you didnt divide the 32, only the first part
#help-13
rustic siren
but the main problem was before that, you didnt factor the top part ideally, it should be (x-8)(x+4)
dreamy lava
but the main problem was before that, you didnt factor the top part ideally, it ...
Gotcha. How exactly did you factorize it to become (x-8)(x+4) ?
rustic siren
Gotcha. How exactly did you factorize it to become (x-8)(x+4) ?
viete formulas
find 2 numbers that add up to -4, and multiply to -32
dreamy lava
.reopen
cedar kilnBOT
✅
dreamy lava
find 2 numbers that add up to -4, and multiply to -32
ok, ehm. But what bothers me that it isnt just -4, but -4x. COuld you show me this example of your factorization?
uneven siren
cedar kilnBOT
dreamy lava
the coefficient is -4
Saw it now. Thanks mate!
uneven siren
....
foggy tendon
The pulley is pulling object A inclined to an angle
Whenever a vector component is inclined to an angle you should resolve it into x and y
But it’s only moving in x direction right?
If you ask me I would solve for the A there, then find the velocity for the B from A
So it’s given that A is moving in x with v0
And how fast the string is moving on the left side = to how fast the string is moving on the right side
v0 is in the x direction, using the definition of trigonometry, you will find the velocity component in the direction of the string, and that should be equal to the velocity of the string falling
foggy tendon
So it’s given that A is moving in x with v0
@uneven siren everything started from here
cedar kilnBOT
@uneven siren Has your question been resolved?
cold briar
In an arithmetic progression where the common difference is 1/2, given S_100 = 145, find S_99.
cold briar
So what I first thought of doing was.
wait nvm
i wasovercomplicating everything
.close
cedar kilnBOT
stiff totem
it doesn't look like it's S_99 by the way
cold briar
oh wait
stiff totem
it's just the odd terms, a_1, a_3, ...
cold briar
.reopen
cedar kilnBOT
✅
cold briar
odd terms
haha
okay
i definitely didn't misread that...
so...
just make the common difference 1 and the number of terms is 50
okay
.close
cedar kilnBOT
cold briar
just find a_1 and i'm done
cedar kilnBOT
Available help channel!
median mason
Greetings can someone help on this system equation have been stuck for 30 minute
median mason
cold briar
why not find xy first?
x^2 + y^2 + xy = 75
x^2 + y^2 - xy = 25
2 xy = 50
xy = 25
@median mason
median mason
x^2 + y^2 + xy = 75
x^2 + y^2 - xy = 25
------------------- -
2 xy = 50
xy = 25
Oh so xy = 25 then replace?
cold briar
but you still don't have any progress tho
you'll end up with
x^2 + y^2 = 50 on both equation
wait... is x and y integers?
median mason
No
median mason
x^2 + y^2 + xy = 75
x^2 + y^2 - xy = 25
------------------- -
2 xy = 50
xy = 25
Bro +xy-xy = 50 is invalid
muted timber
So did u find any solution
it's not about us finding any solution
It's about you learning how to find every solution
you start by getting two different equations.
The first one is the sum of both equations:
2x^2 + 2y^2 = 100, which means that x^2 + y^2 = 50
The second one is the difference of both equations:
2xy = 50, which means that xy=25; That means that y=25/x
You substitute that in the previous equation:
x^2 + (25/x)^2 = 50
When solving these you will get a biquadratic equation, which means 4 solutions of x.
Each solution of x will get a unique solution of y.
Each (x,y) pair will give you one of the four solutions of the problem
junior hollow
cedar kilnBOT
wraith daggerBOT
calculus is fun
dim tiger
do you know table of sign ?
dim tiger
do you know table of sign ?
?
junior hollow
do you know table of sign ?
nope
junior hollow
mhm
dim tiger
for a product of 2 factors to be positive we need either both factors to be positive or both be negative right
junior hollow
yeah
dim tiger
do you know how to solve inequalities
junior hollow
3
junior hollow
do you know how to solve inequalities
kind of-
since i mean usually we need to bring all values to one side
solve it as normal
dim tiger
ok if i have x-3>0 then where does x lie
junior hollow
get 2 values
dim tiger
in which interval
junior hollow
plot it on a number line
junior hollow
in which interval
3?
junior hollow
nope
confused
cant we just find the values, put them on a sign diagram, and find out the answer?
dim tiger
what is a sign diagram
junior hollow
oh-
like, usually, we plot the values after factorising the equation
on a numberline
we sub in a value greater than the positive value, smaller than the negative value, or somewhere in between the two values
to find out which applies to the signs : < or > or equal and > <
dim tiger
something like this
junior hollow
YeAHH
dim tiger
what are the roots
dim tiger
and ?
junior hollow
since theres a x infront- of the brackets
dim tiger
roots are the zeros of the equation
dim tiger
the values of x where the expression becomes 0
junior hollow
Oh
dim tiger
$x(x-3)\geq 0$
wraith daggerBOT
calculus is fun
junior hollow
so sqrt 3?
dim tiger
when does x(x-3) become 0
junior hollow
when?
dim tiger
at which values of x
junior hollow
or like a value greater than 3 and smaller than 3?
dim tiger
we have a product of 2 factors
junior hollow
yes
dim tiger
if one of them is 0 what happens to their product
junior hollow
oh so equate x to 0?
