Yeah then after that I need the angle here
#help-27
acoustic plank
acoustic plank
gray axle
Did u find q?
acoustic plank
Did u find q?
I did 90 + 90 + 40 - 360 and got 130 then q was 65.
Since tangent and raidus
acoustic plank
I did 90 + 90 + 40 - 360 and got 130 then q was 65.
Mb 210 from 360 and got 150
gray axle
Angle ABO = 360⁰ - angle O - angle q
Is this enough for u?@acoustic plank
It is possible:
angle B = 180⁰ - Angle q - (Angle O)÷2
acoustic plank
Is this enough for u?<@1088620222627450981>
Ig
acoustic plank
.close
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deep marsh
Help
solid osprey
!15m
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grand warren
lethal pollen
Form a system of two equations
deep marsh
Omds i posted the wrong image i meant this so srry
solid osprey
@ adoniszgks reference??
lethal pollen
Omds i posted the wrong image i meant this so srry
Assign a variable for each person
Let's call the income of adonis D
Short for drakes kid
The income of apollo P
And aphrodite L
deep marsh
Please somenoe help
lethal pollen
I'm tryna do that cuh😭
lethal pollen
Omds i posted the wrong image i meant this so srry
So we know that Mr adonis earns 7200 more than apollo
lethal pollen
We can make an equation from this
D-P=7200
lethal pollen
We can make an equation from this
D-P=7200
As we know the difference between D and P is 7200
deep marsh
yea
lethal pollen
@deep marsh try making two other equations in a similar manner with other info in the qn
deep marsh
yea
lethal pollen
Lastly form an equation based on their total income
deep marsh
Lastly form an equation based on their total income
what would the euation be
lethal pollen
P+L+D=303 200
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atomic glade
hello, does someone mind verifying a solution i have for a calc 3 question
regal moat
Send
sand dove
I believe your counterexample works yes
an even easier counterexample : f(x,y) = (x-y)^2
atomic glade
perfect! i also have another similar question i am a bit more unsure of, can i send it here too?
sand dove
also it is on R = [0,1] x [0,1]
you mean D = ... instead of R = ... right?
atomic glade
yes haha my bad
thanks
my intuition was kind of along the lines of 2^0 = 1 so can it be less than 1?
since it's continuous along D and the area of D is 1 can it be below 1?
atomic glade
some people i know thought it was false, so i was a little confused on the proof
would my intuition be correct?
sand dove
it's growth of the integral
sand dove
since it's continuous along D and the area of D is 1 can it be below 1?
the answer is it cannot
but try the proof
sand dove
it's growth of the integral
again it's all here
atomic glade
yeah it seems pretty straightforward
sand dove
$\iint_D 2^{|f(x,y)|}dA \geq \iint_D 1dA = 1$
woven radishBOT
rafilou is not not born in 2003
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dull thunder
is my reasoning for part (d) valid? if not how can I fix it?
devout snowBOT
is my reasoning for part (d) valid? if not how can I fix it?
dull thunder
tropic skiff
You should also mention R(t) - W(t) = 0
tropic skiff
what bout W(t)-R(t)=0?
Either works
tropic skiff
You must also state that W(0) - R(0) < 0 and W(8) - R(8) > 0
dull thunder
You must also state that `W(0) - R(0) < 0` and `W(8) - R(8) > 0`
is that a must?
then why?
why is that condition necessary?
to show that it exists in that interval?
tropic skiff
where should i mention that?
where R(t) - W(t) = 0 -> R(t) = W(t)
tropic skiff
why is that condition necessary?
Bc the IVT only guarantees stuff in between f(a) and f(b)
It seems obvious to you, but the scorers will be strict about this
dull thunder
You must also state that `W(0) - R(0) < 0` and `W(8) - R(8) > 0`
should i mathematically find the value to state it cause otherwise I wouldn't know...?
tropic skiff
should i mathematically find the value to state it cause otherwise I wouldn't kn...
I dont think you have to mathematically find the value, you can literally just write those statements
dull thunder
I dont think you have to mathematically find the value, you can literally just w...
is it cause that must be true for the IVT to do the stuff...?
but the question says "explain why or why not" so that means it could either exist or not exist...?
tropic skiff
but the question says "explain why or why not" so that means it could either exi...
Well youre given W(t) and R(t) at t = 0, 8
Ig you can solve for W(t) - R(t)
Also its very likely you can use a graphing calculator
devout snowBOT
tropic skiff
its calculator allowed
The nature of W(t) makes it exceedingly likely so
dull thunder
yeah its kinda impossible to calculate with hands...
