Then it will be C it's impossible
#help-42
hushed knot
glass heart
I mean you could do some weird stuff like $x^{y^z} = x^{y\cdot y^{z-1}} = \left(x^y\right)^{y^{z-1}} = C^{y^{z-1}}$
potent lotusBOT
Denascite
woeful nimbus
Yeah hence my example you need a value to put an exponent upon
hushed knot
This problem x⁹-x³=24
I was trying to solve that
So if x^3=y then x^3^2 would be y²
But it's not possible
So I was thinking what should I do
woeful nimbus
Oh seems redundant then
night torrent
so thats y³ +y =24 then 
hushed knot
Yeah
night torrent
well uh y=3 is immediate observation
then u can to synthetic division to get rest of the roots
hushed knot
Yeah but a method or mathematical way
night torrent
?
hushed knot
then u can to synthetic division to get rest of the roots
Ohhhhhh
Ok
I should factor this eq
y³-y-24=0
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remote mural
definition of linear independence works
yeah
yes
you might even have a theorem to do with rank somewhere in your notes
(full rank iff rref to the identity)
the same way you did part 2, but with the orthogonal vectors instead of B
,w orthogonal [1,1,0], [2,0,1], [2,4,5]
you need to use the orthogonal basis from part b
calm coralBOT
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remote mural
yes, thats the right method for 2cii
what is your answer to 2b
thats not how gramschmidt works
oh ok
ok thats good
now use that instead of B for 2ciii
if you add those up, you dont get (7,17,13)
remote mural
do exactly the same as you did for 2cii, but with the basis u1 = (1,1,0)
u2 = (1,-1,1)
u3 = (-2,2,4) instead
so make the augmented matrix and rref
calm coralBOT
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remote mural
Did I write the inequality for part B right? The context is at the TASK
calm coralBOT
Did I write the inequality for part B right? The context is at the TASK
@remote mural Has your question been resolved?
calm coralBOT
@remote mural Has your question been resolved?
calm coralBOT
@remote mural Has your question been resolved?
potent igloo
@remote mural no not really
remote mural
oh
remote mural
<@456226577798135808> no not really
do u know how i would write it then
potent igloo
Oh sorry I read it wrong
Yes you got it right
I thought it was asking for set of points that meet the height requirement
remote mural
Yay thanks
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eternal mason
Hello
calm coralBOT
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tawny raven
can someone help me
Yes this correct becz tri ABX and Tri AXC are congruent
tawny raven
Becz AB= Ac (given )
Ax=Ax (common side ) and angle B is equal to angle C (adcent angles ) so by SSA theorem u can say that both triangle are congruent
tawny raven
what theorem
.
tawny raven
That's correct i think
remote mural
I need help
calm coralBOT
I need help
prisma mango
I need help
• Show your work, and if possible, explain where you are stuck.```
oblique current
People aren't gonna download random files
remote mural
Yeah i just need help on how to solve for y=mx+b
last time i did this was in middle school so i don't remember anything
woeful nimbus
So you have the slope m=-3/2 for the first one
Then plug that into y=mx+b
Plug in y and x to solve for b
remote mural
y=-3/2x+b?
remote mural
so -6-+2 then -3+3 cause both are negative then negative with an negative is an postive?
woeful nimbus
Idk what you mean here but you turn y=(-3/2)x + b into -6=(-3/2)(-3) + b then isolate b to solve
Then plug b back into y=(-3/2)x + b
And that is the function/answer
For the first one answer is y=(-3/2)x - 10.5
Also gose is actually spelled goes
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remote mural
can anyone help with this
calm coralBOT
can anyone help with this
remote mural
In physics, a formula for movement with constant acceleration is given by 𝑠=𝑣0𝑡+12𝑎𝑡2.see distance in meters, v0 is the initial speed in meters per second, ter time in seconds, and aer acceleration in meters per second2. The teacher shows a solution on the board, but has made a mistake. What is the error? Explain why this does not work.
Image
ember oxide
right side of the second equation should be s/t shouldnt it
since it looks like youre just dividing both sides by t
remote mural
okay thank you
calm coralBOT
proud lintel
how would i find the time?
calm coralBOT
proud lintel
would i have to take the log
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vivid idol
Hello
calm coralBOT
@vivid idol Has your question been resolved?
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stable bolt
HI
stable bolt
Im doing question (iii) and i dont know how to solve it
i know that the probabilty of getting 28000 and greater is .6587
how would i solve for it?
edgy raven
well, its the chance for it to be over 60000, and you definitely know its over 28000
what can you deduct from that?
@stable bolt
stable bolt
what can you deduct from that?
would it be the probability that I get if its below 60000?
edgy raven
would it be the probability that I get if its below 60000?