dim tiger
nice
dim tiger
and equate x-3 to 0
junior hollow
and equate x-3 to 0
positive 3
dim tiger
ok so the roots are 0 and 3
dim tiger
these are values of x when the product is 0
junior hollow
**calculus is fun**
but isnt this one equation
and if we equate it to 0 its o
0*
wraith daggerBOT
calculus is fun
dim tiger
now x(x-3) is a product of x and x-3
junior hollow
yeah-
dim tiger
if x=0 then x(x-3)=0(0-3)=0
dim tiger
and if x=3 then x(x-3)=3(3-3)=3(0)=0
dim tiger
so x(x-3) is 0 when x=0 or x=3
junior hollow
oh
dim tiger
but where r u getting these x values?
i will tell you
dim tiger
$x(x-3)=0\implies x=0$ or $x-3=0\implies x=0$ or $x=3$
wraith daggerBOT
calculus is fun
junior hollow
do we just takr the answer from the brackets only
junior hollow
ok
dim tiger
we want z=0
junior hollow
ok
dim tiger
now xy is a product of x and y
junior hollow
ye
junior hollow
yeah
dim tiger
the factors of z are x and y
junior hollow
uh huh
dim tiger
so z=xy is 0 when at least one of its factors is 0 so x=0 or y=0
did you get the concept
junior hollow
ok
but where did the 3 come from
like i get that theres a 0
but
why did u take out the (x-3)
and equate it to 0
oh wait
nvm
ok
i got it
i understand now
so the x outside of the brackets is individual
correct?
so its -0
=*
and (x-3)=0 is positive 3
and then we have the values for the
dim tiger
exactly
junior hollow
okok
dim tiger
the factors here are x and x-3
dim tiger
niceee
junior hollow
i was confused at first since i thought they were a whole one
ok what abt the second one tho
dim tiger
np
junior hollow
x^2<4
dim tiger
we didnt solve the inequality yet
dim tiger
we still need to solve the inequality
dim tiger
now plot 0 and 3 on the number line
sub value less than 0 a value between 0 and 3 and a value greater than 3
junior hollow
yup
the answer is
x is greater or equal to 3
and x is smaller or equal to 0
yayy
ok
dim tiger
great
now for the second one
x^2<4
so x^2-4<0
now factor x^2-4 into product of 2 factors
junior hollow
u cant rly factor it tho
dim tiger
why cant you
dim tiger
what is sqrt(4)
cedar kilnBOT
@junior hollow Has your question been resolved?
hearty vector
Any idea how to solve this
cedar kilnBOT
Any idea how to solve this
spice folio
Solution does not exist in real numbers
cerulean harness
It seems x is an irrational number
cerulean harness
U do it by urself first
Letting 3^x as a
Then applying the quadratic equation
hearty vector
What?
cerulean harness
?
cerulean harness
Wdym?
spice folio
it is actually 0 if you go trial and error
hearty vector
How do i get to that
cerulean harness
forgot the log
No need of that tbh cuz x is the exponent of 3 in the ques
Also,
0 can't be the ans
spice folio
yes
cerulean harness
hearty vector
.close
keen nova
i am struggling to see how this can be right
cedar kilnBOT
i am struggling to see how this can be right
wraith daggerBOT
keen nova
yet, here they are treating MP as if it was the hypotenuse
taking MP^2 - r^2
TP will always be larger as long as TMP is 90 degrees
i don't get it
more context :
THIS HAS TO BE WRONG
YET THEY MAKE ME SPEND HOURS ON THIS BUT THE QUESTION HAS TO BE WRONG
oh my god i am so mad
please someone tell me i'm wrong
okay i realized my mistake
.close
cedar shale
Only got the center correct other two are wrong, even tho a site says I'm right
cedar shale
cedar kilnBOT
@cedar shale Has your question been resolved?
cedar kilnBOT
@cedar shale Has your question been resolved?
worn forge
Hi there! I'm trying to figure out how to build a formula that explains a bunch of variables, but I'm very new to math... I'm passionate about video games and always get "lazy" about math.. I figure it's time to fix this problem... I never got a proper education in mathematics, but since I'm finding myself doing wiki pages for games I love, I'm now finding I can't run from this any more. is anyone willing to help me figure out how to write down a "Chance to hit" formula?
I know how it works logically, I just don't know how to explain it using mathematical symbols... it's the notation that's the problem here. Should be easy to answer for someone who's involved in this. 🙂
narrow wagon
A chance to hit is a percentage often like 84% this means it's a ratio. You could think of it as 84 hits / (84 hits + 16 misses), or 84 hits out of 100 tries.
I'm not sure if you're asking how to design a more interesting formulation using more variables (attack level, evasion of enemy etc), if so you could mention them here
Ah ok I think I misread your question, you're asking for symbols so you can write a wiki page?
I think as long as the ratio is clear (It should have a numerator and denumerator) I think it makes sense
I don't think you need anything fancy symbols
worn forge
Sure, so, here's the way this works.
the game is Final Fantasy XII: The Zodiac Age (The remaster)
Evasion comes from shields and weapons in this game, and if you're playing the original on PS2, there's an accessory that conditionally adds chance to avoid.
the game does a series of checks.
