#help-23
1 messages · Page 89 of 1
wait so it works if we do 1 + cos(theta) = 1 - cos(theta)
and then for the left side
we flip the signs
-1 - cos(theta + pi)
= -1 + cos(theta)
set that = to 1 - cos(theta)
and that works out
but what if we do it the other way?
1 + cos(theta) = 1 - cos(theta)
we do the stuff on the right side
1 - cos(theta)
= -1 + cos(theta + pi)
= -1 - cos(theta)
1 + cos(theta) = -1 - cos(theta)
2 = -2 cos(theta)
cos(theta) = -1
wtf am i doing wrong?
should i write this on paper
this is getting very lengthy lol
oh no his sleeping pills kicked in 
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“The equation x2 = -1 has real solutions.”
Would that be true or false?
Graph x^2 and y = -1 and see if they intercept on the Cartesian plane
or try finding the square root of -1 
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Each number in a list is obtained as follows: The first two numbers are 2 and 3; then each number is the units digit of the number obtained by multiplying the previous two in the list. For example the first 5 numbers in the list are: 2,3,6,8,8. What number appears in position 2023?
extend the pattern and see what happens
2,3,6,8,8,4,2,8,6?
keep going
2,3,6,8,8,4,2,8,6,8,8,4,2,8,6,8,8,4,2
okay so clearly a pattern
yep 6,8,8,4,2,8
How?
I dont get it, I mean what is the relation there, both are divisors of 3? but 2023 is not
well you know it repeats
so you can use the fact that 3 + 6n will be 6
so the start of the pattern
Yes, but how do that helps?
I understand why, but how that helps with that 2023 term
Well you can find a term near 2023 and finish the sequence
Like if you know term 2022
Go to the next number in the pattern
Is it 4?
okay so
3rd term is 6
9th term is 6
2019th term is 6
becuase (2019-3) % 6 = 0
so
2020th is 8
2021th is 8
etc
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I need help with this please
.close
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I forget how to do 1b with variables on both sides. Help?
transpose is just a fancy word for performing teh same operation on both sides
instead, you could say, subtract 2n from both sides
then add 4 to both sides
which is what you're doing here
once your doubt is cleared, remember to close the chat.
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Need some help with Complex Exponentiation
how would you find (z1)^7
Consider rewriting z1 in polar coordinates
haven't learnt all of those yet
i think the expectation for us atm is to just do it step by step
like this was what the professor did during lecture
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Find $\sin [\arccot {\cos (\arctan 1)}]$
bettim
Is it $\frac{1}{\sqrt{2}}$
bettim
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✅
Wait no
So
Cos of pi/4 is 1/√2
I entered this in a triangle
I got base and opposite to be 1
And hypote5to ne root 3
Hypotenuse is root 2
Now cot is
1
Arccot is pi/4
Sin of that is 1 by to2
Root2
@thin bridge
I got base and opposite to be 1
you don't really care about the triangle where cos(pi/4) is 1/sqrt(2)
So what do I do
So theta is pi/4 ?
no
you determined that arctan(1) is pi/4
and that cos(pi/4) is 1/sqrt(2) right?
Ye
ℝamonov
no
let $\theta = \arccot(\frac{1}{\sqrt{2}})$ \
(do NOT make any attempt to determine the numerical measure of $\theta$) \
draw a right triangle where $\cot(\theta) = \frac{1}{\sqrt{2}}$
ℝamonov
So opposite is root 2 , base is 1, hypotenuse is root 3?
yeh,
and what's the sin of theta in that triangle
$\sqrt{\frac{2}{3}}$
bettim
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Hello, limx->pi/3 sin(3x)/1-2cos(x)
I did that and got 0, am I correct?
Is that really sin(3x)/1-2cos(x) or is it rather sin(3x)/(1-2cos(x))?
You means x tends to 0?
He wrote x->4 so no
x means to? Don't you mean x tends to?
Direct substitution
Another error haha, sorry
Wait
doesnt seem correct
So I don't need to use sin3x = 3sinx -4sin^3x?
