Yes
#help-10
sage geode
obtuse pebbleBOT
serene mural
.reopen
obtuse pebbleBOT
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stoic yacht
you get 10^x / 4^x = (10/4)^x
sage geode
a^x/b^x = (a/b)^x
serene mural
It will become fraction is that ok? Like 2.5 are fine, or 1/4?
I still didn't got it, sorry
sage geode
10/4 becomes 5/2
So keep it as (5/2)^x for now
Now think about what to do with 25^x/4^x
serene mural
What we do?
sage geode
25^x/4^x = (25/4)^x = ((5/2)^x)^2
serene mural
Am I following the right path?
I know I might be too dumb, but I'm still learning, right?
sage geode
Why are you multiplying?
serene mural
I don't know what I'm doing.
- My mother language is different
So I'm kinda lost.
We actually never did Exponent Equations with fractions with teacher, lol..
Still have youtube tutors at least
sage geode
\begin{align*}
2\cdot25^x - 5\cdot10^x + 2\cdot4^x &= 0 \
2\cdot\frac{25^x}{4^x} - 5\cdot\frac{10^x}{4^x} + 2 &= 0 \
2\cdot!\left(\frac{25}4\right)^x - 5\cdot!\left(\frac{10}4\right)^x + 2 &= 0 \
2!\left(\left(\frac52\right)^x\right)^2 - 5!\left(\frac52\right)^x + 2 &= 0 \
\end{align*}
warm shaleBOT
A Lonely Bean
sage geode
Now you have a quadratic equation where (5/2)^x is the unknown
serene mural
That's what I needed, thank you
a lot simpler to understand
Can you also help me with Discriminant?
I've got -41, this is not good
<@&286206848099549185>
Oh, I wrote -25 instead of 25 because -5 x -5 = 25, not -25
Nobody will help me with this.
.close
obtuse pebbleBOT
obtuse pebbleBOT
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barren flax
i need help on dipole movements
the bond S--P
is it ^δ-S --> P^δ+, or P^δ+ --> ^δ-S?
another question:
in this pair, which species is larger? (explain your reasoning in terms of the electron strucure of each species)
Mg^2+ or Mg
obtuse pebbleBOT
i need help on dipole movements
the bond S--P
is it ^δ-S --> P^δ+, or P^δ+ --> ^...
worn yoke
the more electronegative element will have the partial negative charge in the dipole
pulsar quarry
i can answer your second question though
barren flax
i can answer your second question though
yes plz
barren flax
the more electronegative element will have the partial negative charge in the di...
yes but my textbook says ^δ-S --> P^δ+
isnt it supposed to be P^δ+ --> ^δ-S?
barren flax
r u clear with that question?
not yet
i think my textbook might be wrong
im not sure though
the dipole movement points to the more electronegative atoms
so why is it pointing to the less electronegative atom in my textbook
is my textbook wrong?
worn yoke
can you post a picture of the problem and its solution?
barren flax
it just says to draw a figure indicating the direction of the bond dipole, including which end of the bond is positive and which is negative
the bond is S--P
my text book says the answer is ^δ-S --> P^δ+
but i think it should be P^δ+ --> ^δ-S
the dipole should point to the most electronegative atom since it attracts more electrons
but maybe im missing something that makes the text book right
worn yoke
well it should look something like this
barren flax
so my text book is wrong
okay thank you sm
may you help with the second question though?
worn yoke
in general, for the same element we would expect the species with more electrons to be bigger
worn yoke
yes
obtuse pebbleBOT
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molten yew
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warm shaleBOT
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@molten yew Has your question been resolved?
stoic yacht
the formula of the volume of a cylinder is V = pi*r^2*h
and the volume of a cone is 1/3*pi*r^2*h
using these, as well as the fact that the heights of the cylinder and cone are x and the radius is x, you can add the volumes of the two shapes to get the total enclosed volume
and by setting that expression of x equal to the volume they gave you, you can solve for x
small pewter
I need help with finding the surface area of a certain shape I have a test on may 21 and i still don't know how to find the surface area can someone help
obtuse pebbleBOT
I need help with finding the surface area of a certain shape I have a test on ma...
stoic yacht
show
for future reference don't ask to ask, just ask the question
makes it faster for everyone
stoic yacht
the question??
small pewter
give me shape
keen verge
give me shape
Yeah, what kinda surface? Like just a normal shape, or are you trying to use surface integrals? You might have to be more specific. Can you find an example of what you're asking for?