The game assumes from a starting point that chance to hit is 100.
there are 4 variables (I think that's what they're called? oop) that go against this
Mechanics of Damage Avoidance
Damage Avoidance has 4 checks as to whether the defender successfully avoids damage, in order:
- Shield Block
- Weapon Block
- Parry
- Miss
narrow wagon
Yeah so you can represent conditional variables by setting some function that evaluates to 1 when true and 0 otherwise
so
20 + I_shield * 40 will give 60 if I_shield is true, 20 otherwise
worn forge
Here's where it gets nasty... this engine doesn't behave like that does.
narrow wagon
worn forge
So, say it's between you and I, you're the attacker using a magic spell.
narrow wagon
need to attend class will try to check later
worn forge
Sure, I'll type it out and you can look when you can. 🙂
cedar kilnBOT
@worn forge Has your question been resolved?
worn forge
The game has augments which are passive skills, and technicks and magicks which are actives (Abilities for shorthand), you have to DO those.
Game has two types of attacks, physical and magickal. (Spelling is old timey)
The attacker has 100% chance to hit unless:
- Windy/Heavy Rain/Snowstorm/Sandstorm and using a bow (x0.5) or crossbow (x0.8)
- Blinded (x0.5)
so, worst case, we're walking in with 25% accuracy, but not always.
the formula needs to reflect these as potential variables.
Outside of this, it's on the defender's side.
This is done in a series as follows:
- defender's shield block
- weapon block
- parry chance
- miss chance (unknown variable, honestly, always been a mystery, miss is pretty rare, though.)
Before the game does any math, though, it asks itself 3 conditionals
- Does the attacker have the Ignore Evade augment (Yes/No?) [if yes, skip shield block, weapon block and parry.]
- [If No] Can the ability be evaded? (abilities can be blocked or evaded, but they cannot miss. this is how you get around bad weather as a blind bowyer, but some abilities like the spell "dark/darkness" have an innate "Ignore Evasion" property as well, so it'll entirely ignore any chance to avoid. [so, it will ignore the defender's shield block, weapon block, parry, and it cannot miss.]
- [If Yes] What type of damage is the defender taking? (Physical or Magickal)
So say after all this, attacker doesn't have ignore evade, the ability doesn't have ignore evade, and we're taking magickal damage.
Conditionals:
- "Shield Block" augment for Defender. (can have up to 3) "adds a flat 5% chance to evade to a shield per stack" but ONLY in categories your shield has.
so if you have 3 SB Augments (+15/+15) and your shield has 15 Physical and 15 Magickal evasion, you'll have 30 of both evasion types from your shield.
- if it has 15 magick evade and 0 physical evade, you'll have 30 magick evade and 0 physical evade.
- if you have 15 and 1, you'll have 30 and 16... it only applies where the shield is positive.
so if we have a magickal attack (Always 100% accurate) and we have 10 Magick Evasion on the shield, and 2 Shield Block Augments, I have 20% chance to evade. which is 80% chance to hit.
THEN
If my weapon has 10% magickal evasion, it takes 10% off of OF 80%
THEN
You can't normally parry, it requires a specific item to be worn as your accessory, if you're wearing it, parry is always 30% chance.
THEN it rolls for a miss. (We don't know the chance of this to occur exactly)
So it then runs a probability chain, Accuracy - Shield's Chance to Avoid = 80%
did that hit? yes.
okay, 80 - Weapon's chance to avoid = 72%
Did that hit? yes
Okay 72 - Parry = 50.4
Did that hit? yes
Cannot Miss
HIT!
worn forge
<@106637056335216640> Has your question been resolved?
For clarity:
Evasion and Block are the same thing, evading is blocking, blocking is evading according to this game, so that's the same variable. (I think that's the name for it)
so, you can't "block" per se, you evade.
So you evade (block), parry, or the attack misses.
"Miss" is a random outlier, you can't modify the chance of it occurring. it basically only occurs as a last ditch before deciding whether you got hit or not.
If anyone has any questions regarding how this works, just ask! 😄
I'm just trying to come up with a formula I can put on the wiki, lmao.
cedar kilnBOT
@worn forge Has your question been resolved?
cedar kilnBOT
@worn forge Has your question been resolved?
worn forge
No
cedar kilnBOT
@worn forge Has your question been resolved?
narrow wagon
so assuming you want to write a wiki page for this game you could write it two ways. The first is very similar to how you wrote it here where you just explain the effects of each conditional, this is honestly probably preferred if you want the people to fully understand what's happening
if you want to write it in a single line of math it will be ugly. However, you can abuse the indicator functions that I mentioned earlier.
Ill just make an example here:
The attacker has 100% chance to hit unless:
Windy/Heavy Rain/Snowstorm/Sandstorm and using a bow (x0.5) or crossbow (x0.8) Blinded (x0.5)
Let the function Weather(X) = 1 when X = Windy, Heavy Rain, Snowstorm or Sandstorm and 0 otherwise. You can defined these function as piecewise (https://wikimedia.org/api/rest_v1/media/math/render/svg/e3977eccbf90d95798f9d4c30f04a8ad7ac45974)
Let the function Bow(Y) = 1 if a bow is used, 0 otherwise, same logic from crossbow and blinded.
Just to make sure I interpret this correctly its if the weather is BAD and you are using a bow OR crossbow you get a penalty, and you get blinded penalty regardless of weather.
We can also drop the X and Y for convenience
Chance to hit = (1 - Blinded * 0.5) * (1 - (Weather * ((Bow * 0.5) + (Crossbow * 0.3)))
assuming you cannot use both a bow and a crossbow at the same time
worn forge
if you want to write it in a single line of math it will be ugly. However, you c...
