I'm assuming you haven't done multivariable differentiation either
#help-13
cosmic steppe
Hm
Oh you know what
Just treat h as a constant
So you're maximizing $\pdv{V}{r}$
wraith daggerBOT
Umbraleviathan
undone star
sure
undone star
i just need to prove that then the turning pointi is concave down when h = r ?
cosmic steppe
Sure
undone star
only problem is when u differentiate it it produces no constants
if i try to equate that to 0 to find turning points
cosmic steppe
If you find $\pdv{V}{r}$ you should get $2\pi r h$
wraith daggerBOT
Umbraleviathan
undone star
yeah
undone star
so just to reiterate
cosmic steppe
Ah I see
undone star
the cone has a fixed surface area with its top missing
prove that the volume is maximised when r = h
undone star
What's the surface area
i rearranged to express h with usrface area in it
*rearranged
ok
thats worded better
SA = 2pi r h + pi r^2
then rearranged h as SA/2pi r minus r/2
cosmic steppe
Are you not given the numerical value of SA?
undone star
no
if i attempt to subsitute h after first derivative
i would yield r^2 = 4pi r h + 2 pi r^2
cosmic steppe
then rearranged h as SA/2pi r minus r/2
This doesn't seem right
cosmic steppe
$S = \pi r^2 + 2\pi rh \implies h = \frac{S - \pi r^2}{2\pi r}$
undone star
yes
cosmic steppe
And I forget a pi somewhere amazing
wraith daggerBOT
Umbraleviathan
undone star
yeah
i split it up to see if i can just get a separate term
to then equate after first derivative
cosmic steppe
Lemme check something
Hm you don't maximize partial V then
You have to substitute into h before differentiation
undone star
oh ok
i figured it out i think
if someone could just check that this is logically sound
cedar kilnBOT
@undone star Has your question been resolved?
cedar kilnBOT
@undone star Has your question been resolved?
soft shuttle
How do I solve this? I’ve tried getting rid of the radicals by squaring everything, but I’m not sure if that’s even how it works. I know the answer is 144/25, but I have no clue how to get there. I am studying for a math test.
royal loom
hmm
wraith daggerBOT
AustinU
soft shuttle
need to get rid of the radicals
can i still get help orrr??
<@&286206848099549185>
cedar kilnBOT
<@&286206848099549185>
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.
bronze phoenix
cedar kilnBOT
bronze phoenix
can someone help me do this
timber bluff
crimson sedge
can someone help me do this
I would try to first change the left side to cos and sin
bronze phoenix
I would try to first change the left side to cos and sin
thats what i did and I got sinx/cosx * 1/sinx * cosx
bronze phoenix
do I then mulitply 1/sinx by cosx or sinx/cosx?
dull oxide
consider $\frac{\sin{x}}{\cos{x}}$ as $\sin{x}\cdot\frac{1}{\cos{x}}$
wraith daggerBOT
SWR
dull oxide
you left out one factor
undone star
i mean i guess it stil proves it correct if u divided both sides by sinx first
bronze phoenix
you left out one factor
dull oxide
yes
dull oxide
How did you get 4 terms in the denominator?
bronze phoenix
dont u have to multiply sinx by both sides?
undone star
no?
dull oxide
both sides?
undone star
think of sin x and cos x as sinx/1 and cosx/1
dull oxide
Remember that $\frac{1}{\sin{x}}$ is the reciprocal of $\sin{x}$
wraith daggerBOT
SWR
dull oxide
So if they're reciprocal, then what should $\frac{1}{\sin{x}}\cdot\sin{x}$ be?
wraith daggerBOT
SWR
bronze phoenix
So if they're reciprocal, then what should $\frac{1}{\sin{x}}\cdot\sin{x}$ be?
sinx/sinx?
bronze phoenix
1
dull oxide
same idea for cos(x)
dull oxide
$\frac{a}{b}=a\cdot\frac{1}{b}$
bronze phoenix
I dont know if im over thinking it or not but this part confuses me
wraith daggerBOT
SWR
celest kernel
i found is 2, want to check answer
cedar kilnBOT
i found is 2, want to check answer
celest kernel
numbers i found is 123654 and 321654
fair geyser
clear grail
how do u convert a 14 bit twos complement back to decimal
cedar kilnBOT
how do u convert a 14 bit twos complement back to decimal
cedar kilnBOT
@clear grail Has your question been resolved?
latent bloom
Wait 11111111001000 in base 2 = 422 in decimal?
