As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.
#help-38
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trim lichen
also completely useless for the "how to find the value" question
you could first find (sqrt(2) + 1)^2 then (sqrt(2) + 1)^4 and multiply them together
both in the form a + bsqrt(2)
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@wide charm Has your question been resolved?
wide charm
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fading bane
help
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@fading bane Has your question been resolved?
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@fading bane Has your question been resolved?
vague pier
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vague pier
I need to find a phi value so this long equation equals 0
(need it for rotation of an equation, ...)
But idk how i should find said phi value
and no im not gonna bruteforce it
heady wolf
what exactly the question is?
vague pier
what exactly the question is?
I need to find a phi value so this long equation equals 0
heady wolf
i dont think it will be zero
heady wolf
Try Hit n Trial method?
vague pier
do you realise how big the equation is and how much time that would take?
frozen plover
The original question would be helpful
heady wolf
The original question would be helpful
Yeaa
heady wolf
there is a method for it, im sure
i mean there must be a specific appropriate question for it
vague pier
The original question would be helpful
What curve is the following equation in the xy plane? Reduce to std. form
Since there is an xy term
I have to rotate
--> use rotation formula
vague pier
and then i become this after applying it
frozen plover
or you can just check the eccentricity
bzzz sorry I meant the
the thing
hold on
frozen plover
pity
Determine the relation between h^2 and ab
h is the coefficient of xy while a and b are the coefficients of x^2 and y^2
I think its an ellipse
,w plot x^2 + xy - y^2 = 1
solid kilnBOT
vague pier
Its a hyperbole
vague pier
i know the final std. form / answer
frozen plover
Rectangular hyperbola
vague pier
just not how to get to it
solid kilnBOT
jan Nejon
frozen plover
Its a neat trick to remember
fading bane
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frozen plover
You cannot undo what was never done
fading bane
Are you talking to me
frozen plover
Yes
frozen plover
This channel is taken now and you cannot reopen it
vague pier
Its a neat trick to remember
Ok thx
winter summit
Fast question, are Alpha and Beta equal to (-2;0) ?
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Fast question, are Alpha and Beta equal to (-2;0) ?
split chasm
what are alpha and beta supposed to represent
winter summit
what are alpha and beta supposed to represent
second-degree polynomial chapter
If a > 0 , f has a minimum for x = α . This minimum is equal to β .
If a < 0 , f has a maximum for x = α . This maximum is equal to β .
split chasm
then yes
wintry crater
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wintry crater
is there an easier way to approac this than expand everything out?
heady wolf
Maybe Try Finding The Discriminant
wintry crater
yes, i mean when you put it in the discriminant
(a^2-9)^2-4(a^2+5a+6)(-17a^2-32a+57)
wintry crater
also it says have more than 2 real roots, so is it still appropriate to use >0
heady wolf
its a good ques tbh
heady wolf
whats this?
wintry crater
its a good ques tbh
even though it says MORE than 2 distinct can i still use the >0
its the answer from an online calculator
to check
heady wolf
even though it says MORE than 2 distinct can i still use the >0
yea ig
heady wolf
do u have its ans?
wintry crater
do u have its ans?
no unfortunately, its just a problem sheet
wintry crater
when its always true?
heady wolf
Identity
- True For Every Value Of x
- Has more than 2 roots
- Coeff Of Each Term Is Zero
wintry crater
ah okay
heady wolf
u know this?
wintry crater
**Identity**
`-` True For Every Value Of x
`-` Has more than 2 roots
`-` Coeff O...
slightly haha, how does it correlate to the question?
heady wolf
See the question clearly mentions
it has more than two distinct real roots
so definetly it is an identity
wintry crater
i see
heady wolf
yea
heady wolf
(a+2)(a+3)
so replace the quadratic eqn given in bracket by these
solid kilnBOT
wintry crater
something that is Identity
- True For Every Value Of x
- Has more than 2 roots
- Coeff Of Each Term Is Zero
😭😭
heady wolf
so i want you to carefully observe the eqn we form and the definations of identity
heady wolf
wintry crater
😂
wintry crater
The coeff of each term is 0
heady wolf
yeaa so ?
heady wolf
What would be equal to zero?
wintry crater
The factorised forms
heady wolf
Exactly!!!!!!!
heady wolf
idk but im feeling much happy
heady wolf
So equate each to zero to give values of a
Yessss
wintry crater
Haha yes thank you!
