@signal marten Has your question been resolved?
#help-10
obtuse pebbleBOT
wanton dagger
I’m having problem in figuring out what I should do here
obtuse pebbleBOT
I’m having problem in figuring out what I should do here
wanton dagger
I was thinking of simultaneous equations but that makes the question complicated and also gives a laborious working out, is there maybe another way?
high lily
shouldn't be that complicated
inland solar
It can be solve very easyly
wanton dagger
Hmmm
high lily
2 variables, two equations
inland solar
Think Right triangle!
wanton dagger
Also,
Are these the equations:
|4|=sqrt(x^2+y^2)
tan(120)=y/x
?
high lily
where are x and y coming from
why aren't you using the variables a and b given in the question
inland solar
General view of your problem
wanton dagger
where are x and y coming from
Ok ya true
wanton dagger
General view of your problem
I see
inland solar
For the direction, I don't know what convention you are using
wanton dagger
So tan(120)=b/a
inland solar
In trigo, 0°is on i, positive going ACW
wanton dagger
Wait what is ‘ACW’
wanton dagger
Oh i see
inland solar
CW Clockwise
inland solar
So use the positive way as your teacher told you, whichever it is, but I think it is ACW positive
The trigonometric way
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
timid silo
The difference between the supplement and the complement of an angle is 90 degrees. Find the measure of the angle.
obtuse pebbleBOT
The difference between the supplement and the complement of an angle is 90 degre...
warm shaleBOT
The following error occured while calculating:
Error: Invalid left hand side of assignment operator = (char 15)
sterile zenith
obtuse pebbleBOT
sterile zenith
this is a discrete math question
so i tried assuming all primitive statements are true
then their combination with connectives should be true for it to be conistent i.e not a contradiction
is that right
sterile zenith
so i tried assuming all primitive statements are true
this assumptions feels illegal
obtuse pebbleBOT
@sterile zenith Has your question been resolved?
obtuse pebbleBOT
@sterile zenith Has your question been resolved?
thick epoch
How can I obtain the probability in the second picture according to the info in the first pic?
obtuse pebbleBOT
How can I obtain the probability in the second picture according to the info in ...
@thick epoch Has your question been resolved?
lunar nymph
help what to do if 2 sets dont have something similar
obtuse pebbleBOT
help what to do if 2 sets dont have something similar
pine sail
You'd say there's no intersection
pine sail
Create two disjoint circles.
pine sail
Create two circles, which do not intersect each other. That's how you'd show no intersection...
proud finch
lunar nymph
ok thanks
final one
how do i make a venn diagram with (a u b) n C and how do i solve it
obtuse pebbleBOT
@lunar nymph Has your question been resolved?
obtuse pebbleBOT
Available help channel!
rain current
Can someone help me out with this?
obtuse pebbleBOT
Can someone help me out with this?
royal basin
oh this looks nasty...
random depot
Is it like this
random depot
Ouh I read it as a du
random depot
Can someone help me out with this?
is it dx or du at the end
wild swallow
wolfram gives the exponential integral 
rain current
It's dx
random depot
ohshi
solar trellis
I would let u=2x-3 then separate the integral and do ibp
rain current
Also what the hell is wolfram , like bro I just learned integrals last month and they gave these sums as hw 😭
I did u substitution and then I'm doing by parts
It's definitely wrong
I forgot to substitute the value of k ugh
wild swallow
did you copy the question correctly
like what you've written is a very nasty integral
random depot
^
rain current
Yes I did
I rechecked it
Is this integral high school level?
Cause I feel like I don't know enough to solve it..
devout sable
Pretty sure no
wild swallow
the 3 is in the exponent?
devout sable
,w integrate (2x-5)e^x/((2x-3)3)
wild swallow
in the denom?
warm shaleBOT
wild swallow
yeah okay even with 3 dropped down it's bad
rain current
It's ^3
warm shaleBOT
rain current
What's Ei
random depot
exponential integral
obtuse pebbleBOT
@rain current Has your question been resolved?
timid silo
-x^2+2x+3
timid silo
if I were to plug in 1 for x
would it be -(1)^2 or (-1)^2
why or why not is it the other and how do I know when to include the sign? Thanks
onyx berry
(-1)^2 is the right one
timid silo
how?
I graphed the expression in desmos and the vertex was 1, 4
not 1,6
still confused myself
onyx berry
-(1)^2 is 1x1= 1 Then we have -1x1=-1 meanwhile (-1)^2 is -1x(-1)= 1
timid silo
yes
so if you graphed -x^2+2x+3 shouldn't the vertex by 1,6
if (-1)^2 is the right one
onyx berry
yea, i think so
timid silo
so why is it 1, 4
onyx berry
i gtg now for a bit, sorry bro
timid silo
ok
timid silo
not sure what to search
obtuse pebbleBOT
@timid silo Has your question been resolved?
obtuse pebbleBOT
@timid silo Has your question been resolved?
upbeat yacht
Can x = 1 mod 4 be split into x = 1 mod 2 & x = 1 mod 2 ?
obtuse pebbleBOT
Can x = 1 mod 4 be split into x = 1 mod 2 & x = 1 mod 2 ?
sage geode
x = 1 mod 2 & x = 1 mod 2?
upbeat yacht
yeah, like x = 1 mod 40 can be split into x=1 mod 5 and x=1 mod 8
desert sinew
Can x = 1 mod 4 be split into x = 1 mod 2 & x = 1 mod 2 ?