Weather bad, if you're using crossbow, lose 20% accuracy. if using bow, lose 50% accuracy. (This effect occurs AFTER blind)
So if you have the blind status effect, it's 50% reduced accuracy.
if you have bad weather and are blinded, and you're using a bow, you have 25% accuracy.
narrow wagon
might have messed up some numbers but does this help
worn forge
kind of? because I'm not even sure how indicators work, may I DM you for the purposes of this question and call this room closed?
It's okay if you say no! I'm trying to learn mathematics and I'm a bit of a scrub.
narrow wagon
I'm a bit busy rn, but I wish some other person would check this
worn forge
Poke em? kekw
narrow wagon
ideally someone who actually does probability lol
let me check
Idk anyone I can ping but perhaps you could use the help forum (because those post stay up for longer) and copy paste what you wrote
alternatively you could post on reddit maybe
worn forge
This doesn't mean anything to me, btw.
It references itself it so many places that it can't do anything.
how can X = -itself if it's less than zero
how can X= +itself if it's greater than or equal to zero?
I don't know what these symbols mean lmao.
woeful flame
|x| means the absolute value of x
if a number is less than 0, multiply it with -1, which give us an ans as the abs value
and if a number is greater than 0, the abs value is itself
-x which means to the ans of the duplication (x*-1), -x mustn't be considered as a negative integer
woeful flame
actually, it is meaningful if 'x*-1' is written instead of '-x', and 'x' instead of '+x'
dapper raven
The vertical line means absolute value which is just how big the number is, not caring about if it is positive or negative
dapper raven
The curly bracket thing { is the notation for a function with two(or more) different conditions. This is known as a piecewise function
The reason it is -x is because when you have |X| if X is negative that means you have a number like '-a' and in order to find the size of the number you add another - in order to just get a
The commas and text after that indicates that for any number X , if X is less than 0 aka negative then use -x
and the same for the bigger than or equal to 0
Where instead of adding a - in front you just take the number as it is
cedar kilnBOT
@worn forge Has your question been resolved?
cedar kilnBOT
cedar kilnBOT
Available help channel!
winter rose
is there any "steps to follow" to find the boundaries of a convex real function of single variable?
winter rose
my notes just have all kinds of proof, but nothing on how to use them and such
given a function f(x) of the form ax^k, bx^(k-1) ... where a, b, ... are constant coefficients, and k is the an integer (that is the order? of the function, if i am using the term right), and no "funny" stuff like trigo for the moment,
i am told f(x) is convex in some interval [a,b] (unrelated to the a and b above), where a < b.
to find a+b
my thoughts are to twice differentiate it?
and then it must be greater than 0
crimson delta
yes
livid tundra
can someone explain
cedar kilnBOT
can someone explain
livid tundra
I want to know how we got ln (1)
tropic oxide
$\lim_{b \to -\infty} \frac{b-1}{b+1}=1$
wraith daggerBOT
Ann
livid tundra
I take the highest degree?
tropic oxide
sure...
livid tundra
-infinity/-infinity = 1?
tropic oxide
yes but you should never write it this way
tropic oxide
u = sqrt(x) => x = u^2, and dx = 2u du = 2 sqrt(x) du
tropic oxide
overthinking it
livid tundra
sorry?
tropic oxide
ok let me write it in full
$\int_0^{\infty} \frac{\dd{x}}{(1+x)\sqrt{x}} \overset{x=u^2}{=} \int_0^{\infty} \frac{2u \dd{u}}{(1+u^2)u}$
wraith daggerBOT
Ann
tropic oxide
agree or disagree?
livid tundra
yes
tropic oxide
this was not a yes/no question
livid tundra
Are you mentally okay?
One of the definitions of exactly is “a reply used to confirm or agree with what someone has just said.” Like absolutely and definitely, you can also add “yes” to this I agree synonym.
tropic oxide
"agree" is only two characters longer
livid tundra
I'm not here for english I'm here for math
tropic oxide
well i've already told you the math you asked about, save for one (1) cancellation
livid tundra
wdym save for one(1) cancellation
tropic oxide
i did not cancel out the u's from the top and bottom.
cedar kilnBOT
@livid tundra Has your question been resolved?
cedar kilnBOT
cedar kilnBOT
Available help channel!
chilly spade
stuck on this calculus question
cedar kilnBOT
stuck on this calculus question
spice kraken
calculate the total profit in terms of x
celest sentinel
be careful; the cost is "per x blankets", while the market value is "per 1 blanket"
celest sentinel
Yeah, that should work
ripe cliff
need to find det(2B^(−1))
cedar kilnBOT
need to find det(2B^(−1))
ripe cliff
i don't understand how to turn A matrix into B or something like that
that's what i got and don't know what to do next
earnest socket
probably better to try transforming B into A
rearrange columns of B, and then transpose
(modifying the sign of the determinant correspondingly)
cedar kilnBOT
@ripe cliff Has your question been resolved?
ripe cliff
.close
strange bronze
cedar kilnBOT
strange bronze
How do you simplify the denominator?
I can't make (tan^2(x)+1) to get to sec^2(x)
Or idk how
Oh wait a minute
.close
crimson sedge
Let A be a 3×3 matrix. Let B be a column vector such that $B^TAB$ is 0.
If I take transpose both sides, then $B^TA^TB$ is 0. I don't know what information I can extract from this. Does this imply A is symmetric?
wraith daggerBOT
- Miles12345
crimson sedge
<@&286206848099549185>
cedar kilnBOT
@crimson sedge Has your question been resolved?
crimson sedge
<@&286206848099549185>
spice spoke
without giving any more infos on B, then not necesarily. Take B zero vector. then B^TAB = 0 is true, but A can be anything.
