then u draw the 1/2 of 60
#help-0
wooden raven
Ye that’s the hypotenuse right
wooden raven
5
alpine sable
u can draw that?
wooden raven
Yeah?
alpine sable
do it
after finishing go in the end of a line and do a good point
round point
cause we going to expand it
so we can draw the second line
wooden raven
Ok
alpine sable
u done that?
alpine sable
can u pic me
alpine sable
this one?
wooden raven
That’s for 30
Ye
Then for the coords of 45 I got 3.53 for x and y
Then I add them to get my coordinates to find p?
lone heartBOT
@wooden raven Has your question been resolved?
errant cedar
lone heartBOT
errant cedar
having trouble with the second part of d
ive got up to
-2(p.q)+p.p = -2(r.q) + r.r
now if p=r then it would work but according to the diagram it doesn't look like p=r?
this is the part of the answer that I don't get
lone heartBOT
@errant cedar Has your question been resolved?
lone heartBOT
@errant cedar Has your question been resolved?
lone heartBOT
@errant cedar Has your question been resolved?
lone heartBOT
@errant cedar Has your question been resolved?
errant cedar
.close
serene karma
lone heartBOT
serene karma
lone heartBOT
@serene karma Has your question been resolved?
serene karma
<@&286206848099549185>
serene karma
Yes @dusty flare `
serene karma
On both
dusty flare
ok so for the first you can use basic trig definitions
sin x = opposite/hypotenuse
do you know that?
serene karma
No this a brand new unit for me, I had attempted it and had gotten C. for the first and B. for the second but I'm not too sure.
dusty flare
so
$$\sin{x}=\frac{opposite}{hypotenuse}$$
$$\cos{x}=\frac{adjacent}{hypotenuse}$$
$$\tan{x}=\frac{opposite}{adjacent}$$ with adjacent, hypotenuse, and opposite being the respective sides to the angle.
ocean sealBOT
sdash
dusty flare
so for the first problem, we are given an angle, 27 degrees, a side opposite to that angle, and we want to find the hypotenuse
we use the formula for cos to get
$$\cos{27}=\frac{34}{x}$$
and just rearrange from there to
$$x=\frac{34}{\cos{27}}$$
ocean sealBOT
sdash
serene karma
So what would be the next step?
serene karma
Oh sorry I thought you were asking me a different question
dusty flare
do you need help on the second too
serene karma
Yes please, I think I figured it out but after that I'm not so sure
serene karma
So the same concept but what would we use for the hypotenuse?
dusty flare
3sqrt5
because it’s opposite the right angle
so using sin we have
$\sin{B}=\frac{3}{3\sqrt{5}} \to \frac{1}{\sqrt{5}} \to \frac{\sqrt{5}}{5}$
ocean sealBOT
sdash
dusty flare
but that’s not an answer choice so it must be cos b
serene karma
There are two cos m<B choices A and C
I personally thought it was B because it was sqrt5
dusty flare
$\cos{B}=\frac{6}{3\sqrt{5}}\to\frac{2}{\sqrt{5}}\to\frac{2\sqrt{5}}{5} \text{which is A.}$
ocean sealBOT
sdash
dusty flare
I personally thought it was B because it was sqrt5
you can’t just guess
you have to actually evaluate it
serene karma
you can’t just guess
None of the other ones made sense to me because sqrt5 was what I got when I calculated
serene karma
I have an idea, but an explanation wouldn't hurt. Originally I calculated sqrt5/5 but then I looked and it wasn't an option but I saw B matched 90% of the criteria so I figured it was a typo.
dusty flare
ah
if it’s not an exact math then you have to try everything
we can’t have a radical in the denominator of a fraction in math so we multiply by $\frac{\sqrt{5}}{\sqrt{5}}$ (which equals 1) to get rid of the radical
ocean sealBOT
sdash
serene karma
Yes I wrote this down in my notes thank you for helping me and being thorough with the explanations 🙂
.close
abstract skiff
Hello
abstract skiff
I am just curious on how to solve this equation
O, I see
H= 2(6) - (1/2) 2 =
H = 12 - 1
H= 11
.close
rich basin
lone heartBOT
lone heartBOT
@rich basin Has your question been resolved?
dry verge
Hello, I've seen some different(?) definitions for accumulation/cluster/limit points of a set.
