naw bro
#help-17
vast shale
Its a human
vast shale
He tryna help you show the answer
I didnt do anything its just unique
My ans is 3 but its wting
It should be root 3
formal pond
It should be root 3
Yea i see
worthy citrus
why did you write 63 as 3*7?
oh its squared
then you dropped the square on the next line
formal pond
Yea you've done some confusing stuff icl
vocal sleetBOT
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hushed oxide
Is there a way to distribute this out, without the redundant repetition of 2?
(2 * 5) * (2 * 3) * (2 * 4)
vocal sleetBOT
Is there a way to distribute this out, without the redundant repetition of 2?
(2...
hushed oxide
Because if I just did 2(5 * 3 * 4) then the order of operations would get messed up and not reflect the same expression as the above
dense stump
exponents I guess
strange crater
order? it's all multiplication
dense stump
= 2 * 2 * 2 * 5 * 3 * 4
= 2^3 * 5 * 3 * 4
strange crater
well of course not, you "lost" two 2s
hushed oxide
For context
dense stump
why does the redundancy matter btw?
hushed oxide
why does the redundancy matter btw?
To communicate effectively that everything is being altered due to the same 'force'/goal
But I am still new to math, so I don't know the standard to these things
strange crater
altered?
hushed oxide
Everything is being * by 2
Due to the same systematic change
(Every side is being divided by 1/2 aka * by 2)
hushed oxide
= 2 * 2 * 2 * 5 * 3 * 4
= 2^3 * 5 * 3 * 4
Oh I see, that makes sense! Does it obscure intent however? How important is it to convey intent when writing expressions?
strange crater
what is being divided by 2??
hushed oxide
Nothing. I said / 1/2, which is the same as * 2
strange crater
OK well IMO saying it like that is communicating the solution less effectively
the answer looks like it should just be 10 * 8 * 6
hushed oxide
That's exactly what it is, but then the reasoning as to why it's done is made implicit in that way.
hushed oxide
= 2 * 2 * 2 * 5 * 3 * 4
= 2^3 * 5 * 3 * 4
This makes a lot of sense to my brain, especially as 2^3(5 * 3 * 4)
It seems like a more intentful way to convey it
dense stump
honestly, I don’t think it matters too much
redundancy of numbers isn’t usually a crime in math unlike programming
urban edge
I would say using (2^3)(345) is the best way to show that a scaling factor to all three dimensions affects the volume three times hence the cubed scaling facotr
hushed oxide
I would say using (2^3)(3*4*5) is the best way to show that a scaling factor to ...
Right, that makes a bunch of sense
hushed oxide
redundancy of numbers isn’t usually a crime in math unlike programming
Right? I just want to make something showing "For n amount of sides, multiply each side by 2 and then multiply every resulting product"
Can math do that?
In the way as it's outlined in my description
hushed oxide
Well then how would you translate that to symbols/notation?
hushed oxide
Why not?
vivid axle
because you cant express everything with symbols
hushed oxide
You can do it in programming, why not math?
Yeah you can
At least for something this relatively simple
vivid axle
its a bad habit not to use any words
heavy plover
it would be redundant, overly complicated and elitist to have a symbol for everything
just use words
hushed oxide
I'm just asking out of curiosity btw, not arguing against the nature of math lol
vivid axle
You can do it in programming, why not math?
math is for other ppl to read and to understand. program is to be executed by a machine that doesnt "understand"
hushed oxide
Right? I just want to make something showing "For *n* amount of sides, multiply ...
That's kinda crazy to me if there isn't a way to represent something like this in a way that makes this logic explicit, as it seems like it would be infinitely useful
strange crater
it's called "human language"
heavy plover
we made it for a reason
hushed oxide
We still design systems to reflect the underlying logic to it.
That's why, for example, HSL notation exists for representing color.
(It's more appropriate for the perception of color, so the representation was reworked to be more explicit to achieve a specific goal)
strange crater
IMO this is probably more suited to a discussion channel
vivid axle
and do you say "im wearing #ffffff t-shirt today" on a daily basis?
like its good for to communicate with computer
not with people
hushed oxide
I think you're missing the point
heavy plover
why would you want to complicate it
hushed oxide
It seems like it would make it infinitely easier
urban edge
It would not
heavy plover
until you realise how big a field math is
hushed oxide
I'll take your guys' word for it at this point
urban edge
You would have to teach numerous people what your notation is
heavy plover
having symbols for everything would need its own dictionaries
urban edge
It becomes more inconvenient at that point
hushed oxide
That's true, everything has its costs & benefits
vivid axle
there already are problems due to inconsistent notation
urban edge
Whats the waste in typing or writing a few more symbols to make it more accessible
heavy plover
we already have a lot of symbols and you have to take courses to understand the symbols to understand the math and it would just suck for anyone trying to take math
vivid axle
most famous, is 0 a natural number? who knows
sudden cloud
lol what is even the question
modest dirge
In ZFC you can technically represent any formula with symbols from the language of set theory
vivid axle
most famous, is 0 a natural number? who knows
depends how you like it
modest dirge
So like, he’s kinda right, but it’s really shit for teaching and understanding
Trying to do formal proofs without words is cringe
strange crater
So like, he’s kinda right, but it’s really shit for teaching and understanding
there's the rub
hushed oxide
🥹
sudden cloud
💀 is there even a question in this channel
vivid axle
i dont think "any formula" is "any sentence" though
heavy plover
teaching everyone your symbol that means this number is prime is definitely less efficient that writing "this number is prime"
modest dirge
Even the set theory book I used called th e chapter that describes the language of set theory “LOST” which is a double entendre lol
urban edge
If you really want a way to represent it, $f(n)=\prod_{i=1}^n{2d_i}$ where $d_i$ is a dimension in a specific... dimension
twin meteorBOT
GarlicBredFries
hushed oxide
My main professional is teaching a technical skill, so I think a lot about how to best frame a system and its workings for easiest understanding, so that's where my mind went for this specific example - but then again I am very ignorant on math so I am completely in the dark on the colorings of its thinking and approach
hushed oxide
If you really want a way to represent it, $f(n)=\prod_{i=1}^n{2d_i}$ where $d_i$...
