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#help-33
still temple
Represent the following numbers as being members of set L: -15, 1, 7, 3, -8, 7, 0,
12, 6, 12
marsh citrusBOT
Represent the following numbers as being members of set L: -15, 1, 7, 3, -8, 7, ...
still temple
I wasn't here at the lesson I was learning this at school so I don't get how to answer this
hazy shard
Is there anything else to the question?
stoic saddle
{-15, 1, 7, 3, -8, 0, 12, 6}
hazy shard
{-15, -8, 0, 1, 3, 6, 7, 12}∈L
hazy shard
{-15, -8, 0, 1, 3, 6, 7, 12}∈L
Ah shoot what did I do wrong
still temple
oh,,
hazy shard
you named an entire set of numbers as an element of L
Ah
stoic saddle
@still temple i just listed all your numbers without duplicates and put them in curly braces lmao
hazy shard
So what, you just write a set and assume the values in it are part of set L?
still temple
<@456226577798135808> i just listed all your numbers without duplicates and put ...
ohhhh
stoic saddle
well the problem statement is a little unclear as written
maybe it had to be translated from a different language so we will never know
hazy shard
I assumed L was a set already given and you had to write that the numbers given were part of it
crystal lintel
maybe {-15, -8, 0, 1, 3, 6, 7, 12} = L
still temple
Do I close this after finished..?
hazy shard
?
royal flicker
Do I close this after finished..?
Yup
crystal lintel
I assumed L was a set already given and you had to write that the numbers given ...
maybe ${-15, -8, 0, 1, 3, 6, 7, 12}\subseteq L$ if you wanted to say that?
elfin berryBOT
layla💜
royal flicker
how should I close this..
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hazy shard
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marsh citrusBOT
still temple
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marsh citrusBOT
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livid maple
no
livid maple
idk where to start
stoic saddle
okay well let's see
what feature can a rational function have at most one of?
...okay, there are more possible answers to this question than i intended, but maybe thinking about this will spark some thought processes in your head.
from this, think about how many functions you need in order to satisfy your constraints.
marsh citrusBOT
@livid maple Has your question been resolved?
cold sequoia
Guys really basic question. It's a graphing question
f(-1) = -2
f(1)= 2
f(0)=0
lim(x -> infinity) of f(x) =1
lim(x -> negative infinity) of f(x) = -1
marsh citrusBOT
Guys really basic question. It's a graphing question
f(-1) = -2
f(1)= 2
f(0)=0
...
cold sequoia
Like I got all the points and have a general idea but for f(0)=0, would I have to connect those two other graphs or would it just be like a floating point
crystal lintel
I'd probably connect them
cold sequoia
yeah but like how
crystal lintel
it's not very clear exactly
cold sequoia
Yeah it really aint
crystal lintel
straight lines or curvy lines or whatever might be fine
cold sequoia
oh
steep garden
Hey guys I have three questions that I need help in
I was wondering if anyone can help me?
cold sequoia
uh you should ask in a available chat
crystal lintel
ya, see #❓how-to-get-help 🙂
steep garden
Ah thx
cold sequoia
so yeah, it's literally can be anything -_- I'm overthinking it again
yeah it's 11 at night. Thanks layla ❤️
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marsh citrusBOT
crystal lintel
np ^-^
marsh citrusBOT
Available help channel!
warm obsidian
marsh citrusBOT
marsh citrusBOT
@warm obsidian Has your question been resolved?
warm obsidian
<@&286206848099549185>
marsh citrusBOT
@warm obsidian Has your question been resolved?
marsh citrusBOT
@warm obsidian Has your question been resolved?
wooden oriole
compare with $\sum_{k=1}^{\infty}\frac{1}{k}$
elfin berryBOT
秋水
wooden oriole
marsh citrusBOT
marsh citrusBOT
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sly plume
Have I multipled the matrices correctly?
marsh citrusBOT
Have I multipled the matrices correctly?
sly plume
The top right corner should be -4+y-x
sly plume
?
nimble canyon
its a 3 x 2 matrix into2 x 3 matric
so it should be a 3 x 3 matrix as an answer
lol
spring tide
Isn't it supposed to be a 3x3 matrix?
nimble canyon
Isn't it supposed to be a 3x3 matrix?
ye
sly plume
so what did i miss
nimble canyon
a whole column and row
sly plume
Which multiplication did I miss? @nimble canyon
spring tide
You go first row first column first row second column first row third column
nimble canyon
then multiply corresponding element to each other
nimble canyon
You go first row first column first row second column first row third column
or that
sly plume
Ok
sly plume
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fossil crown
Hello, I found the two demarcation but i don't know how to continue
marsh citrusBOT
Hello, I found the two demarcation but i don't know how to continue
fossil crown
I know that i should find this equation but I don't know how to find it
marsh citrusBOT
@fossil crown Has your question been resolved?
fossil crown
<@&286206848099549185>
marsh citrusBOT
@fossil crown Has your question been resolved?
fossil crown
<@&286206848099549185>
jolly saffron
Is this supposed to be geometric progression?