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feral agate
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feral agate
(a) part is easy, the rank of A is 3 and Ax=0 has solutions s(2,3,1,0) where s is a parameter
not sure how I would go about doing b
I know that the rref has only one non-zero row
and hence only one pivot
no wait, we have three pivots
vernal monolith
and hence only one pivot
shouldnt this give it away
it says "reduced row echelon" not "row echelon"
feral agate
yeah
there'll be three pivots, not one
there's one free variable
which is x3
so the pivots are in the first, second and fourth column
pastel pasture
what's a pivot
feral agate
the first non-zero number in a row after elimination
woven radishBOT
kheerii
pastel pasture
oh
woven radishBOT
kheerii
feral agate
should be this then
hard ocean
no, there's a 1
Fourth row
hard ocean
Oh mb
feral agate
For (c) it's just that rank = no. of rows so the range is all of R^3
hard ocean
Then yes
feral agate
it's full row rank
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sturdy mango
yo chat how do i solve a system of two quadratic one in terms of x and another in terms of y
devout snowBOT
yo chat how do i solve a system of two quadratic one in terms of x and another i...
sturdy mango
but both have x and y terms
faint gorge
!original
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Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.
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restive river
(ignore the blue stuff)
devout snowBOT
(ignore the blue stuff)
twin thunder
4 or 5?
twin thunder
ok lemme go through it
restive river
Ay thank you so much
restive river
Yeah I got my maths exam tomorrow and I cannot understand anything related to this sin,cos,tan inverse blah blah thing I am so cooked 😭
sonic parrot
you used inverse trig?
How did you do it without inverse trig
restive river
Bro 😭
restive river
Which question 💔
twin thunder
yeah because i approximated the values at last
restive river
Bru 😭 so is the answer right or naw?
Atp I gotta accept fate and understand I am cooked tomorrow
<@&286206848099549185> anyone else vro 💔💔
restive river
(ignore the blue stuff)
A
restive river
what’s wrong
Check the messages above
rapid pagoda
alright
restive river
To find angles sin inverse cos inverse and tan inverse is used
But like I kinda forgor what to do if I got three values like let's assume
ABC
AB is hypotenuse
BC is perpendicular
BA is base
So like now let's assume I got Value of all three of em
If I had to find out like <BCA or something what inverse would I use sin cos or tan and then those questions above make it more confusing so now I don't understand anything atp 💔
rapid pagoda
mhm
restive river
Bro what is "mhm" 😭😭
restive river
Which question 💔
restive river
Vro I already got the answers I needa see the working
rapid pagoda
relax
restive river
BRO I AM SO COOKED FOR TOMORROW 😭😭🙏
rapid pagoda
since LNM is 90 degrees
restive river
Hm
rapid pagoda
it had a 90 degree angle
restive river
Lnm
rapid pagoda
lmk if u dont so i can expaain deeper
restive river
From 90° do you mean angle L or angle N?
rapid pagoda
From 90 i mean MNL
restive river
Actually go on
rapid pagoda
see how its a right triangle
all right triangles are 90 degrees
the square in the conor is a sign its 90
restive river
all right triangles are 90 degrees
Only angle <N is 90°
rapid pagoda
N woudlent be a angle by itself
restive river
the square in the conor is a sign its 90
Bro I know that 😭
rapid pagoda
that would be considerd a point
restive river
Okay okay go on
restive river
okay now 90-39 is 52
39?
restive river
Yeah oki
restive river
since HM=9.2
Hm
restive river
Hm
restive river
so tan38 HM/HL
Isn't that only used on right angles triangles but that another triangle ain't right angled
rapid pagoda
no
even if the other parts dont form a triangle we only applyed the tan fuction in the right triangle
restive river
Oh
restive river
Hm
rapid pagoda
yes
restive river
The answer is 8.04 tho behind the book
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kindred mauve
Help differentiate these and put in the simplest form
devout snowBOT
Help differentiate these and put in the simplest form
restive river
hi all , how are you?
restive river
Do you know chain rule?
restive river
Apply that, take as much time as you can. Don't rush
restive river
Help differentiate these and put in the simplest form
you can bring them to a same base
kindred mauve
So
restive river
e^y=e^2t^2+1
kindred mauve
can u check?
restive river
First one is correct
2nd is correct
Ayo what u did in the third question
How did u cancel those two with the red pen?