(mod 4) case implies (mod 2) case, but (mod 2) case does not imply (mod 4) case. Consider 3 mod 2 and 3 mod 4 as a counter example.
In short, what you write is not equivalent statement about (mod 4).
In general, you cannot decompose exponent power like that in the context of mod.
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
woeful fiber
Hello, is this correct?
obtuse pebbleBOT
Hello, is this correct?
timid silo
yes
obtuse pebbleBOT
@woeful fiber Has your question been resolved?
obtuse pebbleBOT
@woeful fiber Has your question been resolved?
obtuse pebbleBOT
woeful fiber
.reopen
obtuse pebbleBOT
✅
woeful fiber
they just skipped the step
Hello, thanks for replying. Question: Is the power rule usually implemented in this on introduction of Integrals? Or is the power rule taught at a later time
timid silo
Hello, thanks for replying. Question: Is the power rule usually implemented in t...
power rule is implemented here
it's one of the first things u learn in integrals
woeful fiber
I see, thanks
What do you suggest when learning calculus 1 and 2?
Focusing on previous math or diving straight into calc 1 and 2
woeful fiber
Please do solve it
Hi, this help channel is taken. There's other help channels available here: #❓how-to-get-help
south dome
Nobody is solving my doubts
woeful fiber
Is this solving linear inequalities?
south dome
No modulus
wanton kraken
just a quick q
obtuse pebbleBOT
just a quick q
wanton kraken
xyz is a 3-digit number
the number in the middle is zero
do I write it as
100x+0y+z
@jaunty stream
<@&286206848099549185>
obtuse pebbleBOT
<@&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.
wanton kraken
man it's an easy question
versed cave
Yeah that makes sense, but you also have to make sure that || 1 || ≤ x ≤ || 9 || and that || 0 || ≤ z ≤ || 9 || and that they are integers
otherwise you'll have multiple digit numbers
obtuse pebbleBOT
versed cave
Yeah that makes sense, but you also have to make sure that || 1 || ≤ x ≤ || 9...
(This is considering the number is supposed to be positive, if it is not, I'm sure you can modify this accordingly)
obtuse pebbleBOT
Available help channel!
rose crater
obtuse pebbleBOT
plain stag
!15m
obtuse pebbleBOT
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.
@rose crater Has your question been resolved?
unique vessel
obtuse pebbleBOT
unique vessel
This question seems too simple to be true, is my answer correct?
plain stag
,calc 15*0.35
warm shaleBOT
Result:
5.25
yep
unique vessel
thank you
plush valley
how did i forget how to solve these
obtuse pebbleBOT
how did i forget how to solve these
plush valley
forgot everything from 8th grade thanks to quarantine
covert crag
The goal here is to eliminate the denominator
So try to modify the numerator so that it is possible
plush valley
oh yeaa
covert crag
Usually in questions like this prime factorization helps
plush valley
after eliminating the numerator i just solve it normally?
covert crag
after eliminating the numerator i just solve it normally?
You mean denominator ?
plush valley
yes
covert crag
Yea just solve it normally after that
The thing is that if you want you can solve the question normally from the start
But wont be very efficient
plush valley
so the final answer will look smth like this?
i might have completly forgot how to work with numbers lmfao
covert crag
Nope thats not the answer
plush valley
i did 3-5 dont know if that works here
covert crag
You will have to cancel 2^19 from both the terms in the numerator
You only cancelled it from the second term
plush valley
You will have to cancel 2^19 from both the terms in the numerator
omg
covert crag
Try writing 4 as 2*2
plush valley
yea
plush valley
Try writing 4 as 2*2
so it would be 2*2^10?
covert crag
No
plush valley
2^5?
covert crag
so it would be 2*2^10?