@crimson sedge
crimson sedge
What if B is non-zero
spice spoke
take any A with A11 = 0, take B=e1. Then again u have the equality but A can be anything up to the A11 entry
and B is not zero
Maybe give more context, is it a part of proof?
crimson sedge
,rotate
wraith daggerBOT
wraith daggerBOT
crimson sedge
Question 2
spice spoke
it literally says for EVERY vector B u have the equation 
crimson sedge
Yea
But like
I don't even know how to proceed or what information to extract if I consider general case. So I thought to consider special cases and get to the answer
spice spoke
if B is a column vector aint a B^TAB just a number?
crimson sedge
if B is a column vector aint a B^TAB just a number?
Yep
Here's my rough work. It may seem weird due to the assumptions I'm making
spice spoke
then why it says BTAB is a zero matrix
crimson sedge
That's what confused me initially but I thought it's taking 0 as [0] (a 1×1 matrix) lol
spice spoke
ye technicaly correct but still weird. Anyway take B=ej for j=1,2,3 plug in into equation B^TAB = 0
what it says about A?
crimson sedge
Well nothing except it's a 3×3 matrix, and some values of its elements
Oh wait
Lemme plug
spice spoke
ye u know the diagonal entries of A
crimson sedge
crimson sedge
Ohh
spice spoke
B = e2 = [0,1,0]
crimson sedge
My bad
spice spoke
a13 a23 a21 are given aswell for free
spice spoke
probably for the rest of unknowns entries, but atleast u know diagonal entries immediately if u plug e1,e2,e3 in
crimson sedge
Perfect
spice spoke
oh ye try plugin [1,1,1] u will find a12 that way
crimson sedge
Thanks a lot!
spice spoke
no problems
crimson sedge
.close
crimson sedge
If......, calculate
cedar kilnBOT
If......, calculate
crimson sedge
I have done this, but I don't know if it's correct
wintry pier
!noclopen
cedar kilnBOT
Please don't repeatedly close and claim a new channel with the exact same question. This erases all previous progress made towards your problem and is confusing for helpers, making it more difficult to help you. Please be patient, even if your channel has not received much attention.
crimson sedge
oh okay, I wanted to pin the question and put then my answer
this is why I opened another one
cedar kilnBOT
@crimson sedge Has your question been resolved?
turbid spoke
Someone can help me
cedar kilnBOT
Someone can help me
turbid spoke
with mathemathic discrate
mild coral
ok im going to read your mind and help you
crimson sedge
crimson sedge
ok im going to read your mind and help you
Tell me too
turbid spoke
Tell me too
.
turbid spoke
ok im going to read your mind and help you
.
turbid spoke
Okay thx
crimson sedge
how i can make venn diagram
Can you make
A universal set as a big box
And then three intertwining circles, name them set A B C
Then like
Keep the commons of set A and B between the common area of circle A and Circle B
Similarly for all
Thinsg that dont come in A B C circles, will be inside the box outside of all the circles
And things that come in all three sets A B C , will be in the commonplace of all the three circles
Whichever you understand the best 👍
@turbid spoke
crimson sedge
Yep
crimson sedge
Ummm idk
turbid spoke
yes i need solve word problem
turbid spoke
with set theory
crimson sedge
What grade are you in
turbid spoke
university
crimson sedge
how i can make venn diagram
This is the easy level medium or hard i mean
turbid spoke
This is the easy level medium or hard i mean
Do you know what the inclusion and exclusion property is?
crimson sedge
Do you know what the inclusion and exclusion property is?
Not by namw, show some example
And i cant find specific site for word problems on solvjng sets using venn diagrams
turbid spoke
Does it always start with the intercept or are there exceptions?
crimson sedge
The words you use go over my head but
Yes
Like youre given n sets
(Add all singletons) - (all intersection pairs) + (3 intersetions ones) - (4intersection ones) .... ±(n intersections)
crimson sedge
The words you use go over my head but
Yes
Like youre given n sets
(Add all si...
A more precise but harder to undsrstand way for what i just said
@turbid spoke
cedar kilnBOT
@turbid spoke Has your question been resolved?
gusty rune
can someone help me with this
cedar kilnBOT
can someone help me with this
digital cliff
do you know soh cah toa
gusty rune
a little
digital cliff
o=opposite, h=hypotenuse, a=adjacent
sin=o/h
cos=a/h
tan=o/a
gusty rune
okay
digital cliff
what would sin(A) be
gusty rune
5/13
gusty rune
no not at all
digital cliff
it is indeed
digital cliff
looks good to me
digital cliff
yup, just from B rather than from A
gusty rune
so where would the adjacent and opposite be
strange bronze
cedar kilnBOT
strange bronze
Why are these not equal
Ax^2-16Ax+64A+Bx-8B+C
1=A, 0=-16A+B, 64A+C=0 so A=1, B=16, C=-64
strange bronze
I just fingured it out a moment before you sent that
But you're right
I hate that little mistakes like that take up so much time
I'm going to write it differently and put it into the formulas while I expand it so that doesn't happen again
Thanks
.close
cedar kilnBOT
muted bear
Youre welcome!
cedar kilnBOT
Available help channel!