Explain pls
restive river
Ye
restive river
Else is correct, also one more thing
What you are doing is quite long process, it's not wrong
But you do these directly let's talk about 3rd example
Just differentiate it with respect to t
restive river
Ye
kindred mauve
Ur not helping
restive river
Correct, but a slight mistake in sign and also I forgot to add brackets
The final result should have -27
devout snowBOT
@kindred mauve Has your question been resolved?
sharp kayak
try rechecking $\frac{dy}{dx}(5x^3 + 4x^2 - 1)$
woven radishBOT
BuilderDolphin
flat surge
On the last step, why did they make it tan(u) instead of keeping it as tan(t)?
flat surge
The guy in the video said, "Obviously change the t to a u," but it's not very obvious to me. If someone could explain it as simply as possible, I'd greatly appreciate it 🙏
tropic skiff
The guy in the video said, "Obviously change the t to a u," but it's not very ob...
One possible justification is that, since u is defined, its technically "clear" that the bottom expression is correct
flat surge
One possible justification is that, since `u` is defined, its technically "clear...
I just remembered this is the equation/formula that went along with the example:
Could I say they changed the "t" to "u" so that it would turn into tan(u), which then becomes tan(x^2), matching the final answer of f(x)?
tropic skiff
Could I say they changed the "t" to "u" so that it would turn into tan(u), which...
They technically didnt "change" the t to u though
flat surge
They technically didnt "change" the `t` to `u` though
yea ik the "u" came up as a substitution for x^2 but visually, that's what it looks like to me, and it's an easier way for me to put it into words 😭
but im sticking w the "matching the final answer of f(x)" explanation cuz i think it makes sense
tyvm
tropic skiff
yea ik the "u" came up as a substitution for x^2 but visually, that's what it lo...
Your explanation works if youre justifying it to yourself. Your explanation does not work if youre justifying it to an exam scorer
flat surge
Your explanation works if youre justifying it to yourself. Your explanation does...
Lmao got it
But for now, it's just for myself
I'm having my teacher explain this topic next class, so I'll have her do the extra explaining and justifying.
tropic skiff
!done?
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flat surge
.close
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opal valley
test
opal valley
.open
I need somebody to take a look at this so-called 'solution' to check whether i've made a mistake, because I dont seem to notice any
nvm i found sth
ok i think I got a prettier answer now
.close
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heavy ravine
wanted to clarify smthn
devout snowBOT
wanted to clarify smthn
heavy ravine
so the limit where x approaches 1, both from the left and right side would approach 1/3 right
even tho theres no point there and itll never reach it, they both approach it
so the limit does exist
runic prawn
yes
heavy ravine
ty one more thing
runic prawn
very true
heavy ravine
if i had the same rgaph but there is a point at x=1 up ther
itd be the same answer right
runic prawn
yes
heavy ravine
im just confused rn bc i learnt this whole section on my own before it came in class but then
the teacher said like some other bs and i didnt have time to ask
heavy ravine
wanted to clarify smthn
he said smthn like LS would approach 0.99 and rs would approach 1.01 here
and he said theres no limit
i think hes wrong but he also knows his stuff
runic prawn
wanted to clarify smthn
the limit deefinitely exists
heavy ravine
weird ill ask him tmrw then
heavy ravine
the limit deefinitely exists
thats what im saying but like i also just learnt this topic yesterday on my own
ty then i apprecaite it alot
.close
devout snowBOT
runic prawn
np
dark tundra
wanted to clarify smthn
ps I hate how this implies 0/0 whoopee limit exists, because that’s not entirely guaranteed
runic prawn
whoopee?
proven sail
.close
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leaden wharf
In the answer part it says that 2 comes out, I tried with artificies but I ended up confused halfway through the solution
devout snowBOT
In the answer part it says that 2 comes out, I tried with artificies but I ended...
supple knot
what does artificies mean
iron kindle
try u-sub
supple knot
probably better to just show the solution
leaden wharf
what does artificies mean
It's like a method of restoring and adding the same amount (I don't speak English, I guess it's another pre-university method), for example +1-1
supple knot
i see
atomic sparrow
In the answer part it says that 2 comes out, I tried with artificies but I ended...
u can find omega directly with the quadratic formula and be able to solve the equation below but that seems to tedius to be the method they would want you to use
leaden wharf
u can find omega directly with the quadratic formula and be able to solve the eq...
uhmm Okay, thank you. It makes sense to me, I finished high school recently and I don´t know how to use integrals, which makes me excited because the exam I want to pass is in 4 months.
leaden wharf
u can find omega directly with the quadratic formula and be able to solve the eq...
I just understood why the answer is 2, thank you again.
.close
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dull thunder
how do i determine if g(x) <=0 from looking at g'(x)=f(x) graph...? whats the rule(?) for this? (part d)
devout snowBOT
how do i determine if g(x) <=0 from looking at g'(x)=f(x) graph...? whats the ru...
tropic skiff
how do i determine if g(x) <=0 from looking at g'(x)=f(x) graph...? whats the ru...