I'll definitely revisit this when I have the know-how to take it in
I am technically on 6th grade math right now lol, I really did not pay math any mind throughout my life until recently so I had to start from the basics
urban edge
Essentially the notation is a compact way of saying "if you want to pack cubes that are scaled by 1/2 in the same volume, you need double the amount of cubes required in each dimension"
urban edge
Ability of expression is more a gained skill over time
hushed oxide
So you were technically able to express that, but does it come across as awkward?
Or is this a good use case?
hushed oxide
I think there's no coming away from that, even programming has its equivalence of having to give context
Like naming things
urban edge
Yeah
Usually, when you write something like what i made above, you would also explain what you said in word form anyway
hushed oxide
That makes sense
urban edge
Basically notation can be handy if you dont wabt to write a long equation (especially multiple time), but you should still explain why
hushed oxide
Thank you for the clarification on this all, it makes more sense to me now
hearty delta
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devout dawn
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devout dawn
(Calculus 3) How to find a,b and c
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@devout dawn Has your question been resolved?
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@devout dawn Has your question been resolved?
summer lichen
note that if you take a trace of the hyperboloid perpendicular to the xy plane, then you'll end up with an ellipse, try solving for the values of a and b. Then you can substitute a point on the surface and find the equation of the line (note that a, b and c are constants)
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vast shale
QUESTION PERTAINING TO PERMUTATIONS AND COMBINATIONS
A group of 12 people want to go to a concert. They can travel in a small car that takes one drive and one passenger and two cars each taking one drive and 4 passengers. If there are 5 drivers in the group, in how many different ways can they travel?
vast shale
I am really really unsure on how to approach this question
really dont have any working to show for
<@&286206848099549185>
.close
sudden cloud
**QUESTION PERTAINING TO PERMUTATIONS AND COMBINATIONS**
A group of 12 people w...
Sorry wdym
vocal sleetBOT
Sorry wdym
sudden cloud
So there are 2 cars?
violet pebble
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violet pebble
how do we know that this has a finite value?
the first integral on the right-hand side
paper depot
$\int_0^1 e^{-x^2} \dd{x}$?
twin meteorBOT
Ann
paper depot
this one?
is this a "i dont know whats going on" or "i think theyre wrong" situation
vocal sleetBOT
@violet pebble Has your question been resolved?
violet pebble
is this a "i dont know whats going on" or "i think theyre wrong" situation
It's a "I don't know what's going on situation"
violet pebble
this one?
yeah that one
how can they just say it'll evaluate to a finite value?
without knowing what the integral of the function is or anything?
paper depot
well we still know that e^(-x^2) is a continuous function
in fact we know that 0 ≤ e^(-x^2) ≤ 1 for all x, and in particular for all x in [0,1]
so we can put bounds on the integral
we may not know the exact value of this integral but we do know it too lies between 0 and 1
vast shale
Sorry wdym
I got my answer from someone else. Thank you so much for your time :) !
vast shale
.close
tough lily
Could I get help on this? The question says "Use the geometry program to mark the points A = (−2, 3), B = (0, −2) and C = (4, 6) in the coordinate grid. Measure to the nearest degree" I have no idea as to how to measure it's degree..
vocal sleetBOT
Could I get help on this? The question says "Use the geometry program to mark th...
raven bough
Could I get help on this? The question says "Use the geometry program to mark th...
u want to calculate the slope ?
vocal sleetBOT
@tough lily Has your question been resolved?
tough lily
u want to calculate the slope ?
it says measure to the nearest degree
regal slate
you can measure the angles once you connect the coordinates with lines ig
tough lily
the answers are 95,85 and 95
regal slate
desmos?
tough lily
how do I do that?
raven bough
it says measure to the nearest degree
degree of what tho ?
regal slate
no, are you using desmos?
regal slate
oh
raven bough
one meaning could be that u have to make a differential equation and find out the degree
or u need to measure the degree from one of the axis
tough lily
yeah but I have no idea as to how to solve it
hence why im asking xD
I mean chapter's name is vector's basics
so I don't think it can be that complicated however I'm still lost
vocal sleetBOT
@tough lily Has your question been resolved?
vocal sleetBOT
tough lily
.reopen
vocal sleetBOT
✅
tough lily
oh yeah....
tough lily
howd u do that😭😭😭
regal slate
plot the points
connect with segments
then use the angle measure tool to measure the angles
you have to select segments and it gives you the angles
tough lily
is it really that simple
I thought I had to do a full calculation or something 😭😭
Thank youuu
vocal sleetBOT
@tough lily Has your question been resolved?
vocal sleetBOT
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Available help channel!
fleet vessel
What did I do wrong?
vocal sleetBOT
What did I do wrong?
fleet vessel
P supposed to be 5
fluid obsidian
What's the actual question
astral pilot
twin meteorBOT
fleet vessel
Have u figured it out?
hard rose
What did I do wrong?
