so what we did is right
#help-10
paper quest
dim(W-1 + W-2) = 4
and check if the 4 vectors are independent
if yes then those vectors are the besis of R^4
timid silo
so u mean the dimension of intersection would be 0?
paper quest
yeah
timid silo
oke so I am mistaken somewhere because dim(W1+W2) cannot be 4
paper quest
I guess what i said is false
dude that's confusing i need to rewatch my lesson again😑
timid silo
its okay do not worry
paper quest
from what our prof said, if you've have the basis of 2 vectorspaces then check only the common vectors between them
limber mauve
How come the volume of revolution for this function, revolved once around the y-axis
obtuse pebbleBOT
How come the volume of revolution for this function, revolved once around the y-...
limber mauve
Is equal to this
How is (sin x)^2 equal to x sinx, I assume the two outside the integral was moved there from the solution, but I have no clue as to how
rocky schooner
It's called the shell method.
obtuse pebbleBOT
@limber mauve Has your question been resolved?
frank belfry
For what value of Θ is tan9Θ=cotΘ
obtuse pebbleBOT
For what value of Θ is tan9Θ=cotΘ
frank belfry
How do i solve this?
forest sinew
what have you tried?
forest sinew
i think id start from like
$tan (\theta) \tan (9 \theta) = 0$
personally
oh, sorry
warm shaleBOT
jan Niku
forest sinew
from here, maybe a substitution?
there are some esoteric but common identities
can you think of how you might be able to use these with a substitution?
frank belfry
Tan(3Θ)3={(3tanΘ-tan^3Θ)/(1-3tan^2Θ)}x3?
forest sinew
i think youre close
its hard to tell, but you cant just multiply like uhh
$\cos (6 \theta) \neq 2 \cos (3 \theta)$
warm shaleBOT
jan Niku
warm shaleBOT
jan Niku
forest sinew
Then $\tan (\theta) \tan (9 \theta) = \tan ( \sfrac{\phi}{3} ) \tan ( 3 \phi) = 0$
warm shaleBOT
jan Niku
forest sinew
idk maybe this is not easier
dawn parrot
**jan Niku**
did you mean =1
forest sinew
oh, yea 😄
frank belfry
My brain was scrambled
forest sinew
whats the trick
ill bbiab
how about
instead of division
$\tan (9 \theta) - \cot (\theta) = 0$
warm shaleBOT
jan Niku
forest sinew
then uhh
$\frac{ \sin (9 \theta) }{ \cos (9 \theta) } - \frac{ \cos \theta }{ \sin \theta } = 0$
warm shaleBOT
jan Niku
forest sinew
which iss
dawn parrot
im pretty sure $cot(\theta)=tan(\frac{\pi}{2}-\theta)$
warm shaleBOT
james ash.
dawn parrot
and you can just take it from there
dawn parrot
Is the answer supposed to be 45
try substituting it
mild ocean
,w tan(x) = 1
warm shaleBOT
obtuse pebbleBOT
@frank belfry Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
restive ridge
I'm genuinely curious, what's the answer to this question?
obtuse pebbleBOT
I'm genuinely curious, what's the answer to this question?
austere moth
there isn’t it’s a paradox
restive ridge
I see
serene rivet
its none of them. cuz the actual answer is dependent on what you answer
timid silo
how do i find differentiate a multivariable function
obtuse pebbleBOT
how do i find differentiate a multivariable function
timid silo
when i have to take both variables into respect
Take a look at B
how do i differentiate like that
do i just treat both x and y as variables
i hold none of them constant?
Why do i never get any help here
this is basic calculus come on
spiral maple
You do partial wrt y then x
spiral maple
Yeah... I just told you how to get B
timid silo
I tell you I have already done that
storm lynx
So A and C are second order derivative with respect to x and y respetively. B is asking for first order derivative with respect to x of the first order derivative with respect to y. (Or vice versa as they are commutative)
spiral maple
You said look at B and asked how to differentiatr
That implies you're unsure how to do B
spiral maple
So A and C are second order derivative with respect to x and y respetively. B is...
They arent commutative unless Clairaut applies
timid silo
So A and C are second order derivative with respect to x and y respetively. B is...
So I first take first order derivative wrt x of the entire function, then i combine that with the deriviative of the entire function wrt y, and the same goes for second order wrt x and wrtx
and then i combine them together?
timid silo
That implies you're unsure how to do B
i have no idea how to do B sorry for not clearing that up
i can't do two variables at once
can you give me an example of what it would look like?