You can try marking the area of the triangles
Or, in other words, finding the area under the curve line segments
dull thunder
so integrate it to go a step backwards and find if its <=0?
tropic skiff
so integrate it to go a step backwards and find if its <=0?
Yes, you might need to use this rule:
$$\int_a^b f(x) \dd{x}= -\int_b^a f(x) \dd{x}$$
woven radishBOT
King Leo
dull thunder
how do i select the bounds (a and b)...?
tropic skiff
how do i select the bounds (a and b)...?
a is already defined as a = 2
b will change based on the value of x
dull thunder
how do i select b...? like which x could make g(x)<=0?
tropic skiff
how do i select b...? like which x could make g(x)<=0?
Why are you trying to make g(x) <= 0
dull thunder
Why are you trying to make `g(x) <= 0`
cause they want to find where g(x)<= from g'(x)=f(x)
tropic skiff
Oh the absolute minimum
tropic skiff
Can you label the area of each triangle
tropic skiff
Ok, now find g at every value where f crosses the t-axis
dull thunder
t axis...?
tropic skiff
t axis...?
Same thing as the x axis in this case
dull thunder
Ok, now find `g` at every value where `f` crosses the `t`-axis
does touching x-axis count or you have to cross it...?
tropic skiff
does touching x-axis count or you have to cross it...?
For now, touching
And then you just see which point is the absolute minimum
Although later, you might need to see where it crosses the x-axis
dull thunder
so 2,10?
tropic skiff
Also make sure to find g(-4) and g(12)
dull thunder
int from 2 to 2 is 0...? and int from 2 to 10 is -4...?
is it like the the interval where g(x)<=0 is where in g' graph the area below the line that is negative or 0?
devout snowBOT
@dull thunder Has your question been resolved?
devout snowBOT
@dull thunder Has your question been resolved?
devout snowBOT
@dull thunder Has your question been resolved?
misty crest
@dull thunder
tropic skiff
Wait
misty crest
still need help?
tropic skiff
How did you get -4
misty crest
brother came back right away wtf
tropic skiff
Nvm thats right
tropic skiff
brother came back right away wtf
I was here for ~15s prior reading what they said
misty crest
you mean 2 hours
misty crest
what’s PWR
tropic skiff
Stands for Ping When Replying
tropic skiff
why do you want pings
Cause there have been too many times ive left someone hanging bc i forgot to check the channel again
dull thunder
what happened...?
dull thunder
yea
misty crest
send it again
dull thunder
how do i determine if g(x) <=0 from looking at g'(x)=f(x) graph? whats the rule(?) for this? (part d)
misty crest
since g(x) is defined in terms of an integral we simply want to find all intervals in which the resulting integral yields a non positive result
you could do this two ways
misty crest
since g(x) is defined in terms of an integral we simply want to find all interva...
either find this directly
or find the intervals in which it’s positive then exclude those parts
and hence construct the remaining intervals
dull thunder
should i try integrating all intervals or...
misty crest
or find the intervals in which it’s positive then exclude those parts
if you do it this way
you don’t need to do much direct computation
dull thunder
or find the intervals in which it’s positive then exclude those parts
how?
i dont get it
like are we finding the areas and then...?
misty crest
well we are shown [-4,12] right
dull thunder
yea
misty crest
now it certainly is true that g(x) is either <= 0 or > 0 yes?
there is no other possibility
dull thunder
yea
misty crest
ok so if we found the intervals where g was positive wouldn’t that mean the other parts of the interval [-4,12] would have to therefore be not positive (<= 0)
dull thunder
yes
misty crest
ok so let’s use this strategy
first let’s consider x > 2
since our lower limit is 2
for the integral
dull thunder
ok
misty crest
clearly the integral is positive for (2,6] right
because we are integrating f
and f > 0 there
we get positive area from that triangle
yes?
no?
questions?
misty crest
yes
exactly
now
let’s continue further right
and see how far we can go until g is no longer positive
i.e find where g is zero for x > 2
so let’s try subtracting the area of the next triangle
since it’s below the x axis
it’ll have negative area
what’s the area of that triangle and thus what is the integral of f from 2 to 10
dull thunder
8+(-8)+(-4) = -4?
misty crest
so we dont cut at 10
wdym?
dull thunder
you said its 2 to 10 but why should it be to 12...? is that cause that triangle extends to 12...?
misty crest
i asked you to stop at 10
because if you notice that g = 0 when x = 10 since the positive and negative area there cancels
it’s negative thereafter
so we’d include the 10 to 12 bit
dull thunder
oh so at 10 its g(x)=0
dull thunder
yeah
misty crest
we don’t need the numerical value
dull thunder
so continue to move one...?