,w convert 11111111001000 from base 2 to base 10
wraith daggerBOT
cedar kilnBOT
@clear grail Has your question been resolved?
native solstice
What is larger, e^pi or pi^e? Need the working out without a calculator ty
wraith daggerBOT
digital cliff
@native solstice
cedar kilnBOT
@native solstice Has your question been resolved?
wild wyvern
Can someone help me understand this statement? A system of n linear equations in n unknowns typically has a unique solution
cosmic steppe
So assuming that the system has a solution
Then if the number of unknown variables equals to the number of linear statements, then there's gonna be a solution
chilly warren
That's not true. If the determinant representing of the linear equations is zero, there is no unique solution.
cosmic steppe
Although by "typically" I think they mean most likely
Or assuming there's a solution of some kind
wild wyvern
How does that relate to linearly independent?
chilly warren
A linearly independent linear equations has nonzero determinant
wild wyvern
but why does n variable with n equation typically have 1 solution? Can you explain what happen when we have n variables with m equation where m > n or n < m?
chilly warren
If there are more than one unknowns, you can at best find a relation between one unknown with another, but not the exact value.
If there are more, it won't be linearly independent.
Prove that a set S of (n+1) vector with length n is not linearly independent!
wild wyvern
Hmm
chilly warren
Hint: use mathematical induction
wild wyvern
My class haven't taught us proof for linear algebra
I am just learning all the jargon of linear algebra right now and trying to understand the relationship between m and n
chilly warren
Isn't vector space the thing that was taught first?
wild wyvern
Yes i've learned that
it means the space n vectors can reach when we apply linear combination of n vectors
chilly warren
Okay, then. Why does two vectors of length 1 cannot be linearly independent?
wild wyvern
Hmm, ain't basis vector [0, 1] and [1, 0] linearly independent? 😮
chilly warren
Hmm, ain't basis vector [0, 1] and [1, 0] linearly independent? 😮
Length 1, not 2
wild wyvern
[1,0] [0,1] is a unit vector tho...not [2,0][0,2]..?
But If both 2 vectors have the same orientation / direction then they are on the same line and cannot be linearly independent
chilly warren
[1,0] [0,1] is a unit vector tho...not [2,0][0,2]..?
But If both 2 vectors hav...
Wait, by length one, I mean with one basis.
wild wyvern
2 vectors that shares the same basis is linearly dependent because they can both be represented as the scalar multiplication of the same basis vector
chilly warren
2 vectors that shares the same basis is linearly dependent because they can both...
Now, we know that n vectors with (n-1) basis is not linearly independent, what about (n+1) vectors with n basis?
wild wyvern
Well if I have n basis vector that are by definition linearly independent, they form R^n, so n+1 vectors imply that one of the vectors must be linearly dependent of the others
wait
chilly warren
Well if I have n basis vector that are by definition linearly independent, they ...
How do you know that it forms R^n?
wild wyvern
because they are linearly independent?
chilly warren
Yes, that still needs to be proven
wild wyvern
It forms R^n because any n vectors can be the linear combination of the n basis vectors and the n vectors can span any space in R^n?
chilly warren
Oh, I guess that's also right.
cedar kilnBOT
@wild wyvern Has your question been resolved?
cedar kilnBOT
@wild wyvern Has your question been resolved?
fervent sandal
How much time would it take the rocket to travel 3.45 x 10^9 metres?
ruby lion
How much time would it take the rocket to travel 3.45 x 10^9 metres?
i think theres some information missing
what is the speed of the rcoket
rocket
ruby lion
do u know index laws
fervent sandal
yes
ruby lion
$$\frac{3.45 \cdot 10^9}{5.3 \cdot 10^5}$$
wraith daggerBOT
Mothy
wraith daggerBOT
Mothy
ruby lion
and the 3.45/5.3
ruby lion
and that speed=distance divided by the time
u want to find time so it would be time = d/s
ruby lion
what is that dot
multiply
fervent sandal
oh
ruby lion
$$\frac{3.45}{5.3} \cdot $$
fervent sandal
now i get it
wraith daggerBOT
Mothy
ruby lion
was about to tytpe something up
fervent sandal
i thought you would times them
cedar kilnBOT
cedar kilnBOT
Available help channel!