hazy depot
I need to find the co-ordinates of the point of intersection of CM (y + 3x = 14) and AD (x - 2y = -2)
hazy depot
<@&286206848099549185> it is such a simple part of the question, but i still just don't know how to do 😭
cedar kilnBOT
@hazy depot Has your question been resolved?
hazy depot
<@&286206848099549185> just to alert again
sweet crest
solve the system to get your point
hazy depot
but how
floral condor
find n
wintry pier
,rotate -90°
wraith daggerBOT
cedar kilnBOT
@floral condor Has your question been resolved?
crimson sedge
,rotate -90°
Logarithms
floral condor
Logarithms
ive not learnt that
floral condor
<@&286206848099549185>
floral condor
.close
buoyant hill
Hi guys, I'm French btw
i want to make an equation of this text
International standards define the danger threshold as : 85 dB for 8 hours. This threshold increases by 3dB each time the exposure time is divided by 2.
It means u can resist 8hours hearing a 85dB sound without ur ears getting hurt.
it s like 85+n3 = ...
buoyant hill
it s a basic thing, plz i need help
cedar kilnBOT
@buoyant hill Has your question been resolved?
buoyant hill
<@&286206848099549185>
onyx dove
$85+3(3-log_2(t))$
wraith daggerBOT
chlamydia
onyx dove
random shore
Hey I dont need help with anything but I wanted to give a big shout out to all the helpers. Im pretty sure I got a solid mark on my calc test and I wouldnt have been able to if it wasnt for you guys and gals. Thank you all so much.
random shore
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winter cairn
cedar kilnBOT
onyx dove
!status
cedar kilnBOT
What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
1
onyx dove
$x\to{\frac{\pi}2}^-$ know what this means?
wraith daggerBOT
chlamydia
winter cairn
No I know when it’s simpler numbers
I’m really confused
@onyx dove do you think you can help me?
cedar kilnBOT
@winter cairn Has your question been resolved?
winter cairn
I got it now
neat dune
Noice
cedar kilnBOT
@winter cairn Has your question been resolved?
upper elm
I am solving something for my company and was wondering if anyone could help.
Basically, I need to write an algorithm to accurately get from an initial % composition by mass, to a desired % composition by mass. For example, if sample A was 100kg initially, and it was made up of 40% carbon and 60% iron, and I wanted it to become 45% carbon and 55% iron, how would I determine suitable amounts of either to obtain that composition. I CANNOT subtract anything that was initially in the sample, nor take away anything that I add. I can only add enough to dilute the sample to its desired % compositions respectively.
If I can get an algorithm for this, I will need to extrapolate a formula to work with, let's say, 12 different materials within the composition.
upper elm
Here is an example of what a final wants list could look like, but I would like to start with a simpler example so I can understand the math behind it.
digital cliff
I am solving something for my company and was wondering if anyone could help.
B...
these % dont sum to 100
upper elm
Typo, sorry.
Obviously, there are an infinite number of answers so what I'm finding difficult is finding the most efficient or first one.
If anyone is interested in doing a voice call for further clarifications that may be helpful
cedar kilnBOT
@upper elm Has your question been resolved?
cedar kilnBOT
@upper elm Has your question been resolved?
cedar kilnBOT
@upper elm Has your question been resolved?
lethal jackal
this seems like a linear programming problem
set x to be the amount you add of each element
minimize c^T x, where c is the cost of each element
your constraint is a little harder, but you can actually write it as A(x_0 + x) = 0
for a suitable A
cedar kilnBOT
@upper elm Has your question been resolved?
upper elm
I don't understand that exactly
cedar kilnBOT
@upper elm Has your question been resolved?
fair geyser
take any amount of final composition e.g. 1 kg
divide every part of the orginal by every part of final
if you take the largest quotient and multiply by
that 1kg every part becomes at least as large as the orginal so you can just add the difference
@upper elm
maybe that's nonsense somehow
can't see the problem if so
lethal jackal
yeah I wonder if some greedy algorithm works here
the thing I'm worried about is if the elements cost different amounts
broken mist
What are typical good techniques of determining reasonable domain and range?
broken mist
Other than the obvious figuring out what fits “reasonably”
Like if your range is distance a ball can be thrown, hundreds of miles are obviously out of the picture, but I have no idea what outliers could be at. Is there a certain number of standard deviations from a mean that is generally used?
buoyant latch
What does standard deviation has to do with range
broken mist
I don’t know that’s why I’m asking
Like are there any general conventions that are followed when determining “reasonable” domain and range?
Or is it just a situation of if I fits I sits
buoyant latch
Like if your range is distance a ball can be thrown, hundreds of miles are obvio...
I would bound this by upper limits
You can do like rough approximations to bound your results
Like let’s say you probably can’t throw harder than a bat swing
broken mist
What if a datum somehow does surpass that
buoyant latch
And a bat swing hits a ball around a baseball court
broken mist
I guess you’d just increase the reasonable range
buoyant latch
So the size of a baseball court is probably a good upper limit on how far you can throw a ball
broken mist
So essentially just what makes sense
I don’t like that lol math isn’t supposed to be subjective in my mind
buoyant latch
Nothing about this has to do with math
I can’t even tell what topic you’re talking about
broken mist
Determining “reasonable” domain and range of a function
buoyant latch
The domain and range of a function has nothing to do with reasonability
broken mist
I’m supposed to teach it with function domain and range and can’t wrap my head around how to effectively determine a “reasonable” domain or range
buoyant latch
They are defined alongside the function with the notation f: A -> B
broken mist
Then why is it in this curriculum lol
buoyant latch
Well I don’t know the context you know
broken mist
So like take a word problem that’s optimizing the area of a fence
classic problem
Obviously your area can’t be negative, so even if the area is modeled by a parabola then you’re not going to include negative intervals of the domain in a “reasonable” domain
It makes sense with cases where you can’t have negative area but I can’t figure out how one would consistently determine a reasonable range for something like throwing a ball
Like the length of a baseball field makes sense, but I’m sure there some outlying person who could yeet a home run
Would they be included in a “reasonable” range?