This is equal to 2^11
covert crag
It would be (2*2)^10
While this is equal to 2^20
plush valley
While this is equal to 2^20
yea
covert crag
So now what did you get your answer as
covert crag
Correct!!
plush valley
While this is equal to 2^20
btw. i might be forgetting something but how did you get 2^20?
did you just multiply (2*2) 10 times?
covert crag
Distribute the exponent
(2×2)^10 = (2^10)×(2^10) = 2^(10+10) = 2^20
I gotta go so if you wanna ask anything else just dm me
plush valley
(2×2)^10 = (2^10)×(2^10) = 2^(10+10) = 2^20
thanks
my brain stops functioning as soon as an exponent is above 3
.close
obtuse pebbleBOT
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lost yew
im getting thrown off by the meaning of the star and the circle, im going to make truth tables of both of them, and im wondering if im going in the right path
obtuse pebbleBOT
im getting thrown off by the meaning of the star and the circle, im going to mak...
lost yew
obtuse pebbleBOT
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lost yew
.close
primal idol
obtuse pebbleBOT
primal idol
This is a hydrostatic force on a plate/dam problem from calc 2
i'm having issues with setting my bounds
for my integral
and not sure if my integral setting is correct.
delta A is the area
P stands for Pressure
obtuse pebbleBOT
@primal idol Has your question been resolved?
next valley
If I have X={0,1}, would {empty, {0}} be a topology on X?
obtuse pebbleBOT
If I have X={0,1}, would {empty, {0}} be a topology on X?
royal basin
no, because it does not include X itself
next valley
It seems like it satisfies all criteria but I’m not sure
royal basin
if you add X to it you get the sierpinski space
next valley
Oh a topology needs the itself. So {empty, X, {0}, {1}} would be a topology?
next valley
Ok seems simple enough thanks
pliant bear
Let a and b in Z* be such that |a|≤100 and |b|≤ 100. Show that: |a√2+b√3| ≥ 1\350 Hint: We can assume that √3/2 is not rational.
Anyone can help?
next valley
.close
obtuse pebbleBOT
pliant bear
<@&286206848099549185>
sage geode
Post your question in an available help channel
obtuse pebbleBOT
Available help channel!
pliant bear
Let a and b in Z* be such that |a|≤100 and |b|≤ 100. Show that: |a√2+b√3| ≥ 1\350 Hint: We can assume that √(3/2) is not rational.
obtuse pebbleBOT
Let a and b in Z* be such that |a|≤100 and |b|≤ 100. Show that: |a√2+b√3| ≥ 1\3...
pliant bear
<@&286206848099549185>
obtuse pebbleBOT
@pliant bear Has your question been resolved?
obtuse pebbleBOT
@pliant bear Has your question been resolved?
pliant bear
<@&286206848099549185>
tardy epoch
Let a and b in Z* be such that |a|≤100 and |b|≤ 100. Show that: |a√2+b√3| ≥ 1\3...
what have you tried?
obtuse pebbleBOT
@pliant bear Has your question been resolved?
drowsy girder
599 yellow and 301 blue balls are given. Can you arrange these balls in a row so that the number of
balls between any two blue balls is different from 2 and 5?
Can i just say
Because that question doesnt give enough info.
obtuse pebbleBOT
```
599 yellow and 301 blue balls are given. Can you arrange these balls in a ro...
burnt geyser
obtuse pebbleBOT
burnt geyser
how would i do this?
hardy widget
Interpret this geometrically, the first is the locus of points equidistant from -10 and $6+4i\sqrt{2}$, the second is the circle with radius 3 centered at $(-1,0)$
warm shaleBOT
enclave wangedrocht
hardy widget
Eh if you want
burnt geyser
is there a quicker way ?
grave oyster
does |z| mean sqrt(a^2+b^2) ?
hardy widget
Yeah, it denotes the modulus of a complex number
burnt geyser
ya im pretty sure, i used that to find the equation in cartesian form
warm shaleBOT
grave oyster
and fin 2 solution (a;b)
obtuse pebbleBOT
@burnt geyser Has your question been resolved?
mint atlas
how do i apply transformations to key points on this graph?
obtuse pebbleBOT
how do i apply transformations to key points on this graph?
@mint atlas Has your question been resolved?
mint atlas
no
tired shell
you have to work from where x is and go out layer by layer
so like the order is
x-1
times -2 inside g
times 3 outside g
+1
tired shell
that's good
mint atlas
i just wanted to make sure cuz my solution sheet was different than what I got
tired shell
oh hmm maybe it's the x part that's off
tired shell
yea that makes sense
mint atlas
this is what i got
tired shell
but the horizontal shift is +2 maybe
mint atlas
isn't the horizontal shift +1 tho outside of brackets?
tired shell
oh ok I think the problem is you don't have to reverse the x stuff
tired shell
when I plug in x=-4
I get y= something with g(10)
so you just apply -1 and *-2 to the x values
er wait is your graph of y or g?