uneven cloud
hi
uneven cloud
the question asks for x
i tried replacing 1 with log 10 and then log(10/x) and so on
but that did not work
tame wraith
use the log rule to make log x^2 to 2logx
now say
y = logx
and subtitute y instead
long mauve
Hi may i know how to do question a? What is meant by commutative matrices?
tawny niche
Check if A and B commute, i.e. if AB = BA
crimson sedge
wassup boys and gals
cedar kilnBOT
wassup boys and gals
crimson sedge
Let $(X,\Omega, \mu)$ be a $\alpha$-finite measure space. Consider the Hilbert space $H = L^2(X,\Omega, \mu) =: L^2(\mu)$. If $\phi \in L^{\infty}(\mu)$, define [
M_\phi : L^2 (\mu) \longrightarrow L^2(\mu) \textss{by} M_\phi f = \phi f]
How do I show that [
M_{\phi} \in \BB (H) \textss{and} \norm{M_\phi} = \norm{\phi}\infty
]
where $\norm{\phi}\infty$ is the $\mu$-essential supremum norm
gilded elm
bruh
crimson sedge
hi derpz
gilded elm
whats up
crimson sedge
just wanted to make sure
wraith daggerBOT
crimson sedge
But the linearity of M_\phi should be pretty obvious
do i just have to show that M_\phi is bounded then
and just
calculate its norm
wait wtf 
how do i proceed from there
gilded elm
a.e.?
gilded elm
bruh
sacred grail
gilded elm
well ive not seen a.e. being used ngl
gilded elm
hmm
cedar kilnBOT
@crimson sedge Has your question been resolved?
cedar kilnBOT
cedar kilnBOT
Available help channel!
cedar kilnBOT
<#903430334681608232>
old lantern
Can someone help me with this? I don't know how to find the complex conjugate for this
vagrant elbow
Rewrite the e^ix using Euler's Formula and then invert the signs on the complex parts
Or or
old lantern
maybe the professor planned this
vagrant elbow
$-i = e^{\frac{3\pi}{2} i}$
wraith daggerBOT
NEONPerseus
vagrant elbow
Oh
old lantern
turns out it's exactly the next lesson
vagrant elbow
You don't need it
vagrant elbow
Do you know how to represent a complex number in polar form?
cedar kilnBOT
cedar kilnBOT
Available help channel!
fringe mauve
How do i find a
cedar kilnBOT
How do i find a
slender jungle
hello
slender jungle
how would you do this wo
would you do
9
times by
32
divided*
I know how to do similaritys but not with the squares
cosmic steppe
Just compare the sides
The ratio between each pair of corresponding sides should be the same
Which they are
slender jungle
3:6
slender jungle
oh
cosmic steppe
So you literally just enlarge it by 2x
slender jungle
oh okay
thx :)
w
what about this sir
X would be 7.8
scale factor 1.3
Im looking for y
rustic siren
Im looking for y
pythagorean
cedar kilnBOT
@slender jungle Has your question been resolved?
halcyon patrol
Hi! Is there a specific formula to solve this?
cedar kilnBOT
Hi! Is there a specific formula to solve this?
harsh sky
vagrant elbow
$\vec{v_{AB}} = \vec{v_A} - \vec{v_B}$
The velocity of A wrt B is the velocity of A wrt the ground minus the velocity of B wrt the ground
wraith daggerBOT
NEONPerseus
halcyon patrol
The physics doesn't really matter! It's more that I'm not sure how to find | Va - Vb | from | Va | and | Vb | alone
vagrant elbow
What I recommend is you draw out a diagram and take components of the velocity vectors along the coordinate axes
cerulean sail
Note that they give you the norm and the directions ("southwest"/"northwest") - can expand out the dot product with
$$
|\mathbf{v}{B} - \mathbf{v}{A}|^{2}
$$
wraith daggerBOT
chartbit
cerulean sail
Damn you small tex 
halcyon patrol
I'm not really sure how to work with the dot product here...
Does the question imply that they're all at perfect 45 degree angles like so?
cerulean sail
Does the question imply that they're all at perfect 45 degree angles like so?