lethal jackal
the concept of signed area is a pretty useful one
broken mist
For high school sophomores?
lethal jackal
yeah in some matters of practicality it is
broken mist
What’s the point in ever bringing this up in a class then?
lethal jackal
as an example, suppose you have two parcels of land that are currently separated by a property curve
there's a proposed redrawing of the property line
compute the amount of land you stand to lose/gain from this redrawing of the property line
you compute signed areas and add them up
broken mist
I’m not trying to condemn “reasonable” domain and range though I’m trying to justify it
lethal jackal
I'm not actually sure what you mean by domain and range here
like domain and range of a function?
broken mist
A word problem that allows for signed area defeats the purpose of it in the first place
Yes
lethal jackal
seems several things are getting conflated here
broken mist
Domain and range of a function
lethal jackal
functions are defined on whatever domain you wish them to be
broken mist
A function that models typically a word problem where signed or extreme values would be, for lack of a better word, “unreasonable” to include in the domain or range
lethal jackal
I think that's a little bit of a rigid way of looking at things
one is generally free to pick whatever mathematical tools they please to solve a real-life problem
for example, even though voltage and current are physically related to the flow of charges, and as such take on real values, people use complex numbers for them all the time
the same goes for things like complex frequencies, even though frequency is just counting the number of times something happens
broken mist
.close
viral plover
hello
lusty grotto
what do u mean by calculate it?
viral plover
like solve it
lusty grotto
it is not possible to solve it, there are too many unknowns
dusky peak
viral plover
thx
cedar kilnBOT
@viral plover Has your question been resolved?
crimson pike
cedar kilnBOT
crimson pike
is this the right way to proceed with this question or is there another way to do the integration
tropic oxide
missing dx but yes this is correct so far
mint raft
Is this the correct inverse function of the problem?
cedar kilnBOT
Is this the correct inverse function of the problem?
primal socket
It is, yes
mint raft
It is, yes
Srsly?
primal socket
Yeah, replace y with $h^{-1}(x)$
Because y= isn't a function
But you can use commutativity to rearrange $2-3x$ to $-3x + 2$
primal socket
x+1 is correct though
cerulean harness
Oh right my bad
cedar kilnBOT
@mint raft Has your question been resolved?
sterile grove
cedar kilnBOT
opal basin
B^T means the transpose of B
sterile grove
B^T means the transpose of B
what is the transpose of B?
opal basin
It's swapping the rows for the columns
sterile grove
It's swapping the rows for the columns
oh
opal basin
So the rows become the columns and vice versa
sterile grove
is the determinant of a transposition of a square matrix always the same as the original?
opal basin
Yes
sterile grove
but a non-square matrix would have to be calculated right?
opal basin
Non-square matrices don't have determinants
sterile grove
Non-square matrices don't have determinants
they don't?
opal basin
No, it's impossible for some of the properties of determinants to hold in that case
sterile grove
I guess that makes sense
strange that I haven't run into that question up until now
opal basin
det(AB) = det(A)*det(B) = det(BA) wouldn't always be true
stiff gyro
-
A particle moves to the right along the curve y = x^3/3 with a constant speed of 4 feet per second. Find a_t and │a_n │as it passes through the point (1, 1/3).
-
A particle moves along the given curve r = 1 + sin^2 Ɵ with a constant angular velocity of 2 radians per second. Find the speed and acceleration at Ɵ = π/2.
-
A particle moves in accordance with the equations r = t^2 + t and Ɵ = t^3 /6 where t denotes the time. Find its position and speed when t = 2.
i really need help....it wasnt discussed yet but the teacher already gave us this math problems...
blazing dune
Can you picture them as there are some numbers that aren't understandable
Like
The first question
Is it
$$y = \frac{x^3}{3}$$
stiff gyro
wait lemme fix it
wraith daggerBOT
Sherif Player
blazing dune
Or $$y = \frac{3x}{3}$$
wraith daggerBOT
Sherif Player
stiff gyro
**Sherif Player**
this is
blazing dune
Also what is $a_n$ and $a_t$?
wraith daggerBOT
Sherif Player
blazing dune
@stiff gyro ?
stiff gyro
hold on i do not know about it maybe it is normal acceleration and tangential accelaration...
blazing dune
Normal acceleration mean you want the acceleration to the right or what ?