Now that I look closer… it appears that the comment was a little late to the party.
fossil crown
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wanton pecan
How can I solve this problem using the method of characteristics?
marsh citrusBOT
How can I solve this problem using the method of characteristics?
wanton pecan
Would applying d'Alembert's formula be considered a solution "by the method of characteristics?" If so, how would I account for the boundary?
marsh citrusBOT
@wanton pecan Has your question been resolved?
viral pilot
is there an official name for “a quad that has no para lines”
marsh citrusBOT
is there an official name for “a quad that has no para lines”
worthy trellis
not really
viral pilot
i see
thats what it seems like too
even though some people suggest that a trapezium is one
worthy trellis
that is not atrapezium
gleaming lance
depends, there are trapezoids that have no parallel sides
worthy trellis
and trapezium has one pair of parallel sides
viral pilot
depends, there are trapezoids that have no parallel sides
i see, what are they called? surely there are ways to differentiate them from the other trapeziums that have at least one pair of parallel sides
gleaming lance
i dont think there is a specific term for that
upper briar
fun talk
viral pilot
oh hey again
this is the person that got what i meant last time, but shes also in the same boat as me
we still dunno how to differentiate it lol
viral pilot
i dont think there is a specific term for that
hmmm, there logically should be wouldnt u agree?
since theres room for discrepancy
gleaming lance
well if yyou consider kite a shape, then maybe you can call it a kite lol
viral pilot
and there are already ways to differentiate other higher numbers of parallel sides
gleaming lance
it is insignificant enough for it to not have a name
viral pilot
like parallelogram for two, and the supposed trapezium for at least one
viral pilot
well if yyou consider kite a shape, then maybe you can call it a kite lol
lmaoo
yeah true that, but kites are special tho
since they have two pairs of equal lengths
while not all quads with zero parallel sides have pairs of equal lengths
so a kite wouldnt work
plus the other properties
like the circle thing
gosh
worthy trellis
why do you think there has to be a name for it?
viral pilot
why do you think there has to be a name for it?
because its a specific property, one thats already earnt other shapes their names
like parallelograms
theyre quads with two pairs of parallel sides
the next down is one pair, which is apparently a trapezium
but then theres nothing for zero pairs
logic whomst?
darn the greeks or whoever did geometry
im no experty, but it seems logical that there should be a name for this
upper briar
well
thrs a lot of stuff with no sepcific names assigned to them
as u can easily write it in terms of other stuff already known
an example would be the set of all ints from 2 onwards
we just use like $\mathbb{Z}_{\ge 2}$
elfin berryBOT
viral pilot
yeah true, could u possibly lead the way? im a noob when it comes to this stuff
upper briar
or similar, thrs a lot of ways to
viral pilot
i see
so like
just find something that shares this kind of property and mix it with quad, or if theres none just translate it into latin and add the suffix -ium to it or smthn?
lmao
i feel like a very dumb scientist / mathmentician pioneering in very ingenius things that humanity has completely overlooked for thousands of years
wooo…
depressing ngl
worthy trellis
just find something that shares this kind of property and mix it with quad, or i...
maybe you could come up with your own name for this if it makes you feel any better lmao
viral pilot
maybe you could come up with your own name for this if it makes you feel any bet...
lmao 😭
sigh is there really no better alternative other than going to sleep at this point?
owndjqjdnkakamda
im kinda interested in this as well since i got distracted with the quadratic equation
worthy trellis
owndjqjdnkakamda
"okay, construct a owndjqjdnkakamda"
viral pilot
yknow, calculus stuff for finding the area
viral pilot
"okay, construct a owndjqjdnkakamda"
😂💀
id be damned if we really called it that
but then again, its not too far off from the likes of those scientists that coined the term “spaghettification”
ahahahaha
worthy trellis
lol
viral pilot
im sorry, i think my brain aint normal at 4am
i guess ill revisit this problem another day, or just do as u say:
just make up a term for it xd
worthy trellis
but then again, its not too far off from the likes of those scientists that coin...
at least it gives you an idea of what that is, owndjqjdnkakamda on the other hand XD
viral pilot
at least it gives you an idea of what that is, owndjqjdnkakamda on the other han...
you place too high of expectations on my interpretation of big words
lmao yeah fine i concede
true XD
aight have a good one mate, thanks for the laughs
worthy trellis
good day to you
agile yoke
Hello Im repeating some stuff about sets. what does "to the power of C mean"
tight furnace
complement
agile yoke
thanks
tight furnace
np
agile yoke
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deft apex
marsh citrusBOT
deft apex
is this just asking for the x coord of the maxima and minima of the y curve?
still temple
Critical points, I guess. $f''(x)=0$.
elfin berryBOT
3317
deft apex
yeah
thats what it is asking right
wait
isnt it just a single derivative
and then where it is 0
cus its a trig function
deft apex
alr ez clap
just making sure thats what the horizontal stuff is
wasnt too sure
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marsh citrusBOT
deft apex
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marsh citrusBOT
✅
deft apex
I have no clue how to format this correctly
oh I forgot the fucking minimum
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subtle pawn
it is right statement right?
