#help-0
1 messages ยท Page 68 of 1
the confusion
which one you solved?
what happened?
I got like
400 something
and my friend got 391.60m
I was asking for the oct
but if you solved the hex its ok
DUDE
Anybody help ?
how?
its for the 8 sides
yeah
so
ok wait
nono ill make it easy for ya
ok
yeah
yeah
now from this we have two options
yeah?
first is directly finding the area of an isoceles trisngle
I dont think I know that because im on seventh grade but ill try
ill just give you the octagon formula
I need to do like pyhtagoras
what did your teacher give ya
ignore it then
ok
so I was doing like c= 11 a= ? b=5
the h is obtained from this
b = a
oh ok
then I got 146
and I need to get the square root
so its
12.08
and then I need A = 8 x 5 x 12.08 over 2
im confused here
could you help on this part?
hello?
omg dude why this always happens
ok so
we have
A = 8 /2 ah
right?
we have a as 10 right?
SO a = 10
that means
A=(8/2) * 10 *h
@alpine sable now whats left is to find h
ok
ok it is good
but wait
arent we finding the apothem or other thing?
because on all shapes my teacher told me just to find area and perimeter, the formula for area was A = N x S x A over 2 and for perimeter was P = N x S
hmmm
thats correct
but
?
what you need to do is find the area of one triangle
octagon is just that triangle multiplied by 8
it goes for all the gon shapes
?
nono its an isoceles triangle a triangle with two equal sides
lol
a is also 11
wait no
you did a right angles triangle
solve it
a = 13
okok
ok let me send you what I was doing
sure
ye just ping me lol
no way
the procedure is tho
ok wait
@alpine sable
no way thank you so much I FOUND IT
I GOT 391.60
m
than u so much
so so so so much
I need to go tho
but thank you so much bye
if you have time can we solve the other just if you have time
just in case you respond me give me 5 minutes becausei m helping my mom
I will be back
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can i get help with 54?
@viscid wren Has your question been resolved?
f can be thought of as the distance from (1, 0)
and R is the upper half of a disc centred on the origin
if you draw a diagram it should be clear where the maxima/minima are
@viscid wren Has your question been resolved?
If you partially differentiate the equation inside the square root of f(x,y) with respect to x, you'll get 2x - 2. Then set this equal to zero, then you'll get x=1.
thats only one of the extrema
i need the absolute max and mins
prof told us to solve the bounded region for y and then plug that into the original function but
Similarly, you can also differentiate wrt y to get 2y, if you equate that to 0, you get y=0
yyup
rewrite the inside of the sqrt as
Therefore, the point (1,0) is a point where there is either a minima or maxima
you can see that its minimised when x=1 and y=0
and that its maximised when its furthest away from (1, 0) in the half-disc
quadratics dont require taking derivatives to maximise/minimise
well this was the method we were taught to find the abs max and mins so I don't really know what to say
I used this exact same method for question 51 and had 0 issues
you can plug in the boundary directly to find the maximum
51 can likewise be done without differentiating
I 100% get that but we have to work it out like this for whatever reason.
like I asked if I could just plug in the boundary points and he said no lol
anyways I'm gonna go ahead and go to bed.
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Is this correct?
also the calculator says ln(x)^2 is 2ln(x)/x
But isnt is 2/x?
like the derivative of it
chain rule
Yes
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Oh do we get a systems of equation out of it?
Cant remember that on one go
Especially when Im trying to practise all the other stuff in my calculus course at the same time
Bound to forget some things here and there
Anyways I reckon I can take it from here
thanks
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Need help trying to rearrange a fraction in order to compute a limit
@rigid tundra Has your question been resolved?
show work
don't unnecessarily expand stuff
I rearrange, but this new form still has same problem
I see ,so something can cancel when I multiply conjugate
i would prefer that you don't, if you have questions make a channel
consider conjugates of the numerator as well
Yh I tried aswell separately
Could u do them at the same time
Or will one succeed in cancelling
Somewhere
If u don't expand
only do the multiplications involving the difference of two squares
and you should end up with a relatively easily identifiable common factor in the numerator and denominator
Ahh I see thanks
I'll try now
I saw the cancel ,thanksm
How did u understand to multiply by both conjugates
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standard idea for these types of problems
I see thanks ,I have it in my tool kit ๐
builds on the same principle of why you'd do the first conjugate
Yh true
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@woeful wind Has your question been resolved?
@woeful wind Has your question been resolved?
