yep i got that
#help-39
brittle wyvern
jolly parrotBOT
MellowDramaLlama
pearl pondBOT
@brittle wyvern Has your question been resolved?
fleet sky
no y is our line y = mx + b. This is called the point slope form.
it's another way to figuring out your line
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modern island
hey I got AB cong CB, and AB cong BC because of bisect, how would I get the angle 3, or 4 to get SSA
modern island
i'd still need an angle
safe drum
U have angle 1 = angle 2
modern island
where does it say that tho
modern island
exactly and I defined that
if bd bisects abc
then ab = cb
oh my god
i just answered my own quesiton
thank you
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faint onyx
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faint onyx
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naive sequoia
I've ran into a problem I don't get. It involves VERY fundamental trig and it's been an issue for quite some time now.
We have a right triangle which has a side of 4 and hypotenuse of 9. I need to find the length of the side I don't know, which funny enough, I already know it's 8.06 thanks to Pythagorean theorum. So what's the problem? Solving it. I decided to solve it in two ways.
The first way is to solve for the angle adjacent to 4 and 9, followed by using the hypotenuse cosine(angle degree) method. As you may have guessed, the angle is merely 90 minute the angle I've already solved, which I work out manually on a calculator anyway to verify I've done everything right up to that point. When I use cosine, to solve the unknown side, I get 6.4. When I use sine to solve for the unknown side, I got 8.53. Will be sending pics in a second.
naive sequoia
The goal here is to solve for x using Y and Z, only using pythagorean theorem to verify my method worked.
9^2 = 81
4^2 = 16
81-16 = 65
Now that we have what x SHOULD be, lets work out z and y
The 90 verifies that the angles are likely correct
rounded to the nearest hundredth
Now to solve x using BOTH angles
^ This is my problem. I'm trying to multiply the hypotenuse by cosine and sine to get the answer which is how I was tought.
Halp pease
The reason I used those methods is that I was told sine(Degree) = Unknown side/Hypotenuse and so I could just multiply both sides by the hypotenuse.
naive sequoia
Ahh you're right
Also I mixed up the angles for sin and cosine for some reason
@.@
Annoying
Thanks fam
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lyric helm
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lyric helm
question 3
pearl pondBOT
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lyric helm
<@&286206848099549185>
plush bramble
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
lyric helm
idk how to start the equation
pearl pondBOT
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hot vortex
How do you solve a?
https://gyazo.com/b7badd89d8a0d0237fb4d41685a3f25d
Says the answer is 245 but no matter how many times I try calculating it I dont get that number?
abstract locust
5 * (s^2)
plush bramble
wary dragon
pearl pondBOT
wary dragon
how to do
plush bramble
there's no question?
drowsy aurora
Was here last night for this question and still am because I didn't get it. Need help with (c) here
drowsy aurora
What are you doing that's turning S(2p) into 2p×{15+2(2p}?
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drowsy aurora
<@&286206848099549185>
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steel smelt
how do you solve the systems of equations 7x+2y=4 and 9x+2y=0 by combining the equations.
flint field
Consider 7x+2y=4 as eqn 1 and 9x+2y=0 as eqn 2, then subtract eqn 1 from 2 what do you have...?
steel smelt
x=1/4 and y=-7/8
jolly parrotBOT
flint field
Not quite
Do like this
9x+2y-7x-2y=0-4
Then the 2y's cnacel out
2x=-4
X=-2
Like this
Get it??
agile maple
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prime hull
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prime hull
<@&286206848099549185>
pearl pondBOT
<@&286206848099549185>
Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
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dapper thicket
How do I continue on the right side to make Botha sides equal? Not sure what to do next
dapper thicket
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midnight haven
I need help with (b) onwards
midnight haven
oops
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midnight haven
<@&286206848099549185>
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winged karma
Can someone help me out with the integrals of trig functions?
winged karma
Like what are the integral of Tan u, cot u, sec u, and csc of u?
I tried looked them up but couldn’t find them.
<@&286206848099549185>
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limpid edge
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timid spindle
..................