In particular, I'm wondering if these two are equivalent (for a subset ( X ) of the real line).\
Limit point: ( x ) is a limit point iff it is an adherent point of ( X \ {x} ).\
Some lemma: ( x ) is an adherent point iff there exists a sequence contained in ( X ) which converges to ( x ).\
(1) Thus, it may be written as ( x ) is a limit point iff ( x = \lim a_n ) for some sequence ( (a_{n}) ) contained in ( X ), ( a_n \neq x ) for all ( n \in \mathbb{N} ).\
(2) ( x ) is a limit point iff ( x = \lim a_n ) for some sequence ( (a_{n}) ) of distinct elements (or pairwise distinct) contained in ( X ).\
I get the impression that (2) is more restrict than (1). Is it true?\
What are the consequences of this? (if they're not the same).
ocean sealBOT
End
vale wigeon
pretty sure (1) is the same as (2), because a sequence verifying (2) can have at most one term equal to x which can be thrown out without affecting convergence
dry verge
pretty sure (1) is the same as (2), because a sequence verifying (2) can have at...
Oh, that makes sense.
If we have a sequence satisfying (1), we can find another which satisfies (2) by throwing out any repeating terms? i.e. since (a_n) converges, we can construct a subsequence (which also must converge) without the repeating terms.
Is then, the only purpose of these two definitions to discard/not consider constant sequences?
scarlet oriole
Hello guys! I don't really have an idea on how to prove that a system has no real solutions. I know I can graph them for example and then show they do not have a point of intersection or maybe I could end up with a quadratic and then show that it has only complex solutions. But this problem can't really be solved using this 2 methods.
lone heartBOT
Hello guys! I don't really have an idea on how to prove that a system has no rea...
@scarlet oriole Has your question been resolved?
lone heartBOT
@scarlet oriole Has your question been resolved?
lone heartBOT
@scarlet oriole Has your question been resolved?
real gazelle
Hello guys! I don't really have an idea on how to prove that a system has no rea...
Which problem are you looking at, 1, 2, or 3
scarlet oriole
The first system
scarlet oriole
No, in class we do some simple stuff
It's just for my training
This problem is from a 9th grade manual
real gazelle
yeah I have no idea sorry :( I definitely don't know how 9th graders solve this..
does the manual give any examples for how to solve it?
you could always just graph it on a calculator and see that there's no intersection points but I guess that's not really a proof
I know you can do it using calculus but I'm guessing that's not what the manual wants you to do lol
oh wait actually I have an idea for number three
never mind it doesn't work yeah I'm stumped
scarlet oriole
Well, no, the manual does not give me solved problems that can help with this. I really don't understand how can a 9th grader solve it tho. I've been looking at it for quite some time now
Yeah, I could graph it, but I think it needs to be solved using algebra
Maybe I could use inequalities to solve it, but I don't know how🤔
scarlet oriole
What is the weighted version?
I know the AM GM inequality but I've never heard of the weighted version
scarlet oriole
Hmm, so how can I use that in my problem?
tawny schooner
@scarlet oriole all the problems have to be solved using AM-GM
Same method for all
scarlet oriole
Oh, I understand now. Thanks a lot for the help (to you and to Eric Tao)!
What a nice way of solving it
kindred cedar
Can someone help me with the following?
Given that p^x = 3 and p > 0, Find the value of
keen pasture
(p^x)^z = p^[xz]
keen pasture
You're welcome
kindred cedar
Another question, how would I evaluate questions like these?
tawny schooner
Use sum of first n natural numbers formula
N(N+1)/2
Then decompose each term into partial fractions
kindred cedar
alright
prisma elbow
how do you get the vert asymptotes from this equation?
lone heartBOT
how do you get the vert asymptotes from this equation?
minor needle
ik it's 3(n-(1/3)) or 3n-1
3n-1
you can solve it in two ways I'd say
first is
$$\cot \Big(\frac{\pi}{3}(x+1)\Big)=\frac{\cos \Big(\frac{\pi}{3}(x+1)\Big)}{\sin \Big(\frac{\pi}{3}(x+1)\Big)}$$
ocean sealBOT
Modus
ocean sealBOT
Modus
minor needle
you can solve for "x" now
2nd way is to start from original (not transformed) cotangent
cot(x) has vert asymptotes when x = πn
now just follow the transformations and modify this equation
alpine sable
hello, can someone help me understand how to solve this quadratic equation 5x( x+2 ) -15 ?
wary stream
Can you post the exact question? Like a screenshot
prisma elbow
$5x(x+2)-15$
ocean sealBOT
Scarecrow
prisma elbow
is this what the question looks likes?