marsh citrusBOT
it is right statement right?
subtle pawn
and does anyone know how can i write this kind of statements in wolfram🦆
devout mauve
,rotate
elfin berryBOT
sage heath
whole number 
subtle pawn
what exactly is w supposed to be?
whole numbers
devout mauve
usually we use Z for that
subtle pawn
i mean i think all integers work even negative but i don't need them 🦆
subtle pawn
usually we use Z for that
Z is for integers not whole numbers
devout mauve
in what world are integers and whole numbers not the same thing
ok nvm just googled. weird stuff
so you want to say that $i^{4x}=1$ for all $x\in w$
that's it?
elfin berryBOT
Denascite
subtle pawn
in what world are integers and whole numbers not the same thing
In Wikipedia
{0,1,2,3,4,5…} = whole numbers
{…-5,-4,-3,-2,-1,0,1,2,3,4,5…} = integers
devout mauve
subtle pawn
that's it?
Yup
devout mauve
if you are gonna quote wikipedia, at least quote everything
subtle pawn
So i^4x = 1 as long as x is an integer
what about
i^4x+n = i^n
devout mauve
also correct
marsh peak
Sure
subtle pawn
i^4x+n = i^4x×i^n = 1×i^n?
devout mauve
well there is a way
but it's not nice
not sure why you wanna write these statements in wolfram
or do you just mean writing "i^(4x)=1" and wolfram solving to show you x in Z
marsh citrusBOT
@subtle pawn Has your question been resolved?
subtle pawn
not sure why you wanna write these statements in wolfram
It's ez way to know if somethin is right
raven wasp
What is the weight of a bowling ball with a diameter of 12 inches given the fact that one with a diameter of 8 inches has a weight of 10 pounds?\
marsh citrusBOT
```What is the weight of a bowling ball with a diameter of 12 inches given the f...
raven wasp
anyone wanna help in this?
eternal tundra
we do this by using the density
assuming they share the same density
for a ball we have:
$V=\frac{4}{3} \pi r^{3}$
elfin berryBOT
~Martin
eternal tundra
where V is the Volume
density is defined as mass/volume
diameter=8 => radius=4
,calc (4/3)pi*3^3
it weighs 10 pounds
so we get a density of
,calc 10/((4/3)pi*6^3)
elfin berryBOT
Result:
0.011052426603604
to get the mass of the bigger ball we first need the volume
elfin berryBOT
Result:
113.09733552923
sry i got some values wrong
raven wasp
(12/8)^3 * 10
you put it to the power 3 since r is cubed right?
eternal tundra
,calc (4/3)pi*4^3
elfin berryBOT
Result:
268.08257310633
this is the volume
mass is 10 pounds
density=mass/volume
,calc 10/((4/3)pi*4^3)
elfin berryBOT
Result:
0.037301939787163
this is our density
for the bigger ball we first get the volume
,calc (4/3)pi*6^3
elfin berryBOT
Result:
904.77868423386
density=mass/volume
therefore
mass=density*volume
to get an exact answer, i wont use the result from before but rather the formula used
raven wasp
you put it to the power 3 since r is cubed right?
@worn nimbus
eternal tundra
,calc (10/((4/3)pi4^3))((4/3)pi*6^3)
elfin berryBOT
Result:
33.75
and there we have our mass
otherwise we could also have used the fact that mass and volume are proportional
raven wasp
why did you cube it?
eternal tundra
that is just the formula for a volume of a sphere
eternal tundra
yes, that's correct
proportionality also works
i must admit this was a bit overcomplicated haha, but i guess it works as well
worn nimbus
why did you cube it?
suppose you have a cube with sidelength one
then now suppose you have a cube with sidelength 2
how much more volume does the cube with sidelength 2 have
this doesnt justy hold for cubes
its for all shapes
raven wasp
how much more volume does the cube with sidelength 2 have
times 2
worn nimbus
np
raven wasp
we then multiply it by 10 since we are trying to find the weight of 12 inch bowling ball compared to the 8 inch one
raven wasp
for these type of problems we would do big to small for ratio right?
worn nimbus
exactly
but beware of what ratio you start with
suppose you start with the ratio of areas
then you wouldnt cube that ratio to find the ratio of volumes
usually though the ratio of lengths is where you start
raven wasp
ic
raven wasp
then you wouldnt cube that ratio to find the ratio of volumes
what would we do then?
worn nimbus
well you have 2 dimensional ratio
so to find the 3 dimensional ratio we would do (2d ratio)^1.5 since 1.5 * 2 = 3
worn nimbus
so square it?
no then you would get the 4 dimensional ratio
raven wasp
so to find the 3 dimensional ratio we would do (2d ratio)^1.5 since 1.5 * 2 = 3
we care about the 3
since we are dealing with 3d ratio right?
worn nimbus
well if you want the 3d ratio you would do that yes
perhaps i overcomplicated it
but i think you understand
raven wasp
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molten venture
marsh citrusBOT
molten venture
i am having trouble with this
i know that its III
i am having trouble figuring out whether its I or II
marsh citrusBOT
@molten venture Has your question been resolved?