The angle between them is a right angle sure
$$
|\mathbf{v}{B} - \mathbf{v}{A}|^{2}
$$
wraith daggerBOT
chartbit
cerulean sail
Ah, hopefully no more 
Anyways, are you familiar with how to expand dot products, and that $|\mathbf{v}|^{2} = \mathbf{v} \cdot \mathbf{v}$?
wraith daggerBOT
chartbit
halcyon patrol
I know the second part, but I don't recall if I've expanded dot products before.
cerulean sail
Hmmm, have you seen something like $(\mathbf{a} + \mathbf{b}) \cdot \mathbf{c} = \mathbf{a}\cdot \mathbf{c} + \mathbf{b} \cdot \mathbf{c}$?
wraith daggerBOT
chartbit
halcyon patrol
ah, yes!
cerulean sail
Basically use something like that, on $|\mathbf{v}{B} - \mathbf{v}{A}|^{2} = (\mathbf{v}{B} - \mathbf{v}{A})\cdot (\mathbf{v}{B} - \mathbf{v}{A})$
wraith daggerBOT
chartbit
cerulean sail
It'll give you a very useful formula that will save you time later!
halcyon patrol
I'll try that
I'm not sure if I'm taking the right approach here...
setting Va = (a, b) and Vb = (c, d)
cerulean sail
setting Va = (a, b) and Vb = (c, d)
Basically you don't need to really consider the components of v_a and v_b here
cerulean sail
**chartbit**
The idea is to just expand this directly without considering them, like this:
$$
\begin{split}
|\mathbf{v}{B} - \mathbf{v}{A}|^{2} &= (\mathbf{v}{B} - \mathbf{v}{A})\cdot (\mathbf{v}{B} - \mathbf{v}{A}) \
&= \mathbf{v}{B} \cdot (\mathbf{v}{B} - \mathbf{v}{A}) - \mathbf{v}{A} \cdot (\mathbf{v}{B} - \mathbf{v}{A}) \
&= \mathbf{v}{B} \cdot \mathbf{v}{B} - \mathbf{v}{B} \cdot \mathbf{v}{A} - \mathbf{v}{A} \cdot \mathbf{v}{B} + \mathbf{v}{A} \cdot \mathbf{v}{A} \
\end{split}
$$
wraith daggerBOT
chartbit
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
cedar kilnBOT
@halcyon patrol Has your question been resolved?
cerulean sail
I don't even know, it seems to render properly 
figure out why it's complaining later
burnt oracle
Monoid is a category with one object. But what kind of object. For example, i have monoid (N, +). I guess, morphism are 1, 2,... and compisition of morhipsms k and m is (k+m). But what object must be on a category?
cunning monolith
A monoid is a category with a single object. Given a monoid (M,), one can construct a small category with only one object and whose morphisms are the elements of M. The composition of morphisms is given by the monoid operation.
burnt oracle
im trying to understand image...
cedar kilnBOT
@burnt oracle Has your question been resolved?
burnt oracle
Sorry, i cant understand image. But is it really matter what object i use for create category from monoid? Looks like i can choose any object. Is it right?
.close
deep sage
Guys I have a question, how would you analyze a multiple regression with some categorical variables as independents? So a combination of numerical and strings (nominal), without the use of dummy or ordinal variables
For example x1=15 x2=red and x3=Europe and y would be numerical too
(I do this analysis in python)
cedar kilnBOT
Guys I have a question, how would you analyze a multiple regression with some ca...
@deep sage Has your question been resolved?
cedar kilnBOT
@deep sage Has your question been resolved?
crimson sedge
and in the second question b) if i want to learn how to make x the subject do i need to practice it more of it?
crimson sedge
can you check my work out
crimson sedge
and in the second question b) if i want to learn how to make x the subject do i ...
this went up about
valid tendon
looks nice
cedar nexus
i nneed help with this question: prove this statement using the rules of inference. (p^(-(-pvq)))v(p^q)=p
vagrant elbow
()))()(()())()))))((()()()()()
cedar kilnBOT
@cedar nexus Has your question been resolved?
cedar nexus
what about this one: is the following arguement valid or invalid explain if x is an integer, then x is rational. if x is rational, then x is real. x is not real. therefore, x is not an integer. <@&286206848099549185>
i converted it into symbol form and determined that it was invalid, but i cant explain why
cursive drift
wraith daggerBOT
cedar nexus
i got p > q q >r -r therefore -p but is not in the valid arguements so is invalid
but idk which error it is, like is it inverse error or distributive error?