small pewter
How to find a surface area of dimensional shape
keen verge
Yeah, I know lol. I mean how? using what method? There are lots of ways to do this, but if your talking about just a cube or smth or something more complex where you have to use surface integrals there is an incredibly huuuge difference
In terms of difficulty anyways
small pewter
wait a sec
@keen verge
so for every shape there has to be a different formula ?
keen verge
Kinda. U pretty much just find the area of all the sides and add them together
small pewter
is that easy ?
keen verge
Depends who u ask ofc. In this case, it just uses a bit of trig. And then the bottom is just and square and the four sides are just triangles, so thise areas are pretty easy to find
small pewter
wait am try to solve it and u check if it's correct ok ?
the answer is 33 am i correct ?
keen verge
Nah, pretty sure it's like 99 or smth
small pewter
what
keen verge
Remember the area area of a triangle is bh/2
So you gotta find the height of the triangle
small pewter
So you gotta find the height of the triangle
its 7
keen verge
Using pythag most likely
small pewter
alr i'm confused
keen verge
No that's the height of the pyramid
small pewter
can you explain in simple words pls if you don't mind
keen verge
Sorry, I gotta get to my lecture. Maybe someone else can explain, otherwise just look up Pythagoras' theorem
brittle lodge
so for every shape there has to be a different formula ?
U can memorise the formula or jst solve it on the spot
The area of this pyramid is made out of a 5x5 square base and 4 5cm x y where y is the height of the triangle
small pewter
the teacher said she will give us a sheet of formula so we don't have to memorise
brittle lodge
Realise that u can find y using Pythagoras
Oh then thats good
But its always better to know how to solve it without the formula
brittle lodge
Break the question down and see what u know/dont know
obtuse pebbleBOT
@small pewter Has your question been resolved?
ripe hazel
how is the inverse wrong
obtuse pebbleBOT
how is the inverse wrong
tame narwhal
plus/minus?
bright inlet
how is the inverse wrong
a function needs to be one-to-one to have an inverse, if you have a graph calculator at your side you can easily check for one-to-one'ness by graphing it and doing a horizontal line test
or you can recognize that it fails the one-to-one property because it's an even function
ripe hazel
obtuse pebbleBOT
wooden cipher
try taking out the F
ripe hazel
i did it didnt work
wooden cipher
also it seems you plugged in the wrong value of C
ripe hazel
i plugged 5 and -10
wooden cipher
show me how you did it for 5
wooden cipher
you got it now?
ripe hazel
yea
have a diff problem tho
i tried graphing this and it didnt make sense
<@&286206848099549185>
smoky vigil
okay, increasing and decreasing has this very neat trick. you know about positive and negative slopes/gradients of lines right?
like y=2x+1 has positive slope/gradient, y=-5x has negative slope, etc
@ripe hazel
ripe hazel
kinda
ripe hazel
this is alg2
smoky vigil
you could say the black line has a negative slope, and red line as positive slope right?
ripe hazel
yea
smoky vigil
and what a bout the green line?
ripe hazel
0 slope
smoky vigil
mhm
ripe hazel
tangent to the point
smoky vigil
so increasing means the intervals where the line has positive slope
ripe hazel
i know that already
ripe hazel
put the equation into desmos and it returns the values i re entered into the problem
but womp womp theyre wrong
so i messed up somewhere
smoky vigil
did you try 1.15? maybe they're rounding down? is it expecting you to use graphing caluclator/desmos? I assume so
ripe hazel
ill try rounding down
smoky vigil
you can zoom in on desmos and it'll show more decimals
obtuse pebbleBOT
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rare raven
AD is double of DG
AB is double of BC
a vector = AB vector
b vector = AD vector
frosty orchid
is there any additional information such as which vectors are parallel?
frosty orchid
what have you done currently?
rare raven
AE = a + b
EI = b/2 + a/2
FG = a + a/2 + b/2 ?
DH + EG = b/2
@frosty orchid I don't know if I am correct
frosty orchid
AE and EI are correct, give me a second to think about the next two
rare raven
👍
frosty orchid
lets start on FG
rare raven
oki
frosty orchid
can you tell me what DF is?
or better how did you get to
FG = a + a/2 + b/2
cause that's pretty close and it's better if you use your method
rare raven
ok
rare raven
or better how did you get to
FG = a + a/2 + b/2
cause that's pretty close and i...