misty crest
ok so we’ve established now that (2,10) will not be in our answer
dull thunder
10 to 12?
misty crest
note that the interval is open since if we included the endpoints we’d get g = 0 which would be part of our answer
dull thunder
10<=x<=12 is one interval
misty crest
10 to 12?
this will be part of our answer yes
mhm
now let’s look towards x < 2
so for x < 2 we have to realize that whatever the resulting area would be, we have to negate it because of how the limits of integration are
dull thunder
anything below 2 is gonna be negative unlesss its already negative cause if we flip the bounds we stick the - sign? right?
misty crest
anything below 2 is gonna be negative unlesss its already negative cause if we f...
well, we need to analyze carefully here
let’s start by rephrasing the problem
dull thunder
ok
misty crest
we have $g(x) = \int_2^x f(t) \dd{t}$
woven radishBOT
knief
misty crest
but for x < 2 the integral will be negative so the areas we’d get will be misleading
so let’s flip it
$g(x) = -\int_x^2 f(t) \dd{t}$
woven radishBOT
knief
misty crest
now
reading from left to right, if the area is negative we have that g is > 0
and aha
dull thunder
yeah
misty crest
notice that the triangle between -2 and 2 has an area of 8 but we must negate it so -8
and what’s the area of the other triangle?
dull thunder
the two triangles eat each other up so the rest is 4 and we stick that negative --> -4?
misty crest
the two triangles eat each other up so the rest is 4 and we stick that negative ...
hmm well tbe triangle from -4 to -2 had an area of -4 which gets negated to 4
so what can we say about g for x < 2?
dull thunder
the two triangle before zero is gone
and after zero is 4 and we put the sign so -4?
dull thunder
so what can we say about g for x < 2?
its -4?
misty crest
that would be the integral from -4 to 2
i see what you’re doing
and it’s correct
but
what can we then say
about g for all of x < 2
dull thunder
i dont know?
misty crest
we’re not so concerned with the particular value
misty crest
i dont know?
it’s always negative isn’t it?
because there’s more "positive area" for x < 2 which then gets negated
dull thunder
yeah
misty crest
notice that no matter how far left we go we still have to go through that larger triangle which has more area
so it’s always negative
dull thunder
yea
dull thunder
-4<=x<=2 and 10<=x<=12
dull thunder
yea
its literally that easy if you understand it
thanks for helping 🙏
😀
have a good night
dull thunder
.close
misty crest
have a nice night
devout snowBOT
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Available help channel!
sturdy zenith
devout snowBOT
sturdy zenith
can someone double check my work
basically since inequality signs flip when we take both limits there must be a value $\pi ^*$ that exists where B passes A
woven radishBOT
Faduzzle
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@sturdy zenith Has your question been resolved?
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@sturdy zenith Has your question been resolved?
vocal pebble
iv'e been stuck on this for a while, especially b, any help?
devout snowBOT
iv'e been stuck on this for a while, especially b, any help?
vocal pebble
i dont really understand interest because i wasnt there for any of the lessons
devout snowBOT
@vocal pebble Has your question been resolved?
vocal pebble
<@&286206848099549185> ?
vocal pebble
im unsure how to start it, (both a and b) and when i try it it is incorrect
olive fossil
So like when you deposit money in a bank the bank usually gives you an interest which is a percentage of the amount you deposited
olive fossil
And the formula of simple interest is P x R x T /100
Kk
So the principal is 4000 pounds
vocal pebble
okay
vocal pebble
so 4000 x 3.5 x 1 year?
olive fossil
We would get 4000 x 1 x 3.5/100
vocal pebble
/ 100 okay
olive fossil
Divided by 100
Now see what you get as the interest
Wait
@vocal pebble
The time here is 6 years
vocal pebble
its compound though?
olive fossil
Is it?
vocal pebble
yeah
vocal pebble
no
vocal pebble
i kinda know simple interest but not compound
vocal pebble
okay
olive fossil
So if u make the denominators same
It would 100+R all over 100
And the rest of the formula I have given u
vocal pebble
and r = 3.5 ?
olive fossil
Yes
This formula is for the total amount
To find ci
First u have to find total and then subtract principal from it
rare helm
Hi
rare helm
Can I ask help for science :cc
glacial violet
sure
glacial violet
wht even is that
rare helm
I'm using a compound microscope
glacial violet
are those cells
rare helm
Cardiac Muscle Section
glacial violet
reminds me of robert hooke looking at onion peels
rare helm
are those cells
Yes
glacial violet
well i know nothing about biology
rare helm
Tissues*
rare helm
Yes
rare helm
yay i guess i do know some biology afterall
I'm dying
glacial violet
anyways i hope you get someone to help you soon! :D
rare helm
I hope so too
devout snowBOT
@rare helm Has your question been resolved?