molten venture
I understand that it becomes ln(n+1) - ln(n)
however the only value remained is ln(1)
still temple
ln(1)+ln(n+1), bc there will be always a last term that doesn't cancel out
marsh citrusBOT
@molten venture Has your question been resolved?
viral pilot
ngl i prefer this over forums
marsh citrusBOT
ngl i prefer this over forums
viral pilot
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marsh citrusBOT
main idol
Did you feel the need to open a help channel just to say this. But I agree
absolutely anyone who has any say in forums/help channels won't read it here
hidden plaza
absolutely anyone who has any say in forums/help channels won't read it here
Wdym?
main idol
i imagine at some point one of these will go away
marsh citrusBOT
Available help channel!
trail quiver
How do I graph a relation in which the "y" is an absolute value. For example, how would I graph |y|=2x^2
marsh citrusBOT
How do I graph a relation in which the "y" is an absolute value. For example, ho...
nova totem
You would graph when y = 2x^2 and -y = 2x^3 simultaneously
Good job Pure
I saw that
hidden plaza
trim matrix
marsh citrusBOT
trim matrix
And the question
trim matrix
0,-4
nova totem
Nope
nova totem
And the question
Look at the information above
It specifically gives you the x-value of the global minimum
nova totem
That's the minimum as a point, yes
Now, if the equation has the minimum at (3, -4) and is a quadratic, then two things:
- Is the parabola concave (opening) up or down?
- What is the vertex?
nova totem
its opening down
Would that make sense
Think about it
Yes the vertex is (3, -4)
But if it's opening down
Yeah no that is not a minimum
This question essentially is checking if you understand parabolic behavior
The vertex is a minimum when the parabola is opening up
The vertex is a maximum when the parabola is opening down
If needed, draw a diagram
But it physically evinces itself
marsh citrusBOT
@trim matrix Has your question been resolved?
trim matrix
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marsh citrusBOT
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languid harness
Can someone explain this graph to me ?
marsh citrusBOT
Can someone explain this graph to me ?
languid harness
How is it going in the negative side,as:
Cos(-x) = cos(x)
acoustic cosmos
How is it going in the negative side,as:
Cos(-x) = cos(x)
cos (2npi + x) = cos (x)
for all n in Z+
languid harness
cos (2npi + x) = cos (x)
that still lies in the first quadrant right ??
if i take n = 1
cos(2pi + x) = cos(x)
and the value is +ve
acoustic cosmos
that still lies in the first quadrant right ??
so cos -90 = cos 270
does that make sense to you
wait did you learn radians yet
languid harness
so cos -90 = cos 270
but we can write cos -90 as -cos90 right ?
acoustic cosmos
but we can write cos -90 as -cos90 right ?
not sure
languid harness
bruh
acoustic cosmos
don't think so
languid harness
isn't cos(-x) = cos(x) ?
languid harness
so cosx is positive
yes so how is the graph going in the 2nd and 3rd quads ?
languid harness
for second quadrant cosx = cos-x
ok going by that too
cox(-x) = cos(x) which again is +ve 💀
languid harness
what
acoustic cosmos
take this
languid harness
take what ??
acoustic cosmos
proved
marsh citrusBOT
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rain wyvern
marsh citrusBOT
glacial hedge
for iv, how is there no 0 polynomial?
0 doesn't verify 0(2) = 1. So it's not in Q. Therefore Q isn't a VP
rain wyvern
sorry i think i have trouble understanding what a 0 polynomial is then
glacial hedge
The constant polynomial equal to 0
It is usual to associate/identify constant polynomials to their value
rain wyvern
so there should be a polynomial in every subspace of the set of polynomials where every output is 0?
and because 0(2) != 0 then this 0 polynomial doesnt exist?
glacial hedge
A subspace is a vector space, which is a group. It must therefore contain the neutral element, which is 0. Therefore if a set doesn't contain 0 it isn't a VP
glacial hedge
and because 0(2) != 0 then this 0 polynomial doesnt exist?
The 0 polynomial does exist. It just isn't in Q. These are 2 very different statements
rain wyvern
nvm it just wouldnt be in the subspace
rain wyvern
The 0 polynomial does exist. It just isn't in Q. These are 2 very different stat...
would it be correct in saying that this 0 polynomial doesnt exist in Q?
rain wyvern
0 doesn't verify 0(2) = 1. So it's not in Q. Therefore Q isn't a VP
can you go over how you input a number into a constant number
glacial hedge
Is not in. Doesn't exist in a set is something we don't say
Because something either exists or it doesn't. We don't want that property to depend on a certain set
rain wyvern
like if 0 polynomial is a constant how would you input a number into it
glacial hedge
can you go over how you input a number into a constant number
As I said, we associate constant polynomials with their values (and polynomials with their polynomial applications, but that's another topic). So when I wrote 0(2) I mean (x -> 0)(2), which is a (polynomial) function evaluated at 2
cloud kettle
can you go over how you input a number into a constant number
5 into (x)^0 I can input any real value of x here, for example
languid harness
How do I proceed :/ ?
marsh citrusBOT
How do I proceed :/ ?
vestal forge
could you post the whole question?
vestal forge
what i meant is the multiple choices
vestal forge
alright, and what have you tried?
vestal forge
ok, so I suppose limits is available to us?
if not, you can brute force it by just solving for y in terms of x
and then find the domain from there
languid harness
ok, so I suppose limits is available to us?