... why?
its less of an math question and more of an English question:
you are given a distribution, find the chance for it to be over 60000 when you are guranteed that it cannot be 28000 or below
in another example
I visit the zoo to see dogs
a Distribution function tells me the amount of dogs per cage
A cage contains at least 5 dogs, so I can discard the chances for <5
left imp
hello can someone help me with this?
remote mural
First 4 non zero terms of the taylor series of $2e^{5x}$ centered around $a=2$
potent lotusBOT
hibyehibye
remote mural
So f(x) = 2e^5x f(2) = 2e^10
So f’(x) = 2/5e^5x f’(2) = 2/5e^10
So f’’(x) = 2/25e^5x f(2) = 2/25e^10
So f’’’(x) = 2/125e^5x f(2) = 2/125e^10
wait i forgot the 2! and 3!
😢
.close
calm coralBOT
remote mural
So f’(x) = 2/5e^5x f’(2) = 2/5e^10
Why 2/5
is that wrong
Ohh
I did that question so wronf
wrong
omg
Lmao when u think integrals with derivatives
remote mural
Lmao when u think integrals with derivatives
it was a two part question too
so there goes 12 points
:(
It's okay always a second time for everything
halcyon pawn
remote mural
It's okay always a second time for everything
it was my final haha
I think I got a B overall now but I’ll find out friday
Ahh I see
flat gorge
riemann helped me
I didn't see a solution, are you sure you got it done?
remote mural
Yeah u factor out the 4
flat gorge
the one with, second smallest repunit number?
remote mural
of the sqrt
flat gorge
not the integral 🤦♂️
remote mural
repunit?
remote mural
the one with, second smallest repunit number?
I don’t remember this sorry
flat gorge
must've been someone else.. nice to know the integral got sorted out
remote mural
Yup
flat gorge
I read it was a different one on the table you could've used
remote mural
Yeah only way it makes sense
flat gorge
mhmm, take care next time
remote mural
u2 tysm for all the help
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quaint harness
I dont understand the constraints that i need to use for the linear programming
quaint harness
question 1
upper sparrow
Been some time since I’ve done linear programming properly
quaint harness
The thing is I understand how to do it but when it is put in wordy form like this it confuses me lol
upper sparrow
Ahh I see! Are you able to do this one, or do you need help with forming the inequalities here?
quaint harness
Ahh I see! Are you able to do this one, or do you need help with forming the ine...
A bit of help forming the inequalities would be very helpful
upper sparrow
Ah, cool cool, then let me try it out
quaint harness
thank you
upper sparrow
You have only 8 members that want to drive, and each vehicle needs a driver (obvs), so you know the number of cars and minibuses can’t be more than 8
You also need the cars (cap. 5) and minibuses (cap. 12) that you do have to at least have a total capacity of 80, to carry everyone
And you want the cost minimised for the amount of cars ($20 ea.) and minibuses ($60 ea.)
Does that make it clearer?
quaint harness
sort of, for the objective it is to minimise cost would it be 20x+60y?
upper sparrow
Yea I think it would be
upper sparrow
5x+12y=80?
Greater than or equal to
You need to have a capacity of at least 80, but it doesn’t really matter if you have free seats in the end
So 5x+12y>=80
upper sparrow
You have only 8 members that want to drive, and each vehicle needs a driver (obv...
This one!
One more 😉
upper sparrow
Yep that should be it!
quaint harness
nice!
upper sparrow
They’re not too bad when you get the hang of deciding what they’re saying haha
quaint harness
yeah haha the problem solving ones are always like that lol
so then i put it in a simultaneous equation right to find the values
oh wait i want to minimise cost though don't I
warm fractal
Hello i have question a bout trigeonamy i need to conform something
warm fractal
The question is about expressing "Show that the area can be expressed by the function"
there is a given function
show that the area of the new pane (the gray-shaded area) can be expressed as a function of the side length x and that the prescription is given by
calm coralBOT
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@warm fractal Has your question been resolved?
calm coralBOT
@warm fractal Has your question been resolved?
median roost
@warm fractal
try to find the equation of the line MN
M = (10,20)
N = (26,12)
y = m x + c
m is the slope of the line (MN)
so $m =\frac{y_M - y_N}{x_M - x_N} = \frac{20 - 12}{ 10 - 26} = \frac{8}{-16} = \frac{-1}{2}$
potent lotusBOT
Mehdi_Moulati
median roost
y = -0.5x + c
to find c try to find the point M :
y(x_M) = y_M
y(10) = 20 = -0.5*10 + c
so c = 25
so far y = -0.5x + 25
so any point in the line (MN) will be in th form of :
(x, -0.5x + 25)
the area of a rectangle is :
A(x) = L * l
= (-0.5x + 25) * x
= -0.5x² + 25x
so A(x) = -0.5x² + 25x
calm coralBOT
@warm fractal Has your question been resolved?
warm fractal
the area of a rectangle is :
A(x) = L * l
= (-0.5x + 25) * x
...
