#help-0
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Same thing?
Hehe-
If you dont mind me asking
How do they get 13.1 cos 67 & 13.1 sin 67

OH they got 13.1
because uh cosine rule
OB= 15^2 + 9^2 -2 15 9 cos60
But I dont know why they write since OB = 13.1
OA = 13.1
and AB = 13.1
Weird no?
Ty anyways :>
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Yo can anyone help me solve this : Find the real and imaginary parts of the following complex numbers:((Sqrt[3+i]) (-1+iSqrt[3]))/(1+i)^2
i have no clue why rez=0 and irez= sqrt[3]
expand and simplify
bro how
like
I put this in wolfram
and get thisL
:
expand denom and use conj
You can't put i inside sqrt
so this is an error in the qstiuon
or what
w8
Depends on ur country i guess
lol
what do u get?
The question is probably meant to be (sqrt(3)+i)*... but you can absolutely put i inside sqrt
u think?
But either way, u should multiply top and bottom by -2i to get rid of i in the denom
Well the answer would be way neater
couldnt u j square the whole thing to get rid of that sqrt anyways?
Then what? You add the sqrt back at the end?
When we do sqrt(a) we take in consideration positive square roots of a
What convention are u using for complex numbers?
Pretty sure there is no simplification for that sqrt part
i guess
sqrt(4)=2 and not -2 cause by convention sqrt is from R+ to R+
It's called the principal root https://en.wikipedia.org/wiki/Square_root#Principal_square_root_of_a_complex_number
Ask whoever gave you this problem if there may be a typo
Hmm ok, good to know ty
You need to solve this equation: a^2 =3+i in order to simplify the sqrt
so I put a^2 i instead of 3+i
I think you replied to the wrong message?
No i mean you should find the square roots of 3+i
That's going to be pretty difficult
yea
but this is 1st task on my list
so i think
You just need to solve a system of equations
this is not to be hard
mean to be hard
In polar form? With a 4th root and some exp and arctan in the mix?
No... wait I'll send it here
kk
the square roots of 3+i are the complex numbers x + iy that verify this system of equations
okay but why in my answers rez =1 and Irez=sqrt[3]
$x^2+y^2=|3+i| \ x^2-y^2=Real(3+i) \ 2xy=Im(3+i)$
Adam Chebil
What's rez??
Real
You said rez=0 earlier
sorry thats polish notation
I thought you had tried something and that was your solution
You have the actual answers?
i mean
yes
what z
rez=real part, irez=imaginary part
yes
Oh ok xd
XDDD
So u got 1 + i sqrt(3) ?
bro im stuck in this position
and not clue what to do
what can i do from this
in my answers rez =1 and Irez=sqrt[3]
Where do they come from?
from my teacher pdf xDDDD
So you're supposed to have them, right?
yes
Multiply top and bottom by conjugate of 2i which is -2i
$\frac{2i\sqrt{3+i} + 2\sqrt{9+3i}}{4}$
Adam Chebil
this is in the end
i put this in wolfram
and i got this:
so what can i do from this
like
I told you already, it's a typo
Yeah there's no way to simplify this unless u find square roots of 3+i
okaaaaaaay
thx guys
i close this
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29h
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tried getting help and realised i was doing it wrong, but i still dont understand
if two shapes are similar then the ratios of their sides are equal
do you know how to start the problem?
well i'd have guessed id do:
20/4 = 5
4x9 = 45
45x5
and get the answer
225
is that wrong? if so are you aware why im doing it wrong 😭
I don't believe this is right, try being more thorough and I think you'll notice why this is wrong
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Proof the inequality for a, b \in |R for a >b >=0
And for which a and b is the inequality equal?
@regal lake Has your question been resolved?
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@regal lake Has your question been resolved?
<@&286206848099549185>
@regal lake Has your question been resolved?
@regal lake Has your question been resolved?
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i need help
7 and 9
try putting 3 into the number of real zeros box
8*
and see if its right
its wrong
still
okay 1 sec
i know you have to get the possible roots and then use synthetic division for it but it didn't work and the teacher never finished the question in class
try 4
and then try 5
see if either is right
there wrong
istg
ik man i hate this shit i don't get it
ik how to get the positive and negative roots
i put it in desmos and there was no roots so i tried to put 0
still wrong
try just putting 1
still wrong
aright man thanks for trying tho
@last dagger i'd say repost the problem and ping helpers
ok thanks
@alpine sable actually nvm i got some people to help me figure it out
thank you for the help tho and 3,1 did work i thought it didn't because i could have sworn i put it in before and it came back as wrong
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hello
give me 1 second im takinga picture of my question
for question 1
i just want to know if my setup
is right
i did cylendrical form so i have the first interrgal from 0 to 2pie , raduis from 1 to 2 and z from 1 to 3
is that right ?