heady wolf
we will get 6 values of a
wintry crater
a=-3 a=-2 a= 3 a=-19/17
heady wolf
lemme see
wintry crater
But when I put the numbers into my calculator I only get 3 roots
One is -3 and the others decimals
heady wolf
which numbers
heady wolf
its telling common value
let it be
now we have values of a
so we just need to make them in a range
then we are done for this question
wintry crater
so we just need to make them in a range
Okay
wintry crater
its telling common value
What does this mean?
wintry crater
Hmm okay 🤔
heady wolf
So GG ?
wintry crater
Do I have to put it in a range or can I leave it like that
heady wolf
just say a = 3 , -3 ...........
wintry crater
Okay perfect
minor thistle
Can I speak here
minor thistle
How do I divide them I forgot the formula
I’ve searched on google but showed me different things
minor thistle
How do I divide them I forgot the formula
(This is not a real exercise I just gave an example)
nimble stone
what is D denoting?
minor thistle
what is D denoting?
Domain of a function
nimble stone
oh
theres no particular formula for this, youd just differentiate them
unless you meant $\frac{d}{dx} \left(\frac{f(x)}{g(x)}\right)$
solid kilnBOT
AℤØ
nimble stone
in which case its called the quotient rule
minor thistle
**AℤØ**
Yes this sorry
I think Ive found out
Its D[f(x)] • g(x) - D[g(x)] • f(x) all divided by (g(x))^2 right
grizzled vortex
<@&286206848099549185>
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<@&286206848099549185>
What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
1
grizzled vortex
how would you solve this if you didn't have `a` but just some number?
factorise the top and bottom ?
solid kilnBOT
artemetra
pale breach
all i understand is you need to get a 0 on the numerator
vagrant prism
all i understand is you need to get a 0 on the numerator
i was trying to get to that lol but okay
pale breach
its gonna solve itself then
grizzled vortex
**artemetra**
what does this mean ?
pale breach
what does this mean ?
well you multiply both sides by b and the b gets cancelled in the lhs and you get a = 0
vagrant prism
what does this mean ?
a/b=0 is only possible when a=0 (and b≠0)
vagrant prism
yes
grizzled vortex
then solve how ?
vagrant prism
then solve how ?
then you just have a quadratic
pale breach
yeah if you divide both sides by a you get 1/b = 0 and by reciprocating, b isnt defined
grizzled vortex
then you just have a quadratic
with 2 unknows
vagrant prism
x^2 - (a+1)x + 2a-2 = 0
first coefficient = 1
second = -(a+1)
third = 2a-2
and just plug those in
grizzled vortex
x^2 - (a+1)x + 2a-2 = 0
first coefficient = 1
second = -(a+1)
third = 2a-2
what do i do from here
vagrant prism
the step between the last 2 is wrong
grizzled vortex
the step between the last 2 is wrong
the discriminate is 0
does that mean it has more then 2 real roots
grizzled vortex
it has one real root
vagrant prism
your discriminant is a^2-6a+9
vagrant prism
ah, yes
grizzled vortex
sub a back
grizzled vortex
if a≠3, then there is 2 real roots
Wait a second
now that i have a
can I sub into quadratic to solve for x ?
Why does it want it , in terms of a ?
grizzled vortex
I dont need to solve for x ?
vagrant prism
I dont need to solve for x ?
you already found x, in terms of a
grizzled vortex
just the denominator
Why
vagrant prism
because if the denominator is 0 the solution doesn't work
vagrant prism
find the solutions to $3x^2+3x-5=0$, and then find what values of a would be equal to those solutions. those values of a will give your entire equation no solutions
solid kilnBOT
artemetra
vagrant prism
its a complex number
wut
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sudden lily
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sudden lily
Need help on the first question
viscid flower
is this the question?
vagrant prism
,rccw
viscid flower
vagrant prism
lmao
vagrant prism
ah
solid kilnBOT
solid kilnBOT
jan Niku
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@sudden lily Has your question been resolved?
fickle arrow
The derivative of a linear function is just the slope
As youve written f'(x) = 4
therefore what is f'(0)?
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warm snow
Is this correct?
trim joltBOT
Is this correct?
normal jasper
Or this one
this answer
warm snow
Oh okay
warm snow
Yeah
normal jasper
warm snow
<@&286206848099549185>
granite saddle
How do you derive this?