<@&286206848099549185> please
.close
torpid urchin
could someone verify my induction
agile osprey
Hello, I have a question about Span in linear algebra that I have been stuck on for hours :/, I am not sure how to find if a vector belongs to span(u,v). w,u,v are all vectors. but the catch is i have a missing variable I have to find. For example w = (23,-19,z) and u = (-3,-3,-4) and v = (16,-5,2) if w belongs to span (u,v) what is z. I have started by making a augemented matrix with w as the right most column and reduced it to the point where the bottom right is -55z+1318 but I am not sure what to do now? so my matrice looks like [(1,-7,-z+19),(0,1,-10z+240),(0,0,-55z+1318)]?
agile osprey
I have tried turning that into a system of linear equations but not sure where to go from there if that is the correct way. For example I did 1-7 = -z+19 and so on
mighty drift
I'd have solved for the unique combination that gets the first 2 coordinates right. Then look at what the 3rd coordinate is
that way the problem is reduced to a 2D problem
agile osprey
how would i solve for the unique combination for the first two coordinates?
mighty drift
that's just a system of 2 equations. If you're talking about augmented matrices, you should know how to do that
spoiler answer: ||a bit of looking around shows that 3u + 2v works||
agile osprey
I am lost. So do you mean solving where we do x1 -7x2 = -z +19 and 0x1 + x2 = -10z + 240? (1 and 2 after x should be subscript)
mighty drift
Hello, I have a question about Span in linear algebra that I have been stuck on ...
the last line already yields 55z = 1318. Which means you made a mistake somewhere since z is supposed to be an integer
but if you did solve it properly like that it would be correct anyways
I just offered a smarter method that requires you to solve a 2x2 system rather than a 3x3
agile osprey
ohhh i see. I had never done that before so the way I am doing originaly should work if i reduce correctly?
mighty drift
yes
vapid lotus
How could you rewrite the equation a^(b+cz) such that z has no coefficient
small dust
How could you rewrite the equation a^(b+cz) such that z has no coefficient
u can divide by c to all the inside terms
but then u get that c can't be 0, if that's not an issue then do it
red pumice
$a^{b+cz} = a^b a^{cz} = a^b (a^c)^z$
wraith daggerBOT
heavy
red pumice
classic
small dust
fr
small dust
what do you find hard about that
vapid lotus
It’s hard to write that as a program
vapid lotus
Well when I tell you z isn’t a real number it will be
vapid lotus
lemme see ur code
I got code only for a^(b+z)
small dust
Well when I tell you z isn’t a real number it will be
that's still not an issue
small dust
I got code only for a^(b+z)
what langueage
vapid lotus
python
small dust
Also not complex
if it isn't real or complex, what do u want it to be
vapid lotus
z is a constant that represents 1/0
I will not answer any questions about 1/0 and why I’m doing math with it
small dust
well that just sounds like a disaster
vapid lotus
Just think of it like an extra dimension just like i
small dust
usually division by 0 breaks math pretty hard
that doesn't quite make sense though
what grade are you in
or like level of math
small dust
,w (1/0)^0
wraith daggerBOT
vapid lotus
But I don’t see how the value of z is relevant
small dust
,w (1/0)*0
wraith daggerBOT
vapid lotus
Just treat z as an extra dimension
small dust
what level of maths are u in
vapid lotus
That’s not relevant
small dust
I'm just curious
vapid lotus
Just trust that z works
small dust
is this research or just pure dedication and ambition
that's not really how math works
I'd need a proof
vapid lotus
is this research or just pure dedication and ambition
Both
vapid lotus
Not professionally
small dust
Ah, so just on ur own
jaunty mural
what in gods name is going on here 
small dust
what in gods name is going on here <:sully:651816820122189834>
I'm being enlightened to new math
it's interesting
vapid lotus
I at some point I plan at documenting how z works with all operations
None the less the fact that z is 1/0 is irrelevant to what I’m doing
dusk finch
lmao
small dust
this feels like
dusk finch
z=1/0
small dust
very interesting
dusk finch
I mean I was experimenting with this when I was younger
only thing that I accepted was sqrt(-1)
small dust
yeah it's definately cool
dusk finch
and later I found out it actually exists
jaunty mural
small dust
I can't raelly understand that there is a use for division by 0 that makes sense
vapid lotus
But to go back to the question I asked
small dust
also wym by dimension
vapid lotus
Is there any other way of doing that
small dust
u said another dimension
dusk finch
Is it true that $z^{2}=z$
wraith daggerBOT
MathIsAlwaysRight
dusk finch
And $z^{-1}=0$
wraith daggerBOT
MathIsAlwaysRight
vapid lotus
Well the reciprocal of z is a gray area as of now
small dust
lmk if u make progress
vapid lotus
Now can we get back to my original question
dusk finch
shhh
vapid lotus
That’s why z^-1 is a gray area
dusk finch
The first one I asked
vapid lotus
It might not be 0
wraith daggerBOT
Requested by Jukelyn#9848
vapid lotus
You can use z to break alot of things in cool ways
small dust
interesitng
vapid lotus
But still is there any other way to rewrite a^(b+cz)
vapid lotus
what do u want it to be in the form of
The output?