<@&286206848099549185>
Thank you so much
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can someone confirm my answer?
@wide marlin Has your question been resolved?
<@&286206848099549185>
didnt you already do this shit
Yea but I’m not sure if it’s what you said
i said a because it matches the normal line at x=0
Ok can you help me check another one then?
sure
hm lets see
im not great at derivatives but that looks correct to me
if its not d then idk what it would be
^
<@&286206848099549185>
I'll check this for ya, seems like you just apply the quotient rule to find the derivative, then compare your computed derivative to those choices
ok please check both thanks
i think D is correct for the second question, here's my work if you want to read it over
i'll check the first
my bad, took me a little longer than i expected to write up
was trying to be thorough so i could check
haven't done calc by hand in a little while so it was nice to brush up on this
wait hold on i miswrote
ok
are you sure this is right
where do you disagree
i can also try to clarify a step if you'd like
idk
Rino
hi
no
I need help
Bruh
I cannot open my own help room. And I have a question that need solving
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oh and btw this is not from an assignment or quiz/test/exam, it's from:
@analog nymph Has your question been resolved?
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Can you someone please explain to me how I can manipulate the left side to equal the right side?
I got 1 + cos(2t) = to 2cos^2(2t)
I did get sin(2t) - cos(t) = to 2sin(t)cos(t)-cos(t)
So my equation looks something like this, 2cos^2(2t) / 2sin(t)cos(t)-cos(t)
What further can I do? I am very confused. You do not need to solve the question for me, but give me a direction to go. Thank you guys!
expanding cos2t and sin2t might help
i expanded 1 + cos(2t) = to 2cos^2(2t)
and i expanded sin(2t) = 2sin(t)cos(t)
so divide it out of 2cos^2(t)?
yes
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Honestly, I had to look up the steps to this problem in Symbolab, but since I don't have the paid version, I cant see the jump here. I must be blanking or something, but I have no idea which Log Rule turns one into the other. Can anyone explain how it gets from the first to the second?
what us log2(4)
idk, i have to verifiy number probably
ye
5-2 is 3- 3/3 is 1 though, no?
yep
and if im just simplifying that down, how does it remove the log from the other side
well log of what makes 1
log2(x) = 1
so that means x-1 = 2
hmm
this was just an example
ohh
ohh i see
it confused the shit out of me when it said "log rule" cause i was expecting it to use some fancy rule instead of like. . . just simplifying it down normally 😭
hahahhaha, nah its just that simple
i was overthinking it!
yeah my brain is just not functioning. im on hour 14 at school rn. got here at 9:30am, and im sitting in an empty campus at bout midnight now trying to get hw done before i go home and get distracted, and my brain is just not wanting to cooperate
why would you stay so late though?
cause i can only get work done at school
as soon as i go home, i have either a comfy bed or my pc to instantly distract me
and i wont ever be able to stay focused, ever
what do u study btw
like major or just level of math rn?
ye like in what are you majoring or like what direction you are going
mechanical engineering atm
im in pre-calc rn
gotta take calc 1, calc 2, calc 3, differential, linear
ohh thats nice, ususally i hear people go on mechanical engeneering
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Hey y’all. Could anyone please give me a tip on how to do this problem. I have already tried completing the square and some other methods but that got me nowhere. I honestly have no clue what to do. Thanks
what "other methods"
Honestly not much I tried doing it integration by parts but that didn’t help
since the denominator isn't factorisable here, you could express the integrand in the form:
$$\frac{m\cdot g'(x)}{g(x)} + \frac{n}{g(x)}$$
ℝαμΩℕωⅤ
What’s n and m
How do I find them
Sorry English isn’t my first language is the denominator the bottom one?
yes
6x-4
for what constants m,n will
5x + 31 = m(6x-4) + n
something off
How so?
nvm
thought wolfram should've simplfied that
anyway integral of the first term will involve log
and you can complete the square for the second term which will get you something with arctan
When you say integrand does that mean the whole function im integrating?
yes
could writing this as $1 - \frac{3x^2 - x -20}{3x^2 - 4x + 11}$ help?
Editing in a ping doesn't ping them
oh 💀
ItzKraken
@gray isle
what do you plan on doing after that?