I know BC is half of AB and AB = a. So a/2 then I know DE is same as AB so its a. Then DG is same as b/2 because AD is b and AD is 2x longer
so a/2 + a + b/2
frosty orchid
ok so I think that this is the one thing you are missing: vectors have direction
frosty orchid
if you have DG is 1/2b so whats GD?
rare raven
-1/2b
frosty orchid
I think you know how to solve the problem
@me if you have any issues
rare raven
so is answer -a -a/2 + b/2?
frosty orchid
that is what I got
rare raven
you got same?
frosty orchid
yes
rare raven
DH + EG = b/2
ok btw
this one i will check too
actually
i dont understand
because
DH + EG
It starts at D
and ends at G
so why cant i just go straigt from D to G?
which is b/2
frosty orchid
if you look at the individual values of DH and EG you accumulate b/2 twice, but you are correct a cancels.
rare raven
ok so
what i did wrong was i didn't use direction
and
I didn't look at each vector
?
rare raven
yeah let me try solve this now
a + b/2 - b/2 - a + b/2
this wrong too
I went to DH
then I went from DH to EG
frosty orchid
what are you getting for DH?
rare raven
frosty orchid
are you not calculating the intermediat value of DH?
rare raven
whats that
frosty orchid
DH = b/2 + a
rare raven
o
bruh
i am supposed to do that
get the value for each vector
then add them togheter
I was going to DH to EG
frosty orchid
ah I see you are probably missing a wierd vector fact, let me find a diagram
rare raven
ok
frosty orchid
hangon that was the wrong one
there it is
the weird vector fact is that vectors do not have a posistion
vectors only have magnitude (length) and direction
so you can think of vectors as being an offset from some point
in this case one of the points A through I
so when you add two offsets you start at the the offset of one and go to the offset of the second
frosty orchid
yes
frosty orchid
well if you say a point is 0, 0 then it's the same as storing a point because you are offeset from that point
that's a bit confusing lets see
you set some point in space as a center 0, 0 all other points can be offset (vectors) from that point
frosty orchid
that's basicaly it
a vector only has how long it is and which way it is going
this is the diagram for DH + EG btw
the second one is how the vectors would be added
rare raven
so what is point of position vectors?
frosty orchid
as opposed to storing coordinates directly?
surreal flicker
drifting wraith
you just gradually add the numbers
for each vertex, the number of ways to reach it from the left side
because we only have enough steps to always go forward
obtuse pebbleBOT
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Available help channel!
keen coral
obtuse pebbleBOT
keen coral
Need help with this
timid silo
!status
obtuse pebbleBOT
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 was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
BDFE
Is the problem
Earlier I assumed the it’s a square
And this simple trig ratio to solve it
But the question gives no evidence that BDFE is a square
It cloud be a kite
keen coral
```
What step are you on?
1. I don't know where to begin.
2. I have begun but go...
3
3
@timid silo
timid silo
ok
keen coral
If it’s a square it’s simple, DE is 6800 and then just use tan30 * 6800 to find CE
But
It’s a kite
@timid silo
timid silo
busyy
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shrewd comet
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<@&286206848099549185>
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umbral robin
How do I find the point of intersection between two polynomial curves of different degrees?
obtuse pebbleBOT
How do I find the point of intersection between two polynomial curves of differe...
umbral robin
These two for example
sharp moss
set the two equations equal to each other, then form a single polynomial equation
inland ravine
These two for example
is the answer (.5, -6.25)
sharp moss
simplify and find the roots
inland ravine
is the answer (.5, -6.25)
no wait that wrong
umbral robin
set the two equations equal to each other, then form a single polynomial equatio...
That’s what I did
inland ravine
how ?
umbral robin
But there’s only one point of intersection when graphing
inland ravine
But there’s only one point of intersection when graphing
yes
you do derivative of both
and set them equal to each other
lemme solve on paper rq wait @umbral robin
umbral robin
ok
umbral robin
np 😂
umbral robin
Let me check
inland ravine
nah i dont think its right
sharp moss
yea it is
inland ravine
i got the imaginary roots
before i got the actual root
my fucking calculator bruh
umbral robin
yea it is
yeah this image is correct
alright so it is the x-value of the root, thx
wonder if there's any other way to do it
inland ravine
When I put put in my Calc I get the imaginary roots
How do I got the normal one 💀
inland ravine
,rotate
warm shaleBOT
umbral robin
oh, but can't there also be 2 separate points that have the same gradient?
