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#help-36
steel gale
i know you probably have to use factorials here but i dont know how to
steel gale
formulate this
the consonants can be arranged in 5! ways
the vowels can be arranged in 4! ways
but i dont get how to apply the whole
vowels cant be next to each other
c_c_c_c_c_
so 6
possible places for vowels to be
sorry im just saying whatever i can think of
trail mango
there are 4 vowels, so the structure of the word will be like V_V_V_V with 2 extra _ inserted between or before any of those 7 positions
robust mulch
steel gale
okay so
grim nebula
and you fill in the holes with vowels
steel gale
thats what i was thinking but it doesnt really seem to matter
either way should work right
grim nebula
there is a difference
grim nebula
its possible to have VCCVCVCVC for example
steel gale
so then i have to account for
trail mango
wouldn't that come up with my method?
grim nebula
would it
grim nebula
your holes need to be filled with either 1 or 2 consonants
not as straightforward to count i think 
trail mango
I may not have said it very well
steel gale
its fine i appreciate the help
so then in that case
the different
the consonants can be arranged in
trail mango
the _ was supposed to represent positions filled by constants
steel gale
seems easier to work around with consonants then
steel gale
the last one has to be a consonant too, right?
trail mango
does that not count double constants at the end?
grim nebula
should probably put another _ then
steel gale
to nbe honest
steel gale
it seems easier to work around consonants
so then yeah the vowels can be arranged in 6C4 ways right?
along with
4!
grim nebula
yes
steel gale
so 6C4 x 4! ?
grim nebula
dont forget to arrange the consonants too
grim nebula
yeah
final saddleBOT
final saddleBOT
Available help channel!
final saddleBOT
spring lava
Let's take the question one sentence at a time
For the first sentence we have a farm that's split into 3 pieces for 3 people
Afterwards we read that John's part is equally divided into 3 for his children
Im pretty sure if paul sells his it wouldnt matter as all of them are being sold in the end,
Jim owns 1/3 of the property but that isnt the common fraction
it's simplified down to that but if common fraction means you need to have it equivalent to everyone elses you need to find a common denominator
so jim would own 3/9 of the property
@tranquil pine does this help?
jovial ermine
Hello, I would appreciate any hints to solve the following question. I'm unsure how to start.
Need to work out the pdf and cdf using the variables.
Thank you!
final saddleBOT
Hello, I would appreciate any hints to solve the following question. I'm unsure ...
coarse yacht
Write $F_{e^{X}}(x) = \mathbb{P}(e^{X} \leq x)$
soft zealotBOT
black_couscous
coarse yacht
Then describe this set $ (e^{X} \leq x) $
jovial ermine
Write $F_{e^{X}}(x) = \mathbb{P}(e^{X} \leq x)$
just to clarify, does this mean that e^x is less than or equal to all values of x? and do I treat this as the pdf or the cdf?
coarse yacht
No $X$ is a random variable and $x$ is a real number. If you want you can chose $y$ instead of $x$ to make things clearer.
soft zealotBOT
black_couscous
jovial ermine
ok and because of the sign '≤' this is the cdf right? if so then i guess for the pdf it would be just <?
coarse yacht
For the PDF it's different
Let's focus on the CDF first because it's easier
Try what I told you and then come back for the pdf
jovial ermine
ok
jovial ermine
Then describe this set $ (e^{X} \leq x) $
also im not sure what this means?
coarse yacht
Then describe this set $ (e^{X} \leq x) $
This is a set
Like $X$ is a rv that goes from a universe to the real numbers
soft zealotBOT
black_couscous
coarse yacht
And the probability is a measure of sets
jovial ermine
hmm is that like the range of values which rv can take? if so then after writing the cdf I should describe its range of values?