My function is R(s, t) = (s - 2t)^2 - 2(2/35 - s * t)
spiral maple
No
spiral maple
Partial of R wrt s is 2(s-2t)-2(-t)
timid silo
i have simplified them
timid silo
You don't know how to simplify what is this
spiral maple
I did the partial directly
spiral maple
Yes.
timid silo
is that all that is to it?
wow
if you had said that at the beginning we could have saved a lot of time
thanks for the help though
i'm under a lot of stress because i suck at math im very sorry that was mean :((
i have this assignment you know, time pressure i need to pass and so on
spiral maple
if you had said that at the beginning we could have saved a lot of time
I did say that.
timid silo
so i need to do it four times?
wait nvm i got it
I need help with b)
lagrange multiplier yes?
obtuse pebbleBOT
@timid silo Has your question been resolved?
obtuse pebbleBOT
@timid silo Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
crystal delta
Need some help here.
timid silo
Need some help here.
x+3pi/4=cos^-1(1/2)
x+3pi/4=cos^-1{pi/3 +2pi(n), -pi/3+2pi(n) where n is a real number}
now I think you just subtract -pi/3 and pi/3 with -3pi/4
same with 2pi(n)
and you should have all the solutions
then it's just finding them specifcally from -pi<x<pi
@crystal delta does that help?
...
crystal delta
Kinda, are you available to write it on a paper or so?
crystal delta
Awhh. Okay! I will try and understand it.
crystal delta
Need some help here.
<@&286206848099549185>
@timid silobut hey thanks so much for helping
imma try and understand yours
polar glacier
can someone pls help me
polar glacier
idk who to ask
timid silo
<@456226577798135808>but hey thanks so much for helping
yea np
obtuse pebbleBOT
@crystal delta Has your question been resolved?
obtuse pebbleBOT
@crystal delta Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
frigid surge
is there a way to write this in the linear approximation formula?
obtuse pebbleBOT
is there a way to write this in the linear approximation formula?
chrome orbit
is there a way to write this in the linear approximation formula?
try using differentials
$\Delta y=\frac{dy}{dx} \cdotp \Delta x$
warm shaleBOT
the.dorkest.knight
obtuse pebbleBOT
@frigid surge Has your question been resolved?
frigid surge
oke thanks
celest sun
Don't troll
celest sun
Rokabe 
upbeat plinth
sup luna
pine flax
Guys don't be mean to dumb people
ocean topaz
i'm not mean. i banned them in the nicest way possible
upbeat plinth
we don't entertain trolls either
obtuse pebbleBOT
Available help channel!
brisk arrow
i have a question
obtuse pebbleBOT
i have a question
dim patio
brisk arrow
so the first thought in my mind is, makes the denominator to 42
so i add 14 on the numerator and denominator to 5/28 so it becomes 19/42
royal basin
19???
brisk arrow
but somehow its illegal
royal basin
19??
brisk arrow
sorry
karmic whale
u cant do that
brisk arrow
typo
royal basin
you tried to add the same number to the numerator and denominator?
brisk arrow
i add 14
royal basin
of course that's illegal
royal basin
0/1 = 1/2 by this logic
brisk arrow
ohhh
royal basin
surely you agree that one half is not the same as zero
karmic whale
when u add +14 in each sides its gonna be diferent
brisk arrow
surely you agree that one half is not the same as zero
yes i agree with this
karmic whale
diferent when we multiply
dim patio
then how i reach the result of (11/42)+(5/28)=
Find the least common multiple of 42 and 28?
brisk arrow
got it
royal basin
then how i reach the result of (11/42)+(5/28)=
42 = 6*7 and 28 = 4*7
so you can take 12*7 as your common denominator
brisk arrow
i have another thought since 42=14*3 and 28=14 * 2, so i think multiply 3/2 on both of the numerator and denominator of 5/28
karmic whale
so u know if
$42=2 /times 3 /times 7$ and
$28- 2^2 /times 7$
warm shaleBOT
IVMC Gaming CH
karmic whale
my laptop doesnt have backslash
royal basin
that's strange, but if it doesn't then you cannot type latex
it's full of backslashes
unfortunately for you
brisk arrow
i think find the LCM of (42,28) is the only method that i can apply here, its the most efficient way to get the answer
brisk arrow
i have another thought since 42=14*3 and 28=14 * 2, so i think multiply 3/2 on b...