<@&286206848099549185>
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write in polar form:
my try:
(1 โ i)^3 ( โ 3 + i) / 4i โ
(1-3i-3+i)(โ3 + i) / 4i โ
(-2-2i)(โ3 + i) / 4i โ
2(-1-i)(โ3 + i) / 4i โ
(-1-i)(โ3 + i) / 2i โ
(-โ3-i-โ3 x i+1) / 2i โ
(-โ3-i-โ3 x i+1) x -2i / (2i x -2i)โ
(2iโ3 - 2 - 2โ3+-2i) / 4 โ
(- 2 - 2โ3)/4 + (2iโ3-2i) / 4 โ
-(1+โ3)/2 + (โ3-1)i / 2
Polรคr form:
r =โ( (-(1+โ3)/2)2 +((โ3-1) / 2)2) = โ2
tanv = (โ3-1) / -(1+โ3) โ v = arctan(โ3-2) <-- this i cant do by hand , is their a better way of going about it?
multiply the fraction by the conjugate of 4i
from the start yea?
yeah then combine and simplify
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โ
well i gave it a try and got the same problem
(1 โ i)^3 ( โ 3 + i) / 4i โ
(1 โ i)^3 ( โ 3 + i) x -4i / 16 โ
(1-3i-3+i)(โ3 + i) x -4i / 16 โ
(-2-2i)(โ3 + i) x -4i / 16 โ
(-1-i)(โ3 + i) x -4i / 8 โ
(4i - 4)(โ3 + i)/8 โ
(i-1)(โ3 + i)/2 โ
(โ3 x i-1-โ3-i)/2 โ
-(โ3+1)/2 + (โ3 - 1)i / 2
Polar form:
r =โ( (-(1+โ3)/2)2 +((โ3-1) / 2)2) = โ2
tanv = (โ3-1) / -(1+โ3)
what is the problem?
i cant do tanv = (โ3-1) / -(1+โ3) by hand
pretty much
that's because you cant, the exact value of arctan(that) is just itself
it's not very nice, but you would have to deal with it
however though, arctan(...) is not your argument
so be careful about that
what do you mean by that?
finding v by taking arctangent on both sides will not give you the argument of your complex number
refer back to principal argument definition
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how do i do this?
i got -8.873 x 10^8
i multiplied 8.2 and -7.9
which was -64. something
then i did
-3-5
which was -8
then i divided -64.78 by 7.3
which was 8.873
then i did -8+16
which was 8
so it was 8.873 x 10^8
,calc 8.210^-3 * -7.910^5/(7.3*10^16)
Result:
-8.8739726027397e-14
you are mixing up positive and negative parts
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Ah sht wait how do u rotate
Forgot how to rotate but basically i need help with number 2.
Where my physics bois at?
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hey good eve can someone give me a easy run down piecewise three sub-functions over a specific interval??
i just want to make a situated problem and answer it myself also
(i can't plagiarize)
something like this
should that function have any requirements?
continuous? differentiable?
$f(x) = \begin{cases} x^2+4x+7 & x\leq -3 \ 5 \cos(x) & -3<x\leq 4 \ -7x & x > 4 \end{cases}$
Denascite
i only have to provide two questions to evaluate the constructed piecewise function and show a detailed solution based on the formulated problem
and create three sub-functions over a specific interval.
thats all
serious questions only, you are occupying a channel that someone else could use.
i am serious
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<@&268886789983436800>
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quick question. Why the anwer is infinity? shouldn't it be 0?
why 0?
limit is infinity because the function gets arbitrarily large when x is close to 1
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In order to differentiate this, I know I need to use product rule
but
Can I treat this function as (6x^2sinx) (tanx)
or are all three pieces independent
You can but then youโll have to use product rule again anyway
Yea i understand that but Its better to do one than two
Youโll see that $$\frac{d}{dx} f(x)g(x)h(x) = fโ(x)g(x)h(x) + f(x)gโ(x)h(x) +f(x)g(x)hโ(x)$$
Pure
good luck
I guess you could factor out some stuff
Can you? The only thing I can see you factoring out is a 6
tanx = sinx/cosx
oh okay. I guess sec^2(x) = 1/cos^2(x) too right
Yes
Okay. Ill factor later but this answer should suffice
Thanks man
have a good one
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We will determine a linear mapping ๐(๐ฅ,๐ฆ)=๐โ
(๐ฅ / ๐ฆ) with ๐โโ2ร2 which "turns the coordinate system around the origin" by 30 degrees anti-clockwise.