It had been literally 2 mins..
limpid edge
im very impatient if u cant tell 😅
dusk trail
You'll need to calculate the monthly salary for 2017 and multiply by 12 to find total income for the year, then divide by weeks and hours per week worked to find the average per hour
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shadow stag
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shadow stag
I took various values and the highest I got was 10.44 (at around x=0.13)
pastel arrow
You can use derivatives to find local minimum and maximum in that x range
shadow stag
I havent learned calculus yet :/ (and this problem is not from a calc class so the teacher probably wants us to use something easier)
dusk trail
What kind of class is this for?
shadow stag
high level competition math
pastel arrow
Oh that makes sense
dusk trail
Well we know that the right expression has a minimum value of 3
And the left expression has a minimum value of 4
No x <= 1
shadow stag
yeah i realized that
abstract ridge
u can use framing
shadow stag
what is that?
abstract ridge
u start from -1<=x<=1
then U do operations in order to reach the expression u have
first u find a framing for sqrt(58-42x)
shadow stag
[4,10]
abstract ridge
yeah
then U find a framing for the expression oj the right side of the plus sign
and u add the minimum values to get the minimum value of the whole thing
shadow stag
but the minimum values wont necessarily occur at the same x
shadow stag
its a problem set from a competition team practice
we do like hmmt, yale mt, princeton mt, et.c
dusk trail
nice
cursive fulcrum
I took various values and the highest I got was 10.44 (at around x=0.13)
ye i graphed and checked, it would be that
pearl pondBOT
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shadow stag
ye i graphed and checked, it would be that
but I need an exact answer
pastel arrow
It looks like the minimum y value is root(109) or at least close to that
Don’t know much more I’ll try
tawdry widget
pearl pondBOT
tawdry widget
Idk how to do 11
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thin lance
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azure terrace
you sure this is the correct figure for the exercise
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gleaming sky
Hey 🙂 I have two independent uniform distributions $T_A$ and $T_B$. I'm interested in their sum $$T = T_A + T_B$$
By linearity I have that the expected value $$E(T^2) = E(T_A^2) + 2E(T_A T_B) + E(T_B^2)$$
But is there anything that can be simplified since they're independent ? I'm mostly concerned about $E(T_A T_B)$, I'm not sure how to calculate that
jolly parrotBOT
Sacha
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tall tangle
\lim _{x\to :0}\left(\frac{\left(1+x\right)^k-1}{x}\right)
pearl pondBOT
\lim _{x\to \:0}\left(\frac{\left(1+x\right)^k-1}{x}\right)
tall tangle
$\lim _{x\to :0}\left(\frac{\left(1+x\right)^k-1}{x}\right)$
jolly parrotBOT
i love to boki
tall tangle
how to prove this without l'hopital since using l'hopital would be circular reasoning
honest bough
Use the binomial theorem to expand (1 + x)^k
tall tangle
Use the binomial theorem to expand (1 + x)^k
k is not a positive integer
it can be any real number
honest bough
plush bramble
That's just the definition of x^k at x=1
plush bramble
Do you know the limit definition of derivative?
The are two equivalent forms, but they look different
Specifically the derivative at a point
plush bramble
That's just the definition of x^k at x=1
Oops I meant definition of the derivative of x^k
tall tangle
Oops I meant definition of the derivative of x^k
yeh
plush bramble
h=x
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midnight haven
midnight haven
any hints
pearl pondBOT
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midnight haven
<@&286206848099549185>
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graceful zinc
pearl pondBOT
graceful zinc
When I do the Gauss on my system I don’t really know how this proves that any 2x2 matrix is a linear combination of my starting matrices because the vector-space must contain the null matrix but this doesn’t satisfy my system of equations
I don’t know if where I’ve start is wrong, the middle or the end tbh
pearl pondBOT
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somber zinc
I thought the answer to this would be 3.95 <, d < 4.05
What am I doing wrong
“<,” is greater than or equal to
grim patrol
er
somber zinc
4.05 would not be rounded off to 4.0
Yeah but 4.0499999999….