sharp moss
wonder if there's any other way to do it
well, can't use rational root theorem here, are you not allowed to use the polynomial solver function in calculator?
umbral robin
idk its just a question in our lesson notes that I'm looking over
probably allowed to use plysmlt tho
umbral robin
what is the rational root theorem?
inland ravine
im lowk confused
inland ravine
i think this might be wrong
sharp moss
any rational root of a polynomial equation with integer coefficients is of the form p/q , where p is a factor of the constant term and q is a factor of the leading coefficient
umbral robin
oh isn't that the product of the roots?
sharp moss
huh
umbral robin
isn't the constant term of a polynomial divided by the coefficient of the highest x^n equal to the product of roots
idk if that only works for quadratics or other stuff too
so like:
for a quadratic,
if you have roots alpha and beta, their product are equal to c/a
like so:
umbral robin
oh ok
obtuse pebbleBOT
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uncut matrix
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uncut matrix
ok nvm what am i doing wrong
this is my profs work
oki found the bearing but its weird
i dont understand
how can i find this other angle?
obtuse pebbleBOT
@uncut matrix Has your question been resolved?
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@uncut matrix Has your question been resolved?
uncut matrix
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@uncut matrix Has your question been resolved?
raw solar
help
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austere sleet
!help
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austere sleet
i dont understand the mistake
you divide both sides by 1/2
you get (x +4)^2 = 16
oh
nvm
to get rid of fractions you have to multiply both sides by the reciprocal
static furnace
yes
obtuse pebbleBOT
@austere sleet Has your question been resolved?
wooden copper
obtuse pebbleBOT
woeful void
No
tidal tangle
obtuse pebbleBOT
tidal tangle
<@&286206848099549185>
sharp moss
what have you tried
robust tundra
just the solution?
tidal tangle
And the work
Like steps to get there
So I can check
if possible can I get it in a simplfied fraction not decimal
thats how I did it
sharp moss
show us your work first
crude lynx
,rotate
warm shaleBOT
crude lynx
It's correct
tidal tangle
the work too?
crude lynx
Yes
tidal tangle
is it sufficent for like a test
tidal tangle
K thanks
crude lynx
Line by line
robust tundra
Just make sure to properly write it with ='s etc
crude lynx
Or use '='
tidal tangle
.close
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twilit dove
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robust tundra
okay so you got $-\frac{1}{2}x^2 + 2x + 6$ correct?
warm shaleBOT
joren
robust tundra
you want to find the y-intersect, so you take x = 0, agreed? When the x is zero, the will intersect with the y-axis.
so you get $-\frac{1}{2}x^2 + 2x + 6 = 0$
warm shaleBOT
joren
robust tundra
then first thing I'd do is get rid of the minus a half like so: $x^2 - 4x - 12 = 0$
warm shaleBOT
joren
robust tundra
thx
oh wait, I mixed them up myself. But just fill in x = 0: $-\frac{1}{2} \cdot 0^2 + 2 \cdot 0 + 6 = 6$
warm shaleBOT
joren
twilit dove
all good i knew what you meant
robust tundra
and the for the x-axis intersect, solve the thing I showed above
twilit dove
x axis intersect?
robust tundra
yeah where the function intersects with the x-axis
i think the paper you showed asked for it
but looks like you already found them
you'd solve $-\frac{1}{2}x^2 + 2x + 6 = 0$, rewrite to $x^2 - 4x - 12 = 0$ and then unbind it into factors: (x - 6)(x + 2)
warm shaleBOT
joren
robust tundra
so your x=6 and x=-2 is correct
robust tundra
that works as well, takes more time
do you know how to unbind into factors?
when looking at this quadratic form: $x^2 - 4x - 12 = 0$ the goal is to find two values that when you multiply them with eachother, result in -12 and when added into eachother result in -4
warm shaleBOT
joren
robust tundra
in our case:
-6 * 2 = -12
-6 + 2 = -4
so our factors are -6 and 2 which you write like (x - 6)(x + 2) or (x + 2)(x - 6) and then you instantly see, x = 6 V x = -2 as solutions
obtuse pebbleBOT
@twilit dove Has your question been resolved?