I'm probably confusing myself sorry
mint atlas
i think the original is g(x) and the transformed one is y
tired shell
gotcha
mint atlas
where did i screw up 😭
mint atlas
how did u get 3 from -4 is my issue
tired shell
ok I think I have a clear answer now
tired shell
i did -1/2(x+1) for all the x values
it's -1/2*x + 1 instead
tired shell
like the +1 is outside the parentheses instead
obtuse pebbleBOT
tired shell
everything else should be good
mint atlas
so the brackets cancel out?
obtuse pebbleBOT
Available help channel!
tired shell
idk what you mean exactly
obtuse pebbleBOT
idk what you mean exactly
tired shell
but like on the inside of the function parentheses you do things backwards, so instead of subtraction first you do the multiplicaiton
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
sturdy wave
i need help
obtuse pebbleBOT
i need help
sturdy wave
tidal hawk
mayb bringing the 3 into the rt will make it easier for u to see
sturdy wave
cube root 7?
sturdy wave
what does it mean to bring the 3 into it then
tidal hawk
okie for eg
if u have 2rt5
it’s the same as square root (5x4)
which is square root 20
sturdy wave
so it would be square root 21
tidal hawk
no
it’s not 7x3
what’s the square of 3
when u bring it into the square root,, u need to square it
so u have to square the 3 when u bring it inside
timid silo
,calc 3sqrt(7)
warm shaleBOT
Result:
7.9372539331938
or u can do that sure HAHAHA
tidal hawk
what is 3 square
tidal hawk
what is 3 square
^^
sturdy wave
9
tidal hawk
now what’s 9x7
sturdy wave
63
tidal hawk
so now u have square root 63
which is the same as 3 square root 7
what is 8 squared
sturdy wave
64
tidal hawk
is 63 more or less than 64
sturdy wave
less
tidal hawk
so it’s between 7 and 8
sturdy wave
where did we get the 8 from
tidal hawk
ur multiple choice
sturdy wave
yeah but if it wasn’t there then where would we get it from
like on a test
i would need to know
distant schooner
whats 8^2
tidal hawk
u have square root 63
so I would see what is the closest square number near 63
in this case it’s 64
so if u didn’t have mcq,, it would still be ok
sturdy wave
so i would just find out which square root the number i get is closest to
like if i get 20
then it would be 25 which is 5
sturdy wave
so it would be between 4 and 5
tidal hawk
welcc!
sturdy wave
.close
rustic moth
proving these two wave functions are orthogonal, any discrepancies here?
tidal geode
It seems correct to me
stable rain
use pytha to find the hypo
then use sin rule to get angle 2
then use
r^2 /2 * angle in radians
tidal hawk
stable rain
hi blob cat
but
OHHHH
yea just
find theta and
ok nvm this is just dumb
why would they ask u to do this is u can find the value directly
but yea
just
use sin rule on theta and angle 1
with the 2 original lengths
to get angle 1 in terms of theta
then use that angle to find area like
r^2 /2 * angle in radians
but is kinda weird
sin like
so like
$\frac{a}{sin(a)}=\frac{b}{sinb}$
warm shaleBOT
stable rain
$\frac{9}{sin(\theta)}=\frac{12}{sin(x)}$ where x is the angle u are finding
warm shaleBOT
stable rain
yes
yes
u can
just find the angle
thats why i said the Q is dumb
but they want u to express it in theta
so just do that
anw
imma get going
atb
lol
wild swallow
thats why i said the Q is dumb
your suggestion is just bad :/
stable rain
what
i said that cuz
they wanted us to express it in theta
i originally said how to not
anw
bey again
bye
wild swallow
you're doing too much work
stable rain
n hi
wild swallow
angles add up to 180
@radiant hornet do you understand what i said here
the internal angles of the triangle should add up to 180
stable rain
theta does not need to be found
i didnt try to find theta?
i wanted to express the other angle in terms of
theta
obtuse pebbleBOT
@radiant hornet Has your question been resolved?
sacred goblet
how many ways are there to insert x objects into a line of y objects? the inserted objects can be adjacent and are indistinct
obtuse pebbleBOT
how many ways are there to insert x objects into a line of y objects? the insert...
zenith raft
are the objects distinct? and by "y objects" do you mean like, y cells that an object can be placed in?
sacred goblet
uhhh i'm visualizing this as like
abcdefg
insert 1,2,3 into the above string in any order
sacred goblet
how many ways are there to insert x objects into a line of y objects? the insert...
this is a different problem but i think i need to understand this first
zenith raft
like 1ab3cde2fg is one way, as an example?
sacred goblet
the way i'm breaking this down so far is just allocating spots for the numbers, then multiplying by the number possible number arrangements
sacred goblet
like 1ab3cde2fg is one way, as an example?
yea
zenith raft
then you can picture it like this
the numbers 1 2 3 can be placed into the blank slots in _a_b_c_d_e_f_g_
so you can view it as 3-permutations of 8 objects
sacred goblet
but that doesn't account for a123bc..etc does it?
zenith raft
oh you're right
sacred goblet
i was thinking something like doing C(7+3-1, 3)
zenith raft
ok so it's like distributing 3 distinct objects into 8 boxes
sacred goblet
hmmm actually yeah
sacred goblet
can we just account for order after
zenith raft
maybe but you'll have to keep track of "numbers in the same box"
sacred goblet
damn this is annoying lmao
im probably approching this wrong if it's this weird
technically we can reword this specific problem as 'how many ways are there to construct a string using the characters abcedfg123'
i think?