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so how do i calculate if
i take a random number (0 to 9) 32 times and put it together.
then i remove all cobinations where the same number is used more than 4 times in a row
how woud i calculate this?
pnc and probability I suppose
pnc?
Permutations and combinations
Okay look
Consider that you get the same number 4 times in a row in the first go
Then you have 28 spaces with 10 numbers, 10^28 possible combinations but multiplied by 10 too as any number can repeat
So 10^29
Then these 4 can be 1-4, 2-5 and so on up till 29-32 which is basically 29 numbers
So 10^29*29 is the possible combinations where you might have the same number repeated 4 times
And 10^32 are the total combinations
So probably 10^29(1000-29) = (10^29)(971)
Not sure
I'm in a car going back home so I couldn't give it much thought but this should be the thought process
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Can someone tell me what they get for part b pls
,rotate
@icy nymph Has your question been resolved?
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✅
I got 8/25 for part a
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Triangle ABC has vertices A(2,1), B(10,4) and C(5,13). Hence find the area of triangle ABC
I already found the exact value of sin angle ABC and cos angle ABC
What are the next steps
Do you know determinant?
No, what is determinant?
No, nevermind.
If you did know, it'd have been much easier.
Anyways, you can find the side lengths too using the vertices.
And then use area = 1/2ab * sin(C)
Or something like that.
Okay thank you I'll try that method
@bleak smelt Has your question been resolved?
Could someone explain the question a bit more
*Explain how to get to the answer of the question a bit more
Because the answer is 87/2 and I am not getting the answer
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Stupid question but Would it be possible for 0x to be equal to anything other than 0 for example 0x=1
no
0x=0!=1
using != for not equals doesn't read well here
What about 1x=0 and 2x=to smth
with
1x = 0
multiplying both sides by 2
2x = 0
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I have to show that left-neutral elements are generally ambiguous. But I can't get any further because, for example, e_1 = e_1*e_2=e_2 and therefore they are always unique?
xD
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well in the first equality you used that e2 is right neutral? what happens if thats not the case
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✅
but both are left neutral but I see ur point. So two left neutral elements aren´t the same?
well you didnt use that e2 is left neutral
Yes I see it
But is it possible to have two different neutral elements
I think so. you just need a less nice operation
Well to be honest I don´t know how to show it properly
what other properties do you need to satisfy for your operation?
you could just take two elements x,y which are not the same and then define all results of one times another so that they are both left neutral
But how does it show that both left neutral elements aren´t unique. Lets assume we have a left neutral element which is e_1 * x = x and the another element e_2y=y . x and y arent the same. But since e_1 and e_2 are left neutral. Doesnt it mean that I can say e_2x = x and e_1*y=y. So e_2=e_1 and they are unique
no
you can for example define xx=x, xy=y, yx=x, yy=y
by definition x and y are both left-neutral
So are u saying since e_1 x= x and e_2 y=y and x unequal y --> e_1 is unequal e_2
e_1=x and e_2=y. they both work
since you can verify that e_1 a=a for all a and e_2 a = a for all a (where a can be x or y)
@alpine sable Has your question been resolved?
I dont understand this man.
How does this show that they are not unique
I have the set M={x,y}
I define the operation $\cdot:M\times M\to M$ by $x\cdot x=x, x\cdot y=y, y\cdot x=x, y\cdot y=y$
Denascite
and then by definition, x and y are both left neutral for the operation
but by definition of them, they are different
Yes
hence, left neutral elements do not need to be the same
Anyone here can help me with quadrants🥲
Ok so the idea is basically just taking two different elements from the set which have different left neutral elements by definition?
the phrasing is a bit off
elements dont have left-neutral elements
the operation has left-neutral elements
which are x and y in this case
pretty much because of how I defined what the operation does. I defined it to be that way
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Can someone help me to solve this
@compact mirage can you help me ?
@flint otter Has your question been resolved?
@obtuse sonnet can you please help me to solve this ?
@flint otter Has your question been resolved?
<@&286206848099549185>
@flint otter Has your question been resolved?
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There is no inverse to this function because the same bit strings can be output from different bit string inputs right ?
(1010101010) and (1111111111) come out with the same output from this function
*I think haha
transitions being (1010101010) -> (1111111111) -> (11111) -> (10101) -> (1100110011)
(1111111111) -> (101010101010) -> (00000) -> (01010) -> (0011001100)
am I correct ?
you apply 4 functions so there should be 4 steps
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need some clarification here because I am confused
i factored all of them out to
14a - 21a^2 = 7a(2-3a)
6a^2 + 13a + 6 = 3a(2a+3)2(2a+3)
4a^2 + 12a + 9 = 2a(2a+3)3(2a+3)
9a^2 - 4 = (3a-1)(3a+2)
Once I rewrite my expression with the new factorization, I am so confused on how I simplify from there.