Would be, wouldn’t it?
cursive fulcrum
So no greater than equal to sign should be there
light helm
why didn't you include 3.95
cursive fulcrum
They said that < stood for ‘greater than or equal to’
somber zinc
With the ,
somber zinc
I didn’t have the correct symbol on my phone
cursive fulcrum
the left has a `,`
Wow I need reading glasses
light helm
phone definitely has = if it has <
cursive fulcrum
<@&268886789983436800>
somber zinc
phone definitely has = if it has <
It does, I didn’t realise that I should use that notation
somber zinc
<@&268886789983436800>
Why ping mods?
light helm
the was inappropriate now deleted content
cursive fulcrum
Some guy spammed an invite
grizzled blaze
pearl pondBOT
grizzled blaze
- it is known that f(x)=e^x-a and g(x)=ax-lnx have the same minimum value
Q: find the value of a
please help
proven hedge
Guys i want help
lapis juniper
22. it is known that f(x)=e^x-a and g(x)=ax-lnx have the same minimum value
take the derivative
find root
grizzled blaze
f(x)=e^x-ax
lapis juniper
Yeah
you would have to solve the last equation XD
I just guessed a = 1 and it works, but I don't know how to find other solutions
lapis juniper
So you showed that a = 1 is the only root since h(x) is increasing for all x>0
lapis juniper
use .close
grizzled blaze
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jaunty fable
pearl pondBOT
jaunty fable
do i just sub 35 and 15 in for x and y
or how do i start this
do i make 3x - 4y = 35 and x - 2y = 15
then find x and y
<@&286206848099549185>
quartz crag
do i make 3x - 4y = 35 and x - 2y = 15
Yes
jaunty fable
i got y = -5
and x = 5
so is the answer just 0?
<@&286206848099549185>
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tepid tree
How can I calculate the expectation?
pearl pondBOT
How can I calculate the expectation?
tepid tree
tropic niche
can you translate to English
timid spindle
Law of the unconscious statistician?
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tepid tree
Given a stochastic variable X, where X is poisson distributed. E is the estimated value that I have to calculate
@tropic niche
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dusky ferry
Can some tell me where i am going wrong?
pearl pondBOT
Can some tell me where i am going wrong?
dusky ferry
3-3=0, not 3
Ah dumb mistakes Ty
dusky ferry
A-lambda * I
Can u point out which line and where?
near echo
it’s just the definition of an eigenvalue. A-lamba*I will probably make it easier not to make mistakes later on
rather than lambda * I - A
it evaluates to the same thing, but in the latter case you’re negating a whole matrix instead of just the lambdas
dusky ferry
Oh my prof has it down as this
near echo
i see. it’s the same thing anyways but i do think the other way around is easier to compute
dusky ferry
I added +1 to second row to make the values 0
near echo
you can’t just add 1
you can add rows together, swap them around, and multiply them by constants
dusky ferry
Or divide by constant?
near echo
yes that’s the same as multiplication
dusky ferry
Gotcha
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sullen drum
Explain how to solve an equation of the form x^p/q =a for nonzero integers x, p, q, and a what is x in terms of a, p, and q?
First raise each side to the __ power by the ____ property, (p/q) ()=1 and x to the first power is x therefore x=
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willow ledge
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midnight haven
i dont understand what they mean here by distance, like in case of 1~2~3 i should take distance equal 3?
pearl pondBOT
i dont understand what they mean here by distance, like in case of 1~2~3 i shoul...
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midnight haven
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foggy canyon
Is my step of taking ln of both sides correct here? I get different answers for x as a result of the second equation compared to the first one
e^(x+7) + 3 = 3^(7-x)
=> x + 7 + 3 = (7-x)ln3
rustic gate
no
wind wigeon
the 3 
jolly parrotBOT
vivid pilot
can i please get help on this
pearl pondBOT
can i please get help on this
midnight haven
I know 2 ways to solve this kind of problems
One by congruence and the other by induction
Which one is needed?
pearl pondBOT
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runic glacier
One by congruence and the other by induction
How does the congruence proof look like?
jolly parrotBOT
turbid moss
Let f be a continuous function from R^n to R^n. I want to show that f(A) is closed, where A is some subset, given that A is closed and bounded. Here's what I have so far.
turbid moss
Let $x_0$ be a limit point of $f(A)$ and suppose that $x_0\notin f(A)$.
jolly parrotBOT
please request a new nickname
turbid moss
Any hints from here?
pearl pondBOT
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merry carbon
My thoughts would be that being a closed and bounded subset of R^n is equivalent to being compact, and then there's a theorem saying that the image of a compact set by a continuous map is compact, from which you know the image is closed (and also bounded)
Unless the idea is to prove it directly?
turbid moss
yeah, i figured doing it directly would help me prepare better for exams
im trying a new approach by supposing that f(A) is open and my intuition tells me that f^-1(f(A)) is open, so im trying to prove that
and maybe I can get an open covering of A using f^-1(f(A)) and find some contradiction there, idk yet
merry carbon
im trying a new approach by supposing that f(A) is open and my intuition tells m...
