Show your work, and if possible, explain where you are stuck.
#help-13
cedar kilnBOT
wary summit
no I just see it and do it
But in this case I wasnβt paying attention
Do I plug in the 3 with the 2
hasty aurora
Let's say I have an equation x+5. x is a variable, so, in mathematical terms its a symbol representing some number (in your case). If I want to give x a value, I may do so. For example, saying x = 5, would mean that x+5 = 10
We can also say x = 4, meaning x+5 = 9
hasty aurora
Yes
wary summit
hasty aurora
That is not correct
wary summit
How would I do it if it was a fraction
wary summit
That is not correct
Oh
wary summit
what
hasty aurora
How would I do it if it was a fraction
Like in the $1-\frac{3}{4}x$ casE?
wraith daggerBOT
Cyrol
wary summit
Ohhhh
hasty aurora
multiplying two negative numbers gives a positive number
wary summit
I forgot to put negative 3
hasty aurora
no you put in the right value
In a function f(x) = x+5 for example f(4) = 4+5
We just replace every x with the value written in the parentheses
wary summit
Ok
hasty aurora
If f(x) = x+5 for example, what do you think f(5) would be
wary summit
0
hasty aurora
No, f(5) = 5+5 which is 10
wary summit
Oh
hasty aurora
If I would've said f(-5) you would be correct, as f(-5) = -5+5 = 0
any questions regarding that?
Just remember that when you have any function f(x), and you put in a value for x you replace every x with that value
f(x) = x+5, f(4) = 4+5, f(37) = 37+5 etc.
wary summit
Both
hasty aurora
Ok let me think of an example to explain them to you
wary summit
Ok
hasty aurora
Lets say we have a magic barn in which we store hayballs. We don't know how many hayballs it can store or what form they have. The doors to the barn are closed, so we don't know how many hayballs are in the barn. So we say, that there are x hayballs in there, x being some number. Once we open the door, exactly x hayballs are in the barn.
Does this make sense?
wary summit
yes
hasty aurora
This is the concept of a variable
wary summit
ok
hasty aurora
Now once we close the door there are still x hayballs in the barn, until we change the value of this x.
We may go there one day and say "There are 4 hayballs in there" and there will be 4 hayballs in the barn. Another day we might say "There are 9000 hayballs in there and low and behold there are 9000 hayballs in the barn.
wary summit
Ok
hasty aurora
I just now noticed they are called haybales
hayball is ok as well I hope
Anyways
We have a working farm, so we need some hay bales to feed our animals. One day we go to our barn and say "There are 4 hay bales in there", so there are 4 hay bales in there. With our animals on the farm however, 4 bales wont be enough. With our wisdom we decide, that we need 2 more bales to feed all of our animals. So we go outside the barn, close the door and say "There are 2 more hay bales in there". We go inside the barn and see, that there are now 6 hay bales in the barn.
Remember when I said that once we close the door that there are still x hay bales in the barn until we change the value of this x
Well here we closed the door to our barn, with 4 hay bales inside. Now we said: "There are 2 more hay bales in there", meaning that there are 2 more hay bales in there than before
So there are 4+2 hay bales in the barn, giving us 6 hay bales.
So far so good?
wary summit
Yeah
hasty aurora
Now we notice, that for any x hay bales we say that we have, we will always need 2 more hay bales to feed our animals. This means, that the number of hay bales needed for our animals to survive is x + 2
The thing is, we don't always know what our x will be, so how do we always get 2 more hay bales than x inside our barn?
Well we can just tell our barn to just put 2 more hay bales in there whenever we say that it contains some number of hay bales.
Our barn is the concept of a function
function in extremely short is just f
According to that discovery, we name our barn f
Now we want to make our barn f do something to any number of hay bales x we give it.
For that, we write f(x)
Now we know exactly what we want the barn f to do to the number x of hay bales. For every number x of hay bales we say it contains, we say it should contain 2 more. So the value of hay bales in the barn is equal to our said value x + 2.