Which questions is it
fleet vessel
Which questions is it
7 a
quartz ginkgo
i think i need help with operations with
cientific notation (adition,
subtraction,
multiplication and division)
quartz ginkgo
i think i need help with operations with
cientific notation (adition,
subtract...
a brazilian helper, please
vocal sleetBOT
@quartz ginkgo Has your question been resolved?
rugged vortex
Let u = x^2
Replace u
If you really hate looking at square roots
Well I typically, if there's like a square root or something, I like to make a substitution so I deal with integer powers
Like in this case, although it's pretty evident there's a case of difference of squares, if you let u = x^2
Then it should end up looking nicer
Now of course you could also recognize that $u - 1 = (\sqrt{u} + 1)(\sqrt{u} - 1)$
twin meteorBOT
Umbraleviathan
paper depot
why are you only showing us this NOW?
little wolf
this is https://xyproblem.info/ i think
gentle totem
It is
little wolf
Your computation is correct, but there's another substitution that makes it a lot easier
u = √(cos x)
try it on paper
that's not how you differentiate a square root
yeah, so if you rearrange, what is sin(x)dx equal to ?
(also you're missing a ½)
derivative of √x is 1/2√x
well yeah, dx would still be there but that doesn't matter in a substitution
if you rearrange you get sin(x)dx = -√(cos x) du
you always have those two
do you mean that you would have both x and u ?
what ?
i don't follow
there's always just one dx on the right
just so we're clear, (ab)×c = (ac)×(bc) isn't true
little wolf
if you rearrange you get sin(x)dx = -√(cos x) du
do you agree with this ?
uhhh
that minus sign isn't a subtraction
it's (-sin x)/2√(cos(x), not 1/2√(cos x) - sin(x)
chain rule yeah
yeah
and so then do you see how to carry out the substitution ?
look at the definition of your substitution again
yeah, so you can subtitute it on the right side
sin(x) dx = -2u du
since u = √(cos x) by definition
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vast salmon
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vast salmon
I don't really understand by what f(x,y) mean
rugged vortex
It's a 3D function
rugged vortex
No x and y are independent variables. f(x,y) is dependent on both, but f(x,y) = 0 for all x and y
f(x,y) = 0 is just the z = 0 plane (Cartesian plane)
rugged vortex
The second line, lemme see
I think it's saying you can split it up because Δx -> 0 is equivalent to Δy -> 0
vast salmon
How
rugged vortex
As something approaches 0 is equivalent to another thing approaching 0
rugged vortex
Uh they just did algebraic manipulation
It could work with any delta variable -> 0
But then that's redundant
So they just made it so the denominators -> 0
If you made the numerators go to 0, then you'd just have the reciprocals, but A • B = B • A
So it's just slight manipulation, I wouldn't worry about it too much
vocal sleetBOT
@vast salmon Has your question been resolved?
vast shale
the zeros of (x+a)(x+b) are x=-a and x=-b
errant briar
x²+7x-3x-21
x(x+7)-3(x+7)
(x+7)(x-3)
outer warren
\textbf{Factoring monic quadratics:}
Consider:
$$\begin{aligned}
(x+m)(x+n) &= x^2 + mx +nx +mn \
&= x^2 + \underbrace{(m+n)}_b x + \underbrace{mn}_c \end{aligned}$$
finding the pair of values $m,n$ that: \
multiply to $c = mn$ and \
sum to $b = m+n$ \
gives the factorisation: $(x+m)(x+n)$
twin meteorBOT
ℝamonov
vocal sleetBOT
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sick willow
There is a 2.5 meter wide path around the square shaped garden. The area of path is 165 sq meter. Let us calculate the area of garden and the length of diagonal
vocal sleetBOT
There is a 2.5 meter wide path around the square shaped garden. The area of path...
elder forge
Do you have a specific question regarding the problem?
sick willow
Do you have a specific question regarding the problem?
Yeah like from where do I start
elder forge
I would draw it first to get a visual aid
Draw the garden as a square, then mark out part of the inner perimeter as the path
Try to mark different lengths of the figure and give them names, then write down the sizes and distances you know
try to make some kind of equation
sick willow
Draw the garden as a square, then mark out part of the inner perimeter as the pa...
Eh so like
Let me consider the side of the outer square as x and y.
So, Area = x²
Length of inner square = (x-5)
Breadth = (x-5)
Area of inner square = (x-5)² = x² - 10x + 25
Area of outer square - Area of path = Area of inner square
x² - 165 = (x² - 10x +25)
-165 = x² -10x + 25 - x2
-165 = -10x +25
10x - 25 = 165
x = 19
Uhhhhh the 25 should've been positive for the answer to be correct..
vocal sleetBOT
@sick willow Has your question been resolved?
trail grail
Let me consider the side of the outer square as x and y.
So, Area = x²
Length of...
ehhh
i got a diff ans
The total width of the garden including the path is (x+5) meters, since the width of the path on each side is 2.5 meters.
The area of the entire square, including the path, is (x+5)^2 square meters.
The area of just the garden, without the path, is x^2 square meters.
Therefore, the area of the path is the difference between these two areas:
Area of path = (x+5)^2 - x^2 = 165
10x + 25 = 165
x = 14
Therefore, the side of the garden is 14 meters, and the area of the garden is x^2 = 196m
The diagonal of the garden can be calculated using the Pythagorean theorem. The diagonal is the hypotenuse of a right triangle with sides of length x, so
Diagonal = sqrt(2x^2) = sqrt(2196) = 14*sqrt(2) meters.