I just wrote these
I suppose for the pdf I need a way to express adding all the individual probabilities being added.
jovial ermine
And the probability is a measure of sets
Need to go but thanks for the advice! 🙂
.close
muted basalt
how do I find the inverse?
final saddleBOT
how do I find the inverse?
muted basalt
The answer I keep getting is (-x-5)/2(x-1)
muted basalt
yeah but when I put it in an oline calculator I get somethin else
muted basalt
it gives me (x+5)/2(1-2x)
I dunno If I have to like factor the negative out or If mine is technically right
here a picture of my work
opaque herald
final saddleBOT
opaque herald
stuck on how to start
tranquil flume
Make x the subject in the first, z the subject ok the second and then plug in them to x/z to solve
tranquil flume
Yeah
opaque herald
then just put both inthe teh fraction?
tranquil flume
Ye
opaque herald
how do i isolate z?
tranquil flume
What do you think
opaque herald
could i cross multiyplu?
tranquil flume
Yes obviously
tranquil flume
I call this algebraic manipulation
opaque herald
can I cancel the 7's in the denonminator before putting into frction
tranquil flume
Yes
tranquil flume
Do you have the correct answer
opaque herald
but II is going to end up with x^2-3x<0
opaque herald
Do you have the correct answer
nope i dont get an answer key
could brute force but i only have 1 reminaing attempt
tranquil flume
What topic is this from if I may ask?
opaque herald
waiting
tranquil flume
In x(x-3)<0 there are quite a few possiblies
opaque herald
there are?
tranquil flume
So the product of x and x-3 has be negative right?
opaque herald
maybe?
tranquil flume
You get negative when: - times + and + times -
opaque herald
yeah but the x^2 couldbe smth else
opaque herald
yeah ig?
tranquil flume
So..
[x<0 and x>3] or [x>0 and x<3]
[False (makes no sense)] or [0<x<3]
Which is 0<x<3
So all of them are equal
opaque herald
ohhh
tranquil flume
Sorry for terrible explanation
I used the logical equivalence method
Because it's what I am learning currently
Plenty of easier methods probably
So the answer is D
Unless they are sick and twisted and set E as correct
opaque herald
would thesse all be true tho?
opaque herald
So the answer is D
worked
tranquil flume
My gut says E
Becuss e
a + b > a-b
<-> a-a > -b-b
<-> 0 > - 2b
<-> 0 < b
@opaque herald you dead?
Our comrade has fallen
Rip
opaque herald
but like, is a and b were option a, and a=2 b=1 the its stillwork
tranquil flume
I don't understand
opaque herald
might just try e tho
tranquil flume
y = a(x-p)(x-q) where p and q are roots you know this form?
opaque herald
wait so i pu he entire thing infromt of x?
opaque herald
or is x^2 the coeeficient
tranquil flume
Sorry I'm a little bit drunk
My man ballerinarata has passed away
Yohojo
@opaque herald you riding???
MD??
opaque herald
still confused
opaque herald
not really? idk
tranquil flume
Otherwise google "quadratic slope intercept form"
opaque herald
that didnt help
tranquil flume
YES
and a smis given as 1
Cleanly
So it can be invisible
YOU GOR IT
@opaque herald
Do you still need helppp
opaque herald
alr will do
tranquil flume
Lemon
Squeezy
Any more questions
Before I did
Die
@opaque herald
MD MY MA
opaque herald
porbably but goin to do his first
opaque herald
are you alright lol
im stuck here
ill be back after i eat smth
<@&286206848099549185>
final saddleBOT
@opaque herald Has your question been resolved?
opaque herald
.close
flat tangle
Given the function y = 2x3 – 3x2 – 5x + 1, which finite differences will be equal (or constant)?
final saddleBOT
Given the function y = 2x3 – 3x2 – 5x + 1, which finite differences will be equa...
spiral quail
What does finite difference even mean??
flat tangle
like would it be the third difference or fourth ?
final saddleBOT
@flat tangle Has your question been resolved?
final saddleBOT
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Available help channel!
static jungle
why does x + |ax + b| = k have one value for k
final saddleBOT
why does x + |ax + b| = k have one value for k
static jungle
why would it have more than 1 answer?
when we modulate x theres a possibility for both a negative and a positive value for k right
summer raptor
no
static jungle
for example in a normal modulation ax + b, ax + b = +/- k
static jungle
no
no?