You may have to but sorry direct sub doesn't work
Hm
Probably wrong... sin(3pi/3) is 0, and 1-2cos(pi/3) is also 0, and since they're both trig-based I would be surprised if the limit was 0 because that'd mean sin(3x) shrinks faster than 1-2cos(pi/3)
@light harness Can you show your workings?
,rotate ccw
Since when does it actually rotate the way I asked it to
Anyways
How did you get that 2cos(x)=2cos^2(x)-1?
Isn't that an identity?
Close enough
2cos
So whats the correct thing?
2cos²x-1 is not correct formula for 2cos x
Afaik there isn't any formula for 2cosx
So, for this problem what am I supposed to use or do?
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could someone help me understand what is going on in this question?
im not entirely sure how to solve?
did you understand what the top part means
i think it may mean i use that in the limit instead of the e^3x^3
but did you understand what it MEANS
not quite
how would you represent e^(x^2) using that expansion?
i have a strong feeling it may be the terms to the right of it?
but will write some quickly
that seems like a good guess
so its that but opposite signs
so assuming the first 3 terms cancel
i now rewrite the summation starting at 3?
possibly like this
):
but you're right
notice that after n=3, all the resulting terms will have a power of x greater than 9
yup
so degree num>denom
or would there be some cancellation i could do?
i dont think so
*except for the first term
right first term is same degree
would it not be inf in this case?
since the numerator is increasing in exponents?
oh
why would it be infinity
yes
no
remember the first term will have the same degree
maybe i messed up
show your work
oh wait
/3
yeah
ok makes sense
so would there be a way to show all other terms tend to 0, or is it sort of trivial by showing deg P >deg Q
you can take an x common in the other terms
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Hey! Why is Pi an irrational number when its clearly depictable in 22/7, a form of p/q where q is not 0?
22/7 is a round-off
fun fact; there are better fractional round-offs too like 355/113 approximation is accurate to six decimal places
High school students can't handle that big of a value
Since 22/7 is mostly used in highschools
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i just need help on what type of shape this is, dont need help solving for variables
<@&286206848099549185>
I don't get what you ask
what type of shape is it
is it a square
or rhombus
i cant tell by the diagnols
A rectangle or a square, in my opinion
how
More likely a rectangle
a rectangle has congruent diagnols
I thought the angles could vary
Well, if the diagonals cannot be touched
Then it is likely a trapezoid
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how do I turn this into a better equation that I can plug into a calculator and solve for. I have a duct tape solution using a spreadsheet that is just awful.
okay so
I think it would be best to write out some terms
its not the simplest sequence that you can figure out in your head
like right out what P(2) would look like?
okay dont do that
do it by hand
the whole point is that you dont simplify anything
I need help
Can you help me plz?
no
\
😔
thats not what I meant
keep a as a variable
dont write any other decimals aside from 0.1 and 0.001
in fact
set 0.1 to a variable
and 0.001 to another
what does that mean
well you still have a recursive sequnce here
you want to not have any value of P be dependent on other values of P
I don't get how you can remove P(2)
if you replace it with something else isn't that just still P(2) with a different name?
not really
the whole point here is that you want to find an explicit function
so for example P3
you dont want P2 in there
you want to use P(3) = (z + q(a^2/z) + q(a^2/((z + q(a^2/z)))
you want P(n) to be a function of just z, q, and a
$P(3) = (z + q(a^2/z)) + q(a^2/((z + q(a^2/z)))$
Kefir
hmm actually idk anymore
?
yeah
I think I got it
instead of z + q(a^2/z)
nope nvm
the issue is that there are two places to use z
so it gets really confusing
cause then you get an infinite fraction
@fair leaf Has your question been resolved?
<@&286206848099549185>
@wheat ospreythis channel is occupied
Ahh
Idk I sent my question much earlier tho when it wasn't occupied
it was though
Idk 😐
Anyways I'll send my prob in another channel
is this hw
solving for Pn, a is some constant I insert
or your own question
my own question
it may not be solvable by hand
I was trying to solve it algebraically
if its your own question ig you can just do what you were doing before and plug into excel/sheets
@fair leaf Has your question been resolved?