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sage peak
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mystic hollow
is someone able to help me with moment of inertia? i tried searching online regarding the different solutions for it but i cant seem to find the right one
vocal sleetBOT
is someone able to help me with moment of inertia? i tried searching online rega...
astral shadow
Did you try anything?
regal bane
Basically calculate the moment of each sphere through L using the parallel axis theorem, then add
Your book should have each sphere's moment so there should be no heavy calculations involved
Oh and the rod, add that in too
vocal sleetBOT
@mystic hollow Has your question been resolved?
mystic hollow
Did you try anything?
i tried using the formulas for the rod and the sphere
mystic hollow
Basically calculate the moment of each sphere through L using the parallel axis ...
my prof didnt teach us that yet
the parallel axis theorem
astral shadow
❌ for the prompt, snow.
And, the theorem is pretty essential for this problem.
You can derive it, then again if you don't know what the theorem states you might have to look that up.
astral shadow
I'll add to it. And you can work stuff out from there.
The theorem is used when you need the moment of inertia of a rigid body about an arbitrary axis.
The moment of inertia of the object about the arbitrary axis is:
Moment of inertia about an axis (parallel to the other axis) passing through the centre of mass of the object + Md^2 where M is the total mass of the object and d is the distance between the two axes.
This works because moment of mass of a body about its centre of mass is zero.
mystic hollow
aaa thank you so much!!
this makes it easier to understand
i appreciate it, thank you again!!
austere bolt
$f(x) = (x+sin(x)*cos(x)), g(x) = x(2 + sin(x)) + 2*sin(x)*cos(x) + cos(x)$
twin meteorBOT
Penca53
austere bolt
limit x->+inf of f(x) / g(x), doesn't exist, right?
river minnow
,w limit of (x + sin(x)cos(x))/(x(2 + sin(x) + sin(2x) + cos(x))) as x goes to infinity
twin meteorBOT
river minnow
Yeah, doesn’t
austere bolt
ok, the question then asks to evaluate it using l'hopital... but it doesn't make any sense?
river minnow
Is the expression written exactly like that?
river minnow
Oh
Then there may exist actually
Let’s check anyway wait
,w limit of (x + sin(x)cos(x))/(x(2 + sin(x)) + sin(2x) + cos(x)) as x goes to infinity
river minnow
Okay nvm it still doesn’t 
austere bolt
,w limit of (x + sin(x)cos(x))/(x(2 + sin(x)) + sin(2x) + cos(x)) as x goes to i...
isn't it the same? 😄
river minnow
No
wary mantle
Okay nvm it still doesn’t <:catThink:526983414226747393>
What you wrote in the denominator still isn't the same as the given g
austere bolt
,w limit of (x + sin(x)cos(x))/(x(2 + sin(x)) + 2sin(x)cos(x) + cos(x)) as x goes to infinity
twin meteorBOT
river minnow
That’s what I typed
Except I used the double angle identity
2sin(x)cos(x) is sin(2x)
austere bolt
I don't know what that is 🙂
river minnow
2sin(x)cos(x) is sin(2x)
It states this
wary mantle
Except I used the double angle identity
Nvm then, I thought you wanted to type it in exactly as it is given
austere bolt
yeah, but I don't know
river minnow
Well either way the limit doesn’t exist
austere bolt
ok. Probably the exercise is then about "try to solve the limit without using l'Hopital", and comment the result, then try to take the derivative of f and g, and try again (which is basically l'hop, right?) and comment the result
little note: we still haven't done l'hop, but I'm already using it because otherwise I'm not able to complete these kind of limits in a reasonable amount of time 😄
river minnow
I guess you could do comparison or smth
austere bolt
I guess so. Either way, how would you determine that the limit doesn't exist, manually?
Is it enough to say: sin(+inf) doesn't exist, so the whole limit doesn't exist?
river minnow
No, that won’t help
Normally you would find the max and min values of those trig functions
But it’s kinda hard here
I guess you can say that the fraction is > (x - 1)/(x + 3) okay nvm this does have a limit
austere bolt
Normally you would find the max and min values of those trig functions
squeeze, you mean?
river minnow
Yeah if you manage to find some function which diverges and is smaller than the expression given then it will be done
But I can’t think of any
austere bolt
But I can’t think of any
Don't worry, I'll try to squeeze my brain for a bit, but I won't stress it too much... thanks a lot 😄
.close
minor root
vocal sleetBOT
minor root
Could you please explain step by step how to reach each result?
sturdy mango
Full workings please?
minor root
Full workings please?
"The solution can usually not be determined closed, but only numerically. For small
numbers this can also be done by trial and error:
By trial and error we get: r = 4. This number represents the smallest r, which satisfies the inequality with 12 < 16.
- This gives the following total packet size: n = 7 + 4 = 11. This size corresponds to the length of the code words in the Hamming code."