okay i think i got it on my own
basically it needs to work both ways
k nvm
.close
modest canopy
Yo
modest canopy
I did bad on a test
And I just wanna go over it
75 - 3 times 7 to the power of 2 + 6 to the power of 3 divided by 12
= -48 right
spiral quail
Yo are u using PEMDAS as order of operations, or something else?
dreamy snow
can someone explain what this means
final saddleBOT
can someone explain what this means
dreamy snow
someone explained it to be like
but I'm so confused as to how they got -12x + 12 = 0
and then how did the deduce that 100 items is maximum profit?
calm laurel
hello
dreamy snow
hi
final saddleBOT
@dreamy snow Has your question been resolved?
dull wadi
final saddleBOT
fossil geyser
For a dilation from the origin, just multiply all the coordinates by the scale factor
fossil geyser
Yeah looks like A is (2,4)
dull wadi
And it's (6,12) dilated right?
fossil geyser
Yep
dull wadi
Ok
dull wadi
Yeah my teacher was saying something about that
fossil geyser
If you do it right, it should look like a scaled up version of the same triangle
Same shape, just bigger
dull wadi
Ohhh
dull wadi
So 12 -6 dilated
fossil geyser
yep
fossil geyser
You should plot and label those points A', B', and C'
Then connect them to form the dilated triangle
Wait
B is not correct
Didn't we say B is (4,-2), so B' is (12, -6) ?
dull wadi
Yeah I forgot to change that sorr6b
Can you help me with a few more questions ?
Please
@fossil geyser
fossil geyser
Go ahead and post them. If I can't, somebody will
final saddleBOT
@dull wadi Has your question been resolved?
final saddleBOT
@dull wadi Has your question been resolved?
final saddleBOT
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Available help channel!
agile jacinth
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half summit
what's the range of cosine wave
agile jacinth
1 and -1
agile jacinth
8 n -8
half summit
mhm, velocity is 4 + 8cos 2t
so it's 8 cos 2t shifted up 4
so what would the range of that be?
agile jacinth
i just dont see how cos t can be substituted for 1 or -1
agile jacinth
right
half summit
so what don't you understand
agile jacinth
cos and son oscilliate between 1 and -1
so how does this explain my question
sorry im just not seeing it
half summit
you didn't ask a question
agile jacinth
i just dont see how cos t can be substituted for 1 or -1
.
half summit
yeah they just did that to illustate
that it's the maximum and minimum
-1 is the smallest value cos x can take
so 4 + 8(-1) would be the miniumum
and same thing for positive 1
agile jacinth
so 4 + 8(-1) would be the miniumum
right so in this case minimum velocity
but if it was just to find the range of values of that eq
what would the minimum value stand for
half summit
range is the just the values the velocity can take
so the range is all the values between minimum velocity and maximum velocity inclusive
agile jacinth
i mean like if we ignore the velocity part
agile jacinth
range is the just the values the velocity can take
than what does that range of values mean
half summit
range is the set of y values a function can be
half summit
👍
final saddleBOT
@agile jacinth Has your question been resolved?
soft zealotBOT
Off_set
finite chasm
,, y = x + 10 / 4
soft zealotBOT
Off_set
finite chasm
,, y = x + 4 // 2
soft zealotBOT
Off_set
finite chasm
.close
final saddleBOT
wraith crater
final saddleBOT
Available help channel!
tranquil pine
How would the function, f(sqrtx) look like with a shift 2 units to the left and 3 units up? Also with a. Reflection over y axis
final saddleBOT
How would the function, f(sqrtx) look like with a shift 2 units to the left and...
tranquil pine
Would it be -(sqrtx+2)+3
ionic glacier
yeah, with correct brackets, you're right
tranquil pine
Thanks
tranquil pine
yeah, with correct brackets, you're right
Wym by that? Brackets like around it?
ionic glacier
-[(sqrt(x+2))+3]
tranquil pine
-[(sqrt(x+2))+3]
Is that necessary? It results in the same thing
ionic glacier
no, -a+b is not equal to -(a+b) because the latter is -a-b
final saddleBOT
@tranquil pine Has your question been resolved?
