what would the integral of this be
#help-33
winged pier
integration by parts perhaps?
true frigate
would that just be (e^P^3)/3?
true frigate
idk
golden cosmos
how'd you know the answer then
true frigate
so i did it in reverse
true frigate
just do u substitution lol
what do u sub in?
marsh citrusBOT
true frigate
oh
yeah
lol
the derivative of that is 3P^2
gives the same anser
sick, ty haha
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hot drum
"Based on the store's purchase data, 40% of customers buy oranges and 33% buy bananas.
How many of the day's 1000 customers buy these fruits (oranges, bananas, or both) in the following cases. Give the answer as a whole number, rounded to the nearest whole number if necessary."
Now I am having trouble in the c section that states
"If buying oranges has no effect on buying bananas."
I can't really grasp the reason on how this affects the outcome and how do I calculate it
Can somebody help?
marsh citrusBOT
"Based on the store's purchase data, 40% of customers buy oranges and 33% buy ba...
hot drum
Okay if buying oranges has no effect on buying bananas, does it mean that those who buy oranges can also potentially buy bananas?
marsh citrusBOT
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hot drum
<@&286206848099549185>
still temple
Okay if buying oranges has no effect on buying bananas, does it mean that those ...
It's one or both
hot drum
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tranquil ice
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night lion
why is it not possible that both are zero is it due to the definiton of cross product?
marsh citrusBOT
why is it not possible that both are zero is it due to the definiton of cross pr...
frank sparrow
give me one minute
glacial hedge
why is it not possible that both are zero is it due to the definiton of cross pr...
these aren't exclusive ors
night lion
these aren't exclusive ors
i know but still
glacial hedge
still what?
night lion
still why isnt it possible that both can be together zero is corss product still defined then?
glacial hedge
0 x 0 = 0
frank sparrow
the condition a x b = 0 implies that either a or b must be the zero vector, or both must be parallel (i.e., the angle between them is 0° or 180°). It cannot be the case that both a and b are zero vectors simultaneously.
night lion
but but is that allowed
frank sparrow
is what i got
night lion
nah i dont want chatgpt to answer me gang 😭
frank sparrow
its not. i just did it.
glacial hedge
0 x 0 = 0
this is a perfectly fine definition
What's your definition of cross product?
night lion
this is a perfectly fine definition
What's your definition of cross product?
like the sin theta is the angle between the vectors but zero vectors dont have a definite direction direct
glacial hedge
you're using trig for the definition?
night lion
nah like the definiton of cross product is
A X B= |A||B|sin(theta) unit vector of n [which is given by right hand thumb rule right]
glacial hedge
0 x 0 = 0
if you ever need to define 0x0, this is the only acceptable answer
most equivalent definitions will let you directly define 0x0 as well
you just happened to take a def that fails in this case
short sedge
A X B= |A||B|sin(theta) unit vector of n [which is given by right hand thumb rul...
for ANY vector a, axa = 0. thus, 0x0 = 0. and the angle between a vector and itself is zero, so |0x0| = |0||0|sin0° = 0.
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fallow furnace
hi i have this quiz for homework
marsh citrusBOT
hi i have this quiz for homework
fallow furnace
ive put 1.True 50 2.False 0 3.False 0 4.True 20
but i only got 5/8 points
what did i do wrong?
wind sinew
<@&286206848099549185>
use chatgpt
wind sinew
what did i do wrong?
everything
marsh citrusBOT
use chatgpt
Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).
marsh citrusBOT
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alpine widget
One message removed from a suspended account.
marsh citrusBOT
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fleet fossil
One message removed from a suspended account.
Wdym by what is it
fervent rampart
,w LambertW[i*pi]
elfin berryBOT
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still temple
how do i do this i have no idea
marsh citrusBOT
how do i do this i have no idea
azure tusk
ye ion know either
still temple
id use chat gpt but i rn out of uploads
azure tusk
me too
azure tusk
i dont know what u said
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swift olive
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smeagol
swift olive
$27w^{-1}+3w=min$
elfin berryBOT
smeagol
swift olive
$-27w^{-2} + 3 = 0$
elfin berryBOT
smeagol
swift olive
$w = 3$
elfin berryBOT
smeagol
swift olive
then solving for l I got 4.5
and the answer didn't like 3 or 3000000 (million) what did I do wrong?