That would be via the preimage characterisation of continuity, right?
turbid moss
yup
merry carbon
Ah, nice!
I'm probably biased but I feel the proof would end up emulating parts of the other theorems above haha
turbid moss
if thats the case, then so be it, at least i'll have an idea of the theorem's proof before I even read about it
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dense badger
You tie up a rope of a length of 5 unit with two pillars whose length is 10 units for each. Find the region under the curve of the rope. (Suppose the rope is hanging there freely.)
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You tie up a rope of a length of 5 unit with two pillars whose length is 10 unit...
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storm bison
I had a thought question I guess. When using l'hopital's rule, I've only done it on a fraction. But, despite that, could I use it if I had a problem with multiple fractions being added. And if I did, I'd differentiate them all at once or not. Right now I'm assuming it doesn't matter since a limit only need one of the terms, but I realized that on the flip side an indeterminate being an addend probably wouldn't make sense
honest bough
Can you show an example
honest bough
Well, you can split them into multiple limits
obsidian hamlet
I had a thought question I guess. When using l'hopital's rule, I've only done it...
yeah you can use l'hopital's rule on the problem with multiple fractions
storm bison
Well, you can split them into multiple limits
Just to make sure I'd take the derivative for lhopital all at once or I'd do the rule respective to each addend
pearl pondBOT
Just to make sure I'd take the derivative for lhopital all at once or I'd do the...
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midnight haven
Linear equations grade 8
pearl pondBOT
Linear equations grade 8
midnight haven
,rotate
jolly parrotBOT
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strong furnace
Hey guys, i have a very stupid question 🙏
pearl pondBOT
Hey guys, i have a very stupid question 🙏
strong furnace
The triangular inequality when you have |x-y| is what ?
In class we wrote that |x-y| < |x| + |y|, is that correct ?
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strong furnace
Can someone try and help me with a question regarding norms ?
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strong furnace
Can someone try and help me with a question regarding norms ?
pearl pondBOT
Can someone try and help me with a question regarding norms ?
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strong furnace
I need to prove that the limit of this is 0 when (x,y) —> 0 but i find 2
<@&286206848099549185>
I’m so fucking stuck please help
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dreamy venture
This is my first time working with product series, and I have gotten into e^some series form, but I am struggling to figure out how to manipulate the series to evaluate it (I can see it converges on desmos). Is my approach correct and if so what steps can I take to evaluate this series? Thanks!
dreamy venture
This is my first time working with product series, and I have gotten into e^some...
accidentally dropped the limit it should say lim n-> inf. of e ^ series from k to n
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dreamy venture
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paper sleet
i need someone to helo me systems of equations
i have no idea what im doing
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blazing shadow
Okay so you said have no clue how to start this right?
paper sleet
kinda
twin ravine
how about trying to get the y and x on each side
blazing shadow
That’s already done on the first equation
blazing shadow
So if x=3y-5, you can replace x with 3y-5 in 2x+12y=-4
paper sleet
ohh ok
blazing shadow
Then, you solve for y and can go back and replace that y value in x=3y-5 to get your x value
blazing shadow
Okay glad I could help, let me know if you have any trouble along the way
paper sleet
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toxic wigeon
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civic river
How can I find the anti-derivative of 1/x^1/4 ?
pearl pondBOT
How can I find the anti-derivative of 1/x^1/4 ?
timid spindle
Power rule
pearl pondBOT
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frozen forge
hello
tacit mulch
,rotate
jolly parrotBOT
frozen forge
Ik something’s wrong but can’t find it
tacit mulch
I'm not sure what Theorem 3-1 and 1-5 are, and you didn't state a specific theorem for step 4
frozen forge
Yea that’s what I’m stuck on
I can’t tell u what the theorems are
But I’m sure there correct
tacit mulch
Also point X kind of came out of nowhere, but the logic seems basically right
tacit mulch
Well, how did you know the triangles are congruent?
frozen forge
Uh
I just wrote it
Cuz we know
Bx and cx are congruent meaning the bottom part of the triangle is congruent. then we also know the given which are the sides and how there congruent.