tranquil pine
-[(sqrt(x+2))+3]
Wouldn’t that be a reflection over x axis? Since that’s outside the bracket
It’s supposed to be inside because it’s a reflection across y
ionic glacier
ah i see, yeah, I misread it
so my equation is wrong, but so is yours
reflection across y axis only flips the negativity of x
so try to come up with the final answer
tranquil pine
tranquil pine
@ionic glacier
final saddleBOT
<@860253495583571977>
ionic glacier
that's not true
ionic glacier
how did you come to that conclusion?
tranquil pine
Because I since were reflecting y
We add a - outside of the
Parentheses
@ionic glacier
ionic glacier
can you write down each progression?
tranquil pine
can you write down each progression?
Oh I made a mistake
Is it plus three?
Since it’s going left 3
ionic glacier
just write down each change and show me pls
final saddleBOT
@tranquil pine Has your question been resolved?
final saddleBOT
final saddleBOT
Available help channel!
tranquil pine
Find the tangent to the curve y=e^x + x^2 at x=2.
final saddleBOT
Find the tangent to the curve y=e^x + x^2 at x=2.
ionic glacier
how do you find the tangent?
tranquil pine
Derivative, then plug in x = 2 to find the gradient of the tangent at x = 2
tranquil pine
e^x + 2x
ionic glacier
ok that's correct too
ionic glacier
idk why you didn't get the correct answer at this point 🙂
tranquil pine
e^2 + 4
tranquil pine
idk why you didn't get the correct answer at this point 🙂
Oh, I'm not sure if it is the correct answer lol
ionic glacier
yeah that's the answer
ionic glacier
I got y = 2(e^2 + 4)(x - 2)
this is wrong though
tranquil pine
this is wrong though
oh
yeah I knew it
lol
What I did was: I found the value of y by subbing in x = 2 in the original equation
tranquil pine
e^2 + 4
Got this again
So then I used y-y1 = m(x-x1)
y-(e^2+4)=(e^2+4)(x-2), then solved for y to get y = 2(e^2 + 4)(x - 2)
@ionic glacier Could you tell me where my mistake is?
ionic glacier
y = kx + c
and when x =2, we know what y value is
then calculate c
because we already know k, it's possible to get c
final saddleBOT
@tranquil pine Has your question been resolved?
final saddleBOT
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Available help channel!
slate garnet
I figured out the zero, sin(x)=-4/5, but I don't know where to go from there
final saddleBOT
I figured out the zero, sin(x)=-4/5, but I don't know where to go from there
@slate garnet Has your question been resolved?
slate garnet
<@&286206848099549185>
final saddleBOT
@slate garnet Has your question been resolved?
slate garnet
.close
zinc fractal
Hi
arctic kelp
final saddleBOT
@zinc fractal Has your question been resolved?
zinc fractal
Same
granite walrus
It is the reflexive property
final saddleBOT
@zinc fractal Has your question been resolved?
sweet summit
abstract algebra
final saddleBOT
abstract algebra
silk wing
Is the red bit something you've written? A solution? What am I looking at?
sweet summit
it's just the set up
silk wing
What is the fundamental theorem in this context?
sweet summit
it's also called the 1st isomorphism theorem
basically that the quotient group $S_n / A_n \cong \mathbb{Z}_2$
soft zealotBOT
MellowDramaLlama
silk wing
Borderline offended by that, but okay
sweet summit
hmm?
silk wing
That's just a weird thing to call the 1st isomorphism theorem
silk wing
But the problem statement gives away the whole game
you know exactly what theorem to use
You need a map from G to Z/2Z that is surjective and has kernel K
sweet summit
right. So then our kernel would have to be the even permutations
but I'm not sure if I"m seeing the connection there
silk wing
connection between what and what? just want to make sure I understand exactly where the disconnect is
sweet summit
well according to the hint, all even permutation of S_n map to 0 in Z_2. I'm just trying to show that's the case, but I'm not sure how
other than just proclaiming it does lol
silk wing
Oh I see. The problem is that the text didn't actually define the homomorphism they're using
There's literally only one option, so maybe the author is just being a dick
sweet summit
if they elements are composed with themselves?