(optimization, system of equations but for calculus)
remote granite
try 3000 and 4500
marsh citrusBOT
swift scarab
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mint spear
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mint spear
im trying to find the angle between AP and the lower part of the shape
obv its vectors
here's my work
the alpha angle is 41.41 i alr calculated it
help :)
marsh citrusBOT
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mint spear
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marsh citrusBOT
@mint spear Has your question been resolved?
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@mint spear Has your question been resolved?
wet oriole
Right or wrong?
Math is so weird because if I were to multiply the top fraction by the bottom fraction reciprocal, I wouldn’t get the same answer
marsh citrusBOT
Right or wrong?
wet oriole
If there is a common factor throughout any part of the complex fraction, can I cancel it?
hollow oracle
Math is so weird because if I were to multiply the top fraction by the bottom fr...
what's the question?
wet oriole
If I multiply the top fraction w/ the bottom reciprocal, would I get the same result?
hollow oracle
like $\frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a}{b}\cdot\frac{d}{c}$?
elfin berryBOT
someone1010
hollow oracle
if so then yes
hardy kelp
This would be what would happen, and here the same stuff cancels out
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stray raven
marsh citrusBOT
stray raven
does this look alright?
tepid temple
does it look right to you?
because if you look right there's something that should make you think
@stray raven
180° + 59 =/= 293
marsh citrusBOT
@stray raven Has your question been resolved?
stray raven
180° + 59 =/= 293
wait what
are you referring to the decimal
and saying to round it
oh wow i just realized for some reason that skipped my mind
239.4 degrees
lilac siren
brief ana2 Q
marsh citrusBOT
brief ana2 Q
lilac siren
regarding the definition of a topological space (X, T)
can for instance
X = R
T = {EmptySet, R, B(0,1)}
?
where B is the closed ball around the origin with radius 1
seems to fulfill the conditions
but I do find it odd as it is also used as an equivalent definition for open sets
meaning V ⊆ X is open <=> V ∈ T
but how shall that apply if I can pick any valid T, especially one which contains closed subsets
marsh citrusBOT
@lilac siren Has your question been resolved?
glass silo
“How is a set different from a door?”
lilac siren
“How is a set different from a door?”
I'm not sure how that answers it :D
lilac siren
can for instance
X = R
T = {EmptySet, R, B(0,1)}
?
since this is a valid topological space,
- a topology may contain closed subsets of X
- the definition of openness of a subset of X via environments is not equivalent to that subset being within the given topology
is what I take away
glass silo
I was in the middle of editing 
was gonna comment that while said closed ball is closed wrt the standard topology (and isn’t open), wrt the new one you just defined, it’s open (but not closed, its complement isn’t in your topology)
lilac siren
ahh
topologies are meant to be the guideline for openness
if T contains all open subsets of X
then a subset is considered open equivalent to the openness definition with environments
so it provides the definition for openness itself ok
ty 🐛
.close
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oak moth
marsh citrusBOT
oak moth
stuck and lost
chilly spoke
do you need to find B(t) or just answer question 14?
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fickle slate
cos(5x) + cos(x) = 2cos(2x)
marsh citrusBOT
cos(5x) + cos(x) = 2cos(2x)
elfin berryBOT
riemann
main idol
Last one with a cleverly chosen x and y
valid cape
at what values of x does cos(2x) = 0?
main idol
cos(2x), not cos(x)
fickle slate
2cos(3x)cos(2x) = 2cos(2x)
im heavily tempted to divide by 2cos(2x) but idk if i can
valid cape
answer my question first
fickle slate
90, 270
fickle slate
45, 135
valid cape
correct, but 2 values arent enough
fickle slate
225
valid cape
now given an integer k, can you give the solutions set of x for which cos(2x) = 0?
fickle slate
45, 135, 225, 315
valid cape
now given an integer k, can you give the solutions set of x for which cos(2x) = ...
as in, the solution set of sin(x) = 0 is x = 180k for any integer k
what about cos(2x)?
fickle slate
for, cos(2x) = 0 solution set is x = 45k
fickle slate
tbh i dont know
fickle slate
90 and 270?
valid cape
correct, but again, im looking for a general solution set
if its hard, use a unit circle
,tex .unit circle
elfin berryBOT
valid cape
at what point on the circle does cos(x) = 0?
fickle slate
90 and 270
valid cape
and...?
valid cape
wrong
valid cape
remember that you can add 360 to any angle and it still doesnt change
fickle slate
90, 270, 450, 630 ...
valid cape
yes
now take your starting point as 90
if you observe closely, you can actually add 180 to 90 however times you want
and cos(x) would still be 0
can you tell me the solution set of cos(x) now?