that's illegal too
i think the question is solved
thank you guys
.close
ancient python
I did.
warm shaleBOT
ancient python
Look at both of them.
celest sun
Oops
ancient python
But when we add pi, where do we move?
celest sun
,w plot y = sin(x)
warm shaleBOT
celest sun
If you add pi, you move pi units to the right
celest sun
Also, consider the unit circle. If you rotate a point (x,y) around the unit circle by angle pi, it becomes (-x,-y). So instead of sin = x/r, you have sin = -x/r
ancient python
If there were an origin of sin(x+pi) and sin(-x), the six(x+pi) will start after pi units in the x-axis after the origin of sin(-x)?
celest sun
I don't know what you're saying
ancient python
See.
celest sun
I am not talking about plotting both graphs. I am saying just look at the graph of sin,what happens if you take a point x and look at the point x+pi, pi units to the right, compare the function values .
ancient python
- If sin(x+pi) had an origin.
- If sin(-x) had an origin.
Will the sin(x+pi) be pi away to the right of sin(-x)?
celest sun
Idk what it means for sin(x+pi) to have an origin
ancient python
Because that would make sense.
ancient python
Idk what it means for sin(x+pi) to have an origin
ASsume that.
celest sun
I don't know what it means, so I cannot assume it
ancient python
OKAy then tell me how are these both equal?
celest sun
See why (1) sin(x+pi) = - sin(x),
and (2) sin(-x) = - sin(x)
This is what I am trying to show
ancient python
I want to know the first one.
ancient python
Because I was asking something else but okay you may go ahead.
celest sun
Look at the graph of y = sin(x). Just that graph. Pick a random point x, then look at the function value at x. Now go to x+pi (move pi units to the right) and then look at the function value at x+pi
celest sun
Also, consider the unit circle. If you rotate a point (x,y) around the unit circ...
Alternatively:
ancient python
Also, consider the unit circle. If you rotate a point (x,y) around the unit circ...
In radians, right?
celest sun
Yes
ancient python
Yeah.
ancient python
Look at the graph of y = sin(x). Just that graph. Pick a random point x, then lo...
Let me try that.
Should I make a circle graph for it?
Like the triangle inside the cirlce?
Or the normal Cartesian plane graph?
ancient python
Also, consider the unit circle. If you rotate a point (x,y) around the unit circ...
It is basically reflected by the axis x, right?
fallow tundra
help please 😦
ancient python
help please 😦
OcCUpied channel.
celest sun
And no, it is not just a reflection in the x axis
fallow tundra
OcCUpied channel.
sorry
karmic whale
@fallow tundra dont take people spot
ancient python
And no, it is not just a reflection in the x axis
Along the line x = y I meant.
celest sun
Also, not that
It is a rotation by 180 degrees, not a reflection
If you insist on it being a reflection, it is a reflection first in the x axis and then in the y axis. But this makes it less intuitive, not more.
celest sun
Uh
celest sun
Do you know the unit circle interpretation of trig functions?
ancient python
Yes.
ancient python
Also, consider the unit circle. If you rotate a point (x,y) around the unit circ...
celest sun
Rotatinf a point by angle pi does not mean add pi to both coordinates
ancient python
Look at the graph of y = sin(x). Just that graph. Pick a random point x, then lo...
ancient python
Rotatinf a point by angle pi does not mean add pi to both coordinates
Yeah.
I messed up and misintrepreted.
Mixed the 1st and 2nd points.
But if we rotate by 2pi, we get back to the original point, right?
celest sun
ancient python
Yes, thank you, I understood it, @celest sun.
celest sun
👍
ancient python
Ah sadge you had to do the hard work for it when I just understood it by the graph.
I will not close this channel since I have multiple questions left.
So I will keep asking them here.
How is this done? Can someone explain this please?