For that we write f(x) = x + 2
All clear?
cedar kilnBOT
@wary summit Has your question been resolved?
wary summit
Yes
cedar kilnBOT
wary summit
Peace out
cedar kilnBOT
Available help channel!
crimson sedge
crimson sedge
Where does 1.25 come from
I know it has to do with going down the center but im still confused
like could someone draw out the way they are walking
cause i cant wrap my mind around it
grand forge
cause i cant wrap my mind around it
2.5 feet wide
crystal raptor
If you walk down the centre of a 2.5 ft wide path, you are 1.25 ft from either side
crimson sedge
I THOUGHT THATS WHAT IT WAS
grand forge
which would be center of the path
crimson sedge
SOME PERSON IN HERE TRIED TO GASLIGHT ME INTO THINKING THE DIAMTER AND RADIUS HAVE NOTHING IN RELATION
BYEEE
π
Thank you both
Sorry
grand forge
who tf was tha
cedar kilnBOT
cedar kilnBOT
Available help channel!
eternal sphinx
hello guys i wanna know how to shrink and stretch a function horizontaly
dull oxide
Shrink/stretch how?
eternal sphinx
bruh no i wana kn ow how tttoo use a table
crimson sedge
https://www.onlinemathlearning.com/image-files/transformation-rules-graphs.png
Keep in mind there can be cases like with exponentials and logarithms where this wouldn't be as clear cut
eternal sphinx
Oh LOLOLOL nvm i get it thanks thoo
cedar kilnBOT
@eternal sphinx Has your question been resolved?
rustic ether
How would I find the perpendicular vector of the normal of a 3d plane?
rustic ether
Vector n is the normal
and vector u is the vector perpendicular to the plane running down/up it
either works
cedar kilnBOT
@rustic ether Has your question been resolved?
cedar kilnBOT
@rustic ether Has your question been resolved?
cedar kilnBOT
@rustic ether Has your question been resolved?
rustic ether
<@&286206848099549185>?
cedar kilnBOT
@rustic ether Has your question been resolved?
cedar kilnBOT
@rustic ether Has your question been resolved?
frail trout
My professor gave a question similar to this on my final.
cedar kilnBOT
My professor gave a question similar to this on my final.
frail trout
I solved it be converting it to the matrix
( 1 1 0 | 2 -1 )
( 0 1 2 | -1 1 )
( 2 0 0 | 2 -3 )
row reducing until I get the identity matrix on the left
and took the transpose of the right side then as the answer for the matrix of l
the answer was right but she said my method was weird and was acting like it was wrong
what method do you think she expected?
and also, is there any situations where my method wouldn't get the correct answer?
cedar kilnBOT
@frail trout Has your question been resolved?
cedar kilnBOT
@frail trout Has your question been resolved?
cedar kilnBOT
@frail trout Has your question been resolved?
proud torrent
it's more intuitive to write general form of the matrix L and figure out it's entries based on the given equations
frail trout
it's more intuitive to write general form of the matrix L and figure out it's en...
wdym?
figure it out how?
proud torrent
$l = \begin{pmatrix} l_{11} & l_{12} & l_{13} \ l_{21} & l_{22} & l_{23} \end{pmatrix}$
wraith daggerBOT
Transparent_Elemental
proud torrent
now substitute given information about how this transformation acts on vectors
frail trout
now substitute given information about how this transformation acts on vectors
i still dont understand the process
proud torrent
now substitute given information about how this transformation acts on vectors
have you done this?
frail trout
have you done this?
no because I don't know what you you mean
just
(2 -1)
(-1 1)
(2 -3)
?
proud torrent
a linear transformation T, if given with it's matrix representation A, can be seen as a matrix-vector multiplication T(x) = Ax
proud torrent
a linear transformation T, if given with it's matrix representation A, can be se...
I've written what this matrix looks like in general form earlier, substitute known vectors instead of x here
cedar kilnBOT
@frail trout Has your question been resolved?
frail trout
a linear transformation T, if given with it's matrix representation A, can be se...
What?
I understand that part
But not how to figure out the entries based on the given equations
And other method than the method I used
proud torrent
have you plugged in the vectors into the equation of the transformation?
this isn't going to end with anything substantial given the pace this talk is going at and I have to go to bed, so you should reread what I was saying earlier and in case you have more questions you should respond to whoever's next going to help more frequently than once every 2 hours
livid tusk
```
( 1 1 0 | 2 -1 )
( 0 1 2 | -1 1 )
( 2 0 0 | 2 -3 )
```
idk i think this is an excellent method
livid tusk
**Transparent\_Elemental**
this certainly works, but i'd never recommend doing it like this tbh. there are more efficient way i think than solving a system of equations in 6 variables
what your method essentially does it determine T(e1),T(e2),T(e3). which is exactly the columns of the matrix you want.
i think it's the most efficient method
livid tusk
and also, is there any situations where my method wouldn't get the correct answe...