omg thank you
median roost
Did you got it ?
warm fractal
Did you got it ?
thanks again
median roost
Anytime brother
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mossy vigil
i need help
calm coralBOT
i need help
sick plover
What have you tried
mossy vigil
6x6x6
sick plover
Why?
upper sparrow
Hint: look at the hint they gave you
mossy vigil
i saw it but idk what use with]
upper sparrow
i saw it but idk what use with]
Part 2: what is 6, in the context of this question?
mossy vigil
Part 2: what is 6, in the context of this question?
like what you mean
sick plover
You're given a length of 6. What is that length? Diameter? Radius?
mossy vigil
the 6 is the radius
sick plover
Why?
mossy vigil
nvm it the diameter
upper sparrow
nvm it the diameter
Does the hint become helpful now then?
mossy vigil
no
upper sparrow
…you’ve just stated that 6 is the diameter, no?
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remote pendant
calm coralBOT
remote pendant
just checking part i is just pi?
and also part 2 doesnt really make sense to me
because what if X is to the left of x
thin wharf
maybe it meant horizontally or assumed x >= X
so what I'm thinking is
wait nvm that won't work
remote pendant
maybe it meant horizontally or assumed x >= X
Probably yeah
remote pendant
I think it’s just Y in that case
thin wharf
not sure what this problem is but I think it'd be better to leave the cost and whatnot out and make it a more abstract problem tbh
remote pendant
It’s an interview question so maybe that’s what they want u to do
Idk
Also do u know if part 1 is correct
?
thin wharf
no clue how the floor function works with limits but I think floor(pi * x) just becomes pi * x as x -> infty
remote pendant
That’s what I was thinking
Cus it’s basically negligible when u take it down to an integer value
remote pendant
Oh that’s smart
pale drift
About the second one , the most logic answer is 0$ because we don’t have X and Y’s values so idk
torn ember
Hello, I'm learning calculus ([redacted personal info from history]). I'm doing a practice test. I've got a question that involves a line intersecting a quadratic, and I have to find the area inside the curve under the line. I've found the points of intersection with the line and the curve, but I don't know how to do the definite integral handling the other line. I've thought about splitting it up into sections, but ultimately it all comes to the same problem. I've attached some screenshots. The question says to find R, but I'm finding that area where R and the curve overlap as a prerequisite.
I've found:
L is y = -(1/2)x + 8
The points of intersection of L and C are 4 and 1.824332802 (my calculator spits out decimals instead of surds, I'll just find a very close approximation).
So what I want to do is the definite integral with a range of 1.824... to 4 of 32x^{-2} + 3x - 8, except I also need to somehow make that only find the values below the line. I'd appreciate some help!
upper sparrow
What were your thoughts re. splitting it up into sections?
Also, why was the indefinite integral you were doing between that 1.824... and 4?
torn ember
Draw a horizontal line from P to y=2, draw a horizontal line from V (what I'm calling the second point of intercept) horizontally to the intersect with C, draw a line from P to V, and there's 3 segments.
1.824 because that's the x where l intercepts c the second time, though thinking about it R is defined as ending at 2, so actually I should be using 2...
I'll grab a photo of my attempt to split it up. It was just me messing with it seeing if I saw anything useful, and I didn't.
upper sparrow
I see, so your thought is to integrate 32/x^2 + 3x - 8 between 2 and 4, right?
torn ember
Yeah, but since not all of that area actually overlaps with R it won't work, and I don't know how to find only the values below that line l.
Actually, no
all of it is inside R, but there's that extra triangle above... which actually I think I can get through normal, non-calculus methods
Thanks 😂
upper sparrow
all of it is inside R, but there's that extra triangle above... which actually I...
Yep, you can do that without calc
(You can also do it with calculus too, if you really wanted, but you should get the same thing!)
...actually wait, above you say?
The red circled bit yea?
torn ember
apologies for the terrible diagram, that lower blue line is meant to intersect with P
I'm thinking of getting a through integration of 2->4, then getting b by just treating it as a simple triangle
pale drift
What’s the point in which the line I reaches the x axis?
torn ember
The equation of the line is y = -(1/2)x + 8. So when x is 0 y is 8
upper sparrow
May I ask why any bit above the curve between x=2 and x=4 is relevant?
pale drift
The equation of the line is y = -(1/2)x + 8. So when x is 0 y is 8
Well it’s solved now
glacial harbor
the integral of C from 2-4 plus the integral from 4 to where x=0 of x
torn ember
May I ask why any bit above the curve between x=2 and x=4 is relevant?
Because I'm finding the area of R, and I first need to find everywhere in that triangle that's not shaded, and that includes that smaller triangle as well
upper sparrow
Because I'm finding the area of R, and I first need to find everywhere in that t...