valid cape
very good!
now that you got the solution set of cos(x) = 0, can you tell me the solution set of cos(2x) = 0 now?
fickle slate
cos(2x) = 45 + 90k
valid cape
very good!
valid cape
2cos(3x)cos(2x) = 2cos(2x)
now lets return to this
fickle slate
cos(2x) = 45 + 90k
i mean thats the solution set for cos (2x) = 0
valid cape
yes, that is correct
valid cape
do you think you can divide both sides by 2cos(2x)?
fickle slate
well idk the angle so i think not
wary kite
well cos(2x) could = 0
valid cape
yes, this is why i asked you to find the values of x in those cases
valid cape
essentially, you need to consider two cases:
- when x = 90k + 45
- when x is not 90k + 45
valid cape
so i substract 2cos(2x) from each side
this also works, its basically the same
wary kite
yes, this is why i asked you to find the values of x in those cases
my fault i didn’t see that message
valid cape
my fault i didn’t see that message
no im supporting your argument, this was directed at op
valid cape
2cos(2x) = 0
cos(3x)-1 = 0
yes
you found the solution set for the former
now do it for the latter
fickle slate
ill be right back, gotta do something quick
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rocky nova
How is the group of integers under addition cyclic?
marsh citrusBOT
How is the group of integers under addition cyclic?
rocky nova
a single member of G should be able to generate all other members
1 can generate all positive ints, and -1 can generate all negative ints. but neither can generate all
rocky nova
I am not looking for a generating set, I am looking for a generator @fervent rampart
Are you saying that if I have 1 as my generator, that includes its inverse, -1?
fervent rampart
a cyclic subgroup is generated by a generating set with a single member (the generator)
rocky nova
I get that
but shouldn't the subgroup be the actual group itself?
so not much of a "sub"group
fervent rampart
a set is a subset of itself, so a group is a subgroup of itself
rocky nova
I am still not really sure where my understanding is off. Can you just tell me what the generator of the group of ints under addition is?
As far as I am concerned, there isn't one
fervent rampart
a generator is just a member of a generating set. so the same rules apply
rocky nova
you lost me at "generating set"
well not really
I am trying to determine if the group is a cyclic group
a single element in G has to be able to do this (create all members of G)
fervent rampart
yes, we like to drop the {} and write <g> rather than <{g}> but they mean the same thing. the definition of a generator does not change
rocky nova
I am not sure why you're mentioning {} that is not what I was confused about, although I am now
can you please just tell me what the g is?
I am not sure what the <> denotes either
is that saying "generator" ?
fervent rampart
using additive notation,
<g> = {ng, n in Z}
using multiplicative notation,
<g> = {g^n, n in Z}
in other words, all elements which can be expressed using a finite number of group operations on g and its inverse
rocky nova
in this example what constant is g
fervent rampart
<g> is the set generated by f
fervent rampart
in this example what constant is `g`
1 would work
fervent rampart
-1 + -1 = -2
rocky nova
note the "and their inverses"
1 is not -1 though, is that why you mentioned this?
fervent rampart
yes
rocky nova
thank you
I get it now
thank you for your help and patience @fervent rampart
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dense smelt
prof accidently put something we havent learned yet on our homework, but insists we do it anyway, which I've only just noticed now, 1.5 hours before its due.
Is anyone able to point me to the relevant reading stuff to solve this problem? Maybe an example? I would like to avoid any stupid mistakes from a hasty google search, and our book is too dense for me to get confident and also do the problem before I have to turn it in.
marsh citrusBOT
prof accidently put something we havent learned yet on our homework, but insists...
@dense smelt Has your question been resolved?
brave marsh
For a), you want to show linear independence.
That means that you want to see whether a linear combination of p1, p2 and p3 can yield the 0 function without all the coefficients being 0
brave marsh
That's the right approach.