I understand how you go from the first expression to second
sturdy mango
Are there any equation relations between n, r, m?
minor root
If I'm not mistaken, yes
sturdy mango
Then (1 + n) 2^m ≤ 2^(m + r)
Divide both sides by 2^m to get:
1 + n ≤ 2^r
1 + m + r ≤ 2^r
minor root
Ah and the right one is just inserting numbers "by trial and error"
Lame
But thanks a lot
.close
upbeat pecan
my mathematics teacher taught that foil is not mathematically correct so i really dont want to use that to solve this
worthy citrus
I wouldn't say FOIL is not mathemically correct, it's just a mnemonic to remember how to multiply two binomials
upbeat pecan
no but
i learned it this way
so -3 goes into 7 and 4 root 2
then -1 root 2 goes into 7 and 4 root 2
then u simplify like terms
how would i do the way i just said?
worthy citrus
That's pretty much foil, but longer
(a+b)(c+d) = a(c+d) + b(c+d)
That's what you're describing
Then you would distribute both remaining brackets
And you'd be left with the terms that foiling tells you to do
So that's why foiling works
upbeat pecan
um if you dont mind
im really paranoid that im gonna get one of the root multiplications wrong
can u do it for me?
like step by step
worthy citrus
Why don't you try it yourself first
upbeat pecan
yea i did
worthy citrus
Then show your work
upbeat pecan
(-21) plus (-12 root 2) plus (-7 root 2) plus (-4 root 2)
-21+(-23 root 2)
is that it?
worthy citrus
,w expand (-3-sqrt2)(7+4sqrt2)
twin meteorBOT
twin meteorBOT
ΣAC
worthy citrus
You need to simplify it
upbeat pecan
im glad i was close
im self learning this so
my school doesnt even teach this kinda stuff
but i appreciate it a lot mate thx for the help
.close
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eternal glacier
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calm light
likely a small mess up
eternal glacier
i don't understand the critical points for this
I found x=5 and x=-1 are critical points
cobalt crypt
,w d/dx (x+2)/(x^2 + 5) = 0
twin meteorBOT
calm light
nvm ur factors are wrong
eternal glacier
wha
cobalt crypt
something is awry
calm light
it’s (x+5)(x-1)
eternal glacier
i thought it must multiply to -5 and add to -4?
can't have negative for first term?
calm light
you didn’t factor the -1 out of the polynomial before factoring the rest
eternal glacier
so the first term must be positive before factoring?
calm light
no all common factors must be removed
eternal glacier
i don't get it
calm light
the full factored form of the polynomial above is -1(x-1)(x+5)
eternal glacier
oh
cobalt crypt
how do you factor x^2 + 4x - 5?
eternal glacier
i know what i did wrong now
i forgot to divide by the first term
1/-1 and -5/-1
ya you're right, it should be -1 and +5
calm light
that technically works too
calm light
of f(x)?
eternal glacier
calm light
this is most definitely not the graph of a quadratic
eternal glacier
it's the graph of the function f(x)
it's asking for the maximum and minimum on interval [-1,3]
so once I know the maximum is x=1 and x=-5 i basically just ignore x=-5, right?
only focus on x=1?
as x=-5 is out of scope?
or do I still want to find both within that interval
calm light
you also need to find the minimum
eternal glacier
again, here is the question:
but when I find the critical points, that's for the entire function
not necessarily within the interval
x=1 just happens to be in the interval
is the question asking for coordinates? (x,y)?
calm light
is the question asking for coordinates? (x,y)?
probably
cobalt crypt
probably not you mean 
eternal glacier
so i would plug in f(1) into the original function to find the y value
calm light
yep
eternal glacier
probably not you mean <:cheeto:1074397590805823582>
huh?
cobalt crypt
the maximum of a function is the value attained by the function
not the point at which it is attained
eternal glacier
so just the x value?
cobalt crypt
no
eternal glacier
oh, just the y value
calm light
the maximum of a function is the value attained by the function
oh crap ur right
forgot about that
cobalt crypt
in that graph you might say that f attains a maximum value of 0.5 at 1
eternal glacier
for the minimum, since the other critical point is outside of interval, do I just test -1 and 3?
eternal glacier
y=0.5 is fine?
for answering the maximum
or (1, 0.5) is even safer
to show exactly where it's located
as for min they want to know what the min is for [-1, 3]
i can tell based on this graph, it's -1
but without seeing the graph, i would just test the other end points of the interval to see which is lower output? for f(x)?
so I would test f(-1) and f(3), whichever has a lower output is min?
since the other critical point is beyond interval [-1, 3]
cobalt crypt
you can check the second derivative to test whether its a local min/max
you can also check the sign of the first derivative
and then you check the boundaries as well
because those are the points where the derivative isnt technically defined
eternal glacier
but checking other x values in the interval should also indicate, right? since i already know (1, 0.5) the slope = 0
so it's either gotta go up or down
or is that risky, doesn't always work?
i think second derivative of f''(1) would just tell me it's concave downward
but I kinda already got that impression if I wanted to test values adjacent, such as f(0) or f(2), they would be lower outputs than f(1)
.close
balmy furnace
Could someone explain to me how to get b? The extra variables are really messing with me.
vocal sleetBOT
Could someone explain to me how to get b? The extra variables are really messing...
balmy furnace
balmy furnace
Is it?
The correct answer was just 8x.
I do not understand.