Figure 1.69.
obtuse pebbleBOT
ancient python
.reopen
boreal plaza
How is this done? Can someone explain this please?
what part dint u understand
ancient python
The RHS formation.
ancient python
Yes.
boreal plaza
Figure 1.69.
so u see this circle right
ancient python
Yes.
boreal plaza
the radius of the circle is 1
ancient python
Yes it is.
boreal plaza
if its an angle theta from the x axis
ancient python
Why square the stuff?
boreal plaza
wait calm
boreal plaza
Figure 1.69.
if u take this example and its an angle theta off x axis
ancient python
What?
boreal plaza
u drop a perpendicular from the point on the circle to the x axis
ancient python
Okay.
boreal plaza
the y part of the image is that perpendicular
and the x part is the horizontal part
ancient python
Ummm.
boreal plaza
since its perpendicular u have a right angled triangle
ancient python
the y part of the image is that perpendicular
Ohhh.
ancient python
and the x part is the horizontal part
Yes it is.
boreal plaza
what part do u not understand
ancient python
Now I do.
boreal plaza
ok
ancient python
So basically like.
boreal plaza
now since its a right triangle u can use trig to describe x and y
ancient python
From the center of the circle, you make a 90 degree angled triangle which is like a quarter of the circle's angle?
boreal plaza
no t
u can make any angle
but u need to drop a perpendicular from the point on the circumference to the x axis
think of it as the height of the point off the x axis
boreal plaza
Figure 1.69.
so we have y which is the perpendicular distance from the x axis
ancient python
What point on the circumference?
boreal plaza
P
ancient python
Can you draw maybe?
obtuse pebbleBOT
Available help channel!
boreal plaza
ok wait
boreal plaza
its gonna be the same thing
so tell me what u dont understand
where are u confused
ancient python
What are you saying and how is it related to the question.
These days the people with Helper's role do be really slacking off.
boreal plaza
did u first understand what x and y are
boreal plaza
Figure 1.69.
in this image
ancient python
Yes.
boreal plaza
do u see how there is a triangle formed
ancient python
Yes.
boreal plaza
a right triangle
this means instead of calling the sides x and y we can use trig to describe the sides
ancient python
Yes.
boreal plaza
what is cos theta
boreal plaza
so sin theta = y/r
y = r sin theta
ancient python
Yes we do.
boreal plaza
since this is a right triangle
ancient python
Yes.
ancient python
Agreement.
ancient python
Figure 1.69.
.
boreal plaza
so x^2+y^2 = r^2
r^2cos^2 theta + r^2 sin ^2 theta = r^2
r^2(sin^2 theta+cos^theta) = r^2
coz x = r cos theta and y = r sin theta
do u agree with this
ancient python
so x^2+y^2 = r^2
r^2cos^2 theta + r^2 sin ^2 theta = r^2
r^2(sin^2 theta+cos^th...
Is not that $r^2((x+y)/r)?$
ancient python
but u get why i squared them right
Yeah Pythagoras my man did some work so you did that.
boreal plaza
so x^2+y^2 = r^2
r^2cos^2 theta + r^2 sin ^2 theta = r^2
r^2(sin^2 theta+cos^th...
so no issues here right
ancient python
No, I have.
warm shaleBOT
Senku Ishigami
boreal plaza
in which part
ancient python
so x^2+y^2 = r^2
r^2cos^2 theta + r^2 sin ^2 theta = r^2
r^2(sin^2 theta+cos^th...
1st and 2nd.
boreal plaza
in 1st and second i replaced x and y in terms of sin and cos
boreal plaza
now since r^2(sin^2 theta + cos^2 theta) = r^2
ancient python
You.
boreal plaza
how do i do it
ancient python
.close
boreal plaza
.close
final python
do u write the absolute value of the length of a vector as |||v|||
obtuse pebbleBOT
do u write the absolute value of the length of a vector as |||v|||
warm shaleBOT
hvna
timid silo
?
final python
absolute value of the length of a vector
final python
really
timid silo
Yes
final python
lol
junior inlet
||v||
junior inlet
do u write the absolute value of the length of a vector as |||v|||
length of vector can't be negative, so... uh, it's the same as the notation for the length of a vector
lunar estuary
i have a question, i have homework due in a bit but i cant solve smth the question is: the answer to a division question is 28
-
use the digits 0, 1, 2, 4 and 5 to find the three digit dividend and the two digit divisor
-
use a written method to show that you are right
obtuse pebbleBOT
i have a question, i have homework due in a bit but i cant solve smth the questi...
timid silo
280/10
What do they specifically mean by "find a three digit dividend and two digit divisor" such that "the answer is 28". There is tons of them.