Limits available as in ? 👀
This is the entire ques
vestal forge
as in, is limit available as a tool for us to use?
languid harness
as in, is limit available as a tool for us to use?
Yea u can use whatever u want as long as u r getting the ans
Preferably something which is quick
vestal forge
actually, there is something quicker than that, nvm then
right, so let us rewrite the constraint as 2^y=2-2^x
languid harness
Pls tell 😈
vestal forge
this is pretty obvious
languid harness
Yep it sure is
vestal forge
now, since 2^y is strictly positive, this must means that 2-2^x>0
do you follow with this statement?
languid harness
now, since 2^y is strictly positive, this must means that 2-2^x>0
How did u assume that y is always positive 👀?
vestal forge
i did not assume that y is always positive, I stated that 2^y is always positive
y can be negative, 0 or positive
but 2^y is always positive
this is just the property of exponentiation
languid harness
Oook got that
vestal forge
right, so it must mean that in order for the equation 2^y=2-2^x to be true for some arbitrary x, then it must mean that 2-2^x>0
for example, take x=2, then 2-2^2=-2, but 2^y=-2 has no real solutions for y
so do you have any question at this point?
languid harness
for example, take x=2, then 2-2^2=-2, but 2^y=-2 has no real solutions for y
What do u exactly mean by real solution of y ??
vestal forge
can you find a value for y such that 2^y=-2?
vestal forge
yes, there is no real values of y such that 2^y=-2
meaning x=2 is not in the domain
languid harness
Ah ok
vestal forge
but anyway, so as long as 2-2^x>0, meaning as long as the rhs is positive, there always exists a real y that satisfies the equation
so all clear?
languid harness
Yes understood
vestal forge
right, so all we need to do is to solve for x in 2-2^x>0
languid harness
Or we can also write it
2>2^x
vestal forge
yes
languid harness
So from this we can conclude that x = 1 and it has got a real solution?
vestal forge
no
languid harness
No, how ?
vestal forge
you could also see why it's not true because 2^y=0 has no real solutions too
vestal forge
have you solved inequalities involving with exponential functions before?
languid harness
Quadratic ones yes
vestal forge
quadratics are polynomials, not exponentials function
languid harness
But those ones were not strictly increasing or decreasing
languid harness
quadratics are polynomials, not exponentials function
Oh sorry
Then no i haven't
vestal forge
alright, nvm all that, if i gave you 2^x<=2, then could you solve for x here?
languid harness
x = 1 ?
vestal forge
that is one of the solutions
languid harness
Isn't that the only solution?
vestal forge
again, we are solving an inequality
languid harness
again, we are solving an inequality
Oh ok
vestal forge
alright, it seems like you are not very familiar with these types of inequalities, let's solve it with me then
oh nvm
languid harness
(-infinity,1] ?
vestal forge
yes, (-infty, 1] is the correct solution
now that is 2^x<=2, what about 2^x<2?
(this is just us removing the equal sign, so remove the solution when the equal sign is true)
languid harness
now that is 2^x<=2, what about 2^x<2?
(-infinity, 1) ?
languid harness
Wow that so freaking smart
Thanks
Never thought of this ques like this
And yes the ans is also right
Thankkkksss
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marsh citrusBOT
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steady mural
hi guys i have a question
marsh citrusBOT
hi guys i have a question
steady mural
what length of tarapulin 3m wide will be requited to make a conical tent of height 8m and base radius 6m? assume that the extra length of material that will be required for stitching margins and wastage in cutting is approximately 20 cm (use pi = 3.14)
pls help
<@&286206848099549185>
marsh citrusBOT
@steady mural Has your question been resolved?
steady mural
<@&286206848099549185>
marsh citrusBOT
@steady mural Has your question been resolved?
marsh citrusBOT
@steady mural Has your question been resolved?
upper briar
what length of tarapulin 3m wide will be requited to make a conical tent of heig...
so as in we just compare surface areas?
then add 20 cm after?
harsh tundra
What should I do to look for the radius and interval of convergence after getting here?
marsh citrusBOT
What should I do to look for the radius and interval of convergence after gettin...
harsh tundra
I got stuck
distant peak
$\sum_{k=1}^{\infty} \frac{2^k}{k² 3^k} x^k$
elfin berryBOT
Ｈｅｒｅｌｓ
distant peak
with $a_k = \frac{2^k}{k² 3^k}$
elfin berryBOT
Ｈｅｒｅｌｓ
distant peak
now to find the radius of convergence, you use d'Alembert
distant peak
why do you want to do that tho
harsh tundra
I'll try it out
distant peak
do you know about d'Alembert tho ?