small dust
yeah and the rest would be just moving these combinations to the denominator with a negated exponent
vapid lotus
In form k+vz (with k and v being real numbers)
small dust
u can take log base a of that and get b+cz
wraith daggerBOT
Jukelyn
vapid lotus
Yea but how would that help solve a^(b+cz)
small dust
well u want b+cz but don't wannt have it to the exponent of some base, so just takeing the log of that base will evaluate to the exponent
for example say a^(b+cz) = 4
then you get this:
$$\log_a{(a^{b+cz})} = b+cz = \log_a{(4)}$$
wraith daggerBOT
Jukelyn
small dust
idk what a b or c is so that's where we stop
vapid lotus
Let’s use the example 3^(2+5z)
small dust
okay then $$\log_3{(3^{2+5z})} = 2+5z$$
wraith daggerBOT
Jukelyn
small dust
we're not solving anything here though
if u wrote something like 3^(2+5z) = x then we'd get
$$\log_3{(3^{2+5z})} = 2+5z = \log_3(x)$$
wraith daggerBOT
Jukelyn
vapid lotus
if u wrote something like 3^(2+5z) = x then we'd get
Even if I knew what x was that wouldn’t help
Because I would just get something like log3(x+yz)
vapid lotus
Wait
vapid lotus
you'd get something in this form
Isn’t x just 2+5z?
vapid lotus
log base 3 of x is 2+5z
And how do I solve for x?
small dust
there isn't much to just magically take something out of an exponent
vapid lotus
I don’t have a problem with z being in a exponent
small dust
**heavy**
u either re-write is as one of these or a fraction with negated exponents, or you'd take a log
vapid lotus
I have a problem with z having a coefficient
vapid lotus
and the only form he gave that works, I have no idea how to code
small dust
lemme see ur code
vapid lotus
I only have code for a^(b+z)
small dust
okay, i'll code it myself then
watch this
...
num = a ** (b + cz)
changed_num = (a ** b) * ((a ** c) ** z)
Ok but then I need to code (a**c)**z
small dust
yeah
you can't do that in many languages
ur not gonna get any kind of math out of z, you're going to get errors
vapid lotus
Yes but I can tell it how to solve that
small dust
then don't assign z
vapid lotus
a^z=1+(a-1)z
small dust
okay then make a funciton that does that and call it whenever u need it to do that
vapid lotus
Bruh
small dust
def expZ(base):
return 1 + (base - 1) * z
(a ** b) * expZ((a ** c))
why not
small dust
yeah
small dust
the coeff of z is 1
vapid lotus
When?
small dust
you are still doing something*z
what does multiplication by z maen
mean*
like how have u defined it
vapid lotus
Yea but you have 1+(base-1)*z
small dust
how is multiplication by z defined by ur system
vapid lotus
here the coefficient is (base-1)
small dust
here the coefficient is (base-1)
yeah
vapid lotus
so you just need to set base-1 as its own variable
Because you can’t directly store anything * z in python
small dust
okay
vapid lotus
i*z=q but this one is less relevant
small dust
you can't raelly code something like this
vapid lotus
You probably can
small dust
show
vapid lotus
outz=a-1
out=a**b
outz=outz*out
print(out," + ",outz,"z",sep='')```That’s for a^(b+z)
small dust
so ur just using strings to represent it
vapid lotus
For the output, yea
small dust
use printf, it'd look nicer and a bit easier to read
but anyways
hmm
then for exponent of z do this
small dust
printf("{a ** b} * {(a ** c)}^z")
That’s not simplified
small dust
yes it is
small dust
how so
vapid lotus
a^z=1+(a-1)z
small dust
a^z=1+(a-1)z
can u show me how this is true btw?