Oh, I see, I get what you mean now, that's one way to do it(!)
torn ember
the integral of C from 2-4 plus the integral from 4 to where x=0 of x
Let's call the line formed by the x axis, the line x=2, and l e
Wouldn't that include a little bit of the curve that's outside of e because the intercept points between l and C aren't x=2 and x=4 they're x=1.82 and x=4?
And thanks for the help 🙂
upper sparrow
Let's call the line formed by the x axis, the line x=2, and l `e`
Wouldn't that ...
It does - but remember that the integral between x=2 and x=4 of the curve C will get you the area under the curve
pale drift
upper sparrow
The red circled bit yea?
See the purple line
You then just have to find the area of the remaining triangle on the right formed by l, the x axis and x=4
torn ember
I think I might have misunderstood what integrals actually are, this is the first time I've done a question that isn't just "integrate this formula between a and b". I thought I'd find a using the integration, not the area under a until y=0.
Referencing a in this diagram
glacial harbor
I think u are over complicating. Think of these two integrals as two separate shapes
pale drift
yea
glacial harbor
It doesn’t really matter where C intercepts x
torn ember
Yeah thanks, I think I get it now.
glacial harbor
For sure, you can even use Pythagorean on the second shape since it’s a right triangle
upper sparrow
For sure, you can even use Pythagorean on the second shape since it’s a right tr...
That's the way they teach it in the book for it, for some reason, I've never got why (and don't you mean the base*height/2 btw?)
torn ember
The equation of the line is y = -(1/2)x + 8. So when x is 0 y is 8
just realised, got this wrong, solved for y intercept instead
upper sparrow
They mention stuff like this, as if integration wouldn't have gotten the answer anyway 🤔
torn ember
Got it! Thanks so much, you've not only helped me with this question but I actually know what an integral is now
upper sparrow
Haha, it took me quite a while to explain integrals when I was tutoring this kid some time ago tbh
unique dust
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mortal breach
need help solving this
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sinful dirge
I need help
calm coralBOT
I need help
sinful dirge
I need help reviewing my test
I understand the problemts
I was tryna see if someone can give me problems similar to these
So i can practice
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strong drift
other then the fact that Every Graph has an Even Number of Odd Degree Vertices , what's the best way to prove that a simple graph does not exist
strong drift
like for example a graph with degrees (1,2,3,4,5,6,7)
i seen some examples online of people drawing out the graph and visually showing it can't exist
is there a more concreate way?
thanks
i found my answer
.close
strange grove
is this regular language?
unreal viper
are L_1 and L_2 also regular languages?
strange grove
are L_1 and L_2 also regular languages?
Yes
unreal viper
Do they have the same alphabet?
strange grove
Do they have the same alphabet?
i dont know, it's not clear form the problem
probably we cant suppose it
unreal viper
I think that it is regular, and im pretty sure it's because, $v\in L_2\circ \Sigma_{L_1}^$, and then that means that $L_1\times L_2=(L_2\circ \Sigma_{L_1}^)\circ L_2$
potent lotusBOT
llspacebarll
unreal viper
I could be mistaken
but this seems like it is a regular language then since it is a concatenation of two Regular languages
the first one being the concat of a regular language and a klein star
which are also both regular
it also seems like L_2 is a sublanguage of L_1 tho
actually nvm
its just a restriction on this set i guess
strange grove
but the word u is from alphabet of language L_1 and not from language L_1, cant it make problem?
its problem from last year exam, personally i thought that this problem was meant for pumping lemma
unreal viper
w is from language 2 and u is from language 1 star
you think its pumping lemma time?
i mean it may be
but i wouldnt be able to help then
but then v is also from language 1
thats what is confusing me as well
strange grove
hmm
maybe we can pump the 'u' word and after that it doesnt have to be in L_1
really idk
strange grove
.close
pine schooner
What would it mean for the difference between iterations of two different initial values to diverge?
pine schooner
I'm iterating a quadratic of form $f(x_1)=ax(1-x_0)$ through 1000 steps of iteration
potent lotusBOT
goobybalooby
potent lotusBOT
Gijs
pine schooner
yes
wintry glacier
alright yeah
pine schooner
i have a program to do it for me on octave, but the results after 1000 steps of iteration neither approach zero, infinity, or a concrete number
pine schooner
and oscillating is essentially diverging right? if a limit does not exist, then it diverges?
glass heart
yes
but maybe a subsequence converges
try plotting the sequence
and change your parameter a
pine schooner
the question i am working on fixes a as a=4
then says to vary the inputs for x_0 for the two different iterations by seeing if they diverge even if they agree through a certain number of decimal places
so the picture above is with initial values for two different iterations with a=4, and one has x_0=0.42, and the other has x_0=0.48
then it asks to make them agree to the hundredths place, then thousandths, etc and to see if they always diverge or if there is a point when they actually converge
calm coralBOT
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pine schooner
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tame coral
Is it okay to use the equivalent sign $\equiv$ when the functions are defined on different domains?
potent lotusBOT
Anders
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carmine sorrel
yeah that's fine. It's just saying that when you restrict to the original domain, then the two functions are the same
tender current
calm coralBOT
tender current
Using the y= equation, and plugging in the values 80 for initial velocity and 45 for theta
[y=x\tan(45) - \frac{16\sec^2 (45)}{80^2}x^2]
[y=(x*1) - \frac{16\sqrt{2}^2}{6400}x^2]
[y= x - 0.005x^2]
potent lotusBOT
dopediscorduser
tender current
Does this look right?
calm coralBOT
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tender current
<@&286206848099549185>
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hallow python
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hallow python
Can someone help me with problem 5 subquestion d?