harsh tundra
Yes, ratio
distant peak
Yes, ratio
ratio of what
harsh tundra
Its the ratio test with the limit
distant peak
yea but ratio of what
harsh tundra
ak+1/ak
marsh citrusBOT
@harsh tundra Has your question been resolved?
river lance
Hey, I am currently searching for a function without condition and defined in R which returns 1 when a number is a solution of n(n+1)/2 et which returns 0 in all the other cases ? Do you have any idea?
marsh citrusBOT
Hey, I am currently searching for a function without condition and defined in R ...
river lance
$f(x) = 1$ if $\exists n \mid f(x) = \frac{n(n+1)}{2}$
otherwise $f(x) = 0$
elfin berryBOT
Lynox
marsh citrusBOT
@river lance Has your question been resolved?
steel basin
This
U want a polynomial function
?
I don think polynomial function exist for this
devout mauve
they don't
the function described is clearly not continuous so you can't get it with polynomials or something like that
steel basin
Yeah
devout mauve
you could do some weird stuff like $f(x) = 1 - \left(\ceil{\frac 12 (\sqrt{8x+1}-1)} - \floor{\frac 12 (\sqrt{8x+1}-1)}\right)$
elfin berryBOT
Denascite
steel basin
How?
devout mauve
if x=n(n+1)/2, then n=1/2 (sqrt(8x+1)-1)
devout mauve
if n is an integer, then ceil(n)=floor(n)=n, so ceil(n)-floor(n)=0 and f(x)=1
but if n is not an integer the ceil(n)=floor(n)+1 and so ceil(n)-floor(n)=1 and f(x)=0
or you could probably find a lot of other functions which are 0 if input is integer and 1 otherwise
marsh citrusBOT
@river lance Has your question been resolved?
worn fractal
i need help on these two geometry questions
marsh citrusBOT
i need help on these two geometry questions
@worn fractal Has your question been resolved?
rose tiger
i need help on these two geometry questions
9: 14x-1 = 12x+17
for 10
the two angles are supplementary
marsh citrusBOT
marsh citrusBOT
Available help channel!
fallow lynx
Please explain to me the step by step process on this
marsh citrusBOT
Please explain to me the step by step process on this
fallow lynx
I'm particularly confused how there is a +2 and how -1 was added in 4cos theta
wet zenith
Please explain to me the step by step process on this
cos theta factored from first two terms, 2 factored from the last two terms
fallow lynx
Ohhh
Aight thanks, got confused and thought you factor cos theta to all
thanks
.close
marsh citrusBOT
marsh citrusBOT
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glad tundra
Which poligon has 35 diagonals? i'd need the steps and the result so i can see how to solf in the future, thank you!
marsh citrusBOT
Which poligon has 35 diagonals? i'd need the steps and the result so i can see h...
glad tundra
polygon*
hidden plaza
In any n-sided polygon, each vertex can be connected to n-3 other vertices (not itself or its adjacent vertices.) Can you come up with the formula for the number of diagonals for an n-sided polygon (careful with over counting.)
glad tundra
yeah i know the formula for that, its n*(n-3) divided by 2
but im getting stuck on how to calculate the n when im given the number of diagonals
hidden plaza
$\frac{n(n-3)}{2} = 35$
elfin berryBOT
Pure
hidden plaza
This is just a quadratic
glad tundra
so
n(n-3)=d/2?
oh wait no
it would be d*2
so now im on n^2 - 3n = 70
what now
marsh citrusBOT
@glad tundra Has your question been resolved?
hidden plaza
Do you know how to solve quadratic equations
glad tundra
sort of, but i'm having problems on this one
can i just get the formula for n so i can have it for future refrence, i am very lost currently
glad tundra
yes, i would like the formula to solve for n
merry terrace
yes, i would like the formula to solve for n
Oh ok
n²-3=70
n=+and-√67
Wait
Shit
What I am doing
glad tundra
Oh ok
n²-3=70
waut hold on wouldnt it be n^2 - 3n =70?
merry terrace
waut hold on wouldnt it be n^2 - 3n =70?
Yeah
That's what I am talking about
It would be the quadratic formula
n²-3n-70=0
glad tundra
ooh right
merry terrace
Yupp you can solve it form here?
glad tundra
yeah thank youu
merry terrace
Welcome 🫂
marsh citrusBOT
Available help channel!
fleet sierra
marsh citrusBOT
fleet sierra
How is it supposed to solve this problem? I mean which formula should i use
I tried different things but can't solve this
upper briar
wait
trim quest
it means arctan
fleet sierra
draw the unit triangle
Yes i can derive arctg12/5 from the triangle
W what am i supposed to do 
Ok, I'll get arccos +arccos. Is there a formula for addition of two arccos?