dense smelt
keep in mind I am cooked 
brave marsh
You likely don't need gaussian elimination though
brave marsh
To have linear independence you need to make sure that the only solution is a1 = a2 = a3 = 0
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brave marsh
b) is somewhat similar
You take some generic $\alpha x^2 + \beta x + \gamma$ and you have to show that there are some $a,b,c$ such that $a p_1 + b p_2 + c p_3 = \alpha x^2 + \beta x + \gamma$
elfin berryBOT
Azyrashacorki
brave marsh
It will look somewhat similar to what you had in a), but the equalities won't be homogeneous (= 0)
dense smelt
thank you so much :)
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muted scroll
find the biggest n where n³ + 100 is divisible by n + 10
marsh citrusBOT
find the biggest n where n³ + 100 is divisible by n + 10
limber hearth
n³ + 100 = (n+10)(n² -10n + 100) - 900
If n³ + 100 is divisible by n+10, it needs you something else here
sleek lake
it means 900 is divisible by n+10
sleek lake
the question becomes how did you factorize it like that
twilit geyser
it's n^3 + 10^2 which wishes to become n^3 + 10^3 🥹
limber hearth
Forced factor by n+10
sleek lake
the technique that needs to be nerfed badly
still temple
where did OP go?
marsh citrusBOT
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muted scroll
n³ + 100 = (n+10)(n² -10n + 100) - 900
I also did that but I didn't know what should I do next
tawdry rampart
Do you know about factor theorem?
true parcel
900 must be divisible by n+10
muted scroll
I have (n+10)(n² - 10n + 100) - 900 ≡ 0 (mod n + 10)
since (n+10)(n² - 10n + 100) is divisible by n + 10
also 900 must be divisible by n + 10
tawdry rampart
Put -10 in f(n)
true parcel
I have (n+10)(n² - 10n + 100) - 900 ≡ 0 (mod n + 10)
since (n+10)(n² - 10n + 100...
yes
you're looking for the biggest n
biggest divisor of 900 is 900
so n+10 = 900
zinc solstice
Let $\mathbb{P}$ be a probability on $(\mathbb{R}^n,\mathcal{B}(\mathbb{R}^n))$. Prove that for any $S\in\mathcal{B}(\mathbb{R}^n)$ and $\epsilon>0$, there are an open set $A\supset S$ and a closed set $B\subset S$ such that $\mathbb{P}(A\setminus S)<\epsilon$ and $\mathbb{P}(S\setminus B)<\epsilon$.
marsh citrusBOT
Let $\mathbb{P}$ be a probability on $(\mathbb{R}^n,\mathcal{B}(\mathbb{R}^n))$....
elfin berryBOT
KOforaf
zinc solstice
I am thinking about the construction of $A$ in terms of $S$.
elfin berryBOT
KOforaf
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sacred epoch
if 25% of an amount is $80 then the total amount is
marsh citrusBOT
if 25% of an amount is $80 then the total amount is
sacred epoch
am i just tripping
my working out says 320
but it sounds wrong
idk
also the value of 8cos28 correct the four deciaml places is 7.0636 right?
<@&286206848099549185>
limpid quartz
how do u get cos here?
sacred epoch
?
limpid quartz
answer is 80 *4
vast sparrow
if 25% of an amount is $80 then the total amount is
If 25% of an amount is 80, then 100% of it is 80 * 4 = 320
Hence you are correct
limpid quartz
do u want the workings?
oak moth
marsh citrusBOT
amber birch
is it D?
no
differentiate x + y = K with respect to t
dK/dt = 0, the derivative of a constant is always 0
marsh citrusBOT
amber birch
it;s a chain rule question
you have $\frac{d F(s)}{dt} = \frac{d F(s)}{ds} \frac{ds}{dt}$
oak moth
i dont get that
oak moth
right side
amber birch
right side
oh have you not seen this notation before
oak moth
no
amber birch
this is the same as $\frac{d}{dt} (F(s(t)) = F'(s(t)) \cdot s'(t)$
elfin berryBOT
south's secret twin brother
elfin berryBOT
south's secret twin brother
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hallow gull
hello , we have an equation of a circle and we ask us to find the center and the radius
but idk how to do it, can someone learn me how please !
marsh citrusBOT
hello , we have an equation of a circle and we ask us to find the center and the...
amber birch
hello , we have an equation of a circle and we ask us to find the center and the...
complete the square
specifically $x^2 - 4x + 4$, $y^2 - 6y + 9$ is already a perfect square
elfin berryBOT
south's secret twin brother
amber birch
so what must the right hand side now be with x^2 - 4x + 4?
elfin berryBOT
south's secret twin brother
amber birch
$(h, k)$ centre and $r$ radius
elfin berryBOT
south's secret twin brother
hallow gull
specifically $x^2 - 4x + 4$, $y^2 - 6y + 9$ is already a perfect square
but why we added 4 and not 3 or 2 or 1
amber birch
but why we added 4 and not 3 or 2 or 1
cause now if we have $(x^2 + 4x + 4) + (y^2 - 6y + 9) = 4$, add $4$ on both sides
elfin berryBOT
south's secret twin brother
amber birch
**south's secret twin brother**
you can complete the square and get to this
and know all of h, k, r
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marsh citrusBOT
amber birch
yes, II is true
wintry gale
My book says only option 3 is possible
amber birch
oh it might depend on their definition of a recurring decimal then
wintry gale
Meaning?