I have no clue about how to approach this problem?
velvet osprey
from part c, divide both sides by $F_nF_{n-1}$ to get $$\frac{F_n}{F_{n-1}} - \frac{F_{n+1}}{F_n} = \frac{(-1)^{n-1}}{F_nF_{n-1}}$$
potent lotusBOT
Ann
hallow python
woahhhh
so the LHS of this equation
is where I should use those test for convergences?
@velvet osprey
potent lotusBOT
Ann
velvet osprey
and the RHS decays exponentially
can probably handwave your way into proving the sum of the rhs converges
hallow python
Okay thank you so much @velvet osprey
calm coralBOT
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velvet osprey
F_{n+1}/F_n = w_{n+1} by defn
hallow python
we have w_(n-1)
got ittt'
sorry
no the lhs is w_{n} -w_{n-1}
right?
@velvet osprey sorry could you check this?
calm coralBOT
hallow python
.reopen
calm coralBOT
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hallow python
hello @velvet osprey
velvet osprey
ah uh. hm.
velvet osprey
no the lhs is w_{n} -w_{n-1}
no, the LHS is what i said it was.
w_n = F_n/F_n-1
so w_n+1 = F_n+1/F_n
velvet osprey
yes
hallow python
In the question its w_(n)-w_(n-1)
velvet osprey
yes
the convergence of $\sum (w_n - w_{n-1})$ is equivalent to that of $\sum (w_{n-1} - w_n)$ though
potent lotusBOT
Ann
hallow python
ohhhhh
got it @velvet osprey
thank you
so (-1)(w_{n} - w_{n+1})
is the same as w_{n} - w_{n-1} right
velvet osprey
not quite
but the difference is not enough to worry about for convergence purposes
hallow python
**Ann**
ohhh okay you meant is equivalent to that of w_n - w_n+1
okay
so just to answer about the convergence of this thing
I can use this
velvet osprey
all three series' convergences are equivalent
hallow python
okay Understood
that was helpful
how to use this info to show that w_n also converges
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lament jungle
Hi, I'm confuse here; CoordinatePlaneTrig
calm coralBOT
Hi, I'm confuse here; CoordinatePlaneTrig
lament jungle
So I found the missing side then I can see the bottom side is 1
but the tan answer is wrong?
adj is 1
hyp is 6
opp is 5.916079783
tan is opp/adj
I also used the opp value to find that side and confirmed it's 1
<@&286206848099549185>
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meager bridge
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meager bridge
Question 8 is where my troubles lie
I already figured out the y portion but i dont understand what im doing wrong with the x portion
I got 1.4
But it says its wrong
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calm coralBOT
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nova fractal
Just a simple question im not sure what i do wrong
calm coralBOT
Just a simple question im not sure what i do wrong
velvet osprey
how do you get -6 - 9i?
velvet osprey
but why are you multiplying anything when these complex numbers are being added?
velvet osprey
(-1+2i)(4+i) isnt the same as (-1+2i)+(4+i)
noble cedar
calm coralBOT
noble cedar
Why is my answer so off? The one provided is $3,777.17
That’s power (30) in the top right
Oh I forgot a zero
Nvm lol
.close
calm coralBOT
brittle jolt
Is this annual compound interest ? We have a test on that tomorrow haha
noble cedar
Yep
noble cedar
Compound and continuously
brittle jolt
I have a question on that in my channel, can you offer help?
It's similar actually, we're solving for "t"
noble cedar
Not sure I’m just following Professor Leonard’s video
calm coralBOT
Available help channel!
safe fulcrum
Yo I need help on a math problem, I need to understand a formula
remote mural
check your book/notes
safe fulcrum
I don't have
The man gave me the formula and we have to understand it
By searching for help in Google or whatever
remote mural
who? for what class?
remote mural
whats the context?
safe fulcrum
Understanding a mathematical law
remote mural
safe fulcrum
We talked about the theory
That human never walked over the moon
And the "teacher" showed us this law
And we have to understand it
remote mural
there is nothing to understand without context
calm coralBOT
@safe fulcrum Has your question been resolved?
remote mural
find out what the context is by asking your teacher
nova fractal
get the sum and the diffrence between the complex equations.