Thank you
Where can I find those formulas?
hushed egret
like
you shouldve calculated the sin and the cosine
of the angles
as was suggested
marsh citrusBOT
@fleet sierra Has your question been resolved?
elfin berryBOT
hushed egret
,w sin(arccos(12/13) + 2arctan(5))
elfin berryBOT
hushed egret
,w cos(arccos(12/13) + 2arctan(5))
elfin berryBOT
hushed egret
hence the top angle is -pi
repeat for bottom one
,w sin(arcsin(8/17) + 2arctan(4))
elfin berryBOT
hushed egret
,w cos(arcsin(8/17) + 2arctan(4))
elfin berryBOT
hushed egret
hence the bottom angle is also -pi
so you're just evaluating arctan(-pi/-pi) = arctan(1) = pi/4
hushed egret
yes
silver matrix
hello guys, im a bit confused with the question, it says
marsh citrusBOT
hello guys, im a bit confused with the question, it says
silver matrix
find value of dy/dx at point (1,-2) which lies on curve 2x^2 +3y^2-6xy=26
what does this question mean? to first input the points to the curve then find dy/dx?
or to first find the dy/dx then then input the points?
ripe rock
or to first find the dy/dx then then input the points?
if you inpt the points first, then you'll now have a number, and can't differentiate the function anymore
silver matrix
ripe rock
asit is no longer in terms of vriables
silver matrix
if you inpt the points first, then you'll now have a number, and can't different...
yess
ripe rock
so differentiate first
ripe rock
it would be the ratio of change in distance in the y direction to the change in the x direction, if you took a small step in the x direction
silver matrix
it would be the ratio of change in distance in the y direction to the change in ...
what do you mean? hehe
ripe rock
so, assume you move a very small distance $\Delta x$ in the x direction on the given curve, then if $dy/dx = a$, it means you will move $a \cdot \Delta x$ distance in the y direction to stay on the curve
elfin berryBOT
Sharl Eclair
silver matrix
so, assume you move a very small distance $\Delta x$ in the x direction on the g...
is this correct?
marsh citrusBOT
@silver matrix Has your question been resolved?
marsh citrusBOT
@silver matrix Has your question been resolved?
fleet beacon
Every natural number from 1 to 15 (incl) is written down on a cardboard card, where each cardboard card has a number on it and none repeat. Four cardboards are drawn at random. What is the probability that among four cards drawn 8 is the lowest number OR 12 is the highest number?
marsh citrusBOT
Every natural number from 1 to 15 (incl) is written down on a cardboard card, wh...
fleet beacon
combinatorics got me good
So 15 choose 4 is what we divide by a
And I have a sneaking suspicion its gonna be 7 choose 3 divided over it + 11 choose 3 divided over it again
at the same time something feels a bit off about it like I have to divide possible all combinations of 8 by only the ones i need
sleek lake
i would do
7c3 + 11c3 − 4c2
fleet beacon
why the 4c2
sleek lake
there's overlap
(it's 3c2 my bad)
fleet beacon
ah right makes sense
wowzers again not so difficult once you see the answer 🤣🤣
thanks mate
fleet beacon
there's overlap
(it's 3c2 my bad)
if you ever have the hearthstone quest do let me know I will do my best to log in an play a friendly game 😝
.close
fleet beacon
there's overlap
(it's 3c2 my bad)
Boss how do you go about determining size of overlap at first glance it seems 3c2 cause if 8 and 12 are fixed that leaves 3 numbers between 2 slots?
marsh citrusBOT
Boss how do you go about determining size of overlap at first glance it seems 3...
sleek lake
4c2 was a mistake yes
fleet beacon
Right
sleek lake
i wrote the numbers to see the sizes
fleet beacon
Little something from class why is 11/36 added again isnt the 11/36 counting both die and the potential swapping in their positions
marsh citrusBOT
Little something from class why is 11/36 added again isnt the 11/36 counting bot...
fleet beacon
Is it all possibilities with 3 and then same for 6 ?
lean flame
,rccw
elfin berryBOT
fleet beacon
then I get the vibe that | 3 | 6 | combinations overlap 🤔
marsh citrusBOT
@fleet beacon Has your question been resolved?
marsh citrusBOT
@fleet beacon Has your question been resolved?
zealous flame
Hi can someone help?
marsh citrusBOT
Hi can someone help?
zealous flame
15th question
trim quest
What's the question?
trim quest
This is just a matrix with an unknown exponent
There must be something else. What do the directions say? There is no question here
zealous flame
Find multiplication of matrices
fleet beacon
Matrix calculators show step by step solutions
marsh citrusBOT
@zealous flame Has your question been resolved?
hybrid belfry
help please
marsh citrusBOT
help please
hybrid belfry
Idk what to do for this
marsh citrusBOT
@hybrid belfry Has your question been resolved?
still temple
here again 😭 dont know how to do any of this
marsh citrusBOT
here again 😭 dont know how to do any of this
@still temple Has your question been resolved?
marsh citrusBOT
marsh citrusBOT
Available help channel!
wide wind
Obtain the differential equation by eliminating the arbitrary constants
y=Ae^(-3x)-Be^(2x)+Cx^3
I tried getting up to the 3rd derivative, but i don't know what to do next
marsh citrusBOT
Obtain the differential equation by eliminating the arbitrary constants
y=Ae^(-...