amber thicket
yo anyone know how to do this
obtuse pebbleBOT
yo anyone know how to do this
warm shaleBOT
veryhuman
timid silo
yo anyone know how to do this
! status
obtuse pebbleBOT
yo anyone know how to do this
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 was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
1
timid silo
So
amber thicket
ok like write down how many solutions for 3sinx= 2cos x right
how do i know
and then like what does it mean to solve
timid silo
ok like write down how many solutions for 3sinx= 2cos x right
Is there an interval
Or just
Any solution
amber thicket
any solution i think
timid silo
???
amber thicket
uhhh sorry
timid silo
Ok
amber thicket
yes
amber thicket
im assuming these might help
i have written down 3sinx=2sin(90-x)
but idk what to do
crude lynx
$3\sin{x}=2\cos{x}$
Tanx=2/3
crude lynx
And since tan X is positive for two quadrants
amber thicket
that makes 2 solutions?
crude lynx
Yes
amber thicket
ok so
solving
it says something abu havinga tleast 1 decimal point
ow
how?
.close
obtuse pebbleBOT
amber thicket
i got it
obtuse pebbleBOT
Available help channel!
wraith barn
hi, need help with 9
obtuse pebbleBOT
hi, need help with 9
versed pier
it only means you also have a card that says 9
If you use 9 can you also use 6?
drifting wraith
you're right
versed pier
Lol
wraith barn
i’m getting the feeling it’s something like
case where you disclude 9 + include 9 x2 for 6
or smth
drifting wraith
yeah 3 cases
wraith barn
but when I try, it’s off
drifting wraith
you use neither
versed pier
Or you don’t use either
wraith barn
yep
versed pier
Yeee
drifting wraith
you need to multiply by n
4×3 counts numbers that start with 9
n times would inclide numbers that end with 9, or have nine in the middle
obtuse pebbleBOT
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wraith barn
hi i’m having trouble with 14b
obtuse pebbleBOT
hi i’m having trouble with 14b
wraith barn
i can see from each point, there are 2 congruent triangles, so I thought that it would be 8x2-1
but the answer is 23
obtuse pebbleBOT
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wraith barn
<@&286206848099549185>
obtuse pebbleBOT
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wraith barn
<@&286206848099549185> the first q is fine can I have help with this instead
narrow quarry
<@&286206848099549185> the first q is fine can I have help with this instead
i can cook better than this lentil soup and rice
red ice
<@&286206848099549185> the first q is fine can I have help with this instead
If all 6 students choose the same flavour, that can happen in 4 ways (4 flavours)
Similarly, if 5 students choose the same flavour and 1 person doesn't, that can happen in 4 * (3 * 6) ways: 6 ways to choose the person who doesn't choose the same flavour, and 3 flavours left after 1 is chosen by all the others
4^6 - 4 - 4 * 3 * 6 = 4020
obtuse pebbleBOT
@wraith barn Has your question been resolved?
novel ore
So I'm trying to prove this inequality seen at the top in the photo by induction for positive integers greater or equal to two. I've done some attempts as you might see but im just not getting any where. "HL" and "VL" is swedish for the right and left side respectively.
obtuse pebbleBOT
So I'm trying to prove this inequality seen at the top in the photo by induction...
warm shaleBOT
obtuse pebbleBOT
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To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.
novel ore
<@&286206848099549185>
dark plover
Ye
novel ore
I should probably clarify one thing here, I realised that not everything fit in the picture, this is only the inductive step
So in the original problem k+2 is actually k+1 and k+1 is k
obtuse pebbleBOT
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obtuse pebbleBOT
@novel ore Has your question been resolved?
timid silo
Hi whats equation for this
obtuse pebbleBOT
Hi whats equation for this
polar fossil
remember how you used to write the equation of a line as Y = mX + b?
do the same here except instead of Y use $\log_8y$ and instead of X use $\log_4x$
warm shaleBOT
hayley
timid silo
Ok thanks
timid silo
hi
timid silo
Is there any way to solve for exponential equations? similar to quadratics
marsh geyser
Using logarithms
timid silo
No
Something like
lemme type
8^{x}-2^{\left(x-5\right)}+4^{\left(x-1\right)}-4^{\left(x+2\right)}-2^{\left(x-5\right)}
yes
expand it
also
...