If someone is able to teach me how that would be great
@wide sable Has your question been resolved?
many of the factors will cancel out
assuming you did your factorization correctly (i didn't check) the denominator of the first fraction will pretty much completely cancel out the numerator of the second fraction
I just watched a video that helped me solved it, thx
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WHERE IS @static tree ?
I Demand an audience.
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what on earth
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So I have the distance from B to the line, how would I then get that closest point on the line to B?
<@&286206848099549185>
find the vector projection and then add it to point A to get a new point C
to find the distance from point B to point C use the distance formula
🤦♂️ so simplee...
thank you!
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so basically im doing this
im on step 4, for step 1 to 3 i wrote a function that worked perfectly
now i get an error here
hi I don't know matlab very well but I am in CS.
So what it's telling you is that the value of z2 is negative
you're trying to call a reference for the position of z2 and it's not liking it because you can't have a negative index with arrays
my value of z2 is z2 = 1 + 2i
can you show the full code?
yeah sure
so thats the code
i can also send you the function version for general cases
which, as i said, works just fine
yeah can you do that too?
is angle() defined somethere or is that something that is given to you by matlab?
its given to me by matlab
another thing is
the first time it stops on line 33
the rest of the time it stops on line 12
if you clear all it once again stops on line 33
yes
so thats the issue i need to solve
but what is another way of getting the angle of a complex number
passing it to polar form maybe
but idk, it works just fine at first
ok, i did something in the main one
i just put
function [results] = rotation_scaling_UO302282(z1,z2,alfa,beta, lambda1,lambda2)
z1 = 1+1i;
z2 = 1+2i;
lambda1 = 2;
lambda2 = 3;
alfa = pi/2;
beta = 3*pi/2;
%function to determine the complex numbers z1 and z2 as well as lambda 1
% and lambda2
% A real number lambda1 to scale z1's modulus
z1 = z1 * lambda1;
...
so basically in the function one
i substituted for values
(so the function is basically useless)
and it works
well
if it works it works
it gets me my results
but im still confused over what went wrong
yeah I'm not sure. I'm looking through forums right now with that error message and using angle() and not getting very far
when deleting the function
here trying running this command real quick and screenshot the results
which angle -all
ok lemme try
where do i run this command? im kinda new in matlab and just know basic stuff
aaaaah
yeah see there where is sasy "angle is a variable"?
you're basically overwritting it
ooohh
can you open that file real quick and see where declaring that?
try changing that reference name (and also all the palces it's called) and try again
what's happening is called a race condition where this variable is defined somewhere and it's a crapshoot whether or not matlab is going to call that or the intended angle() function
ohhh
thats why it lets it run 1 time in z1
then blocks on z2
and then blocks again on z1
function p = angle(h)
%ANGLE Phase angle.
% ANGLE(H) returns the phase angles, in radians, of a matrix with
% complex elements.
%
% Class support for input X:
% float: double, single
%
% See also ABS, UNWRAP.
% Copyright 1984-2010 The MathWorks, Inc.
p = atan2(imag(h), real(h));
this is what says
so i should clear the angle(z1) after doing angle(z2)
yes
there ya go
amen
okay glad you got that resolved!
u2, u really helped me understand some matlab better
good rest of the day!
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for this problem, to find acceleration would it be sum of u-direction forces so Friction - Wu = ma?
there are 2 forces that drag it down (negative) friction (0.1)(mgcos12) and gravity mgsin12 so they would add up instead of that
@deft sage isnt friction positive since its pushing up the incline?
to prevent the crate from slipping down the incline
but the initial velocity is going up
so friction will slow it down instead of pushing it
ohh i see
could you help me draw a free body diagram?
so ican understand this better
sure
i thought it was something like tthis?
where going up the incline is the positive direction
generally the friction would be opposite to the gravity
but in this exact case, the direction is 'up', so friction would push it the opposite way 'down' gravity here does the same thing
after the body reaches a velocity of 0, then the friction pushes 'up' against gravity
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I’m just lost
yup
so since that line divides that one big triangle into two triangles
you have 45 degrees for both automatically
cuz 90/2=45
Well then i have no idea what else it could be, but let me solve the y and x for you and try putting it in
look at the two tick lines
i solved a stupid way mb
what does it mean when a triangle has two similar sides
it’s isosceles
good, so whats an easy angle we can find for that isosceles triangle
hes getting at that the two base angles are equal
dunno
a straight line is how many degrees
180
So x is 20
think we can find the missing part of that?