silk wing
But you need to send everything in the kernel to 0 and everything not in the kernel to not 0 for obvious reasons
but there's only one option fornot 0
so the map is completely determined
sweet summit
hmmm
sweet summit
OH I THINK I SEE IT. Yeah if we do something like f((12)(12)) = f((12))f((12)), then f(()) = f(12)f(12)
silk wing
So the statement you're proving is "there exists a homomorphism from S_n to Z/2Z with kernel exactly A_n". This statement forces the definition of this homomorphism on you -- there is only one set map that can do the thing you want it to do. What you have to prove is that this is a homomorphism
sweet summit
so yeah the evens composed with themselves sends them to the kernel
oh okay
sorry I'm typing it out
okay I think I got the first justification down the fact that A_n = ker(f)
silk wing
Okay so the red is your solution. You never defined your homomorphism from S_n to Z/2Z. You can't just take "a homomorphism", you need to present a specific one that does what you wany
sweet summit
oh sorry first line
G = S_n
and (Z_2, +)is the same as Z/2Z I think
(and yes sorry red is my answer)
silk wing
You can't just say "let f be a homomorphism" because I will come back and say "okay let f be the map sending everything to 0"
then everything you say afterwards will be totally wrong
You need to point to a specific homomorphism and say "this particular function is surjective with kernel A_n"
your job is to define that function
sweet summit
oooh I see
okay
So how about something like if the permutation is odd map it to 1 and if it's even map it to 0?
like a piecewise function
silk wing
cool, that certainly has the correct kernel. But is it actually a homomorphism? You can only apply the first isomorphism theorem to homomorphisms
sweet summit
yeah I think so! To prove that we would need to prove that f(xy) = f(x)f(y) for x, y in S_n right?
silk wing
yup
sweet summit
hmmm
yeah I guess that works
if x and y are both even, then their composition is even, which maps to the kernel
if x and y are both odd, then their composition is even, which maps to the kernel
if x is odd and y is even (or vice versa), then their composition is odd which maps to not the kernel (lol)
...I think that works
so then f(xy) for example, if they're even would be 0 + 0 = 0
silk wing
you are correct. The idea is that homomorphisms to Z/2Z are sort of like identifying parity in your group
the same way odd + odd = even and even + even = even, etc
odd and even permutations have that same relationship, so they define a hom to Z/2Z
final saddleBOT
@sweet summit Has your question been resolved?
sweet summit
hey so I haven't finished yet
but I want to make sure the logic I have so far is sound
I still need to do the final case
mostly I wanted to see if the 0 = 1 + 1 could be inferred. The goal is to show the two sides are equivalent
or is that weirdly put?
silk wing
no you need to also do even * odd, doesn't follow from the others
sweet summit
no I know
I'm working on that one right now
I just wasn't sure if the 0 = 1 + 1 made sense or it was weird
silk wing
Oh I see what you mean. No that's weird
silk wing
just remove the implication arrow
sweet summit
is there a better way to phrase that?
okay
also this shows that this is surjective too yeah? Since all elements of S_n are accounted for and they all map to every element of Z_2
silk wing
What you've written has no clear logical flow. "So 0 = 0" is cool and all, because that is in fact true, but it's not actually a conclusion that you are proving
f(x) + f(y) = 1 + 1 = 0
f(xy) = 0 because xy is even
so f(xy) = f(x) + f(y)
silk wing
modulo irrelevant nitpicking, what you have here makes sense
silk wing
Why is (1) "f is a surjective homomorphism" and (2) " ker f i s A_n" ? Why aren't t homomorphism and surjective two different points?
Also not sure why you're bothering to cite that the kernel is normal. I feel like that's baked in to the 1st isom theorem
sweet summit
Why is (1) "f is a surjective homomorphism" and (2) " ker f i s A_n" ? Why aren'...