amber birch
cause right, 0.2000000... is indeed a recurring decimal
but it terminates cause 0.20000... = 0.2
amber birch
it's really silly I know
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charred panther
Hi, I'd like to ask for some help on finding the equation of a plane
charred panther
so in this figure i'm looking for the plane
So the edges that make up the tetrahedron is
(0,0,0), (1,0,0), (0,2,0),(0,0,3)
my idea was to take one point and then subtract two others from there
for example (0,0,0)-(1,0,0) and (0,0,0)-(0,2,0)
and then use the cross thingy to get a normalvector to the plane
but that'd be (0,0,2)?
and 0*(x-x0)+0(y-y0)+2(z-0) = 0
doesn't really uh..
produce something that i think is correct
so where did I go wrong ;P
ah it should be end point vs start point
but even then does that really change a lot?
(1,0,0) and (0,2,0)
still gives (0,0,2)
and then we get 2z = 0 as the normal equation for the plane
or would I have to select coordinates that aren't 0?
like (1,0,0)-(0,5, 0,5, 0,5) and (0,2,0)-(0,5, 0,5, 0,5) from which we get (0,5, -0,5 , -0,5) and (-0,5, 1,5, -0,5)
(0,25-(-0,75), 0,25-(-0,25), 0,75-(0,25)) = (1, 0,5, 0,5) and plugging back our values we get 1(x-0,5) + 0,5(y-0,5) + 0,5(z-0,5) = 0
x-0,5+0,5y-0,25+0,5z-0,25 = 0
x +0,5y + 0,5z = 0,5+0,25+0,25
2x+y+z-2=0
which ain't it :/
ah wait im completely gone
XD
-1,2,0
-1,0,3
6, 3, 2
6(x-1) + 3(y-0) + 2(z-0) = 0
6x + 3y + 2z - 6 = 0
yeah
idk what i was thinking
.close
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spare badger
ive been stuck on this problem for awhile now
marsh citrusBOT
ive been stuck on this problem for awhile now
spare badger
im new to this so i dont rlly understand it all
spare badger
ive seen tht to and i dont understand it
pliant willow
ive seen tht to and i dont understand it
ok look
the slope of the curve is determined by the coefficient of x
called m
still temple
pliant willow
and you find that coefficient taking two points of the curve
pliant willow
yes
spare badger
what does slope mean?
still temple
State ur points which is ob the graph
crude wadi
the ratio of rise to run. How much a line increases in height for every one unit is moves across
still temple
So like
(-2,24) and (2,8)
Label them if u want to make it easier to read
X1 y1 x2 y2
crude wadi
the ratio of rise to run. How much a line increases in height for every one unit...
so you can see in the photo, for every one unit that the line moves across, it moves down by two units
that's a ratio of -2/1, so the line has a slope (or gradient) of -2
the intercept is where the line crosses the y-axis
spare badger
how do i get the equation
pliant willow
how do i get the equation
well
crude wadi
a line is always in the form:
y=ax+b
pliant willow
use the form y = mx+p
crude wadi
a is the slope, and b is the intercept
pliant willow
with the slope you find the val of m
still temple
pliant willow
ok lets use a and b
crude wadi
use the form y = mx+p
ignore that our letters are different, we mean the same thing
crude wadi
okay, so from there, you can choose one point to be (x1,y1) and the other to be (x2,y2)
Either point can be (x1,y1) and vice versa, it'll give you the same answer
Which one do you want to do?
spare badger
the points are the dots right
crude wadi
Yes the ones on the corners of the triangle
And then those points are written out on the sides there
as (-2,24) and (2,8)
crude wadi
probably
chuck "what is slope intercept form" into youtube and something will come up
but i'll give it one more go
from the top
So, the slope intercept form of a line is in the form:
y=ax+b,
where a is a number that represents the slope (or gradient), and b is a number that represents the y-intercept
Do you know how to find the y-intercept?
spare badger
where the line crosses the y axis?
spare badger
8
crude wadi
Yes, when the red line crosses over the y-axis
still temple
spare badger
24
spare badger
oh then its 16
crude wadi
Yeah!
spare badger
i was looking at the blue one
crude wadi
And another way of saying that is that the red line intercepts the y-axis at the point (0, 16)
crude wadi
And another way of saying that is that the red line intercepts the y-axis at the...
does that make sense?
spare badger
yes
crude wadi
Cool
okay we're getting somewhere
And now the only other thing we need to find is the slope
spare badger
so b is 16?
crude wadi
To find that, you can pick any two points on that red line
spare badger
and -4 is y?
crude wadi
so b is 16?