Where does the 3Tx^2 go?
vocal sleetBOT
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stone scroll
first of all whether or not you multiply by 4 or -4 the range and domain would be same for both because it is a periodic function
as you can see the domain is still (-inf,inf) and the range is still [-4,4]
my bad i took pi/4 instead of pi/2
but it still makes no difference
you should be multiplying with -4 because the other graph would not be of this function
vocal sleetBOT
@shy cosmos Has your question been resolved?
stone scroll
i think its a calculation mistake
im still kinda confused how you are getting the y coordinate of that point
but once you have x coordinate of the point you are trying to find just plug into the function to get the y coordinate
i dont think its a matter of accuracy
if its correct then it will give the exact answer
potent delta
This is written horribly but do I have the correct idea ?
vocal sleetBOT
This is written horribly but do I have the correct idea ?
vocal sleetBOT
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dusty crescent
vocal sleetBOT
dusty crescent
I NEED YOUR HELP
I AM LOOKING FOR GEOMETRY PROS
paper depot
WHY ARE YOU SHOUTING
dusty crescent
to grab attention
dusty crescent
A and B
paper depot
okay
you are told that TU = UV
you also know ST = SU = SV (why?)
from this you can assert that two triangles (despite not being drawn in the diagram) are congruent
can you say which ones
dusty crescent
SR and SW
paper depot
doesn't answer my question.
but that will follow from triangles STU and SUV being equal.
yes, so SR = SW.
do you understand how to find the value of x from this?
dusty crescent
x + 19 + 4x - 11 + 52
paper depot
what's this meant to be
dusty crescent
To find the value of X
paper depot
what is the value of SR as given to you in the problem?
dusty crescent
4x - 11
paper depot
and that of SW?
dusty crescent
RS is 4x - 11
paper depot
no that is not the answer to part b.
dusty crescent
Oh
paper depot
me: what is the value of SR?
you: 4x - 11
me: and that of SW?
you: x + 19
what do you get when you put these into the equation SR = SW?
do not do any algebraic simplification yet. do only the replacement i ask you to do.
dusty crescent
> me: what is the value of SR?
> you: 4x - 11
> me: and that of SW?
> you: x + 1...
4x - 11 = x + 19
paper depot
correct
do you see now that this is an equation in x that we can and should solve for x?
dusty crescent
yes
paper depot
can you solve this equation for x?
dusty crescent
15
dusty crescent
x = 15
paper depot
i think you screwed up. show your work.
dusty crescent
What I did was
4x - 11 = x + 19
= x + 19 + 11 + 4x
= x + 30 + 4x
= 5x + 30
x = 6
paper depot
= x + 19 + 11 + 4x
what's meant to be on the left of this equals sign?
dusty crescent
4x - 11
dusty crescent
Sorry
paper depot
so, let me get this straight
you go from
4x - 11 = x + 19
to
4x - 11 = x + 19 + 11 + 4x
is that what you're doing?
dusty crescent
yes
paper depot
you realize this is nonsense, right
dusty crescent
oh
paper depot
do you know how to solve a linear equation?
paper depot
stuff like "add the same thing on both sides"
or "multiply by the same thing on both sides"
etc.
dusty crescent
I'll check
paper depot
ping me once you are done checking and have an attempt to show or want me to guide you
paper depot
keep going
dusty crescent
4x = x + 30
-4x -4x
3x + 30
paper depot
where did the equals sign go
dusty crescent
3x = 30
x = 10
paper depot
correct manipulations, wonky description
dusty crescent
What about the B now
paper depot
you know the value of x
now it is time to plug that into the expression you had for RS
vocal sleetBOT
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hushed atlas
can anyone explain the best way of doing part c
vocal sleetBOT
can anyone explain the best way of doing part c
hushed atlas
nvm i got it but just wanna check if id get working marks
u can sub in x/5 instead of x into the original expansion?
paper depot
h(x) = f(x/5)
vocal sleetBOT
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vast shale
In set theory, is it possible to easily tell if the type of a relation represented by a binary matrix is reflexive, transitive, symmetric or antisymmetric (translating from Portuguese - hope those terms are correct) just by looking at said matrix and looking for certain properties?
vocal sleetBOT
In set theory, is it possible to easily tell if the type of a relation represent...
dark kiln
you can tell if it's reflexive, and you can tell if it's symmetric. Antisymmetric is harder to see, transitive probably can't tell at all
glossy maple
Why not? It's just hard to see isn't it
dark kiln
much harder than what i would call hard
vast shale
What are the characteristics I should look for in the matrix?
glossy maple
Well you probably have to check all possibilities
glossy maple
What are the characteristics I should look for in the matrix?
Depending on what property you want to check for
glossy maple
Yeah, just look at the diagonal
vast shale
🙂
glossy maple
If it's all filled in, it's reflexive
Right? Because the diagonal is just the pairs <x, x>
vast shale
That makes sense
Does the matrix need to be equal to its transpose?
Or do you just need to check for all 1s in the diagonal and that’s it
vast shale
What about if you have a non square matrix?
glossy maple
For symmetric, just take each element in one side of the diagonal, reflect it on the diagonal, and make sure that one is also 1
Can that even happen
Isn't the relation from a set to itself?
vast shale
If you have a relation between 2 sets with a different number of elements I think the resulting matrix is non square
vast shale
Isn't the relation from a set to itself?
Relation from any set a with any set b
glossy maple
Yeah, but how can you call such a relation reflexive or symmetric then
Symmetric is:
aRb => bRa
But that would mean both sets are the same
vast shale
Oh so these types are only for when you have a relation from a set to itself?
glossy maple
Because if you had for example, a relation between the set {1, 2} and {3, 4}
And you have 1R3
You cannot say 3R1, because 3 needs to belong to {1, 2}
But it doesn't
vocal sleetBOT
@vast shale Has your question been resolved?
vast shale
For symmetric, just take each element in one side of the diagonal, reflect it on...