alpine sable
i was able to do it for the first two
prisma elbow
by the greatest common factor
alpine sable
but im confused by the ()
prisma elbow
but im confused by the ()
it's a way to write multiplcation
wary stream
Distribute the 5x, and then use quadratic formula or whatever factoring method you know
alpine sable
like 5x multiple x + 5x multiple 2?
wary stream
Yes
ocean sealBOT
irenee
alpine sable
i got the discriminant as 14 and when i use the formula -b+√d/2a
it will be like -√2-√14/2
lone heartBOT
@alpine sable Has your question been resolved?
alpine sable
me?
alpine sable
.reopen
lime tartan
What...
lone heartBOT
Available help channel!
turbid sigil
lone heartBOT
turbid sigil
I'm doing an epsilon delta proof of a) and am stuck , I let $|z-i|<\delta$, then get to $|(iz^3-1)|(z-i)|/|z^2+1|$
ocean sealBOT
cali5nia
fallen verge
oh im not good with epsilon delta sorry
turbid sigil
np me either
The limit's zero
that might be all they want but I was curious for practice how epsilon delta would go
wanton musk
Can someone check if my work is correct for this problem
lone heartBOT
Can someone check if my work is correct for this problem
wanton musk
lone heartBOT
@wanton musk Has your question been resolved?
wanton musk
.close
quaint karma
trig identities problem, first i tried getting cos(4x) by cos(4x) = cos(2x)^2 - sin(2x)^2 and i found that cos(2x) = 4sin^4(x) - 4sin^2(x) + 1, i don't know where to go from here (using x instead of theta for convenience)
frigid rune
trig identities problem, first i tried getting cos(4x) by cos(4x) = cos(2x)^2 - ...
did you mean cos^2(2x) by any chance?
real gazelle
try simplifying using $$\cos(2x) = 2\cos^2 x - 1$$
ocean sealBOT
Eric Tao (he/him)
real gazelle
and pythagorean identity $$\sin^2 x + \cos^2 x = 1$$
ocean sealBOT
Eric Tao (he/him)
real gazelle
that should be enough info
frigid rune
try simplifying using $$\cos(2x) = 2\cos^2 x - 1$$
since the answer wants in terms of sine will probably be easier to use cos(2x) = 1-2sin(x)^2 in this case
frigid rune
yes lol
real gazelle
yeah those two identities should be enough to simplify the entire thing
quaint karma
since the answer wants in terms of sine will probably be easier to use cos(2x) =...
that is how i got that cos^2(2x) = 4sin^4 - 4sin^2(x) + 1
frigid rune
yep so now you need to simplify sin(2x)^2
real gazelle
?
quaint karma
more like make it more complex...
real gazelle
**Eric Tao (he/him)**
@quaint karma since you already have the answer for cos^2(2x), try using this identity initially
and then all you have to do is simplify and you're done
quaint karma
i need to somehow get b*sin^3(x)
frigid rune
wdym nathan
their first step was to say cos(4x) = cos(2x)^2 - sin(2x)^2 so im just following on from that
yes ik it can be done by using one of the other cos double angle formula
real gazelle
b can be 0
frigid rune
i need to somehow get b*sin^3(x)
what if b=0?
frigid rune
no, i think d should|| also be 0||
quaint karma
well the issue is that i need to subtract sin(2x)^2 in order to get cos(4x), but i already used the exponent of 2 "cos(2x) = 4sin^4(x) - 4sin^2(x) + 1"
frigid rune
there are 2 ways to deal with the sin(2x)^2
you can either use that sin(2x) = 2sin(x)cos(x)
or that sin(2x)^2 = 1-cos(2x)^2
quaint karma
but i can't use cos...
real gazelle
you already know how to simplify cos(2x)^2 into sines though
quaint karma
yes
real gazelle
so if you get it into that form then you are done
frigid rune
thats true but if you do the first method then you will end up with cos(x)^2 which can be simplified to 1-sin(x)^2
and if you do the 2nd method then you have cos(2x)^2 which you have already found out how to write in terms of sin
frigid rune
even though you only want sin in your final answer you may have to introduce some cosines at some points in the working to get to the answer
quaint karma
there are 2 ways to deal with the sin(2x)^2
you can either use that sin(2x) = 2s...
so i would need to use the half angle identity (sin(x/2) = sqrt((1 - cos x)/2)) and then use the half angle identity on cos(2x) = 1 - 2sin x (cos(x/2) = sqrt((1 + cos x)/2)), and multiply right?
and then i would get the values i need?