Sure is
spare badger
which one do i use
still temple
A
spare badger
urs?
crude wadi
Yeah they're just different letters that mean the same thing
Just up to personal preference
What do you prefer
spare badger
ill use the a one
crude wadi
Okay
still temple
Okok
crude wadi
In the equation y=ax+b, we leave the y and x as is
spare badger
so b is 16 how would i get a and y
crude wadi
So we're only needing to find a and b. Since we've found b, we just need a
crude wadi
so b is 16 how would i get a and y
You don't need it. When we have a and b, (I'll just give the example that a is 2 and b is 3):
then our equation would be: y= 2x+3.
We can then find what y would be equal to by inputting any number for x
For example, if we set x to 1, we would have
2x1 +3
so y would be equal to 5 in that case
but y isn't always equal to 5, so we need to keep it as just y to make sure we can find all the other values it could take
if that makes sense
crude wadi
Probably the easiest way is the rise over run formula
spare badger
can u teach me rise run?
crude wadi
Yeah I'll give it a go
So we want to see how fast the line goes upwards compared to outwards
If a line goes up as fast as it goes across, then its gradient is 1
This is a 45° line
The formula you use to find the gradient is:
You need to pick two points that are on the red line
And they can be any points, so don't worry about having to pick specific ones
They will always give you the same answer
Did you want to pick two points on the line?
spare badger
mk
crude wadi
you can pick that point to help you find the slope, because it lies on the line
the yellow dot is the point (1, 12)
does that point lie on the line?
spare badger
yes
crude wadi
so we could also use that point to calculate the slope
but we aren't limited to using only those two points
we could use the corners of the triangle
or we could use the y intercept and a corner
there's infinite possibilities
but you can't use the green dot
because it doesn't lie on the line
spare badger
how will the point calculate the slope?
crude wadi
because it will show us how fast the line has spread both vertically and horizontally
Can you tell me what point that brown dot is?
spare badger
4,3
spare badger
so 3,4
spare badger
-1,20?
crude wadi
Okay yeah we can do that
So, to use the formula, we need to substitute one of our points for x2 and y2, and the other for x1 and y1
spare badger
can u explain the x2 y2 stuff a bit more
crude wadi
I'm drawing something up
spare badger
mk
crude wadi
So the y1, y2, x1, and x2 are all just placeholders
You put the numbers from your points in their place, and then you can solve the formula
spare badger
ok so 3 is x and y is 4
crude wadi
x2 is 3 and y2 is 4, yeah
but you can swap them around if you'd like
it wouldn't make a difference
spare badger
i think x1 3 and y1 4 would be better for me
spare badger
ok so what now?
crude wadi
So all we have to do now is swap those numbers into the formula
so in place of x1, put 3
and in place of y1, put 4
make sure to be careful of the minus 1!
spare badger
So all we have to do now is swap those numbers into the formula
what formula?
crude wadi
spare badger
20-4?
spare badger
1-3
spare badger
16
spare badger
-4
spare badger
-4
spare badger
a is -4 and b is 16?
crude wadi
what that number tells you is, your line moves down four spaces before it moves one space to the right
sure is
crude wadi
what that number tells you is, your line moves down four spaces before it moves ...
or, it goes down four times faster than it goes outwards
spare badger
oh my gosh tysm😭
crude wadi
that's okay man
got one more thing
now that we've gone through it once, tell me how you'd figure out the equation for this line
spare badger
is it ok if i go back and read?
crude wadi
that's okay, it would be good to see how much you can remember
i can ask you prodding questions if you'd like?
spare badger
whats that mean?
crude wadi
like for example
i'd ask you, what is the equation of a line ?
or, what form does it come in?
spare badger
what other forms are there?
spare badger
y=mx+b
spare badger
m and b
crude wadi
what does b mean?
spare badger
y intercept
crude wadi
and can you tell me what that is on this line?
spare badger
where the line crosses the y axis
crude wadi
yes hahah, what number does that happen at?
spare badger
3?