@tacit mulch
tacit mulch
Do you know like SAS, SSS, etc
tacit mulch
Then, which one can you use to justify the triangles being congruent?
tacit mulch
Yep 👍
tacit mulch
I might add one more step at the end and actually state that AX is a perpendicular bisector
Just because that's the thing they asked for basically
But yeah the rest looks good, as long as theorems 3-1 and 1-5 are appropriate
frozen forge
Yea
Didnt I already do that tho?
I wrote AX perpendicular to Bc
??
@tacit mulch
tacit mulch
That's not the same as perpendicular bisector
It's a perpendicular bisector because its perpendicular and X is the midpoint of BC
tacit mulch
You could just say "Definition of perpendicular bisector"
frozen forge
Bruh
It can’t be words I’m pretty sure
Wait I’m confused
So everything I have rn is wrong or right?
@tacit mulch
What do i replace for def of perpendicular bisector
tacit mulch
Wdym, you can use definitions
What you have is right, but you didn't actually state that it's a perpendicular bisector
just that it's perpendicular to BC
frozen forge
How do I do that
Is there a symbol for it
Cuz u can’t put words in the statement part
@tacit mulch
frozen forge
It’s like that idk lol
Only for the reasoning I’m pretty sure
Sooo
Should I leave it how it is
@tacit mulch
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eternal mural
Question regarding variance, for a continuous random variable, I'm wondering why the following is equal.
eternal mural
midnight haven
expand (x-mu)^2, then apply the definition of a density function and the mean
tall echo
idk if this is clear enough o ask but i need help with Hesse diagrams and creating them from sets
runic condor
tall echo
im not sure what that is
ill just post the question i have
this is what i need help with i dont understand how to do it
midnight haven
hasse diagrams? https://en.wikipedia.org/wiki/Hasse_diagram
naive pilot
Need geometry help. Question incoming:
pearl pondBOT
Need geometry help. Question incoming:
naive pilot
ABCD is a "Right Trapezoid". the points "B" and "D" are symetrical to the line [AE]
What is Area(ABE) divided by Area(AECD)
from what i understood, we can never ever know the values of AD and BE
so we have to do some kind of magic
midnight haven
Are u given any length side? @naive pilot
Like any side?
Oh I see
You don't need it
naive pilot
You don't need it
a friend of mine said that
we can find "AD" or "BE" thanks to the information that B and D are symetrical to AE cuz it would make it square they said
but i said "no"
because it could also be like this
symetrical, but just not square
midnight haven
What are u trying to find again
naive pilot
Area(ABE) divided by Area(AECD)
midnight haven
I see
naive pilot
AD and BC are parallels if that helps lol
i even tried assigning X to those edges but still couldnt come up with an answer
it came down to this but i cant make out an answer
cinder shadow
because it could also be like this
no it can't
symmetry means B and D coincide if folded along the line AE
midnight haven
i tried going this
Well angle DAE also has to be 60 as well
naive pilot
no it can't
symmetry means B and D coincide if folded along the line AE
in the pic i sent, cant B and D coincide if folded?
midnight haven
And you can continue from there I believe
naive pilot
Well angle DAE also has to be 60 as well
hmm why is that
cinder shadow
in the pic i sent, cant B and D coincide if folded?
no, they don't in a rectangle
midnight haven
hmm why is that
The side opposite to it is sqrt(3)
cinder shadow
in the pic i sent, cant B and D coincide if folded?
only if it's a square
naive pilot
The side opposite to it is sqrt(3)
could you try explaining by drawing? im not really good with math english terms
oh nvm i got what u mean
midnight haven
I believe you speak Turkish yes? I can explain in Turkish since I know a bit
naive pilot
i mean yes the side opposite to it is sqrt3 but that doesnt mean it is 60 degrees
naive pilot
I believe you speak Turkish yes? I can explain in Turkish since I know a bit
no worries we can continue english as long as it goes lol
naive pilot
no it can't
symmetry means B and D coincide if folded along the line AE
hmm that makes sense, how to solve it then assuming its a square? cuz i tried and still couldnt
midnight haven
i mean yes the side opposite to it is sqrt3 but that doesnt mean it is 60 degree...