this is trivial
zenith raft
does the order of abcdefg have to be preserved?
sacred goblet
hmm
actually yes i think, because i'm trying to generalize this to if abcdefg were any letter a-z
and keeping order makes sure i don't overcount i think
for having same letter multiple times
okay so if the order of 123 doesn't matter, this is just stars and bars i think?
but if it does i'm kinda stuck
the more general question i was trying to answer was 'how many ways can i create a string using 7 charas and 3 numbers, neither of which are neccesarily distinct "
zenith raft
maybe you could do a few applications of stars and bars
taking cases of all the letters being in distinct boxes
and having one in one box, two in another
and having all three in the same box
and you can consider permutations easier that way
zenith raft
sacred goblet
i refuse there must be a way 
wait does just starting with 10 slots and choosing 3 of the 10 to designate as numbers work
so 10c3 x 10^3 x 26^7
this should work, right...?
obtuse pebbleBOT
@sacred goblet Has your question been resolved?
sacred goblet
<@&286206848099549185> sorry for the ping, just wanted to get a quick sanity check before closing this thread.
Say I have a string of characters of length 8 with the following restriction:
Vowels appear in exactly three positions in the string
can i solve this by doing 8 choose 3 * (5^3) * 21^5
where it's just like #ways to choose slots for vowels * #ways to allocate vowels into slots * #ways for remaining slots
nvm im pepega 
.close
rocky plank
Can someone help me understand the "otherwise" part of this proof?
obtuse pebbleBOT
Can someone help me understand the "otherwise" part of this proof?
jaunty jewel
No idea about this, but I suggest you to get a better picture
This one is too small
rocky plank
This one is too small
I mean it's very viewable if you click on the picture and then click "open original'
jaunty jewel
Oh... I usually never click that option, sorry 😅
rocky plank
Oh... I usually never click that option, sorry 😅
No worries 🙂
Anyways would love if someone could help explain the "otherwise" part of the proof
tardy epoch
No worries 🙂
Anyways would love if someone could help explain the "otherwise"...
Again, you need to be more specific. Read the definitions again of all the symbols in the proof and ask where you're first lost
rocky plank
Again, you need to be more specific. Read the definitions again of all the symbo...
I'm confused about what how R(A,beta) o R(A,beta)=R(A,alpha+beta)
And how that proves it's a rotation when A=B
tardy epoch
I'm confused about what how R(A,beta) o R(A,beta)=R(A,alpha+beta)
And how that...
That's a typo. One of those betas should be alpha
Probably the second one like it says in the proposition.
obtuse pebbleBOT
@rocky plank Has your question been resolved?
rocky plank
That's a typo. One of those betas should be alpha
Shouldn't we have R(B,beta) o R(A,alpha)(P)=R(A,alpha+beta)(P)?
Where alpha+beta=2πn where n isn't a integer
tardy epoch
Shouldn't we have R(B,beta) o R(A,alpha)(P)=R(A,alpha+beta)(P)?
That's probably what it says. It just got cut off in scanning
rocky plank
That's probably what it says. It just got cut off in scanning
I think there was a mistake 🤔
There's nothing close to that written on the paper
I think what we have is correct tho
rocky plank
Gotcha. So now we move to the non-trivial case (when A isn't equal to B)
A figure is created
It's said that <XAB=<CXD and <ABX=EXP<BXD
I'm confused as to how these equalities were created (does it have something to do w/Alternate exterior, Alternate interior, etc.?)
obtuse pebbleBOT
@rocky plank Has your question been resolved?
rocky plank
<@&286206848099549185> or @tardy epoch 😅
obtuse pebbleBOT
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.
rocky plank
!15m
Whoops, didn't know I was only allowed to tag people with the helpers role. Just wanted some help with the question I had above. I worked through the non-trivial case with riemann, but I also need help understanding the trivial case of this proof.
rocky plank
Read it again
Whoops my bad, it's my first day here lol
obtuse pebbleBOT
@rocky plank Has your question been resolved?
obtuse pebbleBOT
@rocky plank Has your question been resolved?
rocky plank
it's just missing (P) part
Is your DM’s open to discuss the question? I’m kinda understanding the angle equality part
obtuse pebbleBOT
@rocky plank Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
flat roost
How did they transion from the second last step to the last ?
Just above the alternatively line is the line which i am referring to as the last line
obtuse pebbleBOT
How did they transion from the second last step to the last ?
Just above the `...
hot sonnet
How did they transion from the second last step to the last ?
Just above the `...
Hello, they multiplied by √(1-x²) on both sides of the equation
flat roost
Hello, they multiplied by √(1-x²) on both sides of the equation
Oh how silly of me 😕
Thanks for pointing it out
.close
obtuse pebbleBOT
knotty crow
gray pulsar
k
Its about slope
So
Do you divide the Rise and the Run
Rise/Run = Slope
right?