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How do you derive this?
marble wharf
start with $\sum_{k=0}^\infty x^k = \frac{1}{1-x}$ and differentiate on both sides
solid kilnBOT
Denascite
granite saddle
That makes sense thanks! Is this just a rule to keep in mind? I probably wouldn't have thought of derivatives if I was just given the summation 😅
.close
swift arrow
How do I approach a question like this?
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How do I approach a question like this?
worthy eagle
,rccw
solid kilnBOT
simple haven
swift arrow
Would that then look like y= -(x-2)^2 -1?
golden bison
no -y you have to distribute -1
swift arrow
I don’t get it 🥲
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@swift arrow Has your question been resolved?
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@swift arrow Has your question been resolved?
vagrant prism
I don’t get it 🥲
it's not -(x-2)^2-1, it's -((x-2)^2-1) = -(x-2)^2+1
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drifting rose
can someone do this? because how I did it I turn the sqrt into power of 1/2 and then expanded it within the bracket to get x^(1/2)+2
drifting rose
but answers do it like this
where did the 1/2 come from
oh you got to factorise the inside also
winged hinge
glad to have helped
but fr do u have any other question cus u seem to have figured it out 
drifting rose
oh yea uh
I did this in another way and i want to ask if it was vaild
give me a second I need to write it in paint because I don't know how to use the Texex or whatever its called
red loom
give me a second I need to write it in paint because I don't know how to use the...
LaTeX?
winged hinge
no
drifting rose
would this have a been a valid way to answer the question
winged hinge
no
red loom
$\int(2x+4)^{\frac{1}{2}}\dd x$
solid kilnBOT
PajamaMamaLlama
winged hinge
Can't split out the 1/2 like that
red loom
$(a+b)^n\neq a^n+b^n$
solid kilnBOT
PajamaMamaLlama
red loom
it's called the Freshman's Dream
drifting rose
ah I see
winged hinge
U could do u-substitution
solid kilnBOT
PajamaMamaLlama
drifting rose
I know how to factorise it the other way so u sub is a but unessesary I think
i'd do it if the x was like squared of cubed
red loom
a u-sub is totally proper here, you cannot expand that :)
drifting rose
also I don't think they would want it to be u subbed
winged hinge
I know how to factorise it the other way so u sub is a but unessesary I think
well you almost forgot to multiply by 1/2 in the antiderivative I think 
, whereas it'd be harder to make that mistake if you u-subbed
red loom
that's a good question what the hell did they do?
drifting rose
red loom
just use u-sub it's the best way to do this
drifting rose
they did that
drifting rose
u sub is different in how I'm thought it
it may be u sub but it's like chain rule but not really?
red loom
$\int g'(x)\cdot f(g(x))\dd x=f(g(x))+C$
solid kilnBOT
PajamaMamaLlama
red loom
that's the inverse chain rule
drifting rose
yea
red loom
i.e. u-substitution
drifting rose
ah
drifting rose
no no I got it, you don't have to explain
solid kilnBOT
PajamaMamaLlama
red loom
no no I got it, you don't have to explain
it's fine typed it out anyways 
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red loom
alright thanks for the help
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dark fulcrum
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dark fulcrum
help pls
red loom
$(a^b)^c=a^{b\cdot c}$
solid kilnBOT
PajamaMamaLlama
dark fulcrum
heady sedge
the cube root of the product is the product of the cube roots right
by exponent properties
dark fulcrum
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lone mauve
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royal remnant
this is wrong
lone mauve
like what exactly is the difference here? it feels like distribution of d/dx to y so why isn't it distribution to the fraction on the right too?
royal remnant
like what exactly is the difference here? it feels like distribution of d/dx to...
you dont "distribute" d/dx since it's not a fraction
lone mauve
you dont "distribute" d/dx since it's not a fraction
but dy/dx is correct
unkempt maple
and if so, why is this considered correct?