no. what you did will always work because it is a linear transformation.
and linear combinations are preserved
<@&268886789983436800> sorry i just really hate having to look at that while i'm scrolling through the messages to see the question
peak relic
Thanks
livid tusk
what method do you think she expected?
you can get the answer through
$\m{2&-1&2\
-1&1&-3}
\m{1&0&2\
1&1&0\
0&2&0}^{-1}$
wraith daggerBOT
nilpotent nix
livid tusk
you can use T(2,0,0)=(2,-3) to say the first column is (1,-3/2)
then doing (0,1,0)=(1,1,0)-(1,0,0), so T(0,1,0)=T(1,1,0)-T(1,0,0)=(1,1/2)
etc.
but... if you notice... this is basically doing the steps you did to row reduce
yeah idk what your teacher expected. lmk if you find out because i'm curious
cedar kilnBOT
@frail trout Has your question been resolved?
molten salmon
- The range of the function f(x) = xβx^2 β 4
is (ββ, β1) βͺ (1,β). To explain
why this is true, you have to do two things:
(a) Show that if f(x) = y for some x, then either y > 1 or y < β1.
(b) Show that if y < β1 or y > 1, then the equation f(x) = y has
a solution in x.
cedar kilnBOT
3. The range of the function f(x) = xβx^2 β 4
is (ββ, β1) βͺ (1,β). To explain
wh...
molten salmon
- The range of the function f(x) = x/βx^2 β 4*
It is a fraction. I am not even sure where to start
scenic stirrup
$\frac{a}{x^2-4}$
wraith daggerBOT
ππΡ³rtΡxπ
molten salmon
@lusty birch
wraith daggerBOT
ππΡ³rtΡxπ
cedar kilnBOT
@molten salmon Has your question been resolved?
wraith daggerBOT
ππΡ³rtΡxπ
molten salmon
yes
scenic stirrup
oh not a but x mb
scenic stirrup
i mean i dont think so
i mean idk how rigorous this has to be
but as x increases when x>2, the value of Y decreases
so when x is very large, like when x is 10000000000 then it's basically $\frac{10000000000}{\sqrt{10000000000^2}}$ and the 4 becomes kinda insignificant
so it approaches just being 10000000000/10000000000=1
wraith daggerBOT
ππΡ³rtΡxπ
scenic stirrup
if that makes sense
it never goes below 1 because the fraction will always be x/(something a little less than x) which gives you the fact that x>1 always, but as x gets bigger, y gets closer to 1
it's the same idea for -1
@molten salmon
molten salmon
Oh okay
scenic stirrup
what grade are you in by chance
molten salmon
Undergraduate in uni, first day
scenic stirrup
also for negative it's the same idea because it's x^2 so yeah
oh ok idk if your teacher wants this to be more rigorous then since this is uni but this is kinda a more intuitive explanation
as x gets really large you have something like $\frac{large number}{\sqrt{(large number)^2 - 4}}$ and the 4 gets insignificant so it starts to become $\frac{large number}{\sqrt{(large number)^2}}=\frac{large number}{large number}$
wraith daggerBOT
ππΡ³rtΡxπ
scenic stirrup
which is virtually 1
it never ACTUALLY gets to or passes 1 because the -4 is always still there but we say that it approaches 1
molten salmon
But doesn't that mean there is no solution for x
scenic stirrup
wdym
molten salmon
never mind
scenic stirrup
i mean $x/(sqrt(x^2-4))=1$ is never gonna have a solution because obviously the numerator doesn't equal the denominator
wraith daggerBOT
ππΡ³rtΡxπ
scenic stirrup
this also doesn't really prove why values like 0 and 0.5 aren't in the range unless you're allowed to assume it's like a decreasing function when x>2
molten salmon
It is a decreasing function...like, it is easy to tell immediately by the range given
You land on Planet X and perform a simple experiment to study gravity on the
planetβs surface. So you pick up a rock and throw it straight up with initial
velocity of v = 10 m/s (meters per second), from the height of 1 meter. You
know that the height of the rock after t seconds is h(t) = 1 + 10t β g/2t^2, where
g is the acceleration due to gravity on the surface of Planet X.
(a) (2 marks) At what time t will the rock come back down to the height of
h(t) = 1 meter? (Your result will involve the unsepecified constant g.)
(b) (2 marks) If the rock came back to the height of 1 meter after t = 12.5
seconds, what is the value of g on Planet X?