nova fractal
3+i and 1+4i
pine topaz
so you just want to add them up or subtract them?
nova fractal
Pretty sure its subtract? But when i Did i didn’t have same answer as in book
opaque minnow
3+i and 1+4i
addition means just add them , so 4+5i
subtraction : 3+i - (1+4i)|
= 2-3i
nova fractal
addition means just add them , so 4+5i
subtraction : 3+i - (1+4i)|
= 2-3i
Yes but we want the sum too
opaque minnow
their sum just add em man
pine topaz
if the question you mean is the question you wrote, then RDT answered it
i also don't really see what else there is to it
just addition/subtraction
nova fractal
Somehow im not doing it right
nova fractal
Sorry im lost
pine topaz
only that the imaginary part of 2-3i is not -3i
the imaginary part of 2-3i is -3
so we get
$\sqrt{2^2+(-3)^2}$
potent lotusBOT
~Martin
nova fractal
Why Did you remove i
pine topaz
two options:
- you think a bit about it and notice that in the complex plane, it functions exactly like a R2 plane
- you just go by definition
and the length of a complex vector is defined as sqrt(Real^2+Imag^2)
nova fractal
Wait i think you complicate things maybe
pine topaz
not really
nova fractal
Because if I put i^2 it becomes -1
pine topaz
and?
nova fractal
So sqrt(-3*(-1))
nova fractal
?
pine topaz
(-3i)^2=(-3)^2 * (i)^2 = 9*(-1)=-9
which is not what we are after
just don't use i in the first place
the length of a vector is just not defined like that
nova fractal
Sorry im not sure How you think
pine topaz
you are not going by the definition
we use the imaginary part here
notice that the imaginary part of a complex number is a real number
the imaginary part of -3i is -3 and not -3i
thin wharf
since absolute value is distance from 0, and complex numbers are on a 2 dimensional plane, it's just defined that way
here the distance of 3 + 4i from 0 + 0i is |3 + 4i| = 5
nova fractal
here the distance of 3 + 4i from 0 + 0i is |3 + 4i| = 5
I think you got my numbers wrong
thin wharf
that was just an example
nova fractal
the imaginary part of -3i is -3 and not -3i
Yeah so basically the absolute value formula has No imaginary number?
nova fractal
here the distance of 3 + 4i from 0 + 0i is |3 + 4i| = 5
How Did you know it was 5
thin wharf
nova fractal
both are real numbers
Okay so IzI= sqrt(4+9) =sqrt(13)
How Did they get 4+5i
timid jay
calm coralBOT
calm coralBOT
@timid jay Has your question been resolved?
upper sparrow
Think so! (I think the markscheme may want you to justify why you're doing that, though?)
calm coralBOT
Available help channel!
tiny condor
based on this image, how can I prove that angle B=angle C? if I can
tiny condor
given angle A=angle D and AB=BC=CD and ABCD is a quadrilateral
tiny condor
actually wait
ripe spade
is the fact that BC equals to AB and CD important?
tiny condor
wait, how does that work
muted spoke
wait, how does that work
This only work if BC and AD are parallel
They don't work if they're not
tiny condor
This only work if BC and AD are parallel
that's not given
tiny condor
you show that triangle ABD is congruent to ACD
how do I know that?
tiny condor
oof
ripe spade
so angles BAD and ADC are equal
tiny condor
goodnight
tiny condor
yeah the triangles are congruent
hushed knot
This only work if BC and AD are parallel
They are parallel
ripe spade
then you know that angles ABD and ACD are equal
tiny condor
yeah that makes sense
ripe spade
To show that angle ABC = angle BCD u just have to show that angles DBC and ACB are also equal right?
tiny condor
yeah
ripe spade
but triangles BCD and ABC are isosceles. so angle DBC = angle CDB, and angle ACB = angle BAC
tiny condor
makes sense yeah
ripe spade
we know from congruence that angles ADB and CAD are also equal to each other. combined with the fact that angle BAD = angle ADC this means angle CDB = angle BAC
can u see it now?
tiny condor
yeah that makes sense
muted spoke
Can't sleep here got bored
ripe spade
so u can show that angle B = angle c?
muted spoke
Gtg
ripe spade
🙂
tiny condor
wait so what was the list of angles we concluded were equal to eachother
ADB=CAD
BAD=ADC=A=B
CDB=BAC
ABD=ACD
are there more
ripe spade
ADB=CAD
BAD=ADC=A=B
CDB=BAC
ABD=ACD
A=D (given)
ADB=CAD (from congruence)
BAD=ADC (from congruence)
u can see from the diagram that
D = CDB + ADB and A = BAC + CAD
coz A = D, we have
CDB + ADB = BAC + CAD.