For the coordinates.
gray pulsar
<:JustAsk:371662163489718273>
Hello?
cedar lichen
Yes
gray pulsar
Oh
cedar lichen
And please be a little more patient when waiting for an answer
obtuse pebbleBOT
fierce lagoon
Bogo
solid pier
google it?
wdym
can I ?
3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 5923078164 0628620899 8628034825 3421170679
obtuse pebbleBOT
nocturne minnow
Sounds like you're trying to cheat
uneven palm
solid pier
shit yeah my bad didn't even think about that
that's really weird though
that's why I didn't even think about that
nocturne minnow
So you're cheating?
solid pier
bruh
obtuse pebbleBOT
Available help channel!
buoyant horizon
obtuse pebbleBOT
buoyant horizon
Could someone run me through? I'm a bit confused
4w=8v -> w=2v
v+w = v+2v
I get to that point but the last box where it says v = _v I just put 1, not sure about that
for second line abs(v+w) -> abs(v+2v) since w=2v
which means it should be abs(3v) which should be 3*abs(v)
but then the laast box I think it's askng what is abs value of v but it was stated it's equal 4 at the top
sullen raptor
How do I solve this problem?
obtuse pebbleBOT
How do I solve this problem?
sullen raptor
I have found the x partial to be 4xycos(xy)+4sin(xy)
The y partial to be 4x^2cos(xy)
plugged in the x and y and got 40.0869 for x and 15.7569 for y
found the magnitude by doing sqrt(x^2+y^2) and got 43.0725
divided the x and y by the magnitude and got <0.9307, 0.3658>
opal trench
try radians instead of degrees?
sullen raptor
.close
willow swallow
obtuse pebbleBOT
willow swallow
I don't know what am I doing wrong
covert crag
Set A is said to be a subset of Set B if all the elements of Set A are also present in Set B. In other words, set A is contained inside Set B.
Example: If set A has {X, Y} and set B has {X, Y, Z}, then A is the subset of B because elements of A are also present in set B.
A ⊆ B; which means Set A is a subset of Set B.
plain stag
I think you may be misunderstanding what $\subseteq$ means
warm shaleBOT
Steakanator
plain stag
It's not a 2-way street like equality, where A=B implies B=A
I see a few times where you have both (for example) $A \subseteq B$ and $B \subseteq A$
warm shaleBOT
Steakanator
plain stag
Both are true only when A=B
willow swallow
SO if D is A then A is not D?
plain stag
More precise language would help
If D is a subset of A, A is not necessarily a subset of D
willow swallow
And A is not a subset of B
plain stag
Indeed it is not
plain stag
Correct
untold yarrow
can anzbodz do graph witch Thesse x? ((4)/(3)) π (((26.6710^(-11) x)/(3*10^(8)310^(8))))^(3)
obtuse pebbleBOT
can anzbodz do graph witch Thesse x? ((4)/(3)) π (((2*6.67*10^(-11) x)/(3*10^(8)...
untold yarrow
in geogebra = 0
untold yarrow
result = 0
fickle turret
result = 0
It's close to 0 for quiet some time
untold yarrow
express the volume based on the content according to the swarchidel radius
tardy epoch
express the volume based on the content according to the swarchidel radius
Show the whole original question
Picture or screenshot
untold yarrow
like what?
tardy epoch
like what?
What don't you understand about picture or screenshot?
untold yarrow
tardy epoch
That's your work, not the question you're solving
tardy epoch
Just fix your axes and range of x
Also do this. Don't plot f and g on the same set of axes
untold yarrow
I'm not solving any question with the Internet, I'm trying to express the volume of what I wrote above
tardy epoch
I'm not solving any question with the Internet, I'm trying to express the volume...
State your whole question with all details. You've only provided a function, not a shape to calculate a volume.
obtuse pebbleBOT
Available help channel!
tribal plover
I was dividing the Polynomial (4x^3-7x+10) by (2x-5) using synthetic division. I got 5/2 as my Divisor and ended up with 4x^2 + 10x + 18 + 55/(2x-5), but I know that's wrong. What did I do wrong?
obtuse pebbleBOT
I was dividing the Polynomial (4x^3-7x+10) by (2x-5) using synthetic division. I...
tardy epoch
Show your whole work
tribal plover
I have it on Paper, I'll make it on Paint 3d
cedar lichen
Am I mistaken, or does synthetic division only work with divisors of the form x - a?
tribal plover
WAIT REALLY?