look that you can transform
in
common base
2^3 = 8
2^2 = 4
Yes
then what
cuz i kinda figured a way to solve them
then after common base you can just not write the base anymore
Then my math teacher said it was rubbish
then solve like a normal equation
timid silo
then after common base you can just not write the base anymore
like 3x -(x-5) + 2(x-1)
like this>
yes
Alright
What if there's no common base
depends
i need example
ok
= to what
in this case expand
so write
marsh geyser
Do you know that is not an equation right
timid silo
=0
3^(x-1) = 3^x - 3^1
huh
use the expansion i just wrote
for each of the parantheses
no
what
ok then use logs
but
u cant
3^(x-1) = 3(x) /3
if it equal to 0
no
3^(x-1) = 3^x * 3^-1
yeah
marsh geyser
Which is the same
marsh geyser
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
timid silo
Hi guys, learning set theories. In Demorgan's law, how does the intersection change into union? What have I done wrong in my proof attempt?
obtuse pebbleBOT
Hi guys, learning set theories. In Demorgan's law, how does the intersection cha...
rough temple
There's a mistake in your derivation from first line to second line
timid silo
the \notin does not distribute to B union C?
Like this is what I found online. From venn diagram, I understand its basically the opposite of the union, but in terms of my above equations/proof, doesnt seem to make sense
polar fossil
if I am not in (chickens U potatoes) then i am neither a chicken nor a potato. this means that I am not a chicken, and i am not a potato.
polar fossil
$x \notin (B \cup C) \longleftrightarrow x \notin B \text{ and } x \notin C$
warm shaleBOT
hayley
timid silo
wait doesnt Union refer to Or, Intersection refer to And?
$x \notin (B \cup C) \longleftrightarrow x \notin B \text{ or } x \notin C$
warm shaleBOT
Infinite Moms
timid silo
Shouldnt it be like this?
polar fossil
no? read my explanation and see that it matches what i wrote
polar fossil
wait doesnt Union refer to Or, Intersection refer to And?
union refers to the elements that are in either set; intersection refers to the elements that are in both sets
they do in some sense map to or/and, but that can be deceptive
let us try an example
timid silo
Is Demorgans law so special that it ignores the definition?
Im reading Munkres Topology
polar fossil
let us look at an example
timid silo
Sure
polar fossil
suppose B is the set of all even numbers, and C is the set of all odd numbers
now what is B u C?
timid silo
All even and odd numbers
warm shaleBOT
hayley
timid silo
Everything that is not all even and odd numbers
I cant think of an actual number sorry
timid silo
Ok irrational numbers?
polar fossil
we just need one example tbh
timid silo
Ok then let it be π
polar fossil
okay, so we've established that $\pi \notin (B \cup C)$
warm shaleBOT
hayley
polar fossil
and as you can probably see, $\pi \notin B$ and also $\pi \notin C$
warm shaleBOT
hayley
polar fossil
everything seems to be working so far
timid silo
Yes, makes sense
warm shaleBOT
hayley
timid silo
Yes
polar fossil
okay. what about $3 \in B$ and $3 \in C$? which of those are true?
warm shaleBOT
hayley
timid silo
only $3 \in C$
warm shaleBOT
Infinite Moms
polar fossil
yeah, so we have that $3 \notin B$ and $3 \in C$ (which means that "$3 \notin C$" is false)
warm shaleBOT
hayley
polar fossil
so let's look at your thing
you said: $x \notin (B \cup C) \longleftrightarrow x \notin B \text{ or } x \notin C$
warm shaleBOT
hayley
polar fossil
if we look at this for 3, we see that $\green{3 \notin B} \text{ or } \red{3 \notin C}$
warm shaleBOT
hayley
timid silo
Yea
polar fossil
green statement is true, and so the "or" is considered true
which means that $3 \notin (B \cup C)$ is true
warm shaleBOT
hayley
timid silo
Yes
polar fossil
but.... 3 is in B u C
polar fossil
it's a bidirectional arrow
timid silo
Same as this right?
polar fossil
yes
now as for your question about demorgan's law
it essentially "flips" or/and:
it states that $\neg (p \wedge q) \Longleftrightarrow (\neg p) \vee (\neg q)$
warm shaleBOT
hayley
polar fossil
"not (p and q), is the same thing as, (not p) or (not q)"
and the same is true the other way around:
"not (p or q), is the same thing as, (not p) and (not q)"
timid silo
So, basically not (p and q) has the meaning of 1. not p, 2. not q, 3. not p AND q
polar fossil
no it does not
it means not (p and q)
p might be true
q might be true
but they're not both true
an example:
p = "i eat a hamburger for lunch"
q = "i eat a salad for lunch"
if i say "not (p and q)" it means that i only had one thing (or nothing!) for lunch
warm matrix
ooooh set theory
timid silo
an example:
p = "i eat a hamburger for lunch"
q = "i eat a salad for lunch"
if ...
which is what I said earlier, implying 3 meanings?