@wide wind Has your question been resolved?
main idol
Looks like a linear algebra problem now
wide wind
yeah, i also tried doing this method, but because of the x variable beside c, i can't add the equations
main idol
Oh hmm I'm stumped then
wide wind
and i can't move the x variable outside since the last equation only has 6C
marsh citrusBOT
@wide wind Has your question been resolved?
wide wind
<@&286206848099549185> help🥺
marsh citrusBOT
@wide wind Has your question been resolved?
marsh citrusBOT
marsh citrusBOT
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half onyx
marsh citrusBOT
vestal forge
the derivative of arctan(x) is 1/(x^2+1) there is not supposed to be any sine in there
vestal forge
too bad you shouldnt have trusted photomath then
half onyx
cuz i tried like 8 times beforehand and got it wronmg every time
vestal forge
try to do it by hand
half onyx
try to do it by hand
vestal forge
have you learnt implicit differentiation?
half onyx
ye
vestal forge
if you are finding it too ugly to differentiate, try taking tangent on both sides first and then differentiate
half onyx
one sec lemme do it again and ill send my work
okay
oh ignore the first bit
that was my last try
half onyx
im nmot sure whats wrong abt it
vestal forge
you didnt distribute correctly
vestal forge
if you wanted to distribute 1/(1+whateverishere) into 1-x/sqrt(1+x^2), it should have been $\frac{1}{1+(x+\sqrt{1+x^2})^2}-\frac{1}{1+(x+\sqrt{1+x^2})^2}\cdot\frac{x}{\sqrt{1+x^2}$ instead
and bot is dead
wonderful
basically, you didnt distribute correctly, the fraction should have been multiplied to x/sqrt(1+x^2) as well
but there was no need for you to distribute, just leave it as is
marsh citrusBOT
marsh citrusBOT
Available help channel!
still temple
How can you solve this with Wolfram?
marsh citrusBOT
How can you solve this with Wolfram?
stoic saddle
,w {{-4,-2,4},{8,4,-10},{2,1,-4}} * {{x},{y},{z}} = {{6},{-12},{-3}}
elfin berryBOT
marsh citrusBOT
Available help channel!
swift cypress
what's a preimage
marsh citrusBOT
what's a preimage
celest wyvern
use gugle
stoic saddle
given a map f: X -> Y and a subset B ⊆ Y, the preimage of B by f is denoted f^-1(B) and is defined as f^-1(B) := {x ∈ X : f(x) ∈ B}
swift cypress
given a map f: X -> Y and a subset B ⊆ Y, the preimage of B by f is denoted f^-1...
ah
thanks
devout mauve
(well tbf you do find the answer with google)
modest idol
marsh citrusBOT
modest idol
Is that right?
cloud iron
Looks right to me
hidden plaza
late geode
should have f(x) instead of f(3) in that main first line
modest idol
Thank you
marsh citrusBOT
Available help channel!
sly plume
Question no. 6 please
marsh citrusBOT
Question no. 6 please
sly plume
,rotate
elfin berryBOT
bleak ibex
Bit of a cheat method, but they could be 1x1 matrices
stoic saddle
Let B be a square matrix such that det(B) = 1 and 2A + B = B^T - A^T. Find det(A+B).
@sly plume
marsh citrusBOT
@sly plume Has your question been resolved?
marsh citrusBOT
sly plume
.reopen
marsh citrusBOT
✅
sly plume
Bit of a cheat method, but they could be 1x1 matrices
What matrices do u have in mind?
sly plume
```
Let B be a square matrix such that det(B) = 1 and 2A + B = B^T - A^T. Find d...
Yes that's the question
bleak ibex
Well, if A is 1x1 it is just a real number a, and it's determinant and transpose are equal to a as well
This makes the equations really easy
@sly plume
sly plume
tell the numbers u have in mind then
sly plume
B is already 1
bleak ibex
A = 0?
bleak ibex
Also works if B is 2x2 identity matrix, but I gtg
bleak ibex
but there should a elegant method
Probably, I dont like this as well
still temple
How can I find the term 2015 of the fibonacci sequence?
marsh citrusBOT
How can I find the term 2015 of the fibonacci sequence?
sly plume
How can I find the term 2015 of the fibonacci sequence?
I doubt it's possible for humans
Unless your allowed to use a computer that is
still temple
I doubt it's possible for humans
I thought there would be a formula in which I could use
sly plume
I thought there would be a formula in which I could use
Nope nothing like that u have to find 2014 th and 2013th term manually..
lime coral
Hey I need help with matrices
marsh citrusBOT
Hey I need help with matrices
alpine imp
marsh citrusBOT
@lime coral Has your question been resolved?
ionic owl
[h = \sqrt{15277^{2} -(4153)^{2}}]
[h \approx 14701.67746]
marsh citrusBOT
\[h = \sqrt{15277^{2} -(4153)^{2}}\]
\[h \approx 14701.67746\]
elfin berryBOT
dopediscorduser
proper lantern