I checked it
stiff gyro
i dont really know to be honest....
blazing dune
Oh so you didn't get it in class
Or you didn't study well to know it ?
stiff gyro
huh?
i really need help....it wasnt discussed yet but the teacher already gave us this math problem - earlier message
kinda like i didnt know how to solve this yet because it wasnt discussed yet
cedar kilnBOT
@stiff gyro Has your question been resolved?
slender dew
hey, sorry for bothering. can someone help me with this question?
scarlet garnet
hey, sorry for bothering. can someone help me with this question?
at which step are you stuck?
slender dew
this step right here, am i on the right track?
i conversed 1/x = a for example, so it changes from lim x to lim a->0
i have tried separating cot a/(1/a) and (2-3a)/(5-2a) but the result is still 0
scarlet garnet
this step right here, am i on the right track?
oh sorry, please ping
slender dew
oop, my bad
scarlet garnet
tbh I would simplify the function first by deleting irrelevant parts
in the nominator you have something like $2x\cdot a - 3 a$, so you know that towards infinity the left term escalates, meaning the right one is irrelevant
wraith daggerBOT
Jigglyproff
scarlet garnet
the same goes for the denominator, you have $5x^2-2x$, which basically is $5x^2$
wraith daggerBOT
Jigglyproff
scarlet garnet
there is a formal way, either big O notation or a play with division by x, whatever your prof/teacher used
slender dew
oh wait okay, so the limit dont change first, but rather simplified it to algebra
scarlet garnet
then you end with\
$\frac{2x\cot{\frac{2}{x}}}{5x^2}$, where you can push out the $\frac{2}{5}$ in front of the limit to get\
$\frac{2}{5}\cdot$ limit of $\frac{\cot{\frac{2}{x}}}{x^2}$
wraith daggerBOT
Jigglyproff
scarlet garnet
limit as x approaches inf, forgor how to do that in LaTex
scarlet garnet
as a hint:
|| cot(x)=cos(x)/sin(x) ||
slender dew
soo
lim $\frac{1\frac{cos\frac{2}{x}}{sin\frac{sin\frac{2}{x}}{x^2}$
mmmkay got it. thank youu
.close
patent pond
Help me pls,I haven't found a solution to this exercise.
cedar kilnBOT
Help me pls,I haven't found a solution to this exercise.
patent pond
help meee
night kite
patent pond
Help pls
errant wasp
projection matrix for
the projection onto its column space, im actually confused what this means
cedar kilnBOT
projection matrix for
the projection onto its column space, im actually confused...
@errant wasp Has your question been resolved?
Available help channel!
errant wasp
is every vector in R^3 orthogonal to the zero vector
cedar kilnBOT
is every vector in R^3 orthogonal to the zero vector
barren forum
can you recall the definition of orthogonal? two vectors v and w are orthogonal when ...?
barren forum
and do you know how a dot product is computed?
errant wasp
in R^3 (1,0,0),(0,1,0),(0,0,1) these are the vectors where if you take the dot product of any, their result will be 0
barren forum
in R^3 (1,0,0),(0,1,0),(0,0,1) these are the vectors where if you take the dot p...
say, vector v = (v1, v2, v3), and vector w = (w1, w2, w3), their dot product is..?
errant wasp
v1w1 + v2w2 + v3w3
barren forum
yep, now what is the zero vector?
errant wasp
v1w1 + v2w2 + v3w3 = 0
errant wasp
(1,0,0),(0,1,0),(0,0,1) is this not the span where the dp = 0
errant wasp
*the zero vector* is just (0, 0, 0)
gotcha
barren forum
gotcha
so to better phrase your question, if we have some vector w = (w1, w2, w3), is it perpendicular to the zero vector (0, 0, 0)?
errant wasp
is it not just a dot at origin?
then any line that goes through the origin will be perpendicular
right
barren forum
I would say at this point it's just by the definition, w1 x 0 + w2 x 0 + w3 x 0 = 0, so yes, they are orthogonal
the intuition of perpendicular arrows breaks down here
errant wasp
i hate linear algebra
barren forum
i hate linear algebra
linear algebra loves you ❤️
errant wasp
fuck being a cs major
this shit suck
anyways
Describe S⊥ by finding a basis for it if --> S is the subspace of R3 containing only the zero vector --> all of R^3
since w1 x 0 + w2 x 0 + w3 x 0 = 0 holds for any vector
in r^3
barren forum
Describe S⊥ by finding a basis for it if --> S is the subspace of R3 containing ...
yep
errant wasp
what if S is the subspace of R3 spanned by (1, 1, 1), how do i think about this
like is this meaning that 1, 1, 1 is the only linear combination?
barren forum
what if S is the subspace of R3 spanned by (1, 1, 1), how do i think about this
S is a line through origin
barren forum
S⊥ (usually called S complement) is a 2-D plane perpendicular to the line (also through the origin)
barren forum
-1, 1, 0..?
yep, that can be one of the basis vector spanning the plane
errant wasp
probably 1, -1, 0 too
and then like ... 1, 0, -1
and then -1, 0, 1
i need to find the entire basis ig
barren forum
you just need two linearly independent ones
south tundra
S is one dimensional, its complement will be two dimensional since we are working in R^3
errant wasp
i just looked up basis defn but in my notes there is nothing about being minimal
barren forum
must be linearly independent
- linearly independent
- spanning
south tundra
Alternatively you can say basis is the minimal set that spans the entire vector space, yes
errant wasp
but if spanning means all the possibilities, why are their just two?
because i just listed like more than 2
south tundra
And 2 pairs of them are linearly dependent
barren forum
The point is, you couldn't find a set of 3 vectors in a plane that is linearly independent
south tundra
S is one dimensional, its complement will be two dimensional since we are workin...
I.e., its (complement of S) basis consists of 2 vectors
errant wasp
The point is, you couldn't find a set of 3 vectors in a plane that is linearly i...
oh wait i se