@fair leaf
@fair leaf Has your question been resolved?
@fair leaf Has your question been resolved?
@fair leaf I responded to you
@fair leaf Has your question been resolved?
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my tired brain can't comprehend. how do u go from top to bottom?
more context
,w (k^(1/3))/(k^(3/2))
ok yeah 1/k^7/6 was what i got
so this is just incorrect?
You can't go from top to bottom
On the second one here, looks like divided to and bottom by cbrt(k)
That would be my guess
yeah, i divided by k^1/3, in order to get it in a format of a P-series test
and i got 1/k^7/6
which converges
and that's what the text book says
so i guess this explanation has a typo or smth then
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In which case A and B can have infinite common multiples?
Where a and b are whole numbers
are you sure you asked exactly the question you wanted to ask?
"Let a, b ∈ Z. When do a and b have infinitely many common multiples?"
Yes
the answer is: whenever they are both nonzero
Well well look who it is again
and i am not convinced there wasn't some kind of mistake
A pair of positive integers always has infinite common multiples

||inb4 it turns out that yes there actually was a mistake in wording||
No there is not, i just reframed one of the questions in our text book.
reframed, you say.
are you 100% certain you did not make a mistake when reframing it?
can you show the original?
I just wanted to see a general case of this, as the answer of this is infinite but i wrote 3
Any two non zero whole numbers will have infinite common multiples
I think you gave the answer 3 since you thought it was common factors
Got it
Yesss
That is what i thought
But even if it was common factors, 3 is not the fight answer
3 and 1*
✅
Yes
So 2 points more to mention in my notes
1 is the factor of all numbers
And number of non zero whole nos will have infinite common multiples
That's not valid English but you got the idea
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Did I get the surface area for this shape correct
*The top side of the rectangular prism isn’t considered
Why is it w^2/4
No I just drew it weird
The slant heights are equal
I think you forgot to include the bottom side as well
Actually it could be isosceles
Because I’m optimising it to have the lowest surface area
Ooooh I see
True
I just wanted to check if my formula was right
Yeah cause w/2 all squared is same as w^2/4
Yup
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@fallow knoll just wondering because you said you want the smallest area what if it an equilateral triangle ?
Hmm
If optimizing for lowest surface area then the triangles are preferred to be turned closer into the flat rectangular surface
@cold thunder Has your question been resolved?
But then he won't have a lowest area for the rectangle ( roof) ?
I don’t really think it matters if I get the smallest one possible
Just my working out
For that specific shape
okkk
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hey
i've been working on this problem: , for all positive integers d, there exists an integer n such that ⌊(n+1)/d⌋ = ⌈n/d ⌉
<@&286206848099549185>
are you asking for values of n?
it's a proof, and i'm asking for the steps
or both n and d
sorry then
all good
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so basically, you want the full proof
which is the solution.
@peak lily do you know mathematical induction?
Is this proposition even true?
@peak lily Has your question been resolved?
no
No what ?
@peak lily
Maybe it's more something like for all positive integers d>2
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I need help solving this. I don't know where to start, I am not skilled in algebra. I will need step by step help from the beginning.
Replace all the x with 2. f(x) means a function that takes in a value and assigns it to x (in this case).
i just did that..
Solve it
..
change it to fraction form
..
6 - 8 + 3 all over 5
!nosols
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.
I'd already solved it genius.
how did u get to 1.4
-1.4
how did u get it
Lexa show your work
Maybe the calculator does not have fraction form. It gives the answer in linear or decimal form
use parenthesis when typing math equations hehe
All of that is over 5, not just the 3
thats not -1.4
it is for me
then keep living in that delusion
use parenthesis
bruh its what im getting
That's why
where
Use parenthesis
@tall bough fuck off nerd
Chilll
Wrap the top part of the fraction with parenthesis
alr
theres no really need to use a calculator for this
Like (…..) / 5
ok well idk math
so
uhuh i got u
alr I got the answer right
thanks @eternal fjord
and u can @tall bough suck my dick
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😆
But yes you don’t need a calculator. Just try 32 - 22^2 + 3 then put that all on top of 5

Aww it messed up my *
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<@&268886789983436800>.
dk if its a joke between friends but inappropriate here anyways...