Sorry I need some time, because what I have read and what you are saying has a teeny bit of contradiction😭
polar fossil
no, there's only one meaning: i didn't eat this for lunch
i might have had this, though:
timid silo
Can it be interpreted this way:
p = "i eat a hamburger for lunch"
q = "i eat a salad for lunch"
z = "non-mentioned food for lunch"
If i say "not (p and q)",
it means I either
CASE 1: Ate p;
CASE 2: Ate q;
CASE 3: Ate z (Which is not P nor Q)
polar fossil
sure, or i ate nothing at all
the point is that either i threw the burger in the cook's face, or i dumped the salad on the ground, or i might have done both
timid silo
This is not a good example but I get what you mean
So Demorgans basically said lets just flip and/or
polar fossil
how about you make up your own? it's lunch time and i am hungry as you can see
timid silo
because you could've thrown the burger in his face, or you could've eaten part of the salad and dump it on the ground
I tend to question these scenarios sorry
polar fossil
you should also make one for the other way around, the "not (p or q), is the same thing as, (not p) and (not q)"
timid silo
the point is that either i threw the burger in the cook's face, or i dumped the ...
like this scenario is "Not P", "Not Q", "Not P and Q"
polar fossil
like this scenario is "Not P", "Not Q", "Not P and Q"
ok pause
the third one is "not P and not Q"
or to be super clear, "(not P) and (not Q)"
timid silo
my mistake, "P and Q" instead of "Not P and Not Q"
Alright back to my question,
Demorgans law basically
changes "And" to "Or"
changes "Or" to "And"
Is that it?
timid silo
"not (p and q), is the same thing as, (not p) or (not q)"
and the same is true ...
the one you mentioned
polar fossil
yes, essentially. it converts "not-and" to "or-not"
timid silo
Alright I understand now
polar fossil
and converts "not-or" to "and-not"
timid silo
Im going to go see why he did that now
You can eat burger king or MOS burger instead of McDonalds
better burgers
Thanks and have a nice lunch
polar fossil
i don't think i want to eat a moss burger, but thank you for your suggestion
timid silo
? Mos burger is a restaurant
I live in Asia so you might not have it (?)
@rough temple did you have anything extra that might help me understand? I saw you typing since 45mins ago
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
wide oracle
how do you do this?
obtuse pebbleBOT
how do you do this?
wide oracle
question 14
dark stirrup
question 14
Distribute it
sage geode
Start by expanding the parenthesis
And keep in mind what vectors being perpendicular tells you about their dot product
sage geode
That's not all of the terms in the expansion, but, yeah, it simplifies to |u|^2 + |v|^2 + |w|^2
Not sure why you set that equal to |u| |v| |w|cos(theta) though
wide oracle
That's not all of the terms in the expansion, but, yeah, it simplifies to |u|^2 ...
yeah, i realized mid way and decided to skip
wide oracle
Not sure why you set that equal to |u| |v| |w|cos(theta) though
what should it equal then?
oh
oh
its the same term
sage geode
What do you mean?
wide oracle
sage geode
In this case yeah, |u|^2 + |v|^2 + |w|^2 = |u + v + w|^2
But with the information given you can simplify |u|^2 + |v|^2 + |w|^2 first
sage geode
Read the problem again, what is stated about u, v, w besides them being mutually perpendicular?
wide oracle
Read the problem again, what is stated about u, v, w besides them being mutually...
oh their value
ok ok
sage geode
The values of their magnitudes, yeah, namely |u|, |v|, |w|
You should know how to calculate |u|^2 + |v|^2 + |w|^2 now
wide oracle
wide oracle
You should know how to calculate |u|^2 + |v|^2 + |w|^2 now
how do i do that lol
sage geode
Again, you are given the values of |u|, |v|, |w|, so you can simply plug them in
wide oracle
1^2 + 2^2 + 3^2 is not 13 though
wide oracle
Yeah, that's it
am i done?
sage geode
Just a quick 1^2 + 2^2 + 3^2 = 14 and yeah, you are done
sage geode
Well, it's wrong then
Also a dot product of a vector with itself can't be negative, so that is clearly a mistake in the book
granite spruce
Hello, does anyone know anything about these 5 topics? I have to write a research project in one of them and so if anyone knows anything about any of these hopefully it will help inform my choice.
obtuse pebbleBOT
Hello, does anyone know anything about these 5 topics? I have to write a researc...