cedar lichen
I mean, I can see how you'd get it to work with ax - b, a ≠ 1
But it'd require an extra step
cedar lichen
If you have f(x)/(ax - b)
You can factor the a from the denominator to get (1/a)(f(x)/(x - b/a))
tribal plover
Oh
cedar lichen
f(x)/(x - b/a) is the synthetic division part, which you got (I'm assuming, I haven't actually checked it)
But there's an extra division by a
cedar lichen
Either long division, or remember to divide your answer by a
And long division is required if the divisor isn't linear
tribal plover
And long division is required if the divisor isn't linear
Oh
cedar lichen
I divided 55 by the divisor because it wasn't 0
55?
tribal plover
yeah, it was the remainder
And I was taught if it isn't 0 divide it by the divisor
tribal plover
Yeah thats what I'm saying
cedar lichen
But remember you have to divide the whole thing by a, since it's of the form ax + b
tribal plover
wdym
cedar lichen
You can factor the a from the denominator to get (1/a)(f(x)/(x - b/a))
There's a 1/a in front
cedar lichen
If you want to use synthetic division, yes
tribal plover
Do I do that before the division or after I get the quotient and the remainder
cedar lichen
Well, you can divide the dividend by a, then do synthetic division
Or you can do the synthetic division and divide the quotient by a
They should both give the same answer
cedar lichen
-7, but yes
That would be before synthetic division
If you do it before, you don't have to divide the quotient
sick osprey
obtuse pebbleBOT
sick osprey
im pretty stuck on this question
im not really sure where to start
it says p is the probabilty that he walks on the first day
so the chance that he could be late is 50%
1/2* 1/2 * 1/2 * 1/2, etc would be the probability he would walk on nth day? (1/2)^n
im confused on the part where if he keeps the same mode of travel the day after, and changes when he gets late
is this a summation problem?
stable rain
hv u learnt matrices
stable rain
i think so
sick osprey
i was thinking if its a binomial distribution
stable rain
i didnt rmb the name i wanted to say eigenvectors
i mean i think markov chain uses eigenvectors right
sick osprey
uh
stable rain
uve to represent the probabilities in a matrice
then get eigenvectors so u ca easily take ^n
i think~
im kinda bad at probability
sick osprey
it was listed under probability section
stable rain
but yea
stable rain
i think its still under probability
sick osprey
stable rain
kinda
hm binomial
idk like
he has the
uk
i
said my piece
im also not the best here so
sick osprey
stable rain
imma just not but
sick osprey
yeah stats hard
sick osprey
stable rain
SONAAA
sick osprey
okay just googled it
im pretty sure
this is a markov chain question
well time to escape library and i'll be home 
n finish this
sick osprey
fierce lagoon
Genshin is for losers
stable rain
WOW
fierce lagoon
"I love genshin impact" 🤓
sick osprey
stable rain
that i donut play
obtuse pebbleBOT
@sick osprey Has your question been resolved?
feral coyote
Find the equation of a surface that consists of all points such that the distance from any point on the surface to the plane x=4 is quadruple the distance as from the point on the surface to the point (1,1,1). Write the equation in standard form and identify it by name.
obtuse pebbleBOT
Find the equation of a surface that consists of all points such that the distanc...
feral coyote
So far I used the distance formula from point P(x,y,z) to plane x=4 (4,y,z) and got x-4 (D1). Then the other distance is from P(x,y,z) to (1,1,1) (D2)
Since the other distance is 4x smaller I set D1=4*D2
But when I set them equal and attempt to make it standard form, I don't get an answer that is right when I put it into graphing software
This is how I started it
obtuse pebbleBOT
@feral coyote Has your question been resolved?
feral coyote
.close
sullen raptor
How do I do this problem?
obtuse pebbleBOT
How do I do this problem?
sullen raptor
I first calculated the partial derivatives of xyz
x is -4x+z+2y-1
y is 4y+z+2x
z is -10z+y+x
What would be my next step in this problem?
hot sonnet
What would be my next step in this problem?
Do you know what the gradient is?
sullen raptor
Do you know what the gradient is?
isnt it just slope?
hot sonnet
isnt it just slope?
for multivariable functions, the gradient is a vector
sullen raptor
for multivariable functions, the gradient is a vector
Got it
hot sonnet
Gradient of f = ∇f = < fx, fy, fz >
you have already calculated those components
the formula for directional derivative is
$D_u f = \nabla f \cdot u$
warm shaleBOT
leonardogtf
hot sonnet
where u is a unit vector with the desired direction
sullen raptor
the 3i + 2j +2k?
sullen raptor
which has the same direction as 3i + 2j +2k
How do I do that?
hot sonnet
divide the vector by its magnitude
then the resultant vector has magnitude = 1, so it's an unit vector
sullen raptor
then the resultant vector has magnitude = 1, so it's an unit vector
the magnitude is sqrt 17
So 3/sqrt(17)i, 2/sqrt(17)j, 2/sqrt(17)k
Is this correct?
hot sonnet
Yes 👍🏽
sullen raptor
What do I do next?
hot sonnet
How is the (1,1,-2) significant?
you have to evaluate the gradient on that point
sullen raptor
you have to evaluate the gradient on that point
How would I do that?
obtuse pebbleBOT
@sullen raptor Has your question been resolved?
obtuse pebbleBOT
@sullen raptor Has your question been resolved?
sullen raptor
<@&286206848099549185>
idle shoal
I'll calculate this now
It may take a few minutes because I haven't done this for a while
sullen raptor
It may take a few minutes because I haven't done this for a while
Totally fine. Thank you for your help.
idle shoal
You're welcome!
idle shoal
How would I do that?