small dust
it doesn't hold for reals tho
$$2^3 = 8 \neq 1+(2-1)3=4$$
wraith daggerBOT
Jukelyn
small dust
,w taylor expand a^x
small dust
I think they're trolling u
vapid lotus
```python
printf("{a ** b} * 1 + {(a ** c) - 1}z")
```
Almost simplified!
vapid lotus
You then need to do the multiplication
small dust
idk how to do multiplication with z
small dust
that doens't help
vapid lotus
What’s the problem?
small dust
I have the RHS form alraedy
but u just sayinf 2*z=2z doesn't make sense
I was asking about what hte actual value would be
vapid lotus
That is the actual value
small dust
bc 2*z to 2z isn't a simplification
vapid lotus
Cuz
small dust
ogh I see
ohh*
so then what I wrote is simplified
u can't simplify further
give me an example and then tell me what u expect the output to be
small dust
nope
small dust
oh python has f"" not printf("")
mb
move the f to the inside
print(f"{a ** b} * 1 + {(a ** c) - 1}z")
mb, I'm used to Java recently
vapid lotus
Ahhhh
See
You give the answer as 9*1+8z
First of all the answer would be 9*(1+8z)
small dust
oh true, I should have wrote that when I changed it earlier
vapid lotus
```py
print(f"{a ** b} + {(a ** b) * ((a ** c) - 1)}z")
```
I assume is has to do something with the fact you put {{a**b}
Or no?
dire geode
I think they're trolling u
oh the irony
small dust
change to ()
small dust
oh the irony
👀
dire geode
okay sorry for interrupting
small dust
xD
jaunty mural
vapid lotus
change to ()
Change what part?
small dust
Change what part?
I changed it, juist copy and paste again
vapid lotus
Ah ok
Oh my
It actually works
Assuming the math is correct
I’ll check that at home
small dust
np xd
cosmic steppe
1/0 = N
1 = N(0)
1 = 0
vapid lotus
1/0 = N
1 = N(0)
1 = 0
What
cedar kilnBOT
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timber turtle
can someone please elp with question 2a?
cedar kilnBOT
can someone please elp with question 2a?
red pumice
t formulae?
cedar kilnBOT
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timber turtle
.close
coarse plover
hey i am confused on Sin(90)=?
cedar kilnBOT
hey i am confused on Sin(90)=?
coarse plover
Sin(90)=?
jaunty mural
you know what sin is?
coarse plover
a little
jaunty mural
in terms of right angled triangle
coarse plover
Yea I know that
jaunty mural
yes - it is?
coarse plover
I think it is 1
wraith daggerBOT
jaunty mural
scarlet garnet
could also know trigonometric functions from a circle
coarse plover
yea
jaunty mural
https://i.imgur.com/55f4JfX.png
sin x = what over what?
if u dont remember just say
coarse plover
I frogot
jaunty mural
coarse plover
Ohhh
jaunty mural
opposite over hypotenuse
coarse plover
ok
jaunty mural
so b / c
Ok, so back to your question
one way to answer it is to consider a triangle where x is close to 90
coarse plover
ok
coarse plover
ok
jaunty mural
Now do you see what sin x must be close to
coarse plover
yea
jaunty mural
its just under 1 right?
coarse plover
yup
jaunty mural
As x gets larger and larger so its almost a right angle
that sin value will approach 1
so thats one way to see sin 90 = 1
You can use a similar argument for cos 90 - try it.
jaunty mural
yeah
so the process looks like this
tan 90 is a bit harder (theres no answer actually) 
do u see why?