coz ADB = CAD, cancel that from both sides, and u get CDB = BAC
so CDB=BAC
tiny condor
okay I think I got it now
rose charm
based on this image, how can I prove that angle B=angle C? if I can
join BD and AC, you get 2 isosceles triangles both of which have their equal sides the same
=> their base angles will be the same, let them be x
=> in BAC
mB=180-2x
in CBD
mC=180-2x
thus mB=mC
ripe spade
coz triangle ABC is isosceles, ACB = BAC
coz triangle BCD is isosceles, CBD = CDB
we know that CDB = BAC, so ACB = CBD also
tiny condor
alright cool then I can just substitute values to get the answer right?
so
gimme like 5 min I think I got it
ripe spade
we know from congruence that ABD = ACD. and we have just shown CBD = ACB. so add these equations together u get
ABD + CBD = ACD + ACB.
but angle B = ABD + CBD
angle C = ACD + ACB.
so angle B = angle C
got it?
tiny condor
I'm trying to the last step myself one sec
ripe spade
I'm trying to the last step myself one sec
take ur time
tiny condor
ADB=CAD
BAD=ADC
CDB+ADB=D
A=BAD+CAD
CBD+ADB=BAD+CAD
CDB=BAC
ACB=BAC
CBD=CDB
B=CBD+ABD
C=ACD+ACB
substitute and we get
B=BAC+ABD
C=ACD+BAC
B=BAC+ABD
C=BAC+ACD
wait now I'm stuck because I can't substitute ABD and ACD for anything
I'm sorry if it's obvious lmao my brain really only works with algebra
ripe spade
well then maybe u shud consider the other answers
ripe spade
join BD and AC, you get 2 isosceles triangles both of which have their equal sid...
does this help?
tiny condor
I was looking at that but I don't know why the base angles will be the same
rose charm
I was looking at that but I don't know why the base angles will be the same
isosceles triangle
tiny condor
join BD and AC, you get 2 isosceles triangles both of which have their equal sid...
oh this adds up]
sorry I didn't understand your explanation silversoldier
I'm flattered you're willing to take 40 minutes out of your day to help me though, ty!!!
tiny condor
join BD and AC, you get 2 isosceles triangles both of which have their equal sid...
wait but wouldn't this only be true if AC=BD
how would you prove that
ripe spade
ADB=CAD
BAD=ADC
CDB+ADB=D
A=BAD+CAD
CBD+ADB=BAD+CAD
CDB=BAC
ACB=BAC
CBD=CDB
B=C...
-
ADB=CAD
-
BAD=ADC
-
CDB+ADB=D
correct upto here -
A=BAD+CAD
its not BAD, it mst be BAC. so A = BAC + CAD.
so then coz we know A = D, we can write
5. BAC + CAD = CDB + ADB.
but now u can cancel CAD from the left-hand side, and ADB from the right-hand side, coz we know they are equal (from 1). then u r left with
6. BAC = CDB.
now because ABC is isosceles,
7. ACB = BAC
because BCD is isosceles,
8. CDB = CBD.
frm congruence, we also know
9. ACD = ABD
Now add ACB to both sides of 9. this gives
10. ACD + ACB = ABD + ACB
but ACD + ACB = angle C, so
11. angle C = ABD + ACB.
from 7, ACB = BAC, so replacing ACB with BAC above we get
12. angle C = ABD + BAC
again from 6, BAC = CDB, and from 8, CDB = CBD, so replacing BAC above with CBD we get
13. angle C = ABD + CBD
finally, ABD + CBD = angle B, so from 13 we have angle B = angle C
sorry if this is too long
tiny condor
reading one sec
that makes sense!!!!!! aaaaaaaaaaaaaaaa
tysm
fuck I don't know how to repay you lol
tiny condor
what math class are you in? if you're in one
ripe spade
im not schooling
tiny condor
oh okay
ripe spade
i guess i am like just out of high school...the school system is kinda different in our coutnry
tiny condor
well if you need help with calculus for whatever reason
actually Idk you're probably like way ahead of me in that area too lmao
in calc 3 rn but can't do geometry lmao
ripe spade
lol thanks
tiny condor
ok ty can I close this now
ripe spade
yea
worthy vapor
Let f : R -> R be a differentiable function.