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toxic spire
devout snowBOT
toxic spire
How do you do this
I first took 31C10-21C10
Stripped away the combinations between the distinct ones themselves since they arent affected
And then (31C10-21C10)/10 since each combination is repeated 10 times
Then i did (31C10-21C10)/10 + 21C10 to get the total
devout snowBOT
@toxic spire Has your question been resolved?
snow merlin
Then i did (31C10-21C10)/10 + 21C10 to get the total
im assuming you're confused because this seems like a pain to calculate?
toxic spire
No its just why my method aint working
toxic spire
what does that leave you with
The combinations that contain the identical numbers
snow merlin
so every single combination that consists solely of identical ones? or all combinatios that include at least one of the identical ones
im assuming the latter
this includes all combinations where one of the balls is from the identical pool, ones where two of the balls, three of them, etc.
for the case where only one of them are identical, then your divide by 10 makes sense, as you ball could be any of the 10
but what if two are? then you have 10c2 ways of selecting those two balls
and if three are? then 10c3 and etc
you can't just divide by 10
its better to try and do casework with the # of identical balls
with 0 identical balls, you have 21c10 ways of choosing the rest
with 1 identical ball, you have 21c9
with 2, 21c8
...
with 10, 21c0
this way you dont even have to consider how many ways there are to choose the identical balls from the 10
snow merlin
its better to try and do casework with the # of identical balls
with 0 identica...
this has an interesting way of adding them up
theres a somewhat well known sequence where nC0 + nC1 + ... + nCn = 2^n
snow merlin
theres a somewhat well known sequence where nC0 + nC1 + ... + nCn = 2^n
if you notice where we stop, (21c10), we have actually traversed exactly half this sequence
and the choose function is 'symmetric' in the sense that like 21c2 = 21c19
toxic spire
Hmmm
toxic spire
Answer is that yes
snow merlin
this includes all combinations where one of the balls is from the identical pool...
anyway i think this is the main problem with your approach
toxic spire
this includes all combinations where one of the balls is from the identical pool...
Do you mean like
If theres AAAA then dividing by 10 won't enough?
Aka more than one identical
snow merlin
If theres AAAA then dividing by 10 won't enough?
yeah, if i get what ur saying
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dusty sigil
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dusty sigil
hey guys what does the y hat mean here?
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robust musk
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robust musk
I guess C is correct?
robust musk
just a guess 😇
pseudo basin
you should not guess
you are not so lucky as to hit that 1/4 chance enough times to pass the exam or whatever
robust musk
Please provide some hints
pseudo basin
(nobody is)
runic prawn
if there are enough people taking the exam then someone is
pseudo basin
try to think about a similar question but with A^3 = 0 instead. it will not be the exact same, but you might have some ideas there.
as in: suppose A^3 = 0; can we say anything about whether either of I ± A are invertible?
robust musk
i need to think of that nilpotent actually
pseudo basin
nilpotence will be crucial, yes
pseudo basin
you did not say anything yet so you are neither on the right nor the wrong way at this moment
are you confused about the word "crucial" itself?
robust musk
I only get hint that a^n=0 looks like nilpotent
pseudo basin
it doesn't just look like nilpotence.
robust musk
I have no idea rest
pseudo basin
A^5 = 0 literally is nilpotence (with a particular index of it, too)
pseudo basin
why am i saying what?
we are getting nowhere with this. you pick my words apart until you confuse yourself, but you have made no progress on this question (nor on the simpler one i suggested).
try calculating (I-A)(I+A+A^2). maybe you will get an idea.
robust musk
try calculating (I-A)(I+A+A^2). maybe you will get an idea.
That is much better
.close
idle tinsel
how do i do this? i don't know how to do induction
devout snowBOT
how do i do this? i don't know how to do induction
idle tinsel
would it be enough to just give an example?
like |u^5| = |uuuuu| = 5 which is the same as 5|u| = 5 * 1 = 5
sinful trellis
no an example wont be sufficient
devout snowBOT
@idle tinsel Has your question been resolved?
idle tinsel
no an example wont be sufficient
Do you know how I would do it?
sinful trellis
Do you remember induction?