I tried to discern that with the last line. We proved that it was a homomorphism, but as a consequence, the cases accounted for all possible elemnts of S_n and they map to all elements of Z_2, so that should showcase that it's surjective, right?
sweet summit
Also not sure why you're bothering to cite that the kernel is normal. I feel lik...
this is our first HW over the 1st isomorphism theorem, so I wanted to confirm all explicit points
I'm sure it's not needed but since the B in A/B has to be normal I figured it warranted mentioning 😛
silk wing
I tried to discern that with the last line. We proved that it was a homomorphism...
I mean those are just two separate statements. I showed this thing is a homomorphism, and then for another unrelated reason, it is also surjective
sweet summit
oh my professor said that the homomorpism has to be surjective
silk wing
and yes, definitely can only quotient by normal. it's certainly not wrong to mention that, just feels weird since I think of "all kernels are normal" as a part of the 1st isom thm
sweet summit
at least in my definition notes
sweet summit
oh lol
sweet summit
yeah I think so
silk wing
but those are still two separate thoughts
1st isom theorem is 3 criteria
- hom 2) surjective 3) has correct kernel
I thought you meant they said all homs had to be surjective and I was afraid
sweet summit
oh no no no lol.
but the homomorphism for the isomorphism is surjective
which I think we we need since we need to show that the quotient groups form a bijective mapping
(I think)
silk wing
I mean really the isom theorem is "f:G -> H gives an isomorphism from G/ Ker(f) to Image (f)" and f surjective is a special case of that
sweet summit
I mean really the isom theorem is "f:G -> H gives an isomorphism from G/ Ker(f) ...
OOOOOH yeah that definition just clicked for me lol
we breezed through this lecture for the sake of time and it wasn't making a lot of sense
okay I appreciate your help! I gotta get some food in me
.close
agile jacinth
A car travels from a point A with position vector (60i - 40j) km to a point B
with position vector (—50i + 18j) km.
The car travels with constant velocity and takes 5 hours to complete
the journey.
Find the velocity vector.
final saddleBOT
A car travels from a point A with position vector (60i - 40j) km to a point B
wi...
agile jacinth
im not sure how to get to the answer
true escarp
what have you tried
true escarp
why would you add them
agile jacinth
cz i need to get from a to b
proven patrol
So yoy add them?
true escarp
so you want to find the distance in between them?
agile jacinth
then find the velocity vector for the whole journey
agile jacinth
So yoy add them?
mb ig
true escarp
if you want to find the distance between 2 and 5 would you do 2 + 5
proven patrol
agile jacinth
so divide both vectors by the hour first then add?
true escarp
no..
true escarp
if you want to find the distance between 2 and 5 would you do 2 + 5
refer to this
and v = d/t
how would you find the distance between 2 and 5
true escarp
how would you find the distance between 2 and 5
you cant do this?
consider a ruler
how many cm between 2cm and 5cm
true escarp
oh ok
true escarp
its all g
agile jacinth
At 12 00 hours, a tanker sails from a point Pwith position vector (5i + 12j)
km relative to an origin O. The tanker sails south-east with a speed of
I2root2 kmh-^
a Find the velocity vector of the tanker
ok im rly not seeing this one
@true escarp
true escarp
ok im rly not seeing this one
try a diagram
true escarp
uhh
well the idea is
you have a direction
and magnitude
you can use it to break the vector back down into components
or you can just express it with the magnitude and direction
final saddleBOT
@agile jacinth Has your question been resolved?
final saddleBOT
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oblique sable
In the text below this definition it states that conditions (2)-(4) are needed in order to make sure both sides of the equation $y' = X(t,y)$ are well-defined. What exactly does it mean that the equation is well-defined?
final saddleBOT
In the text below this definition it states that conditions (2)-(4) are needed i...
soft zealotBOT
Anders
final saddleBOT
@oblique sable Has your question been resolved?
robust sedge
Maybe you can reverse it to have that being well-defined means those things. y needs to be differentiable for the first order DE to make sense. Not sure what D_x means though.