I understand. And what are the characteristics I need to look for to check for the other types?
glossy maple
Just look at the definitions
For example, anti-reflexive is when xRx never holds for any x
vast shale
Thanks!
vocal sleetBOT
@vast shale Has your question been resolved?
vocal sleetBOT
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split swallow
The antidifference of x^-m where m = 0 to 20 except 1 is X^−m is x^−(m-1)/(m-1). But what about if m=1? Is it H(x) = 1 + 1/2 + 1/3 + ·· 1/x or H(x+1)−H(x) = 1/(x+1)
vocal sleetBOT
The antidifference of x^-m where m = 0 to 20 except 1 is X^−m is x^−(m-1)/(m-1)....
woeful stream
anti... derivative?
split swallow
anti... derivative?
or something like that. sorry in my module it is called antidifference
wraith python
What class is this for?
A quick Google search suggests antidifference is the same thing as an indefinite sum, the latter of which is a term most of us are more familiar with.
split swallow
What class is this for?
Um for Numerical Methods
magic surge
is that discete somethign something
vocal sleetBOT
@split swallow Has your question been resolved?
hoary solstice
this is for a revision sheet but yeah idk how im supposed to do it. its not in english but i dont think the words rlly help at all
Translation :
Consider the polynomials P(X) and Q(X)
If P(X)=Q(X) then what is a^2+b^2
vocal sleetBOT
this is for a revision sheet but yeah idk how im supposed to do it. its not in e...
vast shale
equate coefficients
vocal sleetBOT
Please read #❓how-to-get-help
bleak prawn
turbid forum
so you know the formula for the area of a trapezium?
turbid forum
so you just need to apply it to those first three
turbid forum
for this one you split it up into two trapeziums and a rectangle
dapper prairie
could u annotate on it for me
turbid forum
which it looks like the question has done
turbid forum
you calculate the area of each of these separately and add them (sorry for the shaky lines)
turbid forum
nice!
turbid forum
the red line on top isn't parallel, or at least it doesnt say
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Available help channel!
vast shale
|x+4| - |x-3| - 8 < 0
vocal sleetBOT
|x+4| - |x-3| - 8 < 0
vast shale
help please
vast shale
yea how
turbid forum
based on if it makes the value inside the absolute value positive or negative
if we have something like |x-2| and x is, say, 1, then the value inside is negative so when we get rid of the signs we would have to change |x-2| to 2-x
if that makes sense
turbid forum
so if x < -4 then both inside values are negative
if its between -4 and 3 then only the second one is negative
if its > 3 then both are positive
dusk briar
Hello all! I was directed to this community by someone on another game server who thought you might be able to help me.
I am interested in running a queer video game club as part of my company's pride, but I haven't been paying much attention to this space recently - my old favorites were made with flash and don't run anymore!
Can anyone help suggest queer games that are:
- Free or PWYW (paid might be OK too)
- Ideally run in the browser
- Short (max a few hours), or can get a meaningful experience without finishing it
- Made by an LGBTQIA+ creator and touching in some way on queer themes
Thanks!
turbid forum
what
vast shale
Hello all! I was directed to this community by someone on another game server wh...
bro noone cares
peak matrix
Hello all! I was directed to this community by someone on another game server wh...
This is not game server + discuss this in #chill
vast shale
get outa my thread
@turbid forum so 4 cases
which first and second are bigger than 0
less than 0
first is less and second is bigger
first is bigger and second is less
?
peak matrix
so if x < -4 then both inside values are negative
one of the cases you mentioned is impossible, so you need to consider just those 3 cases
vocal sleetBOT
@vast shale Has your question been resolved?
scenic sandal
Can someone explain to me how langrange multipliers help us find the minimum distance between a curve and the origin? I know how to do it but I don't see the correlation.
vocal sleetBOT
Can someone explain to me how langrange multipliers help us find the minimum dis...
scenic sandal
It is my understanding that when we have a bounded curve in mutlivariable then we have to check if the min & max are on the edge just like we check if the end points are the max and min in single variable. To do that we can use Langrange function right? When it comes to the distance, I don't see how we can possibly use Langrange? The distance function we find lets say d(x,y)= sqrt(x^2 + y^2) but this function is not bounded by the curve we are trying to find the minimum/ maximum distance of.
main spade
Why does it need to be bounded?
scenic sandal
Why does it need to be bounded?
I don't really know what word to use, but I mean like we are only interested in the function f in some particular neighborhood/ area.
And thus there will be a max and min if the function f is continuous
main spade
Lagrange multipliers works by finding extrema on a curve not a region.
scenic sandal
Lagrange multipliers works by finding extrema on a curve not a region.
yeah Ik but that is not what I meant.
the extrema we find is on the edge of a function right?
And the way we do it is thru langrange multipliers.
the edge is given by the bounding function
Did I make sense so far?
main spade
We minimise sqrt(x^2 + y^2) subject to (x, y) on the curve g(x, y) = 0.
We in effect solve g for x or y as a function of the other variable and substitute it into the function we want to optimise. We then have f(x) or f(y) in one variable only and require f’ = 0.
scenic sandal
We in effect solve g for x or y as a function of the other variable and substitu...
Still don't get it.
main spade
To minimise the distance between a curve, g(x, y) = 0, and the origin we must minimise the function d^2 = f(x, y) = x^2 + y^2 subject to the condition g(x, y) = 0.
It's hard to help tbh.
Maybe some theory will help but maybe not.