ok
i have run into an issue
it results in 1
somehow i got 4sin^4(x) - 4sin^2(x) for -sin(2x)^2
i don't understand
help
quaint karma
somehow i got 4sin^4(x) - 4sin^2(x) for -sin(2x)^2
and i just checked wolfram and i said that this was true
also it said that cos(2x)^2 = 4sin^4(x) - 4sin^2(x) + 1 is true
lone heartBOT
@quaint karma Has your question been resolved?
lone heartBOT
quaint karma
.reopen
lone heartBOT
✅
quaint karma
why use the half angle identity?
i was using the half angle identity on sin(2x) to get sin x....
wait
that is how i messed up...
real gazelle
wait I'm confused on what you're stuck on
you know that $$\cos(4x) = 2\cos^2(2x)-1$$ and you also know that $$\cos^2(2x) = 4\sin^4(x) - 4\sin^2(x) + 1$$ right
quaint karma
oh.........
real gazelle
oh wait sorry the second equation isn't right lemme fix that
quaint karma
i was trying to solve for sin(2x)^2
ocean sealBOT
Eric Tao (he/him)
quaint karma
since i know cos(2x) is terms of sin i can just use cos(2x) = 2cos(x)^2 - 1
i was trying to use cos(x)^2 + sin(x)^2
i think that is how i messed up
real gazelle
ah gotcha, yeah the cos(x)^2 + sin(x)^2 = 1 is how you get that cos(x)^2 - sin(x)^2 is the same thing as 2cos(x)^2 - 1
quaint karma
oh....
yeah i accidentally use pythagoras lol
so the answer is cos(4x) = 1 - 8 sin^2(x) + 8 sin^4(x)?
yes it is
thank you
real gazelle
no problem!
lone heartBOT
@quaint karma Has your question been resolved?
short comet
so the answer is cos(4x) = 1 - 8 sin^2(x) + 8 sin^4(x)?
that's correct!
vivid bronze
lone heartBOT
placid axle
frigid hatch
yes
gray isle
what will be the height of the rocket when it lands?
gray isle
I know...
frigid hatch
what will the height of the rocket be when it lands?
lone heartBOT
@vivid bronze Has your question been resolved?
frigid hatch
maybe reply to our questions?
alpine sable
lone heartBOT
alpine sable
allr
alpine sable
Notice that 6 of those angles will draw a whole circle
what would the measure of the angle next to it be
also 60?
placid zinc
Everything happens to be 60, yes
hushed oxide
naive valley
is this a true/false question or something?
$\mathbb Z_2[i]$ and $\mathbb Z_2$ are not the same thing
ocean sealBOT
OurBelovedBungo
hushed oxide
is this a true/false question or something?
sorry i mistype it, i think it should be ismorphic. How can I show it tho
$\mathbb{Z}_2[i] \cong \mathbb{Z}_2$ is a field of order 2
ocean sealBOT
wil
real gazelle
unless I'm going crazy, doesn't the former have four elements? 0+0i, 0+1i, 1+0i, 1+1i
lone heartBOT
@hushed oxide Has your question been resolved?
torn isle
Hi, for this, may I know how to find the limit for triple integral of x, y and z?
lone heartBOT
@torn isle Has your question been resolved?
rugged sun
Hi
rugged sun
I got something like this but I don’t know how to find the limit for x y and z
It will be helpful to use cylindrical polars here
In this coordinate system, the surface z=sqrt(x^2+y^2) becomes just z=r
The enclosed volume has this sufrace below the plane z=4
Therefore we need to let r vary from 0 to 4 to reach the plane
torn isle
Therefore we need to let r vary from 0 to 4 to reach the plane
I was thinking don’t change dz first
Then find out the limit of z only use rdrd theta
rugged sun
But the limits of z are from z=r to z=4
torn isle
Hmm so must change to cylindrical polar at first?
rugged sun
Yes, I think so
torn isle
Yes, I think so
Okay nvm, let me think how to change first
rugged sun
Ok
lone heartBOT
@torn isle Has your question been resolved?
rugged sun
Hmm so must change to cylindrical polar at first?