I think (3) means that all the points (y, y(t)) are points of the domain of the solution.
(4) means it actually satisfied the DE.
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lofty kindle
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lofty kindle
i tried multiply from the left (ab)^-1 to get rid of the ab and then multiply from the right (ab) to get rid of the inverses but that leaves me with X=(AB)^-1(I+A)(AB) which i dont think is right
wraith crater
(AB)^-1 ≠ A^-1B^-1
Your first step is right tho
Consider just getting rid of A^-1 and B^-1 one by one
Then you can do some simplification
lofty kindle
so instead a^-1 then b^-1
and then from the right, b and then a
so = a^-1b^-1(i+a)ba
wraith crater
Yes
lofty kindle
alright thank you
wraith crater
so = a^-1b^-1(i+a)ba
Also you can simplify this further
lofty kindle
how so, would it just be simplifying the a^-1 and b^-1 into (ab)^-1
wraith crater
Distribute the A^-1B^-1(I+A)
wraith crater
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tranquil pine
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ionic glacier
which one? d?
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tranquil pine
which one? d?
yes
tranquil pine
but where do i get the 25 16 from
soft zealotBOT
luckydongdong
ionic glacier
you can apply sqrt to numerator and denominator
tranquil pine
100 and 80
so
i need to divide then by 2?
and them simplify it?
so the anwser should be 1,25
right?
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runic frost
I understood the (cos X)2 + (sin X)2 =1, not sure how to prove it using the given values. please help.
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I understood the (cos X)2 + (sin X)2 =1, not sure how to prove it using the give...
deft ravine
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tranquil pine
hey
amber holly
It's 5
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uncut totem
how to get intuition of this
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how to get intuition of this
uncut totem
why are we able to cross multiply
supple copper
first you multiply both sides by 4, and then (x+2)
that’s all cross multiplying is
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lucid wasp
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lucid wasp
how come when they factor out the minus from the arg the isin stays -pi/4 isntead of pi/4
ocean lintel
It's wrong
tranquil flume
Hejsan
tranquil flume
It's wrong
Are you sure?
ocean lintel
,w arg(cos pi/4 - i sin(-pi/4))
soft zealotBOT
ocean lintel
,w arg(cos(-pi/4) + i sin(-pi/4))
soft zealotBOT
ocean lintel
Yes
ocean lintel
It's clear since cos is even and sin is odd
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ocean lintel
Yes
lucid wasp
thank you :P
ocean lintel
A + doesn't juste become a - at random. Unless it was adding 0 in the first place
tranquil pine
How do you factor
final saddleBOT
How do you factor
tranquil pine
X^4-x^2-12
tranquil pine
OH wow that’s rlly good TYSM
supple copper
np
small mortar
I was wondering how to integrate 2+tan^2 is it tanx - x
final saddleBOT
I was wondering how to integrate 2+tan^2 is it tanx - x
small mortar
i first thought maybe it's 2tan x because of 1+ tan^2 x = tan x but that doesnt make much sense to me
so i wanted to make sure
but I think it's the first one
vital crag
I was wondering how to integrate 2+tan^2 is it tanx - x
use tan^2(x) = sec^2(x) - 1
small mortar
ohh my bad, I did to many deritiv tasks recently oppsi
i did the deritiv instead
so 2 becomes 2x then
2x + tan x as final answer
vital crag
,w integral 2 + tan^2(x)
soft zealotBOT
vital crag
you missed a -x from integral of tan^2(x)
small mortar
oh so 2x + tan x - x which is x + tan x then?
yeah i think so 🙂
Thanks for clearing it up 🙂
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hexed atlas
how would i solve further
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hexed atlas
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west valley
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west valley
is this ratio test valid? im unsure about the end part and the formatting of that
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limpid minnow
Can someone explain why this is wrong
final saddleBOT
Can someone explain why this is wrong
@limpid minnow Has your question been resolved?