crude wadi
yeah!
spare badger
but i dont see 3
crude wadi
that's okay
crude wadi
that's right
spare badger
so b is 3
spare badger
thats the one i forgot
crude wadi
that's okay, you can look at the formula
spare badger
im lost again
crude wadi
that's the equation of a line
the formula im talking about is the formula you use to find out what m is
spare badger
oh
crude wadi
so id have to do the y 2 and y1 stuff rii
what you said here is right
we're thinking about the same thing
spare badger
can 1 7 be a point?
crude wadi
yep!
crude wadi
yeah you can do that
spare badger
then x2 2
crude wadi
and then what else do you need
crude wadi
and what are they
spare badger
y1 is 7 and y2 is 11
crude wadi
put it all together?
spare badger
y=4x+3
spare badger
man your a life saver
crude wadi
is it making sense? are you getting the hang of it?
spare badger
yes
spare badger
yes pls
crude wadi
and i don't ask you anything, but you tell me everything that you're doing
spare badger
ok
crude wadi
so that i can point things out if you make mistakes?
crude wadi
wait
i also think it's very good that you figured out where you went wrong here by yourself
spare badger
ye i put the xs on top
crude wadi
yep!
spare badger
x1 1
and x2 0
y1 2 y2 5
2-1 1
wait
itd be 0-1
so -1
5-2 is 3
3 divided by -1
-3
so
y=-3x+5
?
spare badger
thanks to u
crude wadi
hahaha
spare badger
fr tho thx i was stuck for like 2 hours
crude wadi
2-1 1
my only recommendation is: it's very normal for people to write down the formula first and then put all their numbers in
just to make sure they get the right answer
are you writing this on paper?
spare badger
no i was using my head
crude wadi
that's okay! just one more thing too
spare badger
?
crude wadi
make sure to practice
spare badger
i will ill look up some
crude wadi
you're very good at it right now, but when you move on to other topics later, it might not come as easily then
so make sure to do a couple questions here and there to make sure you've still got it
spare badger
ok ty for the advice
spare badger
also do yk any books i could read im tryna get some reading in and cant find any?
crude wadi
i probably wouldn't know. if i recommended anything, it might not fit exactly what they're teaching you at school
i recommend searching it up on youtube, there's some very good maths youtubers out there
and also just ask your teacher if they have any recommendations
spare badger
homeschooled
crude wadi
they might be able to loan you a textbook
ohhh
well there you go
yeah have a go on youtube!
spare badger
mk ty
crude wadi
you're welcome to dm if you get stuck
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sly hare
Is it possible to take the infimum (or min) or a multivariable function subject to only one of the variables, like for example trying to get infimum of f(x,y) subject to only x? If so, how is that defined?
marsh citrusBOT
Is it possible to take the infimum (or min) or a multivariable function subject ...
past maple
Yes, it is possible
In the example, for each y, you get a function f_y(x) = f(x,y) which depends only on x
So you can take the inf as usual
sly hare
In the example, for each y, you get a function f_y(x) = f(x,y) which depends onl...
So I understand that the result of $\inf_{x} f(x,y)$ would be a function of y, I guess I just don't really get what you're supposed to do with the y when taking inf based on x
elfin berryBOT
Risa
past maple
So I understand that the result of $\inf_{x} f(x,y)$ would be a function of y, I...
I don't think you are supposed to do anything with the y
You get a different result for each y
sly hare
so essentially for all values of y, the infimum of f(x,y) based on x should be an appropriate lower bound
devout mauve
for each fixed y you get a different thing
so for example for y=2 you get the infimum of f(x,2)
for y=3 you get the inf of f(x,3)
and so on
that defines a new function g(y) = inf_x f(x,y)
past maple
so essentially for all values of y, the infimum of f(x,y) based on x should be a...
What does appropriate mean in this context?
devout mauve
for each value y you want, you can plug it into this and get some new value g(y)
sly hare
What does appropriate mean in this context?
like satisfies the defininition of an infimum
past maple
like satisfies the defininition of an infimum
It is only an infimum for that value of y
Not for the whole function
For example, take f(x,y) = x^2+y^2
I will find the inf in x when y = 4
The functions becomes x^2 + 16 and the inf is 16
So g(4) = 16
But 16 is not the infimum of f, as it is 0
16 is the infimum of the function f(x,4)
sly hare
Soo if you have something like $\max_{y} \inf_{x} f(x,y)$ you take the max first to figure out what the inner y should be?