Did that work out ok?
worthy igloo
wondering if the answer for this question is wrong
lone heartBOT
wondering if the answer for this question is wrong
native cloud
What's wrong
worthy igloo
is that graph incorrect
native cloud
?
worthy igloo
so would it not just be a series of points at integers along the x axis
native cloud
Why is it undefined
worthy igloo
because would it be negative or positive
native cloud
Plug in 1.5 in -2^x
worthy igloo
online cas calc does not make a graph either
worthy igloo
I see
I think i misunderstood
would you agree with my previos points for f(x) = (-2)^x
native cloud
This?
worthy igloo
no but on your sketch if you included the negative sign in the bracket, I don't believe it would sketch
only real for the x integers
trim wagon
,w (-2)^1.5
ocean sealBOT
worthy igloo
HOW
no way
ohhh, imaginary
there we go, perhaps it can only be sketched on the complex plane
trim wagon
Yeah idk if it’s continuous in real, correct me if I’m wrong
worthy igloo
,w (-2)^(-3)
ocean sealBOT
lone heartBOT
lone heartBOT
Available help channel!
wind bloom
um ok so i think i did this wrong i did 12^2 + 9^2 = x^2
lone heartBOT
um ok so i think i did this wrong i did 12^2 + 9^2 = x^2
wind bloom
to find AE
vale wigeon
angle ABE does not look like a right angle.
so the pythagorean theorem does not apply like you tried to.
also... the problem statement appears to list the measure of angle ABO, but i see no point named O on the diagram
what's up with that?
wind bloom
i think that says ABD
wind bloom
so the pythagorean theorem does not apply like you tried to.
hmm, so what should i use?
vale wigeon
the first thing i'd suggest you do is mark all known measurements on the diagram
wind bloom
ok i did that
vale wigeon
vale wigeon
@alpine sable this channel is occupied, please open your own. #❓how-to-get-help
alpine sable
Ok
vale wigeon
@wind bloom are you familiar with the law of cosines?
wind bloom
<@844979182701379585> are you familiar with the law of cosines?
no
i havent learned that yet
wind bloom
yeah
vale wigeon
so in fact
ABE is a right triangle, so the pythagorean theorem does apply, but you misidentified which angle is the right angle.
wind bloom
oh.
vale wigeon
...hang on what the hell
wind bloom
?
vale wigeon
the problem appears to be inconsistent
wind bloom
wdym?
vale wigeon
considering triangle AEB, the given lengths imply that cos(ABE) = 3/4, but cos(55°) is about 0.58, not 0.75 as it would appear
wind bloom
i dont think im supposed to use trig here bc my teacher didnt teach it to us yet
vale wigeon
ok so your teacher did not teach you trig but they're hitting you with angle measures that make no sense and you're supposed to just eat it up?
wind bloom
i guess so
i mean everyone else in my class got it correct except for me
by using the pythagorean theorem
vale wigeon
i mean ok like
we CAN just ignore the angle inconsistency
and just apply the pythagorean theorem
and the "angles in a triangle sum to 180°" thing
i guess without trig we will not run into contradictions anyway
carmine harbor
vale wigeon
AE is not a side of the rhombus
again
do apply the pythagorean theorem to ABE
but keep in mind it's E that is the right angle
vale wigeon
sure
wind bloom
ok
lone heartBOT
@wind bloom Has your question been resolved?
lone heartBOT
lone heartBOT
Available help channel!
native cloud
lone heartBOT
native cloud
I don't know how to start
frigid rune
what do you know about the velocity of a particle when it is just about to change direction?
native cloud
v = 0?
native cloud
So I should find x'(t)?
frigid rune
yep
native cloud
frigid rune
correct
native cloud
What do I do next?
frigid rune
v = 0?
you already told me that when the particle is changing direction v=0 so you can set cos(t/2) * 1/2 = 0 and solve for t
ebon bloom
Please help. What these things even mean? how it defines that there're exactly a and b?
ebon bloom
i'm acquainted with the used notation, but i can't understand it anyway
vale wigeon
for any two things there exists a set whose elements are those two things and nothing else
lone heartBOT
lone heartBOT
Available help channel!
austere compass
Do matrices $A,B \in Z \backslash 2Z$ exist, so that AB - BA = $I_n$ is true?
ocean sealBOT
Levens
austere compass
So I've proven that AB - BA = I_n is not true for a field with natural numbers, but what makes Z\2Z different?
placid zinc
Is that supposed to be A,B with entries in Z\2Z?
austere compass
Is that supposed to be A,B with entries in Z\2Z?
yes
vale wigeon
So I've proven that AB - BA = I_n is not true for a field with natural numbers, ...
can you show your proof?
er, wait.
do you mean Z\2Z or Z/2Z?
austere compass
sorry yeah the second one
vale wigeon
right
so can you show your proof that AB - BA = I is impossible?