This one is correct
lone mauve
but dy/dx is correct
isn't this distribution to y?
lone mauve
it's not a fraction
but why do we treat it as a "fraction" in the sense of (dy)/(dx)
shouldn't it be (d/dx) y
it's the same thing as rise over run, right?
slope
m
royal remnant
but why do we treat it as a "fraction" in the sense of (dy)/(dx)
we dont, it's not a fraction, it's just dy/dx
lone mauve
we can't use that as rise [(24 + t)] / [run (53 - x)]?
it wouldn't make sense?
as per any variables
royal remnant
dy/dx can be understood as rise by run but that's still not the proper meaning of dy/dx
lone mauve
it seems like a bad habit to say "dy/dx" or "d/dx" is not a fraction, even though it looks like a fraction
wouldn't it have been better to use different syntax?
to be less confusing
royal remnant
it seems like a bad habit to say "dy/dx" or "d/dx" is not a fraction, even thoug...
bruh it literally isnt a fraction
royal remnant
wouldn't it have been better to use different syntax?
some places use y'
royal remnant
it LOOKS like a fraction tho
but it isnt one
lone mauve
that's like saying this looks like a 0, but it's an "oh"
abuse of notation imo
bad mathematicians whoever did this
too late to change now
also the fact that we can cancel out any u-sub by "fraction" totally makes my point here too
it's not a fraction but we can sometimes treat it like a fraction, which is abuse of notation imo
royal remnant
it's not a fraction but we can sometimes treat it like a fraction, which is abus...
we cant treat is as a fraction, all the ways in which you do treat is as one have been proven to work without considering it a fraction
it's not any abuse of notation
i recommend watching this video to understand it
https://www.youtube.com/watch?v=u-I3kF3Drkk&ab_channel=blackpenredpen
dense breach
d is an operator
dense breach
The problem here isn't treating dy/dx like a fraction, it's treating dy like a product
d(a/b) is not (da)/b
daring karma
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daring karma
not really sure where to start.
scarlet badger
not really sure where to start.
start by finding r'(t)
scarlet badger
start by finding r'(t)
plug into arc length formula and integrate, your bounds of integration are t1(t value at initial point given) and t2(what youre trying to find )
daring karma
okay so wait. The velocity is < 5 cost(t), -5sin(t), -12 >
daring karma
start by finding r'(t)
do i also need to find the length of r'(t)?
for the length i got 169
scarlet badger
so the arc length formula is S = ∫sqrt(((dx/dt)^2+(dy/dt)^2+(dz/dt)^2))dt
S is given to us, 26pi
and you found the velocity components, so use those in the formula
next we integrate from t1 to t2
you need to find t1 by setting a component equal to the point given
daring karma
t1 is 0, and t2 is unknown, right?
scarlet badger
yeah
daring karma
i have this integral set up so far, is this right?
scarlet badger
exactly
daring karma
forgot to take sqrt, is it 13?
scarlet badger
there you go
daring karma
so then the t2 is 2pi, right?
scarlet badger
yeah
daring karma
got it, thank you so much. that makes a lot of sense
scarlet badger
np
daring karma
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drifting rose
could someone help me understand the logic of this
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could someone help me understand the logic of this
drifting rose
for further context, a guy is throwing two dice and recording the sum on the numbers both dice lands on
forest egret
let P(n) be the possibility of getting sum of 9 before sum of 7 at the nth throw
drifting rose
alright
forest egret
then P(sum of 9 before sum of 7) = P(1)+P(2)+...
drifting rose
ok I understand that
forest egret
could someone help me understand the logic of this
this is calculating the infinite sum
drifting rose
wait so just one is 1/9 +26/36
forest egret
try to find P(n)
drifting rose
I am confused by the (26/36)^2
and how to get the difference
I understand its a infinite sum but how did they get to an infinite sum
forest egret
26/36 is the probability of not getting sum of 7
forest egret
P(1) = getting sum of 9 at first roll = 1/9
P(2) = not getting sum of 7 on first roll and getting sum of 9 on second roll
P(3) = note getting sum of 7 on first and second roll and getting sum of 9 on third roll...
drifting rose
so P(n) is just how many roles until he gets a sum of 9
so that would cause it being 1/9 + 26/36*1/9 +....
ok i get that bit now
so the r is the just the sum of 26/36*1/9 divided by 1/9
ah I got it now
thanks for the help
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wise heart
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wise heart
Not sure if i did this right
for Q1)
A = 2pi*rh + 2pi(r)^2
with variables height and radius
ionic pendant
remember that the can has both a top and a bottom
wise heart
Q2) V= (pi)(r^2)h
this is so messy
(pi)(r^2)(h) = 330cm^3
so from V
h = 330/((pi)(r^2))
Q3) substituting to area eq: 2(pi)(r)(330/(pi(r^2))) + 2(pi)(r^2) = A
we can cancel some things
660/r + 2pi(r^2) = A
Q4) dA/dr
i'd rather rewrite the expression: 660r^-1 + 2(pi)(r^2)
using power rule: dA/dr = 4pi(r) - 660/r^2
oh for Q3 i forgot to state a reasonable domain
so D_A: {r of R| 0cm<r<=5cm}
to find in this interval where there is a minimum
forest egret
I'd say r>0 but I guess that's not reasonable
wise heart
we could, why not
i'd definitely buy a can of coke if i saw it had a radius of 1 cm
there
uh so yeah, in this interval not exactly sure how to find the minimum point
to not forget, f'(r) = 4(pi)(r) - 660/r^2
wise heart
what if there aren't any stationary points?