o
think you can find y now?
the equilateral triangle has all angles being 60 degrees
yup
you cant assume its isosceles
same concept
180-60=120
then bonglord is right we cant assume its isoceles but idk how to find x in any otehr way
Is it isocolese
if all size is 40
And other is 40
and 2 sides congruent
That means is isocoles
x would be 30 if it was isoceles
think about the big triangle
what big triangle
the two together
it ok we done with that
teamwork made dream work
next
only one more after this trust
cmon guys
more teamwork
simultaneous equation
no can do?
can u do simultaneous equations?
one triangle is equaliateral and one is isoceles
np
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some help me wt all questions plz
<@&286206848099549185>
oh
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"Test the pairs" means plug in the numbers to each of the equations in a,b,c
wdym by that im dum
(0, -5) is a pair of (x,y)
Plug it into y = 3x-7 and the other equation to see if they're both true
True for that point (0,-5) would mean
-5 = 3 * 0 - 7, does it equal?
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Well first one is not bad
Just write it as a sum of 4 vectors
Then combine all of those vectors into rref
See if there is any nullity columbs
If there is
Get rid of those vectors
Then the basis would just be the remaining vectors
Dimension is the amount of elements in the basis
a + 2b - c = 0
2a + 3c = 0
You can easily find the matrix whose kernel is that
It should be
1 2 -1
2 0 3
@royal crystal Has your question been resolved?
oh shoot
dont even know what this means
When i rref it has 3 pivots
A column without a pivot
doesnt that mean that S isnt a span of a set of 4 vectors in r4
idk
thats what the questions asking me to prov
dont i need 4 pivots to prove that its a span of 4 vectors in r4
<@&286206848099549185>
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<@&286206848099549185>
@royal crystal Has your question been resolved?
what???
absolutely not
they don't have to be linearly independent
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you didn't identify all the products that result in a y^3 term
wym
how many is there god dayum
(5) (2y) (4y^2)?
that's one of the ones you missed
that seems to be it
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what about it
@rapid basalt Has your question been resolved?
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pretty sure its -3/4 but my teacher says its 3/4?
Your teacher would be right here.
if both, cosine and sine of an angle are negative, wouldn't their ratio be positive?
oh wait
sorry i misread
sin a
i thught that meant sin a > )
0
oh ok thanks
!close
how do u close?
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I'm trying to follow a proof for this, but I am missing what is going on at one of the steps
it states
Austin
I'm confused about how in the third integral, they got the absolute value sign on f
could anyone explain?
i don’t understand the confusion
should i try to help
ill probably be wrong, but isnt this just from absolute value
like a < |b| -> -b < a < b
yes that is what we want to use
but I don't see how they got the absolute value sign, inside the 3rd integral in my first textit
oh, im dumb
austin take the thing before the implication
yes
just with the negative sign
then multiply by -1
I tried that
but I did it wrong
poop brain
ty
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2w√80w+√(45w^2 )
!nosols
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wot I just say
this is how far I get.
what si the question asking?
Then just seperate √5 and √w^2
for the second root
!nosols
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Jesus
Ok
I'm sorry this is a little hard to follow
What would √(w^2) be
ok thank you
I do need to
i just put it in and it's like
do it again
the problem is
how do I factorize when one side is \sqrt(5w) and the other is \sqrt(5)
I'm not sure what you mean?
if you have (ab+ac)
you get a(b+c)
same thing here, the variable w is in both terms
yeah so like
if it's 8w√5w+3√(5w^2 )
how can I factorize
if one side is squared and the other is not
we got to this step right
sorry a better question is
in both terms, it is multiplied by w, in 8w and 3w
Put an absolute sign around the w
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broski we get it
Then stop
Stop what
Giving sols
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how is this wrong>
case of all
- case of 1
- case of 2
the fuck
anyways yeah
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The city council estimates that a typical house uses 64 Litres of water a day just in the kitchen. This is 9.2% of the total household water usage. Estimate the total use of water by a typical household in one year. Round your answer to the nearest 1000 Litres.
I did $9.2/100 * x = 64$
`
Then i got 16000/23
then i multiplied the result by 365
and i got 254000L rounded
but chatgpt says its 23000L
what did i do wrong
!nogpt
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that is correct
but what is the x you are calculating