280/10 is the most obvious answer
"using the digits" is unclear to me, but 2 * 5 = 10 and then the obvious solution comes about
timid silo
there is multiple numbers for this scenario th ough
i thought of 2 quickly
28 is a multiple of 2 so a good start would be for our dividend and our divisor to be multiples of 2
lunar estuary
but it should be a 3 digit number like 100 not 2
lunar estuary
LESS GO
timid silo
are you supposed to find all of the numbers?
there is more than onenevermind I don't think there is more than one solution. I did math error in brain
timid silo
ok
obtuse pebbleBOT
storm acorn
you saved me from getting spanked by my mom
ahahaha
obtuse pebbleBOT
Available help channel!
uneven gate
Question + my working
obtuse pebbleBOT
Question + my working
obtuse pebbleBOT
@uneven gate Has your question been resolved?
dim patio
What's you question?
uneven gate
I am just confused in general on where i went wrong
dim patio
Lemme solve it then you check?
uneven gate
That would be great thanks
uneven gate
I will try thanks a lot for the help
dim patio
Do you need help with ii) too?
uneven gate
If thats okay with you then sure
dim patio
If thats okay with you then sure
I will give you a hint. Try calculate vector BP depend on u and v.
uneven gate
Quick question, how would i know that they are collinear?
dim patio
Quick question, how would i know that they are collinear?
If vector AB=k. vector BC , then A,B,C are collinear.
uneven gate
So basically i need bp to equal py?
dim patio
No
You need BP=k.PY ( k is a constant)
k can be any number
So try to turn BP into a.u+b.v
uneven gate
I got -2/3u + 1/3v for BP, idk if it is right
dim patio
I got -2/3u + 1/3v for BP, idk if it is right
This seem right
uneven gate
So do i solve for the constant?
dim patio
Yeah
uneven gate
Oh alright ill try now
dim patio
Kk , I will see it you got it correct.
uneven gate
2?
dim patio
Yep
uneven gate
Alright thanks a lot for the help you saved me big time haha
dim patio
uneven gate
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
agile star
obtuse pebbleBOT
agile star
I can't wrap my head around this one
does the incur charges depend on what type of participants I pick?
so if I pick poster presentation with 3 poster instead it would be
1500 + 450 * ( 2 ) + [(5/100) * ( 1500 + 400 * (2))]
for the credit charges
am I in the correct path? 😵
sick crystal
Hello!
high lily
division by something that could potentially be 0
cunning quiver
u have done a mistalke
sick crystal
lol where
cunning quiver
lol
sick crystal
let me check
high lily
and also ^
cunning quiver
yea
sick crystal
and as x=y x-y = 0?
cunning quiver
np
sick crystal
.close
tulip ginkgo
obtuse pebbleBOT
tulip ginkgo
If the degree is odd shouldn't it mean that as x --> -inf., y --> negative inf.?
high lily
not necessarily
tulip ginkgo
not necessarily
do i have it the other way around lol
high lily
whether y approaches pos or negative infinity depends on your function
specifically the coefficient of the leading term
tulip ginkgo
well i was told the degree correlates with the -x side of the axis, and the sign of the leading coefficient correlates with the +x side of the axis
high lily
vague and unclear wording
tulip ginkgo
😦
tulip ginkgo
specifically the coefficient of the leading term
i wasnt given a function
just this graph
tulip ginkgo
ik the leading coeff. is negative since the right side of the graph goes down
high lily
as you're going towards the left of the graph. what's happening to y values
tulip ginkgo
they decrease for a little bit, and then increase infinitely
high lily
yes
tulip ginkgo
i was told that when y --> pos. inf., as x --> negative inf., then the degree is even
high lily
that assumed that the leading coefficient was positive
,w graph y=x^2 + 1 and y=-x^2 - 1
warm shaleBOT
high lily
both functions have an even degree,
and approach infinities of different signs
tulip ginkgo
both functions have an even degree,
and approach infinities of different signs
so if the leading coefficient is positive, and y --> +inf. as x --> -inf, then that means the degree is even. if y --> -inf as x --> -inf. the degree is odd. Would it therefore be vice versa for if the leading coefficient was negative?
obtuse pebbleBOT
@tulip ginkgo Has your question been resolved?
obtuse pebbleBOT
true rampart
How does the first question relate with the second
i am a bit confused on this
since the first ones anwser is r = 23 mod (77) and the second ones anwser is 23 but im confused why they are related
obtuse pebbleBOT
@true rampart Has your question been resolved?
true rampart
!close
obtuse pebbleBOT
true rampart
.close
obtuse pebbleBOT
Available help channel!