The task should be to determine the matrix ๐
a) A turn of 30 degrees counter-clockwise transfers the vector (๐ฅ๐ฆ)=(10)
to ๐โ
(10)=(((โ3)/2)/(1/2)). Where is the second coordinate direction mapped to, i.e. what is the image of (0/1) under the mapping f? (x and y direction, write โ3 as sqrt(3) if you need to.)
b) Based on information from part task a), it is now possible to determine matrix ๐
Task descrpition:
We will determine a linear mapping ๐(๐ฅ,๐ฆ)=๐โ
(๐ฅ / ๐ฆ) with ๐โโ2ร2 which "turns the coordinate system around the origin" by 30 degrees anti-clockwise.
The final goal is to determine the matrix ๐
Task:
a) A turn of 30 degrees counter-clockwise transfers the vector (๐ฅ/๐ฆ)=(1/0)
to ๐โ
(1/0)=(((โ3)/2)/(1/2)). Where is the second coordinate direction mapped to, i.e. what is the image of (0/1) under the mapping f? (x and y direction, write โ3 as sqrt(3) if you need to.)
b) Based on information from part task a), it is now possible to determine matrix ๐
Cant figure out how to do task B, does anyone know how I can do this?
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hello, I'm trying to calculate linear approximation of this data
that's the formulas I'm using
but the result is simply wrong
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Help
-x-3+2x
What are you trying to do?
Simplify
$-x - 3 + 2x$
lexitorius
What are your like terms in this equation?
1x
Nah
$x - 3$
lexitorius
There you are
Thank you
๐
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hi
just ask the question
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โ
is vertical shift and vertical translation the same thing
yeah
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I m kind of lost on what steps to take on the first problem I can find the derivative of x= 121/6 after that I tried plugging it into the original function to find C and got 20959.91667 as the number but it aint right..
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Is molar mass and formula mass asking for the same thing?
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!15m
Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
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problem: secx*cotx - sinx
You gotta simplify??
yep
So secx is the reciprocal of cosx
yep[
So secx is equal to??
1/cosx
Yes
and 1/cosx*cosx/sinx
1/sinx-sinx
On Simplifying the fraction you get??
Yes
is that it
No
cosx/sinx *cosx
Cosx/sinx * cosx
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help
the T stands for transpose, which means switching the rows and columns of the matrix
once you do that, it's just matrix multiplication
ah ok thanks
the first two are basically the same exact operation and are basically like finding a dot product, -10
i am not sure what the bottom two matrix answers are asking for though
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@urban pendant Has your question been resolved?
think about how matrix multiplication works. Yes, if you multiply a row vector by a column vector, you'll get a single number. What happens if you multiply a column vector by a row vector?
Oh hmm
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Why can we use SAS here?
It doesnt look like DCA is included angle on the bottom triangle
you're right, that looks improper
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https://cdn.discordapp.com/attachments/814945818217152623/1032137200571260969/unknown.png
I have no clue what the end behavior is for this graph
What function is that?
Its a polynomial
Finding the end behavior of the function
Gimme a min to paste it
Cubic?
By "end behavior", do you mean the limit of the function as it goes to infinity?
ye
It will diverge to $\infty$
BlokirKominfo
mhm
Just look at the leading coefficient.
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Set A={ ( [-1,0] โฉ Q ) โช [0, 1] }, what is the unordered sum on A? ( โx, xโA )
@jade canyon Has your question been resolved?
<@&286206848099549185>
I'm not sure how much convention there is on what it means to sum over an uncountable set
I only know that the uncountable sum of a non-negative set is the supremum of the sum over its finite subsets.
dont know when it have negative numbers
I don't know if there is any convention for that, but there might also not be any useful way to define it anyway
because its โ-โ?
if you take this
wouldn't the negative numbers not affect the sum?
If it is a finite number of negative numbers, it has nothing to do with the order. If there are infinitely many negative numbers then the order will matter.
but the sup won't change
ok actually I'll ask why do you ask this?
ok I was thinking that the cardinality of R is much more than Q, might this affects the result to be positive infinity?
well... let $$A= [-1,0]\cup ((0,1)\cap\bQ).$$ Then $$\sup\left{\sum_{x\in F}x:F\subseteq A, F \text{ is finite}\right}=\infty$$
actually let me rewrite that
layla๐
How to prove that this formula holds even with negative numbers?