So for this part
You have the gradient function from those partial derivatives
And you just plug in the point you are looking at, $(1,1,-2)$.
warm shaleBOT
ninjahuman
idle shoal
**leonardogtf**
Because this relation is being used
Well this is probably the simplest way to do it
So you have the partial derivatives from above
You get $(\nabla f)(x,y,z)=(-4x+2y+z-1, 2x+4y+z, x+y-10z)$
warm shaleBOT
ninjahuman
idle shoal
So $(\nabla f)(1,1,-2)=(-5,4,22)$ if my calculations are correct
warm shaleBOT
ninjahuman
idle shoal
Then you calculate $(\nabla f)\cdot u$ where $u=v/|v|$
warm shaleBOT
ninjahuman
idle shoal
And that should give you the answer
sullen raptor
so v is (-5,4,22) and the triangle f is (-5, 4, 22)?
idle shoal
$v$ isn't that but $(\nabla f)$, the gradient at that point $(1,1,-2)$, is $(-5,4,22)$
warm shaleBOT
ninjahuman
idle shoal
So 3/sqrt(17)i, 2/sqrt(17)j, 2/sqrt(17)k
$v$ is this
warm shaleBOT
ninjahuman
sullen raptor
ohh okay
sullen raptor
nono totally fine
idle shoal
Ok and I have $\frac{59}{\sqrt{13}}$ for the calculation
warm shaleBOT
ninjahuman
sullen raptor
Okay let me try
idle shoal
Ok!
sullen raptor
Ok and I have $\frac{59}{\sqrt{13}}$ for the calculation
Can you clarify how you got this please? Im sorry i just got lost in the multiplying.
Like the exact process?
idle shoal
Ok
Ok I made a mistake before
Oh nevermind I didn;t
didn't
$u=\frac{1}{\sqrt{13}}(3,2,2)$ and $(\nabla f)(1,1,-2)=(-5,4,22)$
warm shaleBOT
ninjahuman
idle shoal
Oh I did
Then $\frac{1}{\sqrt{13}}(3,2,2)\cdot (-5,4,22)=\frac{1}{\sqrt{13}}(-15+8+44)=\frac{37}{\sqrt{13}}$
warm shaleBOT
ninjahuman
idle shoal
Originally I had $u$ as $\frac{1}{\sqrt{13}}(3,2,3)$ for some reason
warm shaleBOT
ninjahuman
sullen raptor
Hopefully this checks out with what you have
ahh that makes sense
idle shoal
Ok that's good to hear!
sullen raptor
Okay and then?
idle shoal
That is the value of $D_{u}f(1,1,-2)$
warm shaleBOT
ninjahuman
idle shoal
$D_{u}f(1,1,-2)=(\nabla f)(1,1,-2)\cdot u$
warm shaleBOT
ninjahuman
idle shoal
This is one way to calculate it
idle shoal
Yes
idle shoal
Ok I'll check it with another method but it will take a while
sullen raptor
Its fine. Thank youuu
warm shaleBOT
ninjahuman
idle shoal
v normalised?
idle shoal
Ok thanks
I'll calculate the definition now
$\lim_{t\to 0}\frac{f(a+tu)-f(a)}{t}$ where $a=(1,1,-2)$ and $u$ is that normalised vector
warm shaleBOT
ninjahuman
warm shaleBOT
ninjahuman
idle shoal
The same answer as before
sullen raptor
ah okay
idle shoal
I mean there was also some problem with the other answer you had before
Could there be something with the system those questions are being asked on?
sullen raptor
Yep I still havent got that one
idle shoal
This is probably a silly question but
sullen raptor
Its a system called mathway. Im not aware of any system errors but idk
idle shoal
It should be referring to rounding to the nearest number right?
sullen raptor
I believe so?
sullen raptor
Ok I can't think of anything else
Alright. Ill try to figure it out. Thank you for your timee
idle shoal
You're welcome and hopefully it will be sorted out soon!
sullen raptor
.close
rocky plank
Does anyone understand this annotated part of this proof? I'm confused what happened to our figure in pg.2 when comparing it to the one in pg.1. Also how does ρm o ρm cancel out?
(Open the pic if you want a better resolution)
obtuse pebbleBOT
Does anyone understand this annotated part of this proof? I'm confused what happ...
@rocky plank Has your question been resolved?
tall tusk
obtuse pebbleBOT