idle tinsel
i did induction many semesters ago but i dont remember it at all
sinful trellis
you need to prove it for some base case
so show that |u^n| = n|u|, when n= 1
and then you assume it holds for |u^n| and show it holds for u^n+1
idle tinsel
okay, so we can show that for n = 1
n = 1
|u ^ n| = |u| = 1
n|u| = 1 * 1 = 1
then we do
|u ^ (n + 1)| = |uu| = 2
n|u| = 2 * 1 = 2
idle tinsel
oh i thought that was still assuming n was 1
sinful trellis
thats for the base case
you need to show for any arbitrary value of n, where your equation works
it'll also work for the next one
idle tinsel
ahh
sinful trellis
and then you have your recursive/inductive proof
since it works for 1 hence it'll work for the next one (2)
but since it works for two it must work for 3
and so on
idle tinsel
|u ^ (n + 1)| = (n+1) * |u|
this is what im getting now, im not sure how to break that down further
sinful trellis
tahts what you need to show yeah
but you need to show that you can get the left hand side to turn into the right hand side
i'm not 100% certain on my definitions with strings
oops
idle tinsel
u^k means string u repeated k times
sinful trellis
yeah so u^k * u is u^(k+1)
idle tinsel
so like hello^2 = hellohello
sinful trellis
right?
idle tinsel
yeah so u^k * u is u^(k+1)
yes i believe thats right
sinful trellis
$|u^{k+1}| = |u^k * u| = |u^k| + |u| = $
oh man idk how to latex in this
you have an expression for u^k (you assumed it worked for u^k)
so you have k |u| + 1 |u|
(k+1) |u| or something
idle tinsel
i am a bit confused on how we went from |u^k| + |u| to k|u| + 1|u|
sinful trellis
by your induction hypothesis
idle tinsel
aren't we still trying to prove that |u^k| = k|u|
sinful trellis
you proved that it holds for some value, 1
you now assume it holds for some value n
and that for some value n where it holds it works for the next one
idle tinsel
you proved that it holds for some value, 1
right, but in this case k could be any number other than 1
sinful trellis
correct
it's just any condition where it holds
but like
if we assume some n where it holds and show it works where
there*
you could say ok it works from 1 to 2
but since it holds for 2, (as it holds for n+1)
then we can start again ok it holds for 2 (n) so it must hold for n+1, which is 3
and so on
so instead of proving it holds for 1,2,3,4,5,6 you just have to show it works for the next value from some arbitrary value, where your expression works
idle tinsel
that makes sense, I just thought we weren't able to use our own hypothesis that |u^k| = k|u| in our proof, i thought it would be like circular reasoning
sinful trellis
thats why induction relies on two parts
a base case and the inductive step
you need to prove that there exists some k where it works
you can use your expression in the inductive step
on u^k that is
idle tinsel
okay I think i understand it now, thank you
neon wagon
yo how can i solve this
4x-3y+2z = 4
6x-6y+3z = 3
12x-11y+8z = 14
tall knoll
tall knoll
How would you do it with 2?
tall knoll
Please answer my question
neon wagon
like
multiply the other, and so on
and subtract it
and solve it so that one equiation has only one unknown variable
neon wagon
but yk
tall knoll
Take a look at the coefficients of the x terms. Those all look like they'll play nicely with each other
neon wagon
when there is 2 unknown variables but 3 equations
neon wagon
Take a look at the coefficients of the x terms. Those all look like they'll play...
okay wait
neon wagon
Take a look at the coefficients of the x terms. Those all look like they'll play...
yeah but like
waiz omg
i can do the first times 3
and the second times 2
tall knoll
Indeed
tall knoll
Use any 2 of your equations to find the other 2
neon wagon
Use any 2 of your equations to find the other 2
ohh
you mean use y
and form 2 new equations?
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lilac crescent
does this needs an integration by parts :
$\int \frac{t}{t+1}dt$
woven radishBOT
<rajel />
woven radishBOT
SWR
lilac crescent
For the numerator, let $t=(t+1)-1$
then i'll have $\int 1 - \frac{1}{t+ 1} dt$
runic prawn
t - log(t+1)
woven radishBOT
<rajel />
woven radishBOT
<rajel />
lilac crescent
.close
devout snowBOT
lusty sapphire
this shuold be the result :
$t - \ln|t+1|$
don't forget your +C
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merry plume
I have to solve for x by completing the square, how do i square root both sides if the 1/9 is negative?
devout snowBOT
I have to solve for x by completing the square, how do i square root both sides ...
merry plume
also for this question how do i show how i got the x-intercepts can i just factor the original equation
north roost
,rotate
woven radishBOT
north roost
also for this question how do i show how i got the x-intercepts can i just facto...
I think they want u to graph x^2 + 4x and -2x -5
And find where they intercept
,w 3x^2 + 4x + 5/3
woven radishBOT
north roost
I have to solve for x by completing the square, how do i square root both sides ...