@granite spruce Has your question been resolved?
obtuse pebbleBOT
@granite spruce Has your question been resolved?
uneven tinsel
obtuse pebbleBOT
uneven tinsel
I've been struggling to set this problem up. I would really appreciate if someone could help me with that part
obtuse pebbleBOT
@uneven tinsel Has your question been resolved?
uneven tinsel
<@&286206848099549185>
obtuse pebbleBOT
@uneven tinsel Has your question been resolved?
mild blade
You can use washer method
mild blade
!show
obtuse pebbleBOT
Show your work, and if possible, explain where you are stuck.
uneven tinsel
I don't have the work with me right now but I'll redo it and send it in a few mins
I used this to set it up
uneven tinsel
@mild blade I hope it's fine I'm pinging you
velvet rover
well revolving around the line x = b is more like revolving around the y axis
usually cylindrical method is easier in those cases
mild blade
<@1021318332978319431> I hope it's fine I'm pinging you
It’s fine
Sorry, I went somewhere
mild blade
There are two semi-circles here
And you are putting wrong limits
As, y is not going from 0 to b, its limit would be -a to a
Subtract this area from orange area to get the light red area in the last image
You only included thia area
Which would give you the volume of this area revolving around x=b
uneven tinsel
i see, thank you.
obtuse pebbleBOT
If you are done with this channel, please mark your problem as solved by typing .close
rare lake
Just need help, should be relatively quick. I need to know whether or not (0,0) is an inflection point here or not. I already have (-1,0), (-0.447,0), (0.447,0), and (1,0) has my inflection points listed here.
obtuse pebbleBOT
Just need help, should be relatively quick. I need to know whether or not (0,0) ...
tidal thistle
Just need help, should be relatively quick. I need to know whether or not (0,0) ...
there are 3 infection point in that graph
one is at 0 and is at about 0.7 and the other at aprox -0.7
i cant see the numebrs well so i cant give excact numbers
obtuse pebbleBOT
@rare lake Has your question been resolved?
glossy yacht
obtuse pebbleBOT
glossy yacht
Is this the correct sufficient statistic?
obtuse pebbleBOT
@glossy yacht Has your question been resolved?
obtuse pebbleBOT
@glossy yacht Has your question been resolved?
obtuse pebbleBOT
@glossy yacht Has your question been resolved?
obtuse pebbleBOT
@glossy yacht Has your question been resolved?
obtuse pebbleBOT
@glossy yacht Has your question been resolved?
obtuse pebbleBOT
@glossy yacht Has your question been resolved?
timid silo
i feel bad for you man hope you find somebody who knows how to answer
nocturne hawk
I think it is a sufficient function, thanks to Fisher-Neyman factorization theorem
obtuse pebbleBOT
@glossy yacht Has your question been resolved?
glossy yacht
i feel bad for you man hope you find somebody who knows how to answer
My exam has already finished 😭
glossy yacht
I think it is a sufficient function, thanks to Fisher-Neyman factorization theor...
It is indeed, but I need to understand why
civic socket
obtuse pebbleBOT
ooops
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).
obtuse pebbleBOT
@glossy yacht Has your question been resolved?
idle rivet
Is this channel open?
drifting wraith
Is this channel open?
available channels are at the top of the list under math help (available)
unless you set things up so that they are hidden
glossy yacht
then why did you need to ask where my calculation was?
bro, its absolutely fine to admit you're out of your depth, but do not pretend you know how to do something in the hope of teaching others
meager swift
Looks like you're first trying to find an mle of alpha. The test statistic T here doesn't make that much sense to me unless you give me a null hypothesis that it can "test"
Are you sure you're not searching for an estimator of alpha here?
glossy yacht
Looks like you're first trying to find an mle of alpha. The test statistic T her...
the question goes
- find likelihood
- give sufficient statistic (which I assume is done by using Factorisation Theorem)
- find MLE of alpha
I'm on the second part
there is no hypothesis to test
meager swift
Then T isn't needed
glossy yacht
What's the sufficient statistic?
meager swift
You've found the likelihood function tho that's good
glossy yacht
This is the only part I need