grizzled oxide
how would i find KE at launch
obtuse pebbleBOT
how would i find KE at launch
spiral maple
how would i find KE at launch
at launch, all the potential energy has been converted into kinetic
obtuse pebbleBOT
@grizzled oxide Has your question been resolved?
grizzled oxide
<@&286206848099549185>
obtuse pebbleBOT
@grizzled oxide Has your question been resolved?
obtuse pebbleBOT
@grizzled oxide Has your question been resolved?
weak cave
How do i solve this?
obtuse pebbleBOT
How do i solve this?
short spruce
what have you done so far?
weak cave
I have no idea what to do tbh
short spruce
it gives you a hint in the last paragraph there
it tells you what the total revenue is defined as and also tells you how much the total revenue is
weak cave
i multiplyed them got -0.5n^2 + 35.5n + 316
oh
i think i know what to do
got it thanks bro just multiplyed wrong the first time
short spruce
👍
weak cave
need to start reading instructions more carefully
obtuse pebbleBOT
obtuse pebbleBOT
old aurora
<@&286206848099549185>
obtuse pebbleBOT
Available help channel!
dim otter
Are polynomials literally just how much terms there are?
obtuse pebbleBOT
Are polynomials literally just how much terms there are?
dim otter
And what are the factors that'll make an equation not a polynomial?
dim otter
restive acorn
A polynomial equation is any kind of equation that is just different powers of "x" or whatever kind of variable you have
Example:
f(x) = x
This is a polynomial
vital pasture
@restive acorn hi can u help me
restive acorn
It has x^1
dim otter
A polynomial equation is any kind of equation that is just different powers of "...
So just how much exponents there are?
restive acorn
The degree of this polynomial is 1
Because that's the biggest exponemt
I'll give you another example
f(x) = 2x^5 + 5x^9 + 2
This is also a polynomial
What's the biggest exponent?
On x
dim otter
9
restive acorn
That's the Degree
dim otter
confusion
restive acorn
There are 2 exponents
Well 3 actually
The 2 has x^0
Then there's 5 and 9
Which is the biggest number
dim otter
9..?
restive acorn
Yea
Correct so we call this a polynomial of degree 9
Try this
g(x) = 2x^7 - 4x^15 + 23x^1000 + 7
What is the degree of this polynomial
dim otter
1000
restive acorn
Exactly
Good
So this tells us a lot
Because
They are broadly grouped into 2 categories
Even polynomial (even degree)
Odd Polynomial (odd degree)
The 2 categories behave very similarly and you can answer a lot about the shape of their graphs
Do you have a more specific question or example from your class
austere grove
what is it called when a variable increases while in a square root
obtuse pebbleBOT
what is it called when a variable increases while in a square root
austere grove
like if you had v = sqrt(m), v would increase in a ___ way as m increases?
obtuse pebbleBOT
@austere grove Has your question been resolved?
obtuse pebbleBOT
radiant roost
@austere grove i think its called sublinear growth
read this if u want https://math.stackexchange.com/questions/3764070/is-there-a-one-word-term-for-grows-by-square-root
obtuse pebbleBOT
Available help channel!
slow verge
obtuse pebbleBOT
slow verge
does antone know how to get the sum of that series
as in the equation for the sum
bec idk how to find the common ratio or the common difference
weak musk
$$\sum_{i=0}^{20}{3nx^n}$$
warm shaleBOT
MaxVGC
weak musk
This is what you need?
obtuse pebbleBOT
@slow verge Has your question been resolved?
vital pasture
@restive acorn hello
slow verge
This is what you need?
yup thanks!
obtuse pebbleBOT
@vital pasture Has your question been resolved?
frozen willow
Does the function f(x) = 4 have an absolute min/max?
obtuse pebbleBOT
Does the function f(x) = 4 have an absolute min/max?
rocky schooner
4
frozen willow
Cuz, the absolute minimum value is defined as f(a) where f(a) >= all other values in the domain
frozen willow
So the maximum value is everywhere?
rocky schooner
Yep
rocky schooner
Yep
tidal scaffold
obtuse pebbleBOT
tidal scaffold
any help ?
mighty geyser
Try drawing a diagram
tidal scaffold
not familiar with these type of ques
mighty geyser
where is |z|=r
chrome orbit
you can use analytical geometry for this
assume that the equation of the circle is x^2+y^2=r^2
and let the point z0 be (x0,y0)
use the concept of power of a point
chrome orbit
just construct a right triangle
that too
obtuse pebbleBOT
@tidal scaffold Has your question been resolved?