Show that ∀x > 0, ∃c > 0, f(x) - f(-x) = x(f'(c) + f'(-c))
worthy vapor
This may be an easy question, but I can't find the answer
visual nimbus
looks like mean value theorem
worthy vapor
Yeah I know, but I don't know what I can do with it
calm coralBOT
@worthy vapor Has your question been resolved?
calm coralBOT
@worthy vapor Has your question been resolved?
valid plinth
f(x) = x; reflection in the y-axis
calm coralBOT
f(x) = x; reflection in the y-axis
calm coralBOT
@valid plinth Has your question been resolved?
potent lotusBOT
tall talon
if p,q,r and s are natural numbers prove that
calm coralBOT
if p,q,r and s are natural numbers prove that
tall talon
$$x^(4p) + x^(4q+1) + x^(4r+2) +x^(4s+3) is divisible by x^3+x^2+x+1$$
potent lotusBOT
notsogood
wanton wave
You mean you divided the polynomials and showed there's no remainder?
tall talon
no i found out factors of x3+x2+x+1
which are 1 +-i
and by the help of factor 4 in power there is use of multiplicity of i so i proved it that way
glass heart
and what's wrong with that approach?
tall talon
i dont feel legitimate
i mean its so easy like that there nedd to be a different approach
any idea?
glass heart
found easy solution
but no lets overcomplicate it and do something else
tall talon
ok
glass heart
but yeah really not sure
it's a bit cursed that there are 4 parameters. not sure yet how to use that all exponents are of the form 4k+something
tall talon
hmm i think thats the only way
wanton wave
I think your approach is what's intended. It's simple and elegant, and it works 🤷
glass heart
like sure it's x^3*something + x^2*something + x*something + 1*something but not sure how to use that
tall talon
actually i think its just testing the knowlegledge of multiplicity of iota
glass heart
well and just general knowledge like knowing that checking the roots is enough and stuff
wanton wave
You showed that the roots of the cubic are roots of the larger polynomial, right?
tall talon
yeah
wanton wave
And you showed that you understand that means the larger polynomial is divisible by the cubic
tall talon
i am not sure if it will secure perfect marks
wanton wave
It should
wanton wave
And simpler is better
tall talon
hmm
wanton wave
A proof in four lines is better than four pages
tall talon
because whenever i use out of box solution they deduct marks giving excuses like we havnt taught that and everything
glass heart
well ok did they teach that checking roots is enough?
glass heart
I mean that's fair that they only want you to use stuff you went over in your course
neat patrol
calm coralBOT
neat patrol
help?
<@&286206848099549185>
hello
<@&286206848099549185> can someone help
its been 15 mins
calm coralBOT
@neat patrol Has your question been resolved?
neat patrol
No
elfin ermine
@neat patrol
elfin ermine
<@428982920292597790> Has your question been resolved?
btw if your question hasen't been resolved you press the ❌
also for this
what does it mean for two variables to be proportional to each other?
neat patrol
???
remote mural
calm coralBOT
remote mural
I need help with this question
calm coralBOT
@remote mural Has your question been resolved?
remote mural
Everything within the two lines
calm coralBOT
Everything within the two lines
remote mural
I think I did the integral wrong
Can somebody help me with this technique
Where we solve for the integral equation in a sense
wanton wave
Yeah something went wrong, I'm not exactly sure where, but you definitely shouldn't have gotten an x^4 back in your integral after the second integration by parts
you had 12x^2, but it randomly became x^4 again
I know the technique you're talking about "solving for the integral"
Like you'd do in the bottom integral there, the one with e^2x
But that's not what you'd do in this one
@remote mural Have you learned about tabular integration?
sinful glacier
<@456226577798135808> Have you learned about tabular integration?
pm pls🙏
glossy eagle
Me too I want help but I don't think much are active so I want @wanton wave to help if they're available, I will make a channel
wanton wave
Me too I want help but I don't think much are active so I want <@490649542077841...
yes, open a channel in the available section
glossy eagle
Yea I did
calm coralBOT
@remote mural Has your question been resolved?
wide phoenix
I have K but not L so would I treat this equation as (100 - (10L + 2L)) or (100 (-10L+2L)) ?
remote mural
<@456226577798135808> Have you learned about tabular integration?
Uh I have had it mentioned to me
remote mural
I have K but not L so would I treat this equation as (100 - (10L + 2L)) or (100 ...
What does this even equate to
wide phoenix
What does this even equate to
Some equation for economics but I'm not sure which way I should read it
remote mural
Do you know mpl
wide phoenix
nah its just a variable
wide phoenix
general equation
not given L so I cant solve
or actally I am I guess
wait no im not
remote mural
Are u just putting the equation in terms of L?
wide phoenix
Like out of these two how would I interpret the equation? : (100 - (10L + 2L)) or (100 (-10L+2L))
from (100 - 10L + 2L)
remote mural
Idek what u are talking about
pure roost
What would a 6kg dog weigh on or near the surface of a planet with double the Earth's diameter and one-third the Earth's mass?
pure roost
.close
half otter
Can anyone help me with this?
calm coralBOT
Can anyone help me with this?
frank gull
use the distance formula: $\sqrt{(y_2 - y_1)^2 + (x_2 - x_1)^2}$
potent lotusBOT
MellowDramaLlama
half otter
But it also says convert to radical form. I don’t know how to do that
frank gull
Radical form just means that you're leaving it as a root. For example $\sqrt{2}$ is in radical form whereas $2^{\frac{1}{2}}$ is in exponential form, but they are equivalent