All books/articles only show that it holds only if it contains only non-negative numbers
the negative numbers don't affect the sup lol
nono
they just don't define it for the case where there are non-negative numbers
there are infinitely many rational numbers greater than 1/2
what is still what?
ok for only non-negative number, its sup; but for only negative number, its inf
sure
while both non-negative and negative numbers are included, I didn't find any definition of summation
yea, that's what I meant with no convention lol
ok but for this, If the answer for any order of summation is positive infinity, then does it not exist or is positive infinity?
not sure what you're asking 

finite sums from A can range anywhere from -infinity to +infinity
it just sorta doesnt make sense
uhm intuitively, this disordered sum should be positive infinity since the R <-> P(Q)โฆ
idk
its no convention
like the uncountable sum on negative integers union positive real numbers
my intuition says there are more worthwhile things to think about than this ๐ฅด
lol
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could anyone help me with a linear equation?
what happened to the 3
set x = 0
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how would u find y-int for 7y = 5 - 2x
I think u need to make x = 0 or something like that?
i did solving for y and got 0.7
Can someone please help me with coordinate geometry? It makes me want to die
Hey could anyone please help me answer C and D
did i do something wrong
yes correct
but
on my sheet
wait no
donโt write 0.7
7/10?
just write y = 5/7
on my sheet
there is an answer list
set x=0
use #help-15
7y = 5
so y = 5/7
5/7 = approximately 0.7
but itโs better to just write
5/7
there's no 5/7 either
then, whatโs the answer?
idk
omg i have my best friend's discord is also mooncakee woahh
try 0.71
,w 7y = 5 - 0
probably
huh
that
on my calculator
i did 0.7
then clicked the S D button
and i got 7/10
yes
because
because
5/7 isnโt 0.7
itโs approximately 0.7
oh
would 7/10 be a valid answer?
nope
wait whattt
,w 5/7
try it
i can't really do that rn
no, but if the teacher accepts it Iโll be surprised
i'm not at school
i got a sheet
oh okay
and i'm at home trying to do it
if you write something like
โ 7/10
maybe the teacher will accept it
maybe
how come
yeah, thatโs why I said maybe
but if this was me I would honestly just write 5/7
oh wait
so i redid the calculator
and i wrote every decimal point
and i did S D
and got 5/7
yeah itโs 5/7
alr thanks for the help guys
np
:)
.close
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So I'm doing a maths paper that is measuring the correlation between core affinity (how many cpu cores are being used) and CPU temp
as well as
GPU temp and CPU temp
so 2 different correlations
both GPU temp AND core affinity impact CPU temp
as they both increase it, is there a way i can model their combined impacts onto a 3d graph of sorts?
basically
there will be a positive correlation between GPU temp and CPU temp, as well as core affinity and cpu temp
from this correlation, i can derive 2 trendlines, and 2 functions
then i wanna run a video game, and using those two functions, try to estimate CPU temperature using both gpu temperature AND core affinity
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i really need help with this question i am so clueless on how to do it
I actually solved it uh one sec lemme find the solution
Correction: Let $\angle AQP=x$
n11
OMG TYSM ILL HAVE A LOOK
i see
but how does the exterior angle property work
let me unleash my artistry
lmao
So basically the exterior angle is equal to sum of interior opposite angles
both are 180 minus the third angle
i see
OHHHH
OMG
THIS IS SO SMART
THANK YOU SO MUCH
btw are you good in geometry?
i have some more questions
that i am struggling
np!
I can give them a try!
should we do it here or dms?
i have to sleep right now because i have been working on the worksheet for the past 3 hours
here should be okay?
np!
just 2 more with 2 sub questions
n11
And now since they're similar, the second part can easily be proven.
โ This is for question 5 btw โ
btw i dont think i understand (angle subtended by a chord to the centre of a circle is double the angle subtended by it on any other point of the cirlcle than the chord)
tysm
n11
Compile Error! Click the
reaction for more information.
(You may edit your message to recompile.)
Its a theorem. Let me see where I can find it
Ah its an arc actually not chord lmao
ohhh okay i understand now
anyways thank you
btw out of curiousity what year are you in?
First
um how does that work???