forest egret
check the boundaries
forest egret
wait no
wise heart
isn't this an expression for surface area? (derivative of volume)
wise heart
oh my bad, for some reason i thought we derived the first expression by substituting surface area into volume equation
its other way around
anyway, so 4pi(r) - 660/r^2 = 0
4pi(r) = 660/r^2
4(pi)(r^3) = 660
r^3 = 660/4pi
= 165/pi?
yes
it has 1 real sltn
hol up
approximately 3.750
forest egret
use the r value to calculate h and A
wise heart
okk
we said V = (pi)(r^2)(h) = 330cm^3
r^2 = 14.0625
h = 7.470, to 3 dp
wow thats amazing
this is correct?
it kind of supports the intuitive idea or thought that
a 3d shape will have the most volume to surface area ratio the more spherical it is
oh rihgt surface area
so A = 2(pi)(3.75)(7.47) + 2(pi)(14.0625)
264.365 cm^2 to 3d.p
is this all correct?
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wise heart
can anyone verify if it's correct
forest egret
looks fine
reef field
I need to find where this series is continuous, differentiable or continuously differentiable
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I need to find where this series is continuous, differentiable or continuously d...
@reef field Has your question been resolved?
reef field
<@&286206848099549185>
reef field
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humble steppe
explain what x, y, and z is (don't ask me why)
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explain what x, y, and z is (don't ask me why)
wraith hinge
some letters
vernal warren
humble steppe
ok
all i know is x is the value of a hidden number or smth example: 20 + X = 25 means x is 5
ok
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humble steppe
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stark bison
It's closed
humble steppe
ok
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pliant briar
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pliant briar
Geometry
severe wave
yes what's your work so far @pliant briar
pliant briar
yes what's your work so far <@680423367223803943>
I'm really lost, the work I've done is worthless
Can I get your help step by step?
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lost barn
Warning: Physics Question incoming. I asked this in a physics discord channel but no response. I'll ask my question here and perhaps someone might be familiar with this chapter of physics...?
lost barn
This is from Electricity and Magnetism chapter of physics:
I made a free-body diagram of B, where there's:
Weight (0.12 * 10^-3 * 9.81 = 0.001177 = 1.177 * 10^-3 N),
Tension (Wcos(20) = 1.106 * 10^-3N),
and a repulsion force away from object A.
I assumed that the repulsion force would perhaps be the same but opposite direction to Wsin(20) = 0.403 * 10^-3N. But I don't think I am going in the right direction here... Am I?
The answer sheet states 4.3 * 10^-4N, but I'm not getting that through Weight - Tension + Repulsion... Perhaps I need to use F = k q1q2/r^2 (q1 and q2 are the same) but we don't know q... hmm?
jaunty scarab
from what i see in the diagram, A and B are on the same horizontal.
Thus, the weight is balanced with the vertical component of the tension, and the repulsion with the horizontal component of the tension
lost barn
Repulsion is balanced with the horizontal component of tension? I tried L * sin(20) =~ 0.2497m...This looks like the length between the two masses, giving us "r" for the equation F = k q1q2/r^2.
lost barn
from what i see in the diagram, A and B are on the same horizontal.
Thus, the we...
But I don't fully understand how repulsion is balanced. It's currently trying to repel away from A, yes?
<@&286206848099549185> Any helper here who understands charges in physics?
thick hull
But I don't fully understand how repulsion is balanced. It's currently trying to...
yh and the horizontal part of the tension is trying to pull it back to the centre
jaunty scarab
Repulsion is balanced with the horizontal component of tension? I tried L * sin(...
this would be correct. Tension on the rope pulls towards the balance (0º), while repulsion balances this.
Since q1=q2, and you have k and r, you can get both q
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coral crystal
how do I even begin this one?