It does since we also know that angle ADE is a right angle
cinder shadow
hmm that makes sense, how to solve it then assuming its a square? cuz i tried an...
yes, still working towards it
naive pilot
It does since we also know that angle ADE is a right angle
but maybe it is 45 45 90 then
midnight haven
45 45 90 doesn't give you sqrt (3)
naive pilot
45 45 90 doesn't give you sqrt (3)
in ADE triangle , there is no edge that is a number
so you can get sqrt 3
midnight haven
We know side DE is sqrt(3), which also happens to be a side of the triangle ADE
naive pilot
you can get this in ADE
naive pilot
you can get this in ADE
doesnt this prove that it doesnt have to be 30 60 90, it can also be 45 45 90
the sqrt(3) in 45 45 90 is only a ratio
but the number sqrt(3) can appear in any kind of triangle
see it doesnt have to be 30 60 90 to be "sqrt3"
cinder shadow
i tried going this
lead with this
midnight haven
you can get this in ADE
If you are going to say that, then you cannot say anything about triangle DEC then. Saying it has length sqrt(3) and 1 would be wrong
naive pilot
If you are going to say that, then you cannot say anything about triangle DEC th...
those are ratios and could be correct
Makhana just proved you're wrong as well 💀
cinder shadow
ya it's A how did u find it
consider each side of square to be sqrt3
naive pilot
consider each side of square to be sqrt3
so it goes like this:
cinder shadow
ya
midnight haven
Makhana just proved you're wrong as well 💀
Okay but that's literally what I was trying to suggest?
naive pilot
midnight haven
He just did it directly
naive pilot
then do i just find ABE area
cuz i tried it and it didnt work, maybe i didnt know where to go
cinder shadow
then do i just find ABE area
yes
cinder shadow
then do i just find ABE area
is it 3/2
naive pilot
3/2
3/2 + √3/2
this is what i get to
cuz area of "ADEC" is just "ADE" + "DEC" right
cinder shadow
√3/2 in place of √3
naive pilot
oh right
cinder shadow
ye
cinder shadow
yes
naive pilot
hmm yeah but my dumb brain cant still find a way to go to A
how can it get to (3-√3)/2 from there
cinder shadow
are u familiar with rationalising the denominator
naive pilot
i dont think so
cinder shadow
k lemme explain
naive pilot
im all ears
cinder shadow
denominator is √3+1
so we multiply and divide by √3-1
apply a²—b² in denominator
naive pilot
sec im doing it rn
cinder shadow
ye ye
naive pilot
dammmnn thank you
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midnight haven
how to find DE?
pearl pondBOT
how to find DE?
proud dagger
midnight haven
how to find DE, if AB=BC=50 AC=60, AE and CD are the heights
<@&286206848099549185>
balmy ember
weak briar
pearl pondBOT
weak briar
can someone explain this to me? I've tried it a few times and gotten it wrong every time so far
midnight haven
can someone explain this to me? I've tried it a few times and gotten it wrong ev...
should be more than 1500
weak briar
how do you get that though?
midnight haven
look 8.50 - 5 is 3.5 so 1 package makes 3.5 $
then you divide 5250 by 3.5 to get the number of packages that is needed to make 5250$
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sick adder
The line dg is parallel to base bc. Are triangles abc and aef similar?
sick adder
This isn't directly for homework or anything so a yes or no would do
I've been working on the assumption that they are similar
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zinc pine
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merry carbon
First off, why not just use $cos(2\theta) = 1 - 2\sin^2(\theta)$?
jolly parrotBOT
chartbit
merry carbon
And why the square root here, at the same time as 29^2?
zinc pine
And why the square root here, at the same time as 29^2?
im using the r^2=sqrt x^2 +y^2 formula
merry carbon
Pythagoras, right? Shouldn't it be either $r^2 = x^2 + y^2$, or $r = \sqrt{x^2 + y^2}$, no?
jolly parrotBOT
chartbit
zinc pine
Pythagoras, right? Shouldn't it be either $r^2 = x^2 + y^2$, or $r = \sqrt{x^2 +...