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Theyre too young to be my friend
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so
i got this problem
ive done steps a-d but the last step is confusing
im given 251.3g mass with a string that is 1.3m long and a speed of 1.3
its a pendulum swinging in a circle motion
i have to calculate the centripetal acceleration with fc=mac=mV^2/r
using the last part i get centripetal acceleration = .33
i find the tension with t=m((v^2/r)+g) and get 2.8N
the last problem wants me to determine the centriepetal force acting on the mass
how did you get this?
so that would be the centripetal force
that is centrieptal acceleration isnt it ? or are they the same thing
no not the same thing, if we say Σ F = ma_r = mv^2 / r , then a_r = v^2 / r
Fc is centripetal force Ac is centripetal acceleration
and im at the Fc=Mac im just confused ngl
sure, and the centripetal force is given by mv^2/r
hence this
i did it backwards
yep
yes
ugh i went and confused myself again
so no.1 says calculate the centripetal acceleration of the mass
is the answer to that just V^2/R ?
yes
and the Fc is m(V^2/R)
yes
okay thanks so i now have ac = 1.3 t = 2.8 and fc = .33
what are you doing for the tension?
t=m((v^2/r)+g)
this
I would disagree I think
oh sorry I see the mass is factored out
sure
👍
and im assuming this is when the pendulum is at the lowest point?
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Name a segment that is a radius. How long is it?
Show or explain your reasoning.
If diameter is 15=2r , then radius is 7.5 cm AC=AD
Radius is half of the diameter
But it asking for one of them
lol I doubt it, this is an online image
oh
Radius is the same from the center point
the diameter of 15cm is given, so radius is half
half of 15?
Divided?
yes, its 7.5
so the answer is 7.5
Yes
u´re welcome
Wait
what?
Its asking to my work
yes and?
how can i show my work
Look
Diameter = 15cm
Diameter/2 = radius
15/2 = radius
7.5= radius
Simple
That's all the work
That you need
you have to measure with the ruler the radius, like if is the G or something else
ok.
Indicating they all are radii
one more thing
Agreed
Ruler is good too
CD is the only diameter in this picture
okay
Yes
But its asking how long is it
its 15
Alright
u´re welcome!
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I feel like this is more of a "am i reading the problem correctly for a mathematical problem", so heres my question. There are the equations given to me: (1st page) and these are the data given to me (page 2) so is ra, r1 rb, r3 and c is c1
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This is what I've done so far. I just wanted to know if I'm going about the problem correctly, as this is the first question of the assignment.
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this looks like pain
see if you can just get a online calc to do it
like wolframalpha
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For part c u get x squared =144
I’m confused about why x would be -12 rather than 12 given the domains
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The function is the composition of f and g, so f(g(x)) = 17.
The function goes from the domain of g to the range of f.
okay hm
Still confused about something?
Better explanation maybe:
If x^2 = 144 (what you said) Is the answer.
x has two possible answers. Check if both these values plugged in g, give a value that is in the domain of f. If both happen to fall in the domain of f, then both values are correct. Since both values can be chosen to get f(g(x)) = 17.
@frosty granite
Always be careful when squaring roots though, since you might get an answer that is not a real number, when plugging that number back into the square root.
ohhh ok
yeah that makes way more sense
calm
thanks
good luck!
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Is TREE(3) closer to TREE(2) or to TREE(4)?
difference between tree(3) and tree(4) is way larger than the difference between tree(2) and tree(3)
Why
The sequence of TREE(n) grows incredibly quickly as n increases
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$\arctan ( 1-x), \arctan (x) , \arctan(1+x)$ are in AP , find $x^3 +x ^2$
bettim
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bruh smh
What is AP?
arithmetic progression
That means that
arctan(1-x) + arctan(1+x) = 2 arctan (x)
Have you seen something about formulas of the sum of the arc?
arctan(x+y) in terms of arctan(x) and arctan(y)
$\arctan x + \arctan y = \arctan (\frac{x+y}{1-xy})$
bettim
this?