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how do I even begin this one?
coral crystal
I have tried to multiply the second line by i but cant find anything else to do at this point
wooden plover
do you know gaussian elimination ?
works just fine with complex numbers also
@coral crystal
coral crystal
I thought using a matrix would make it more complex
wooden plover
it's already complex badum tss
instead of being unsure what to do, just use something you know tbf
@coral crystal
wooden plover
if you want, no problem
wooden plover
madlad exercise
coral crystal
are there any other ways?
wooden plover
there's a million ways to solve systems
gaussian elim is the most standard tho
,w solve {{15+10i, 4.8-7i,3},{-3,-4i,-2-2i},{3-7i,-9,-2+8i}} * {{a},{b},{c}} = {{5+8i},{-i},{2}}
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wooden plover
yeah it's just ugly af I guess
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hollow pilot
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hollow pilot
So I believe I have f(x&y) = f(x) $ f(y), as well as f(x$y) = f(x)#f(y). What I need to prove is f(x&y)=f(x)#f(y)
So I should need to show that f(x$y)=f(x)$f(y), correct?
That would imply G' is an automorphism, but I do not know how I would go about doing that
mint wasp
So I believe I have f(x&y) = f(x) $ f(y), as well as f(x$y) = f(x)#f(y). What I ...
Don't use the same f for all 3 homomorphisms. They don't even act on the same domain
hollow pilot
I say f. Instead of phi, but I see
mint wasp
Given a surjective homomorphism f from G to G', and a surjective homomorphism g from G' to G'', what do you think a possible surjective homomorphism from G to G'' can be?
hollow pilot
So f(xy) = f(x)$f[y) and h(xy) = h(x)#h(y)?
So something along the lines of f(g(x)$g(y)) = f(g(x))#f(g(y))?
mint wasp
"something along those lines" mhm
btw I can't tell which homomorphisms your f and h are, and which group operations that $ # & are
I'm just telling you the general idea
you can work out the details yourself
hollow pilot
Well all the question states is that homomorphism from G to G' and G' to G''
So I denoted the G operation &, the G' operation $, and the G" operation #
mint wasp
Given a surjective homomorphism f from G to G', and a surjective homomorphism g ...
Do you know how to answer this question?
All I did was rephrase the original question
gray hound
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gray hound
I get it to rref but it doesnt give straight forward answers
Im looking to get help with a breakdown
dull temple
what did you get when you row reduced it?
gray hound
one seconf
dull temple
because of the integers constraint this might require some manual checking
gray hound
what is an integer constraint
multiple in row?
x -z = 4
y-z=-4
is what i got
so x = z+4
and y= z-4
i honeslty want to know how to solve for x y and z
dull temple
there isn't just one solution
you can pick any value of z and get an answer for x and y
gray hound
x -z = 4
y-z=-4
1 0 -1 4
0 1 -1 -4
gray hound
you can pick any value of z and get an answer for x and y
actually?
why is that
i thought it was only infinte when the bottom row is all 0s
dull temple
well because you started with two equations and three unknowns
gray hound
ah
dull temple
i thought it was only infinte when the bottom row is all 0s
that's true in a square matrix like if you start with 3 and 3
because all 0s means you've effectively killed one of the equatiknsy
equations
gray hound
i see
so in order to find y
i need to isolate
and make z equal something
?
i get confused because when i make z equal something it always has X in it, so when i put for x then it was z and its an infite loop
dull temple
yeah, what's the smallest value of z such that x and y are both positive integers?
dull temple
what do x and y equal in that case?
gray hound
1 and negative
dull temple
that's what I'm seeing as well :)
dull temple
yep and then ofc you can calculate x and y
gray hound
i dont get why we can just choose though
like on a test (next week) imstressed because sometimes we can do that
but i dont get why i cant do that everytime
dull temple
if you have more variables than equations then there won't be a solution
like if I told you that a + b = 17
and nothing else
then you can pick whatever you want for a
dull temple
b will be determined by a, or you can pick whatever for b and that will determine a
gray hound
so in this equation
would i ever think to make x or y something random
or since the question is z is as small as possible i have to adjust that?
dull temple
or since the question is z is as small as possible i have to adjust that?
yeah exactly - it's easier to see how to minimize z if you have it simplified like you did
but with just those equations you have "one free variable"
gray hound
ok ill solve now but if you have time i have anohter quesiton
how could i go to solve x or z
dull temple
meaning you can pick whatever for x, or y, or z; and it'll constrain the others
gray hound
oh ok
dull temple
how could i go to solve x or z
wdym
gray hound
like lets say i wanted to solve for Z and x is the smallest
dull temple
what you did before was good, where you put the free variable on the right
see how you had x = z-4 and y = z+4 (or whatever it was)
that way you could pick z and quickly compute x and y
dull temple
yeah, that seems to work well
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hollow pilot
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hollow pilot
I am on portion b.