Oh. I think I might understand you now.
scenic sandal
To minimise the distance between a curve, g(x, y) = 0, and the origin we must mi...
I understand that we need to minimize d^2 but what do you mean by "subject to the condition"?
main spade
The condition is that we are defined on the curve g(x, y) = 0.
g(x, y) = 0 implicitly defines the curve.
g(x, y) = 0 doesn't have any end points to test like you might for a function defined on some domain.
If you wanted to have the curve y = x^2 but only for 0 <= x <= 1, you would need to consider the function f(x, x^2) = x^2 + x^4 on the domain 0 <= x <= 1 where you would then check the end points.
scenic sandal
but how can we know that that is the mimimum distance. As in the formula for distance d is a generic one so like I'm lost rn lol
main spade
We can minimise the square of our distance to save algebra.
We are minimising the squared distance f(x, y) but we are constrained in terms of the (x, y) points we have such that they are on the curve g(x, y) = 0.
Let's do a example problem.
Lets minimise the distance from the origin to the curve y = 1 - x. We must minimise f(x, y) = x^2 + y^2 subject to g(x, y) = x + y -1 = 0.
We could have considered to minimise to be f(x, 1 - x) = x^2 + (1 - x)^2 = 2x^2 -2x + 1, defined for all x.
We would then calculate f_x and set it equal to zero.
We would obtain 4x - 2 = 0, x = 1/2, which corresponds to y = 1/2. The distance is minimise between the origin and the point on the curve (1/2, 1/2).
Alternatively, you could have solve for y and calculated f_y and set it equal to zero and found the same result.
The theory above does this in general for a curve g(x, y) = 0 and you find what it shows.
scenic sandal
kinda getting it right now
main spade
The theory I gave uses the implicit function theory to show it can be solved as a function of x or y so you might not be aware of that and it writes the end part as a jacobian which if you're familiar with the text is not a problem but again you might not get the same result. But it basically boils down to you get the same result as if you performed the procedure done above.
The problem though is you can't really use it for a curve such as y = x defined only on -1 <= x <= 1, as you can't write this as g(x, y) = 0.
If you were to use the method and ignore the restraint of the curve being on -1 <= x <= 1, you would get the result as if it didn't have this constant on it.
You'll have to let me know if the wall of texts are useful or not but I don't know how else to help lol.
vocal sleetBOT
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merry python
$x=1+\sqrt[5]{2}+\sqrt[5]{4}+\sqrt[5]{8}+\sqrt[5]{16}$ Find the value of $\left(x+\frac{1}{x}\right)^{30}$
vocal sleetBOT
$x=1+\sqrt[5]{2}+\sqrt[5]{4}+\sqrt[5]{8}+\sqrt[5]{16}$ Find the value of $\left(...
twin meteorBOT
B-eard
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static ore
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static ore
How to solve
queen shoal
static ore
.close
magic canopy
magic canopy
.close
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magic canopy
.close
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foggy pier
How can I put these values into the calculator to get that number? (4.25)
foggy pier
I know it's chemistry but I'm just trying to use the calculator here
brazen sun
you would do -log brackets and then put that 5.6 x10^-5 value into the brackets
at the bottom of ur calc should be a x10^x button
foggy pier
you would do -log brackets and then put that 5.6 x10^-5 value into the brackets
My calculator has a blank spot as a subscript after the log, what do i put there?
brazen sun
wdym
foggy pier
wait
brazen sun
ok
heavy nova
is this how i find the critical points? and is it correct?
f(x) = 18x^5-15x^3+5x
frozen bobcat
where did the points come from?
vocal sleetBOT
@heavy nova Has your question been resolved?
heavy nova
where did the points come from?
i subbed in 1/3 for x in f(x) = 8x^5-15x^3+5x
same thing for 1/6
frozen bobcat
1/3 is t, not x
heavy nova
1/3 is t, not x
yeah but i said let t = x^2
frozen bobcat
right, so x^2 = 1/3, not x
heavy nova
right, so x^2 = 1/3, not x
but someone else said "x^2 = t = 1/3 or 1/6"
vocal sleetBOT
frozen bobcat
ok. You currently have t = x^2 = 1/3
totally fine.
You cannot then say x = 1/3
Because x is not what you have as 1/3, you have x^2 is 1/3
so if you want to substitute back into the equation, you need to either get x =
or rewrite the equation in terms of t = x^2
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heavy nova
so if you want to substitute back into the equation, you need to either get x = ...
how would i do that?
vocal sleetBOT
how would i do that?
frozen bobcat
how would i do that?
if x^2 = 1/3 then x = sqrt(1/3) or -sqrt(1/3)
heavy nova
if x^2 = 1/3 then x = sqrt(1/3) or -sqrt(1/3)
and are the other 2 solutions x = -1/sqrt(6) and x = 1/sqrt(6) ?
heavy nova
if x^2 = 1/3 then x = sqrt(1/3) or -sqrt(1/3)
ok so now i can find the y value by plugging in these numbers?
frozen bobcat
yes
frozen bobcat
yep
heavy nova
yep
okayy, i have another question, lemme just post it
its the same problem, different question
heavy nova
yep
so i need to create a first derivative test chart. it looks something like this and i believe all of the critical numbers are supposed to go on top and on the sides are the factors
i need help setting it up
ik it looks like this on the side
these are factors of the derivative
vocal sleetBOT
@heavy nova Has your question been resolved?
frozen bobcat
set up your 0's and then plug in values in between like you did in the picture above