elfin berryBOT
Risa
past maple
No, you take the inf first
And get a function g(y)
And then find the max of that new function g
sly hare
yeah I mean that's what I was thinking
idk i'll go see if I confused myself somehow
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sharp sedge
marsh citrusBOT
sharp sedge
my working out will be expand out (3+bx)^3 so u get bx^2 which u then multiply by -x to make x^3 and mutiply x^3 by 2 and then do equation
but this isnt the case
how do i do this???????????
sum1 tell me step by step please
<@&286206848099549185>
vernal yoke
<@&286206848099549185>
yes
sharp sedge
how do i do this
vernal yoke
the answer is confusing im confused
chatgpt 
marsh citrusBOT
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leaden depot
I am doing this question and I am quite confused about the use of Advisory and the use of probability that if a Advisory can distinguish two codes. This is the question:
Suppose MAC is the tag-generation algorithm for a secure Message Authentication Code. Define a new tag-generation algorithm MAC′ as
MAC′(k, m) = MAC(k, m)∥MAC(k, m),
where k ← {0, 1}n is a fully uniform key string of length n. Does MAC′ also yield a secure Message Authentication Code? Prove your answer. You may assume that for both MAC and MAC′, the corresponding Key Generation algorithms take as input the security parameter 1n and output a uniform key k of length n. Here, by secure we mean that the Message Authentication code is existentially unforgeable under an adaptive chosen-message attack.
And my attempt is as follow:
Let the adversary receive any valid message-tag pair (m, t∥t) where t = MAC(k,m)
The adversary can verify that the tag consists of two identical halves
And accept only if both halves are identical (t = t')
Hence Pr[𝙼𝚊𝚌-𝚏𝚘𝚛𝚐𝚎𝒜,Π(𝑛) = 1] > 1/2
Hence MAC' does not yield a secure message authentication code
marsh citrusBOT
I am doing this question and I am quite confused about the use of Advisory and t...
sharp sedge
chatgpt <:bleakkekw:913344117981999125>
^^^^
marsh citrusBOT
@leaden depot Has your question been resolved?
charred panther
marsh citrusBOT
charred panther
How do we get to -2 sinh(1)??
like how is it the case that sin(1) - sin(1) doesn't cancel each other to begin with? o_O
and shouldn't e^-1 - e^1 be 1?
like in my head this is = 1
main idol
and shouldn't e^-1 - e^1 be 1?
,calc e^(-1) - e^1
elfin berryBOT
Result:
-2.3504023872876
riemann
charred panther
ah wait i see
what i did wrong
kek
or now im confused
1/e - e/1
1/e - e^2/e
ah no it probably checks out
but nonetheless how do we get to -2sinh(1)?
fervent rampart
,, \sinh x = \frac{e^x - e^{-x}}2
charred panther
or ah it flips it
elfin berryBOT
cloud
charred panther
yeah ok and we have 1-e^2/e
or we had e^-1-e^1 to begin with before i started doing this stuff
fervent rampart
use that original one j think
charred panther
so then you can say 2(sinh(1))?
ah no its -
since it's the wrong order
ok i see what they did then
thank you!
felt so lost for a second there..
have a nice evening/day!
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still temple
Let’s say i have a pizza and cut it up into 8 equal pieces. Is there a difference in the fraction 8/8 and 0/8
marsh citrusBOT
Let’s say i have a pizza and cut it up into 8 equal pieces. Is there a differenc...
red nimbus
Let’s say i have a pizza and cut it up into 8 equal pieces. Is there a differenc...
what do you think?
still temple
Yeah
red nimbus
explain
still temple
7
Im just kidding
Thanks man. I just got confused for a second
And im trash at math
And i always imagine there is a secret rule i dont know about
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limpid bison
marsh citrusBOT
limpid bison
completely lost on how to do c
the circle is ez pz
but idk what they did here
😱
mystic ledge
you get the inspiration from the pythagoras theorem
in the equation of circle there is sum of two squares as in pythagoras theorem
and also sin^2+cos^2=1
limpid bison
oh its not a right angle triangle there tho
mystic ledge
what is not right angle triangle
limpid bison
ah im lost
oh wait
i think i get it
u make a right angle out of this right?
so then 3 cos t squared plus 3 sin t squared = 3
mystic ledge
no no i mean we have equation of circle like this:
(x-4)^2+(y-3)^2=9
it's like pythagoras theorem right?
limpid bison
yea
mystic ledge
can you see where the parametric equations come from?