it may not require the characteristic of the base ring to be 0 at all
and carry over to Z/2Z word-for-word
austere compass
for my proof i basically took the trace of AB - BA and the trace of I_n and since the trace of BA and the trace of A are equal to each other, you can say that the trace of AB - BA is 0 which should mean that the trace of I_n should be 0 too but it can't, since its always n
vale wigeon
can't say rn
perhaps the slightly painful route of writing AB-BA entry by entry could be fruitful
oh yeah
such matrices do exist
$\bmqty{0&0\1&0}$ and $\bmqty{0&1\0&0}$
ocean sealBOT
Ann
lone heartBOT
@austere compass Has your question been resolved?
keen python
does this - imply to n^2 and 3 ?
lone heartBOT
does this - imply to n^2 and 3 ?
keen python
bc im trying to rewrite it to
(a-b)*(a+b) / (a+b)
so would b be n^2 - 3 ?
the minus does not have an impact to n^2 and 3 ?
b_n = sqrt(....) - n^2 - 3
equal to
b_n = sqrt(....) - (n^2 - 3) ? I guess not ?
only this would be equal
b_n = sqrt(....) - (n^2 + 3)
so by actual b is n^2 + 3 ?
.close
kindred anchor
lone heartBOT
kindred anchor
$(\frac{3}{4}(\log_2{x})^2+\log_2{x}-\frac{5}{4})\cdot\log_2{x}=\frac{1}{2}$
ocean sealBOT
QuantumBee
kindred anchor
considering $\log_2{x}=t$
$\newline \frac{3t^3}{4}+t^2-\frac{5t}{4}=\frac{1}{2}$
ocean sealBOT
QuantumBee
kindred anchor
$3t^3+4t^2-5t-2=0$
ocean sealBOT
QuantumBee
kindred anchor
how do i go further?
mortal trellis
probably best if you just google it
maybe you know it under a different name
but it tells you that if x is a rational root of a polynomial with integer coefficients then there aren't that many options for x
and then you can check them by hand
kindred anchor
,w solve [3t^3+4t^2-5t-2=0]
ocean sealBOT
kindred anchor
mortal trellis
or do that
kindred anchor
im not allowed to use this in exam
how do i solve it by hand
by factoring?
i guess it doesn't work here
mortal trellis
like I said rational root theorem
kindred anchor
possible rational roots = $\frac{\pm{1},\pm{2}}{\pm{1},\pm{3}}$
ocean sealBOT
QuantumBee
mortal trellis
bad notation but yes
then you can go through these
best bet is to start with the integers
kindred anchor
is there any other method by which i can solve the equation?
mortal trellis
well you could learn the cubic formula
but I wouldn't recommend it
by the "law of nice questions" the rational root theorem is hopefully enough
kindred anchor
well you could learn the cubic formula
perhaps @vale wigeon can help
but however im not asked to find the roots of the equation
the answer is just the number of solutions which is 3
mortal trellis
I don't know if there is a nice number to check the number of solutions of a cubic like there is for quadratics with the discriminant
I guess maybe there is with the cubic formula
mortal trellis
gilded citrus
if the questions asks for you to factorize a cubic its likely that one of the roots is as simple as +-1, 2, 1/2
if you find one root, you can divide the cubic by x - a to get a quadratic and factor it normally
vale wigeon
lone heartBOT
@kindred anchor Has your question been resolved?
rustic hazel
lone heartBOT
strange fractal
help
strange fractal
part b
compact cedar
looks right
compact cedar
ovvv
if the triangles are similar, and any of the sides are the same length, that means all are the same length
strange fractal
yes
compact cedar
i'm not sure if there's some goofy terminology you're forced to use to get the right answer but that's the logic in normal words
compact cedar
what is
strange fractal
to watch a video on it
compact cedar
ok listen
strange fractal
yes
compact cedar
it's asking you why DE and AB are the same length. if they're the exact same triangle, they have to be the same length, right?
compact cedar
we already proved they're identical
strange fractal
oh
i thought it meant similar
but i got confused
wait im so freaking confused isnt || similar
compact cedar
no no
strange fractal
oh or is it
compact cedar
a || b means a is parallel to b
strange fractal
|||
compact cedar
the 3 stacked lines means identical. 2 vertical lines means parallel
compact cedar
can't lie im not sure. it doesn't really specify whether AE is a line (if it were it'd be easy to prove). i mean they could be identical triangles and ACB could be tilted, and then AB and DE aren't parallel
@ the helpers rq
strange fractal
<@&286206848099549185>
lime tartan
What
strange fractal
help
lime tartan
We know ABC is congruent to EDC
strange fractal
yes
strange fractal
yes
lime tartan
Use SAS for part a
We know that DC = BC as the sides are given. Same goes for AC = EC. And angle C is vertically opposite which means it should be equal in both sides. So that's SAS
Now coming to part b
We proved ABC is Congruent with EDC so shouldn't it automatically mean AB || DE?