Continue with this
Sqrt of -1/9 is 1/3i
merry plume
Sqrt of -1/9 is 1/3i
wait i thought u couldnt square root negative numbers
acoustic helm
You can, just need to introduce another dimension (imaginary numbers)
merry plume
You can, just need to introduce another dimension (imaginary numbers)
oh i didnt learn that yet😭 i dont think im supposed to use it
acoustic helm
I’m guessing the equation was written wrong and 5/3 should be negative
merry plume
i had a similar question on another assignment and they took marks off bc i square rooted the negative number
but idk what else im supposed to do
acoustic helm
Just ignore it for now and focus on the other questions
Your teacher will probably omit it from the final mark since you haven’t learnt complex numbers yet
devout snowBOT
@merry plume Has your question been resolved?
velvet coral
devout snowBOT
velvet coral
how ddi they go from the (extS)^c cap (S^o)^c?
did they just use lots of distribtuive laws?
and then like some are contradiction/just false so they get rid of those?
devout snowBOT
@velvet coral Has your question been resolved?
dense lynx
how ddi they go from the (extS)^c cap (S^o)^c?
it's by definition, interpreting the factors of the union as sets
a point x is in ext(S)^c if and only if for all positive radii (e) the ball B(x, e) is not entirely contained in S^c (in set theoretic language, B(x, e) intersect S is non-empty)
a point x is in S^o^c if and only if for all positive radii (e) the ball B(x, e) is not entirely contained in S (in set theoretic language, B(x, e) intersect S^c is non-empty)
combining these two conditions gives the result in the image you posted at the start
more explicitly, $x \in \left((S^c)^{\circ}\right)^c \Longleftrightarrow \forall \epsilon > 0, B(x, \varepsilon) \nsubseteq S^c \Longleftrightarrow \forall \varepsilon > 0, B(x, \varepsilon) \cap S \neq \varnothing$
woven radishBOT
Mqnic_
dense lynx
^ for the first factor, and likewise for the second
royal laurel
Is f^-1(x) a common expression of the inverse of function f
devout snowBOT
Is f^-1(x) a common expression of the inverse of function f
storm gyro
very much so
devout snowBOT
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Available help channel!
flat ibex
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faint gorge
!status
devout snowBOT
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 was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
I see but isn't the set Ext(S) = ${ x \in S^c : \exists \epsilon > 0 \text {such that} B(x, \epsilon) \subseteq S^c }$. Therfore shouldn't $(Ext(S))^c = {x \in E : x \in S \text{ OR } \forall \epsilon > 0, B(x, \epsilon) \nsubseteq S^c }$?
woven radishBOT
LXDL
flat ibex
I see but isn't the set Ext(S) = $\{ x \in S^c : \exists \epsilon > 0 \text {suc...
wrong question buddy
this is the wrong channel
<@&268886789983436800>
faint gorge
its just Dg(f(0,1,0)) Df(0,1,0) right
yea basically
velvet coral
I see but isn't the set Ext(S) = $\{ x \in S^c : \exists \epsilon > 0 \text {suc...
sorry for late rpely i was thinking about it and it kinda made sense but then i not really
velvet coral
wrong question buddy
yea h sorry ill move
devout snowBOT
idle carbon
How do i find C in this
woven radishBOT
Marshall The Gamer
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
devout snowBOT
misty crest
you didn’t need {} around the x^n dx part
idle carbon
Oh
misty crest
$\int x^n \dd{x} = \frac{x^{n+1}}{n+1} + c$
woven radishBOT
knief
idle carbon
Ok, but how do i know what C is?
drifting mauve
you don't
misty crest
youd need more information
idle carbon
Say you input a value for n, how do you calculate C?
solar goblet
the antiderivative is not a function, it's a class of functions
idle carbon
…
drifting mauve
Say you input a value for n, how do you calculate C?
any constant C differentiated yields a 0
so you just
can't "find out" C
misty crest
Say you input a value for n, how do you calculate C?
still not enough information
woven radishBOT
Marshall The Gamer
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)
solar goblet
what
misty crest
you don’t
drifting mauve
**Marshall The Gamer**
Compile Error! Click the <:errors:504266556054962196> rea...
you still can't 😭
misty crest
the n isn’t the issue
idle carbon
So how would you calculate this?
misty crest
you just did
drifting mauve
So how would you calculate this?
you can't 😢
idle carbon
😭
misty crest
the + c serves as a vertical shift which doesn’t affect the derivative
idle carbon
the + c serves as a vertical shift which doesn’t affect the derivative
What does that mean?