ohh shit i see
hot canyon
im using the r^2=sqrt x^2 +y^2 formula
use cos(2x) formula ._. it's hard otherwise with the plus/minus sign
zinc pine
use cos(2x) formula ._. it's hard otherwise with the plus/minus sign
idk i wasn't taught it with that formula
merry carbon
idk i wasn't taught it with that formula
Looks like how you tried to do it was by using $\cos(2\theta) = \cos^{2}(\theta) - \sin^{2}(\theta)$, no? If so, just recall that $\sin^{2}(\theta) + \cos^{2}(\theta) = 1$, so you can get $\cos(2\theta)$ in terms of only $\sin(\theta)$
jolly parrotBOT
chartbit
zinc pine
**chartbit**
ok the first part yes... im using that formula... second part is new for me... i did the calculations again and my answer is stil wrong
ill send a pic of my work
zinc pine
Looks like how you tried to do it was by using $\cos(2\theta) = \cos^{2}(\theta)...
answer on the review packet is -41/841
merry carbon
ok the first part yes... im using that formula... second part is new for me... i...
Wait, as in you don't know that $\sin^{2}(\theta) + \cos^{2}(\theta) = 1$? Surely if you know the first part, you would have been taught that at some point?
jolly parrotBOT
chartbit
zinc pine
Wait, as in you don't know that $\sin^{2}(\theta) + \cos^{2}(\theta) = 1$? Surel...
nah bro im telling u I wasn't told abt it
merry carbon
Also what did you do here fam?
zinc pine
Also what did you do here fam?
wym i did the r=sqrt x^2 + y^2
I was given Y and R from the sin fraction at the start
merry carbon
x should be 20?
merry carbon
Pythagoras, right? Shouldn't it be either $r^2 = x^2 + y^2$, or $r = \sqrt{x^2 +...
Rearrange the former of this $r^2 = x^2 + y^2$ to $x = \sqrt{r^2 - y^2}$
jolly parrotBOT
chartbit
zinc pine
Rearrange the former of this $r^2 = x^2 + y^2$ to $x = \sqrt{r^2 - y^2}$
ok so it's 8 again.... sqrt 29^2 + 21^2 is first/// but then the ^2 cancels because of the square root... so u can subtract 29 with 21 and u will get 8
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zinc pine
.reopen
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old rain
what is 3490432480394 ^239030
keen elbow
Can a countably infinite set contain an uncountably infinite subset?
keen elbow
(Cantor)
I'm looking at Discrete Mathematics with Applications Edition Four - and it sounds like it is impossible
But the book is 2010
valid raptor
I think so
but idk about any of it
im thinking of the example whats bigger, all integers or all numbers between 0 and 1
and 0 and 1 is uncountably infinite
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keen elbow
"Page 435, Theorem 7.4.3 Any subset of any countable set is countable." A representation of the numbers between 0 and 1 is an infinite decimal expansion. The best representation of the composite integers is the canonical form of prime powers. The book goes into Cantor's diagonal argument on an infinite decimal expansion to prove there's a number between 0 and 1 not already enumerated - a proof by contradiction. How is this different from enumerating the subset of all relatively prime numbers to 3 then taking a diagonal of all the prime power exponents and applying a similar mapping to achieve another number relatively prime to 3 that's not already in the enumerated list - a proof by contradiction?
Or create a one-to-one mapping of 2^k to every integer because there are infinitely many powers of 2 that are integers. We will never be able to map another prime power p^k to some integer but there are infinitely many primes . Fundamental theorem of arithmetic guarantees these are all unique. It just feels like Cantor defined a set of rules that would guarantee a paradox to get an infinity bigger than infinity
And the arguments he used can be used to create a similar paradox with the integers just by using the canonical form of integers
Every rational number can be represented as the 2-adic valuation over the 3-adic valuation of some n.