tidal scaffold
ohk ill try thanks
trim hinge
can anyone help with this?
obtuse pebbleBOT
can anyone help with this?
trim hinge
dont really know where to start
trim hinge
.close
obtuse pebbleBOT
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sour lantern
I'm supposed to fiund limit of that at infinity
obtuse pebbleBOT
I'm supposed to fiund limit of that at infinity
warm shaleBOT
Erzis エルジス
jolly ginkgo
Why?
jolly ginkgo
Idk about the graph but it doesn't show anything as x tends to infinity
jolly ginkgo
U don't get what you men
sour lantern
it's the power
junior inlet
(there'll be an asymptote but else i think it's possible)
alpine raven
^
sour lantern
oh, so there is no limit?
alpine raven
5n^3 +2 is equivalent to 5n^3 at infinity
jolly ginkgo
This diverges
alpine raven
2n^3 - 5 equivalent to 2n^3
you can simplify
alpine raven
This diverges
indeed
junior inlet
2n^3 - 5 equivalent to 2n^3
you can simplify
just take the highest power when calculating llimits towards infinity
jolly ginkgo
Reaction to your own comment 
sour lantern
can someone write that in latex? I know that limit of $\frac{3n^3+7}{2n^3-5}$ at infinity is 1.5 but it doesn't tell me too much
warm shaleBOT
Erzis エルジス
sour lantern
I need the e^x form
jolly ginkgo
I need the e^x form
Is that necessary?
sour lantern
well I'd say so, how would you solve it?
obtuse pebbleBOT
@sour lantern Has your question been resolved?
rocky schooner
can someone write that in latex? I know that limit of $\frac{3n^3+7}{2n^3-5}$ at...
Did you check it using app/computer?
Oh wait
I thought it's the whole thing lol
rocky schooner
I'm supposed to fiund limit of that at infinity
Is the answer just positive infinity?
sour lantern
I think it's 1
sour lantern
.
rocky schooner
Hint: (2.5)(2n³-5) = 5n³-12.5
,w ((5n^3+2)/(2n^3-5))^(2n^3-5) n tends to infinity
warm shaleBOT
rocky schooner
Just as I expected.
rocky schooner
The graph is like that because the numbers overflowed.
strong vale
obtuse pebbleBOT
strong vale
Apparently, it's not necessary for $P = R$ for this equality to be true. But I cannot see any other solution that will make this true if we don't use 0 matrices
warm shaleBOT
azeem321
obtuse pebbleBOT
@strong vale Has your question been resolved?
obtuse pebbleBOT
@strong vale Has your question been resolved?
jolly ginkgo
What do you think about non invertible Q
strong vale
What do you think about non invertible Q
Would that mean Q would have to be inverse of P? Resulting in $I - RQ = 0 \rightarrow I = RQ \rightarrow I = RP^{-1}$
warm shaleBOT
azeem321
jolly ginkgo
**azeem321**
I wasn't thinking th8s
strong vale
I suggested that $Q = P^{-1}$
warm shaleBOT
azeem321
strong vale
no more hints pls. brain not working.. ill comeback to this after some rest
thanks
.close
jolly ginkgo
no more hints pls. brain not working.. ill comeback to this after some rest
I'll give you an example beforehand you can check it whenever you want
obtuse pebbleBOT
I'll give you an example beforehand you can check it whenever you want
warm shaleBOT
it's Sam
timid silo
Is there any change in sign of inequality if I reciprocal the inequality on both sides?
obtuse pebbleBOT
Is there any change in sign of inequality if I reciprocal the inequality on both...
celest sun
You cannot do this in general unless you know the signs of the things involved.
If they have different signs, then taking the reciprocal won't change the inequality
If they have the same sign, then taking the reciprocal will flip the inequality
Examples:
- 2 < 2 and -1/2 < 1/2
2 < 3 but 1/2 > 1/3
-3 < -2 but -1/3 > -1/2
@timid silo
timid silo
[1/{(x+1)(x+2)(x+3)}] >= 0
I was doing a problem which is almost done but am stuck at the above step
don't know how to proceed further to solve x
celest sun
You can say (x+1)(x+2)(x+3) > 0. Note it cannot equal 0 or you would be dividing by 0, and it cannot be less than 0 since 1 divided by a negative number would be negative.
