation "y = (x - 4)² + 2" but I have to transform it to the form of the quadratic equation (ax²+bx+c), somehow I have to remove the parenthesis but I have no idea how I could do it, I would appreciate some help.
final saddleBOT
Hello, I need some help with a quadratic function, I got the equation "y = (x - ...
frail vigil
do you know the formulas for squared parenthesis? not sure what its called in english, something along the lines of binomical
sick agate
do you know the formulas for squared parenthesis? not sure what its called in en...
You speak Spanish?
frail vigil
nope, german
frail vigil
you know, $(a+b)^2=…$
soft zealotBOT
DerTheo
soft zealotBOT
DerTheo
sick agate
$(a+b)^2=a^2+2ab+b^2$\\
does that ring a bell?
Nope, sorry, I don't remember.
frail vigil
yeah and then you get to that
polar salmon
or use newton binominal
sick agate
You only have to distribute
So it's (x-4) (x-4)?
sick agate
(x-4)(x-4)+2
But that isn't ax²+bx+c.
solar glade
It is
The value of a, b and c can be negative or possitive
In this case, a and c will be possitive
And b negative
sick agate
Ohhh, so I can write (x-2²) (x-2) + 2?
solar glade
No
solar glade
(x-4)(x-4)+2
You have this
sick agate
You have this
Yes.
sick agate
Do you know how to do it?
I don't remember.
solar glade
FOIL
First term of the first parenthesis multiplied by the first term of the second + first of the first multiplied with second of the second + second first times first second + second first times second second
Dont forget to adjust the sign minus or plus according to the product
This might be more visual for you
sick agate
x×x + x×-4 + -4x + -4×-4?
I tried.
sick agate
How much is x times x?
x²
solar glade
Ok and x times -4?
sick agate
Ok and x times -4?
-4x
solar glade
And -4 times x
sick agate
And -4 times x
-4x too.
solar glade
And finally -4 times -4
sick agate
And finally -4 times -4
-8
solar glade
Not even close
sick agate
Sorry again.
solar glade
(x-4)(x-4)+2
The first is correct
sick agate
-8x
solar glade
Nice
Now you have x^2-8x+16 but
This is from the (x-4)^2 but remember the original question.
sick agate
This is from the (x-4)^2 but remember the original question.
it's + 2 too.
solar glade
So add it
solar glade
Why -2x
sick agate
I got confused with all the terms...
sick agate
Now you have it in the form ax^2^+bx+c
Oh yes.
solar glade
Where a = 1; b = -8 and c = 18
sick agate
Where a = 1; b = -8 and c = 18
Thank you very much.
Now I can finish my homework.
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river garden
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river garden
Yes I tried using sin but it wasn’t making sense
soft zealotBOT
w
river garden
Oh ok
river garden
Isn’t it one of them 15.90
wind glen
wdym
river garden
16.5*sin(39)=TU
I did this I got that answer
wind glen
I did this I got that answer
degrees?
wind glen
I did this I got that answer
ah
it interpreted it as radians
u need to specify its degrees
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trail river
how do I solve this
final saddleBOT
how do I solve this
formal trail
use properties of logarithms to get the right side into one logarithm. then you can set the inputs equal (since logarithm is one-to-one)
trail river
use properties of logarithms to get the right side into one logarithm. then you ...
this is the answer in the book but I don't understand how we got rid of the log
formal trail
log is a one-to-one function, so each output can be produced by only one input. in other words, if the outputs are equal, the inputs must be as well
equivalently, we can think of it as applying the inverse function (which is 10^x) to both sides of the equation
polar salmon
this is the answer in the book but I don't understand how we got rid of the log
log x= log y means x=y
normally
@formal trailright
pseudo knot
Watermelon cat
pseudo knot
this is the answer in the book but I don't understand how we got rid of the log
Do you know the properties they used
trail river
$\log\sqrt{xy} = (\frac{x+y}{5})$
soft zealotBOT
rynite
pseudo knot
Loga + logb is log(ab), and nloga is log(a^n)
polar salmon
**rynite**
where did u get that from
trail river
well this
polar salmon
$\log\sqrt{xy} = log (\frac{x+y}{5})$
soft zealotBOT
nrf
trail river
and I equaled it to the other side of the equation
wait
I forgot there's a log
on the right side
polar salmon
hahahahahhaha
trail river
lol I see now
trail river
yeah one sec let me solve
polar salmon
solve whar
polar salmon
it's literally in what you sent
trail river
$xy = \frac{(x + y)^2}{25}$
that's what I get when I square both sides though
wait
trail river
yeah right
polar salmon
what
trail river
fixed it
polar salmon
ye
trail river
wait still no
soft zealotBOT
rynite
polar salmon
there
trail river
like that
polar salmon
ye now u can solve easily
trail river
then $25xy = (x+y)^2$
polar salmon
25xy
soft zealotBOT
rynite
soft zealotBOT
rynite
trail river
take root of both sides
trail river
wym
polar salmon
develop (x+y)²
trail river
expand it you mean?
polar salmon
ye
soft zealotBOT
rynite
polar salmon
ye
trail river
then
trail river
yeah right
polar salmon
you need to sleep dawg
soft zealotBOT
rynite
polar salmon
you good
trail river
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sleek dragon
hello fr <@&286206848099549185> $\sum^{27}_{k=1}\floor{\sqrt{109\cdot k}}$ am I watching you
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hello fr <@&286206848099549185> $\sum^{27}_{k=1}\floor{\sqrt{109\cdot k}}$ am I ...
sleek dragon
fck
soft zealotBOT
Username3
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)
sleek dragon
how
would it be right if someone said like
$\sum^{4x-1}_{k=1}\floor{\sqrt{((4\cdot(4x-1)+1)\cdot k}}$
soft zealotBOT
Username3
soft zealotBOT
Username3
sleek dragon
is that $\lfloor 4 \cdot \sqrt{x-3} \rfloor + \lfloor 4 \cdot \sqrt{x-3} \sqrt{2} \rfloor + \ldots + \lfloor 4 \cdot \sqrt{x-3} \sqrt{(4x-1)} \rfloor$
soft zealotBOT
Username3
sleek dragon
**Username3**
so like that idk
<@&286206848099549185> if someone pings helpers 2 times does something happen
idk
fr
e I mea
fck
tranquil pine
**rynite**
type shiii
sleek dragon
shiii
same
that's why I needed help
like $\sum^{27}_{k=1}\floor{\sqrt{109\cdot k}}$
soft zealotBOT
Username3
obtuse flame
@sleek dragon what's the original problem
final saddleBOT
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sleek dragon
<@1117253392016883762> what's the original problem
the one above you
like $\sum^{27}_{k=1}\floor{\sqrt{109\cdot k}}$
soft zealotBOT
Username3
sleek dragon
@obtuse flame
flat zealot
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wise glacier
Hi, I really need with this any help is appreciated
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Hi, I really need with this any help is appreciated
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wise glacier
<@&286206848099549185>
tranquil pine