alpine sable
since the triangles are congruent, we can consider the line DB that joins the lines DE and AB, and since the 2 triangles are congruent, the angles EDB and BAE are equal, therefore since alternate interior angles are equal, DE || AB
the same argument can be made for the other line that joins DE and AB that is AE
strange fractal
im confused can u make a drawing
lime tartan
im confused can u make a drawing
What he means is that
Congruent means the two triangles are same.
The line DB is joining the lines DE and AB
Do you understand till here?
strange fractal
yes
lime tartan
Then he clarified the angles EDB and BAE are equal
First look at EDB alone then BAE
As separate lines
Get it?
Their angles are equal
alpine sable
lime tartan
Nice drawing lol
Better than mine 
Now since alternate interior angles of the triangles are equal therefore DE || AB
lime tartan
If you're done write .close
lone heartBOT
@strange fractal Has your question been resolved?
native cloud
lone heartBOT
native cloud
How can I approach this problem?
marsh rapids
find r as a function of V, then use the chain rule
marsh rapids
V = 4/3πr^3
it's 4/3, not 27
the derivative of x^1/3 is 1/3 * x^(-2/3), so I don't think your r' is correct
tight locust
Why are you solving for r
That defeats the whole point of differentiating implicitly
native cloud
What should I be doing?
tight locust
The equation
native cloud
27π?
marsh rapids
yeah that also works
native cloud
Yes, hold on
marsh rapids
it's faster I think
native cloud
V' = 4/3π * 3r^2
native cloud
I don't know
tight locust
Remember that r is just short for "r(t)"
The radius is a function of our time parameter
native cloud
r = 27πt
tight locust
Nope
Can you find the derivative of sin(x)^3 using the chain rule
Theres the problem
Recall what chain rule actually is
native cloud
3(sin(x))^2 * cos(x)
tight locust
Yes
Let me rewrite that
3(sin(x))^2 * sin'(x)
Now can you find the derivative of:
r(t)^3
native cloud
But I don't know what's r(t)
tight locust
Doesn't matter
native cloud
3r(t)^2 * r'(t)
native cloud
Yee
tight locust
Now plug in known values and solve for r'
native cloud
27π = 4/3π 3(3)^2 r'?
tight locust
27π = 4/3π 3(3)^2 r'?
If you can solve 5=3x then this equation should be no problem now
tight locust
Sure
tight locust
Draw a diagram
native cloud
Oh wait
I think I might know a shortcut
(60x3, 0) and (0, 80x3)
These are the two points after three hours
I just need to find the slope?
tight locust
Not quite
The pythagorean equation is quadratic in 2 variables
Finding the slope of a line is meaningless
native cloud
Okay
tight locust
Ok
Let's let A and B be our displacements
Then A' and B' will be our velocities
What are A and B at t=3?
native cloud
(80x3)^2 + (60x3)^2 = √Ans
tight locust
Lol
Let's back up for a sec
We have a triangle with vertices at (0,0), (0,80), and (60,0)
What is the length of its hypotenuse
native cloud
80^2 + 60^2 = c^2
native cloud
100
tight locust
Yes
So let's take our equation relating A B and c
A^2 + B^2 = c^2
Take the derivative
native cloud
2A + 2B = 2C?
tight locust
Chain rule
native cloud
2A * (A') + 2B * (B') = 2C * (C')?
tight locust
Lol
native cloud
Isn't it 60x3 and 80x3?
tight locust
Our values of A' and B' at t=3 are 60 and 80
Our value of C is 100
So we take:
2AA' + 2BB' = 2CC'
2(180)(60) + 2(240)(80) = 2(100)C'
native cloud
Ohhh
What happens if the triangle/diagram wasn't a right triangle?
We wouldn't be able to use pyha
tight locust
Law of cosines ig
native cloud
Ohh okie
tight locust
Thats the general pythagorean theorem
native cloud
2(180)(60) + 2(240)(80) = 2(100)C'
Also, shouldn't 2(100)C' be 2(300)C'?
tight locust
Yeah
native cloud
Btw, a bit of a personal question, but how did you get to be this good at math?