limpid minnow
I was trying to solve the one in the left. The one in the right is my answer
Original question
granite walrus
D
obtuse grail
Can someone explain why this is wrong
the 8 goes on top
obtuse grail
yea 8 is 8^1
limpid minnow
Ahhhhhhh
Okay
Yes
Thanks a lot guys thanks 🙏
Btw I love Kevin durant and go for okc
limpid minnow
yea 8 is 8^1
Thank you
granite walrus
No i hate okc
obtuse grail
No i hate okc
W
limpid minnow
Lol
granite walrus
Im going to boston
obtuse grail
impossible
granite walrus
Watch
granite walrus
Im aleady 100% snake i cant become more snake
limpid minnow
Lol
unborn rune
anyone have a clue how to prove this?
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anyone have a clue how to prove this?
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ionic glacier
what did you try?
hybrid raptor
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hybrid raptor
<@&286206848099549185>
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sturdy cypress
why does x even matter
it's a triangle with one leg twice the other
oh wait it's not 90°
i hate geometry
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graceful island
hello does any of you provide help in french?
final saddleBOT
hello does any of you provide help in french?
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Available help channel!
foggy otter
so if i know that f(1) = 3 and f'(1) = 7, and also that g(x)=f(x^3), how would i find g'(1)?
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so if i know that f(1) = 3 and f'(1) = 7, and also that g(x)=f(x^3), how would i...
tired walrus
chain rule
eternal temple
$1.1 = \frac{500 + 1.2x}{500 + x} \implies 550 + 1.1x = 500 + 1.2x$
final saddleBOT
$1.1 = \frac{500 + 1.2x}{500 + x} \implies 550 + 1.1x = 500 + 1.2x$
soft zealotBOT
P0lyAga1n
tired walrus
multiply both sides by (500+x) then expand 1.1(500+x) on the left
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eternal temple
,w 500 * 1.1
soft zealotBOT
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Available help channel!
torn vale
GOOD MORNING, COULD YOU PLEASE HELP ME WITH THE FOLLOWING EXERCISE?
a bucket with water rotates in the form of a conical pendulum, suspended from the ceiling by a rope of 2 meters whose angle with the vertical is 30 degrees. If the bucket is dripping, find the radius of the circle described by the drops on the floor 4 meters below the ceiling.
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GOOD MORNING, COULD YOU PLEASE HELP ME WITH THE FOLLOWING EXERCISE?
a bucket wit...
@torn vale Has your question been resolved?
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torn vale
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tired walrus
@tranquil pine please open another channel
@tranquil pine it's unclear what we're looking at
what are these arrows and circles
astral ice
it’s just a system of equations in disguise
tired walrus
ah, so 4 different people took 3 shots at the same target
and each shot scores based on what ring it lands in
right
well we could assign letters to the three parts of the target
for example, a for the outer ring, b for the middle ring and c for the center
then the first target shows that a + 2b = 29, the second shows that a + 2c = 43 and the third shows that b + 2c = 47
and we need to find a+b+c
do you know in general how to solve systems of equations?
there are some tricks that we can pull here
so i suppose that won't be a huge obstacle
from b + 2c = 47 and a + 2c = 43, we can get that b - a = 4
i.e. that the middle zone scores 4 more points than the outer
we can of course also write that as b = a+4
and we can plug that into the equation for the first target, a + 2b = 29, to get a + 2(a+4) = 29
do you understand how to continue from here?
you missed the a at the beginning
yes, you copied the last equation correctly :p
the equation a + 2(a+4) = 29 is an equation in one variable (a). you can solve it to find the value of a
from this and what we have discussed above you can find b
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void valley
what's your slope and coords of which point have you chosen
a
you've already answered mb
it should be
soft zealotBOT
Modus
void valley
check your slope
keen lodge
.reopen
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keen lodge
void valley
still wrong
void valley
it is
void valley
but P = (-sqrt(11), 15)
keen lodge
Oh sorry yes
I did that kek
Oh
But I didn’t include that in the final answer
My bad
😭 brainfart
Thanks a lot ❤️
You are breathtaking
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tranquil pine