I know the requirements for subgroup are closed, contains identity, and each element has an inverse
The big question is phi inverse. I do not fully understand the rules with that
hollow pilot
Just how it opperates
I've never experienced it, so I am unsure if it is direct in meaning or there is particular paths I have to take
Like since phi (e) = e', can I just say phi (e') = e?
wooden plover
phi^(-1)(K) = the elements g in G for which phi(g) is in K
that's phi^(-1)(K)
it's a set
hollow pilot
Phi^-1(e')=e I mean
I see, so I may say that there are elements e', u, and v in K, to where if phi(e,x,y,) = e',u,v, then phi^-1(e',u,v) = e,x,y, under the notion e,x,y are in G
wooden plover
Phi^-1(e')=e I mean
phi doesn't have to be bijective, it's just an homomorphism, so an actual inverse function might not even exist
wooden plover
phi^(-1)(K) = the elements g in G for which phi(g) is in K
the best you can do is this
hollow pilot
I see, that is interesting
wooden plover
the proof should feel pretty similar to part a) prolly
hollow pilot
The proof for part a, which was mostly done with the professor, went through definition of subgroup
wooden plover
- show the identity of G is in phi^(-1)(K)
- if you take two elements of phi^(-1)(K), their product is in phi^(-1)(K)
- the inverse of something in phi^(-1)(K) is also in phi^(-1)(K)
just try it out
hollow pilot
So while I cannot say through means of equation, there is an implication if x, x^-1 e in G, yes?
hollow pilot
Sorry if I am not getting it right away. Little burnt out and trying to get this done tonight. I think I get the idea
hollow pilot
Since phi(g) is in K, then phi(e) is in k, so phi^-1(phi(e)), is in G, so G is nonempty?
wooden plover
well phi(e) is in K, so e is in phi^(-1)(K), that's it, by definition
the identity of G is in the set
hollow pilot
G is a group, meaning that G is closed, associative, contains e, contains x^-1
Hmmm
hollow pilot
Yeah, just listing out what we know
wooden plover
ah right
hollow pilot
I usually finding it as a good means if forming a path
wooden plover
yeah it helps
hollow pilot
Since G is a group, it contains an identity. Since phi is a homomorphism G into G', by a rule of homomorphism, phi(e) =e', where e' is in G'. Since K is a subgroup of G', it must contain e'.
Since phi^-1(K) returns back to G, and e' is in K, then the identity of G must belong to the phi^-1(K), so e is in phi^-1(K)
wooden plover
yup
hollow pilot
That works?
Writing it down rq
I could use similar logic to say that x belongs to G if phi(x)=u, and u belongs to K, yes?
wooden plover
not sure what you're trying to say
but yeah such an x is an element of phi^(-1)(K)
hollow pilot
Yes, that's what I meant. Ty
Since K is a subgroup, it is closed, thus if u is in K, v is in K, then uv is in K
With that notion, there is element x in G, y in G, such that phi(x) = u, phi(y) =v. Homomorphism definition says phi(xy) = phi(x)phi(y) =uv
Since x and y are in G, G is closed by group definition, xy is in G
uv is in G', and then uv is in K
Since there must be an element that results to uv in K, and it is xy in G, and we stated x,y are in phi^-1(K), then xy must belong to phi^-1(K) and thus must be closed
hollow pilot
Then finally inverse proofing
Since xx^-1 =e, e is in G, e' is in G', e' is in K, and x belongs to G, phi(x)=u belongs to G', u belongs to K, there must be an inverse in all sets
x^-1 in G, u^-1 in G', u^-1 in K
Since e belongs to phi^-1(K), and x belongs to phi^-1(K) then there must exist x^-1 in phi^-1(K)
And with setting the inverse for any term using x/u, that should satisfy the subgroup definition and making me done
Thank you for all of your help
wooden plover
um
hollow pilot
Oh, an issue?
wooden plover
your conclusion pretty much falls from nowhere here
like sure you're stating all the hypotheses
how does that tell me why x^(-1) is in phi^-1(K) ?