Formulas like that
I would try to consider this to write arctan(1+x) + arctan(1-x)
Considering 1+x instead of x and 1-x instead of y
im getting $\arctan(\frac{2}{-x^2})$
bettim
is that right?
Maybe arctan(2/x²)
we have that
2 arctan(x) = arctan(x)+arctan (x)
So 2 arctan x = arctan (2x/(1-x²))
you told to consider the other two arctans
i did this
1-xy = 1 - (1+x)(1-x) = 1-1 +x²
In the denominator yes
bettim
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helo
find $\frac{dy}{dx}$ if $ 2x+y =\sin y$
bettim
bettim
i think is -2 not 2?
how?
oh nvm i just did it the other way around 💀
i got -2/1-cos(y) which is the same so i dont know lol
can you show what you're entering into the system
nvm the pdf's fuked up i guess
?
thought you were entering that into some online thing and that came out as wrong
also $2x + 3y = sin x$
bettim
it as a practice pdf
through what steps?
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i need help here
D=0
what are the conditions for the discriminant if the function touches the x -axis at one point
that the discriminant = 0
I would say no.
Look at your expression of b
That would just make b = 0
your a value is the coeff of your x^2 term, your b value is the coeff of your x, and then c is the rest of the jargan , just constants
k still exists
But the coefficient in x isn't 0, is it?
c is 8 + k then?
b = 0?
no.
.
oh k
close
You want to write ax² + bx + c
So far we have a = 1
C = k+ 8
So that's x² + bx + k + 8
the coefficient of x in b is k right?
not just k
That would make it x² + kx + k + 8
-k?
yes
Yes!
ah nice
let me solve now
so the eq looks like
-k - 4(1)(k+8)^2
just to make sure
oh one sec
wait what's wrong here
what do your notes say the discriminant is given by
b-4ac^2?
no, did you refer back to your notes
oh I think I wrote it wrong
its given by b^2 - 4ac,
k^2-4(k+8) =/= k^2-4k+32
^
is that the same?
Not equal bro
ohh
What is negative 4 times k? what is negative 4 times 8?
oh -32
keep going you almost have the solution.
???
right?
(k+4)(k-8) is indeed the factor but not the roots
the factors would be (k+4)(k-8) = 0 yes
If we are looking for k we need to find the roots.
-4 and 8?
alr sure 
Broooo
lol
same concept
I think you could do this one on your own
𝐁𝐎𝐌𝐁𝐀𝐒𝐓𝐈𝐂 
My dumbass set it equal to (x-a)^2 and then had to undergo 2 variable changes.
lol
and?
3 and -3?
yes
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Can someone help me/tell me what is missing in my proof?
I've been told it does not cover all cases, but I don't see it.
The proposition I'm trying to prove is
Show that no number n with n ≅ 3 (mod 4) can be written as a sum of two integer squares
present your proof
yes that's essentially the proof
actually I don't see a problem with it
let me check again
The feedback I got was
"The assumption that m and n have to be odd and even respectivly does not cover all cases."
uhh
I don't understand that feedback, what you wrote seems perfectly fine
(odd, odd) (odd, even) (even, odd) and (even, even) are the possibiltiies for m and n and you covered all of them
Yeah that's what I thought as well. I'm not sure what's wrong
if anything is wrong at all. I was only given 50%
I believe whoever gave you that feedback is mistaken
Is there any cases at all where this doesn't apply?
perhaps they expected you to explain why both m and n having the same parity does not work
But why give me that feedback then?
It spesifically said that id doesn't cover all cases, which is weird
the only perceivable issue I can come up with is what I just mentioned
there are no other possibilities for a pair of integers, so you need not worry
Ok, thanks!