I tend to forget 50% of the things I learned last year
tight locust
Shitposting on discord
limpid ingot
x^y=2
x^t=16
what is x^(y-1)
lone heartBOT
x^y=2
x^t=16
what is x^(y-1)
tight locust
This system of equations is underdetermined
limpid ingot
yea idk what to do
limpid ingot
answers are -18, -4 1/8 8 and 32
tight locust
Are we to assume integer values
limpid ingot
idk
imma just so 1/8
since it cant be negative
and x^y is already less than 8 and 32
is that ok
@tight locust
limpid ingot
tried that
but
how u gonna get y-1
cause that would be x^y/x^1
yet we cant find x^1
raven dagger
answers are -18, -4 1/8 8 and 32
Is it an mcq or something?
lone heartBOT
@limpid ingot Has your question been resolved?
livid raven
Why is my answer incorrect?
lone heartBOT
Why is my answer incorrect?
lone heartBOT
lone heartBOT
Available help channel!
versed crater
this isnt exactly a maths question but i didnt know where else to ask
versed crater
when writing a resarch paper as a student
what qualifies as impressive
and are new findings necessary
keen pasture
when writing a resarch paper as a student
Like in school?
keen pasture
and are new findings necessary
No, usually not
versed crater
what ive done is written a programme on dsmos to analyse something and talked about how i went about creating it etc etc and it a useful visual aid in visualising a conjecture
is that good enough
for a centrepiece to the paper
lone heartBOT
@versed crater Has your question been resolved?
lone heartBOT
@versed crater Has your question been resolved?
surreal lichen
lone heartBOT
surreal lichen
for this limit i divide the numerator and denominator by x^2
to get
(1 + sinx/x^2 )/ (1+ cosx/x^2 )
from here
i tried evaluating the limit of (1 + sinx/x^2 ) as x approaaches infinity first
here's where i'm stuck
i know sinx is always between 1 and -1
so would the sinx / x^2 go to zero or a negative no.?
edgy flare
We’ll think
1/infinity
And -1/infinity
They both approach 0
So sin(x) /x^2 and cos(x) /x^2 terms turn to 0 as x approaches infinity
lone heartBOT
lone heartBOT
Available help channel!
nocturne marsh
lone heartBOT
nocturne marsh
find for X and Y
lone heartBOT
Available help channel!
livid raven
lone heartBOT
livid raven
In the sixths step, how do they get rid of the anti derivative if that last step is the same as the 1st
That is finding the anti derivative of sin(3x)cos(5x)
lone heartBOT
@livid raven Has your question been resolved?
livid raven
<@&286206848099549185>
real gazelle
In the sixths step, how do they get rid of the anti derivative if that last step...
treat the integral of sin(3x) * cos(5x) dx as a variable in that equation
they brought it over to one side
and then they divided by (1 - 9/25)
(also this is a terrible way of solving this problem, if you want to know a better way, look up the product to sum formula)
teal matrix
lone heartBOT
teal matrix
I got 900-590 because doesn’t a heptagon equal to 900?
And all the #’s added equal 590
Nvm I figured it out
Ty
.close
fast copper
ok so maybe this is too simple for this discord. Our store has 197 reviews and an average 3.6 rating. How many 5 stars do we need to be 4.5?
remote heron
so say you need $n$ more reviews, at 5 stars each
ocean sealBOT
jan Niku
remote heron
you want to solve $\frac{ (197)(3.6)+5(n) }{ n + 197} = 4.5$
ocean sealBOT
jan Niku
fast copper
got it
355 5 star ratings needed to get us to 4.5 apparently
75 to 4.0, more achievable
thanks!\
remote heron
np
lone heartBOT
@fast copper Has your question been resolved?
alpine sable
Why is 5 = to 3 radical 3
lone heartBOT
Why is 5 = to 3 radical 3
real gazelle
Why is 5 = to 3 radical 3
try calculating what $\sqrt{4^2 + 3^2}$ is
ocean sealBOT
Eric Tao (he/him)
chrome plank
@alpine sable ?
real gazelle
its radical 27
how did you get 27?
chrome plank
@alpine sable can you show your work?
alpine sable
oh
BRUH
this makes a lot more sense now
i was legit so confused
radical 25 is 5 yes yes
chrome plank
$\sqrt{4^2 + 3^2}\\
\sqrt{4 \cdot 4 + 3 \cdot 3}\\
\sqrt{16 + 9}\\
\sqrt{25}$
ocean sealBOT
Nonna