I don't see any explanation in what you wrote there
hollow pilot
Okay, thank you for the catch
There must be elements in G such that xx^-1 =e. Since we know x is in phi^-1(K), and e is in phi^-1(K), that x phi(x^-1) = e is in phi^-1(K)
By definition of e, phi(x^-1) must be x^-1, so x^-1 must be inf phi^-1(K) due to phi^-1(K) being closed
wooden plover
it's better but you lost yourself a little
hollow pilot
Hmmm
wooden plover
phi(x^-1) = x^(-1) i don't see any universe where that's true
they're not even in the same group
hollow pilot
Phi(e) = phi(xx^-1) = phi(x)phi(x^-1)
wooden plover
ok fine there we can talk
hollow pilot
=u phi(x^-1) = e', so phi(x^-1) must be u^-1
wooden plover
exactly
hollow pilot
By the definition of e
hollow pilot
Yeah that was my mistake with the translation
I much more prefer talking over writing
wooden plover
explaining a proof vs writing a proof, that's different standards also
hollow pilot
So since u^-1 is in K, and we see that x^-1 translates to u^-1, then logically x^-1 must be in phi^-(K), yes?
wooden plover
it's easier to be picky as a reader in writing
hollow pilot
Definitely, but math and logic needs to be picky
wooden plover
So since u^-1 is in K, and we see that x^-1 translates to u^-1, then logically x...
yep
real saddle
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real saddle
what am i missing here?
would it not be
y = x + 223 if 2012 is y and 2011 is x
nvm
i didnt read a lol
.close
rare cradle
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rare cradle
Any advice on how to integrate with respect to either
ionic pendant
could start by integrating wrt x with u-sub
ionic pendant
- bounds should not be constant here
- try lettjng u = the entire expression inside the square
rare cradle
When you say bounds shouldn't be constant, I changed them when I substituted for x², does that still apply
ionic pendant
the region of integration is not rectangular so the bounds of the interior integral should be a function of the outer variable
ionic pendant
there are two different sets of bounds you could choose depending on the order of integration, but the inner bounds should be a function of the outer variable and the outer bounds should be constant
ionic pendant
rare cradle
Thanks a lot
Very much*
I think I'm still making a mistake with the bounds
I got ln(0) at the end so I don't know where I went wrong
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torn pagoda
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torn pagoda
is this right?
shrewd ridge
i think that makes sense
curve shape is defined by speed and acceleration, there's nowhere to put the mass
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wait, but the speed is not equal
obsidian needle
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obsidian needle
how do i solve this question, pre calc 12 trig
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obsidian needle
<@&286206848099549185>
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@obsidian needle Has your question been resolved?
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@obsidian needle Has your question been resolved?
wraith hinge
is this a function or no?
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is this a function or no?
supple copper
!original
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Please show the original problem, exactly as it was stated to you. A picture or screenshot is best.
If the original problem is not in English, then post it anyway! The additional context might still help helpers help you. Do your best to translate.
wraith hinge
theres no question we were tasked if this is a function or not
supple copper
Just show the full question
wraith hinge
what question
supple copper
Show the full document
wraith hinge
supple copper
Then yes
wraith hinge
the prof said transfer all function used
supple copper
Well it depends what you count as a function
wraith hinge
is this a function or no?
so how will i write this as a function
supple copper
Did you do any of the other ones?
wraith hinge
no because thats a circle
conic sections are different from a function
theres a seperate file for conic sections
supple copper
Well
wraith hinge
what's the domain, what's the range
wraith hinge
ohh
wraith hinge
what's the domain, what's the range
of what
supple copper
So it depends
supple copper
what's the domain, what's the range
On this
You can’t ask what’s a function if you don’t specify the domain and range
I think for your purposes the answer is probably no
They are not functions
wraith hinge
ohh
supple copper
But they could be if you opened your minds to more possibilities of what you count as functions
Which is why it’s an ambiguous question
Hence why I wanted more information before giving you a definite yes/no answer
supple copper
It’s a weird question to ask
But usually the limiting condition is that a function mustn’t map 1 thing to 2 things
It’s got to map every element of the domain to something (singular) in the target
It’s why you would conventionally not call x = y² a function
Because now 4 maps to both 2 and -2
That’s 2 things
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tidal forge