$\frac{\nu_2(n)}{\nu_3(n)}$
Using only 2 prime powers of n gives us "2 degrees of freedom in a sense?" How does the infinitely many primes with the fundamental theorem of arithmetic not allow us to uniquely identify everything?
jolly parrotBOT
CalicoJackRackham
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keen elbow
.reopen
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keen elbow
With Donald Knuth's up-arrow notation - we can bake in recursion within the prime powers as well. Relations can be baked in by numbers having prime factorizations in common. It just seems arbitrary to have a rule like the notion of defining everything between 0 and 1 and then to use a decimal "representation" when I can use a canonical "representation" of integers to prove the same contradiction. Basically, arbitrary rule around representations + trying to talk about infinity seems like you're guaranteed a paradox around representing an element not already in your infinite set
plush bramble
Maybe try #foundations or #elementary-number-theory
rich fractal
quick question its in alg 2 i forgot the name of this but is it
(x-h)^2=4p(y-k) OR (y-k)^2=4p(x-h) ?
rich fractal
😭 please help bru its 12:27 and i got a test tommorow
ivory swallow
Depends on orientation
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rich fractal
😭 yes i found out ty
old marsh
austere jasper
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deep thorn
pearl pondBOT
deep thorn
Idk where to start 😭
deep thorn
Nope im so lost
cinder shadow
I don’t I’ll ever get this question I tried using a, a+d, a+2d…
did you try what I said?
if a,b,c are in AP, then:
2b=a+c
merry carbon
if a,b,c are in AP, then:
2b=a+c
May I ask if a,b,c have to be consecutive, or if that works for any that are in the sequence?
That “in some order” tho 🤔
cinder shadow
a,b,c don't have to be consecutive
they have to be in an AP
for the property 2b=a+c
merry carbon
Oh, never knew that, you learn something new every day 🤔
merry carbon
a,b,c don't have to be consecutive
Meant “consecutive” as in they’re consecutive terms in the AP
As in a+nd, a+(n+1)d, a+(n+2)d
In that case I can see why it holds, but not yet in general haha
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midnight haven
pls help
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midnight haven
.close
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grizzled lodge
Derive an algorithm to find maximum k s.t. p^k | n! where p is a prime >1 how are you meant to answer this?
midnight haven
this is a standard theorem..don't remeber the derivation though
grizzled lodge
tropic saddle
check all the obvious factors of n! and how many factors of p they each contribute
grizzled lodge
This was my interview question and I kind of explained to them that you need to find how many factors of p then p^2 blah blah are in n!
But couldn’t get to the formula
tropic saddle
like they said, derive an algorithm
which you apparently did
count factors of p
count factors of p^2
...
grizzled lodge
Yeah but how can I represent this as a formula?
opal moss
with some use of floor brackets i guess
shrewd basin
so you got asked to derive legendre's formula (ish)
grizzled lodge
shrewd basin
Sum of floor (n/p^i) from i=1 to infinity?
this works
but its probably fine that you didn't get to the actual formula
grizzled lodge
It’s calm I probably didn’t get it
Another question
I basically got this graph
And they ask how many ways
You can colour the vertices such that no two connected vertices share a colour
If yOu have n colours
opal moss
look at vertex t
grizzled lodge
Okay
opal moss
so what’s the number of colours you need :p
grizzled lodge
n
opal moss
but it’s just this graph no?
grizzled lodge
Wdym
opal moss
you have n colors but only 5 vertices
so you’re not gonna need more than 5
but can you use less than 5?
grizzled lodge
4
opal moss
so can t share a colour with any of the other vertices
grizzled lodge
Yes
opal moss
and show a construction
grizzled lodge
Ah wait but like do we have to consider a lot of cases
opal moss
no, just any construction
grizzled lodge
so can t share a colour with any of the other vertices
I meant no
opal moss
ye, so you always need and only need 5 colours
and now it’s a simple combinatorics problem
plush bramble
"simple combinatorics" is an oxymoron
grizzled lodge
Hm
opal moss
intuitive combinatorics, i guess?
it’d be funny if i got it wrong though
the way to think about it is to break it down to two parts:
-
knowing we only need 5 colours, how many ways can we select the 5 colours to colours the vertices
-
given we’ve chosen 5 colours, how many ways can we colour the vertices
shrewd basin
maybe you can ignore the t for now and consider just a square. if that is f(n) then you just want n*f(n-1)
opal moss
isn’t square more annoying
opal moss
n(n-1) + n(n-1)(n-2)(n-3)+2n(n-1)(n-2)
ye but i think vertices are distinct
so some missing factors
shrewd basin
wdym
opal moss
for a given set of colours you can permute the colours on the vertices
shrewd basin
opal moss
so for 2 colours on a square you already have 2n(n-1) ways using 2 colours since the first colour can be on either diagonal
shrewd basin
is that right?