that wasnt my math question lmao
i was asking n11 because he was so good at explaining
and he seems good at math
What a lad
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wdym
you just entered a really good approximation of the golden ratio
its (-1 sqrt5) /2
maybe even the approximation the calculator used
how is that the reciprocal of phi
the golden ratio is a root of x^2-x-1=0
by vieta then the second root is -1/phi
but you can also calculate that the other root is (1-sqrt 5)/2
$\frac{1-\sqrt 5}{2} = -\frac{1}{\varphi}$, so $\frac{1}{\varphi} = -\frac{1-\sqrt 5}{2} = \frac{\sqrt 5-1}{2}$
Denascite
the two roots of $x^2-x-1=0$ are $x_1=\frac{1+\sqrt 5}{2} =\varphi$ and $x_2 = \frac{1-\sqrt 5}{2}$
Denascite
o yeah
by vieta $x_1x_2=-1$, so $\varphi x_2 = -1$
Denascite
or $x_2 = \frac{-1}{\varphi}$
Denascite
and then this
is x2 -1/phi
ye
but um
why is(sqrt 5 - 1)/2 the reciprocal of phi
$\frac{\sqrt 5-1}{2} = -x_2 = -\frac{-1}{\varphi} = \frac{1}{\varphi}$
Denascite
Simplify
$\frac{1}{\frac{1+\sqrt{5}}{2}}$
Pure
thats 1/phi right
Yes simplify that
Pure
what conjugate
Conjugate of $1+\sqrt 5$
Pure
You want to rationalise the fraction
or as a third method, if you know that $\varphi$ is the root of $x^2-x=1$, dividing by $x$ gives $x-1=\frac 1 x$, which is exactly what we want. $\varphi-1 = \frac 1 \varphi$
Denascite
do we multiply this by 1 - sqrt5 or smth
we conjugate 1+sqrt5
how
$\frac{2}{1+\sqrt{5}} = \frac{2}{1+\sqrt{5}} \times \frac{1-\sqrt 5}{1-\sqrt 5}$
Pure
so
How to Rationalize a Denominator
Watch the next lesson: https://www.khanacademy.org/math/algebra/exponent-equations/radical_equations/v/solving-radical-equations?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraI
Missed the previous lesson?
https://www.khanacademy.org/math/algebra/exponent-equations/simplifying-radical-expressions/v/simplify...
1-5
2(1-sqrt5)
wait
2(1-sqrt5)/-4
so
minus?
ooohhhh
oohhhhhhhhhhhhhhhh
conjugate
making the denominator not have sqrts
oh
my first language is not english so
thank you

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Really having time with finding rates change
try plotting the one in the bottom right
@alpine sable Has your question been resolved?
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Can someone please explain to me how to represent irrational numbers on a number line (Class 9 Math)
depends on what kind of irrational
if it's made from integers or rational numbers by means of square roots then you can construct it exactly with some pythagoras bullshit
otherwise youll have to make do with a decimal approximation
roots yeah
but how to take the units
wdym by "take the units"?
...can you just send the entire question
will be easier this way
represent root 2, 3 and 5 on a number line
maybe you're not required to draw the triangles?
yeh, use right triangles and pythagoras as ann mentioned
just put it approximately betwee 1 and 1.5
yeaa
and what else about the โ3 and โ5?
what measure should i take
?
if you just want an approximation, just use a ruler and calculator
because you don't draw circle arcs to represent 0.5 do you
nah just right angled triangles
,calc sqrt(3)
Result:
1.7320508075689
,calc sqrt(5)
Result:
2.2360679774998
this is the mesaure i shoul take
if you just want an approximation, just use a ruler and calculator
if you want something as close to the desired value as humanly possible with the tools available, draw triangles and use compass
represent this on a number line
with using a ruler and a compass
doubt you'd be required to plot sqrt(9.3)
but it really comes in a lot of our book questions
,w a^2 + b^2 = 930 integer solutions
lmao
well there you have it ig. you can plot sqrt(929) using a 20 by 23 right triangle, then plot sqrt(930) using a 1 by sqrt(929) right triangle, then divide that into 10 equal parts and have one of them be sqrt(930/100) a.k.a. sqrt(9.3)
oh what the hell
it's hacky but it works ยฏ_(ใ)_/ยฏ
nah this not the method we used to do
OH SORRY YOU DIDNT SPECIFY A METHOD TO ADHERE TO
you already had a method outlined for you?
yea ig it works
what method were they using
and then?
you have โ9.3
no?
but i don't understand that HOW!?
because you don't get sqrt(9.3) from what you described in two lines?
can you show exactly what the book is saying?
WAIT I'LL SHOW THE SS
by this method ig
yeh.. that's pythagoras
as Ann described
there's no nice way to apply that for sqrt(9.3)
there's no nice way to do it
:(
hence why Ann had to go through all those hoops
well there you have it ig. you can plot sqrt(929) using a 20 by 23 right triangle, then plot sqrt(930) using a 1 by sqrt(929) right triangle, then divide that into 10 equal parts and have one of them be sqrt(930/100) a.k.a. sqrt(9.3)
and dividing into 10 is also a pain depending on how much precision is expected
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1 sec
double checking whether that actually works
ohh