@timid silo
timid silo
celest sun
?
timid silo
attached my work if u needed to check
timid silo
You can say (x+1)(x+2)(x+3) > 0. Note it cannot equal 0 or you would be dividing...
but how I can write (x+1)(x+2)(x+3) > 0? reason?
celest sun
I explained why it cannot be 0 and why it cannot be negative
Then the only alternative is that it is positive
celest sun
👍
timid silo
1/0 is undefined
what about 0*0?
is that equal to 0 or it's also undefined
@celest sun
celest sun
0*0 is 0
vale urchin
obtuse pebbleBOT
vale urchin
i have no clue how this is supposed to work
checked yt and checked the textbook and still cant figure it out
brave bramble
The power series simply add
And then multiply by 1/2
However, it might be helpful to actually write out both series and then add them
In this case
vale urchin
well when i just entered it and multiplied by a half it said it was the wrong answer
obtuse pebbleBOT
@vale urchin Has your question been resolved?
mild niche
I have a quick question regarding spherical coordinates, I know theta starts on the z-axes at z=1 for r=1, but in which direction does it go? Should it be in positive direction, so counterclockwise?
obtuse pebbleBOT
I have a quick question regarding spherical coordinates, I know theta starts on ...
mild niche
mild niche
I have a quick question regarding spherical coordinates, I know theta starts on ...
sorry i didnt mean theta, i mean cos(theta)
for the z-component
woven stirrup
I have a quick question regarding spherical coordinates, I know theta starts on ...
well if you let theta =pi/2 and perturb phi in the positive direction, (cos(phi),sin(phi),0) is counterclockwise in X-Y.
however, let phi=0 for now, then you have the cross section of X-Z which forms (sin(theta),0,cos(theta))
then for phi=pi/2, you have the cross section of Y-Z which is the same
(0,sin(theta),cos(theta))
So when phi = 0,pi/2, you have clockwise rotation when theta is changed in the positive direction
with respect to the X-Z and Y-Z axes
woven stirrup
sorry i didnt mean theta, i mean cos(theta)
^ is a roundabout way of saying that it depends on the value of phi, as you can show that when cos(phi),sin(phi) < 0, then you have counter clockwise
mild niche
thanks for the answer, i'm gonna reply to that in a few mins, just need a bit to process that
woven stirrup
yeah, it’s mostly depending on the way that you look at it because clockwise and counterclockwise doesn’t have a good interpretation in R3
mild niche
ok, im still kind of confused, im trying to imagine it but its not really working 
mild niche
well if you let theta =pi/2 and perturb phi in the positive direction, (cos(phi)...
i do understand what you're saying here
mild niche
So when phi = 0,pi/2, you have clockwise rotation when theta is changed in the p...
but this i dont understand yet
woven stirrup
okay, so when you change phi, you change the circular cross section that you’re looking at. When phi = -pi,-pi/2,0,pi/2 it will always have a 0 x or y component
mild niche
okay yes🤔
woven stirrup
the direction of the circle in those cases is dependent on what direction is facing you though
if you allow only the positive part of y and x to face you (when it’s 0), when cos(phi),sin(phi)>0, it’ll appear to move clockwise, but counterclockwise when they’re negative
when I say the direction that’s facing you, think that the positive x or y axis is coming at you
mild niche
ahhh okay, yeah, that makes sense
woven stirrup
Yeah, it’s mostly something just to draw out, is there a particular reason you asked?
mild niche
yeah, im trying to figure out the boundary conditions on a physics problem
but right now i think im too tired to continue haha
but thank you, that helped a lot
woven stirrup
yeah, you just need to specify what into and out of the board is, then you can kinda understand clockwise and counterclockwise
in that context
mild niche
yeah, you just need to specify what into and out of the board is, then you can k...
ok, gotcha!
thanks!
woven stirrup
ofc
mild niche
.close
obtuse pebbleBOT
obtuse pebbleBOT
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lilac valve
is this the correct domain and range?
obtuse pebbleBOT
is this the correct domain and range?
spiral maple
looks right
obtuse pebbleBOT
@lilac valve Has your question been resolved?
timid silo
im not sure how to write this solution, as im new to newton's method. any help would be appreciated
obtuse pebbleBOT
im not sure how to write this solution, as im new to newton's method. any help w...
timid silo
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