coarse plover
so tan= a/b
coarse plover
yea
jaunty mural
So it turns out tan x gets massive as you increase x and get close to 90 degrees
you can check tan 89.999
and see its very big
because you divide by a very small number
coarse plover
that makes a bit more sense
dire geode
.close
waxen crater
y=5x+7
waxen crater
to write down the gradient of this line is it 5?
dire geode
yes
waxen crater
just look at mx to get the answer?
cedar kilnBOT
cedar kilnBOT
Available help channel!
proven ermine
how to write the following in Matrix notation:
$$\frac{1}{2n(n-1)} \sum_{i=1}^{n}\sum_{j=1}^{n}(x_i-x_j)^2$$
where $X=(x_1,x_2,...,x_n)$
and $x_i,\ x_j\in X$
wraith daggerBOT
Kedi
cedar kilnBOT
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proven ermine
<@&286206848099549185>
cedar kilnBOT
@proven ermine Has your question been resolved?
proven ermine
<@&286206848099549185>
cedar kilnBOT
@proven ermine Has your question been resolved?
proven ermine
<@&286206848099549185>
proven ermine
<@&286206848099549185>
nimble veldt
is your questiion a question how to do something in latex?
proven ermine
is your questiion a question how to do something in latex?
no I want to write the formel in Matrix notation
worldly iron
Are you here?
@proven ermine
The question simply asks you to write the matrix notation for a nxn matrix
cedar kilnBOT
@proven ermine Has your question been resolved?
proven ermine
The question simply asks you to write the matrix notation for a nxn matrix
i am puzzled, do u know how to do it?
worldly iron
i am puzzled, do u know how to do it?
desecrate this wiki article
and extract the answer
cedar kilnBOT
@proven ermine Has your question been resolved?
whole lake
@proven ermine where are u from
cedar kilnBOT
@proven ermine Has your question been resolved?
cedar kilnBOT
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storm mantle
I can't understand it, pls can someone explain it?
cedar kilnBOT
I can't understand it, pls can someone explain it?
lapis meadow
how so I calculate the surface area of a hexagonal prism with a cylindrical hole?
lapis meadow
like what would be the formula for that shape
violet flume
probably just one less the other
lapis meadow
wdym
like i really don't get how to do surface area and volume
also thanks for da help
my teach keeps explaining it in like confusioning ways
livid hound
add up the area of the individual faces
livid hound
?
lapis meadow
what do I do after adding up the individual faces
livid hound
adding up the areas of the individual faces, if done properly will give you the total surface area
lapis meadow
ok thanks man
livid hound
and don't ping helpers before 15 minutes
cedar kilnBOT
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Available help channel!
crimson sedge
im doing proofs right now
cedar kilnBOT
im doing proofs right now
crimson sedge
the gcd of this is always 1 right
and its just desmos bugging out
or is my proof wrong
because a power of 2 could never share a common factor with 3
small dust
is there a condition where a is not b?
crimson sedge
no
crimson sedge
but how
small dust
holon, sorry my brain turned off for a sec, u legit just posted it at 12 and 17
gimme a sec
can I see ur proof
crimson sedge
oh lord
i cant do that
but i cant see how they would share a common factor
because 2^17 is 2 * 2 * 2 * 2... * 2
small dust
ur proof is wrong
crimson sedge
and 3 ^ 17 is just 3 * 3 * 3 * 3 ....
small dust
,calc 2 *17
wraith daggerBOT
Result:
34
Result:
1.7179869184e+10
,calc gcd(2^34, 3^34)
wraith daggerBOT
Result:
8
crimson sedge
🙏
crimson sedge
L
cedar kilnBOT
cedar kilnBOT
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crimson sedge
may i get some help on the values of z
cedar kilnBOT
may i get some help on the values of z
@crimson sedge Has your question been resolved?
small dust
Show ur work so far @crimson sedge
cedar kilnBOT
dire geode
Show ur work so far <@456226577798135808>
your words are magic
cedar kilnBOT
Available help channel!
vocal raptor
Abc is 1/4 of circle. AD radius = 4 = AB = AC. DE =2√3. I need to find DC circle size. (I know answer if that helps)
livid hound
is that the exact wording of the question?
because DE isn't relevant to what's being asked
you have the radius and that's pretty much all you need
if you know how to find the area of a full circle given the radius,
its not a huge leap getting the area of a quarter
crimson sedge
by "DC circle size" I'm assuminig you are trynna find the area of sector DC?