.closed
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
stray orchid
Hi everyone! I tried to calculate the 4th derivative of tan x, could someone double-check if it's correct? It's below the red line. Thank you very much!!
orchid mural
no just put a 1
crimson sedge
sec^2 X is the derivative of tan x :)
stray orchid
We're not allowed to use sec yet, haven't defined it :(
crimson sedge
:(
clear berry
wdym not defined sec yet?
crimson sedge
We're not allowed to use sec yet, haven't defined it :(
but derivative of tan would be sec
you can try
1 / cos^2 X
1/ cos^2 X = sec^ 2 X
crimson sedge
.yea
stray orchid
wdym not defined sec yet?
Didn't have it in a lecture yet so I'm not sure if my prof will allow it
crimson sedge
Didn't have it in a lecture yet so I'm not sure if my prof will allow it
you can use 1/cos^2 X
clear berry
If this is supposed to be a practice for product rule of differentiation then it's kinda okish
otherwise this is a waste of time
stray orchid
Alright, thanks everyone!
crimson sedge
Alright, thanks everyone!
no probs
stray orchid
.close
distant bridge
is this the right way to decide if this equation is divergent (n-2)/(n+2)
hasty fulcrum
in what context are you talking about divergence? as in the limit as n approaches infinity?
wraith daggerBOT
blanket
distant bridge
yes
hasty fulcrum
have you tried factoring out an n from the top and bottom?
distant bridge
oh ty now i learned something
hasty fulcrum
oh
distant bridge
i just did
wraith daggerBOT
blanket
hasty fulcrum
right?
hasty fulcrum
yeah
clear berry
That's one way to do it
distant bridge
i though i could do it another way
distant bridge
lhopitals how does that work
clear berry
you can also write it as $1 - \frac{4}{n+2}$
wraith daggerBOT
numbpy
hasty fulcrum
lhopitals how does that work
it's a calculus thing; don't worry about it if you don't do calculus
clear berry
then as n -> infinity the fraction becomes 0
hasty fulcrum
you can do lhopitals by taking the derivative of both the top and bottom function
distant bridge
have not learned it
hasty fulcrum
with respect to n
what happens when you take the derivative of n-2 with respect to n?
what do you get
distant bridge
n
distant bridge
1
hasty fulcrum
right
so we bring down the 1, and then we have the power as 1-1
and anything to the 0th power is wat
clear berry
Using l hospital is a bit circular so I'd suggest you avoid it now @distant bridge
distant bridge
okei
distant bridge
you can also write it as $1 - \frac{4}{n+2}$
didnt really get how you got this
distant bridge
**blanket**
il try this
mellow loom
How bout series? I think calc use it
clear berry
oh that, I just added 2 and subtracted 2. But anyway if you understood using your method it's fine
You'll later encounter similar stuff in partial fractions
wraith daggerBOT
Sas
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
crimson sedge
$\displaystyle\lim_{n\rightarrow\infinity}\frac {1-\frac2n}{1+\frac 2n}$
wraith daggerBOT
Wither
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mellow loom
$\lim_{n\to \infty} {\frac2n}=0$
calm sierra
\infty
distant bridge
so how do i prof this is converging
wraith daggerBOT
Welf
clear berry
That works
mellow loom
If it's calculus, I gues you can use it
clear berry
Have you learned that $\lim_{n\to \infty} {\frac1n}=0$
wraith daggerBOT
numbpy
distant bridge
yes
clear berry
then $\lim_{n\to \infty} {\frac2n} = 2 \lim_{n\to \infty} {\frac1n}$
wraith daggerBOT
numbpy
distant bridge
if $|\frac 1n| <1$
wraith daggerBOT
Sas
distant bridge
how did you go from $\displaystyle\lim_{n\rightarrow\infty}\frac {1-\frac2n}{1+\frac 2n}$ to $\lim_{n\to \infty} {\frac2n}=0$
hasty fulcrum
they didnt go from the first limit to the second
they're just talking about a specific part of the limit
wraith daggerBOT
Sas
mellow loom
$\lim_{n\to\infity} {\frac {1-\frac2n}{1+\frac 2n}} \
= \frac{\lim_{n\to\infity}{1-\frac2n}}{\lim_{n\to\infity}{1+\frac2n} \
= frac{1-\lim_{n\to\infity}{\frac2n}}{1+\lim_{n\to\infity}{\frac2n} \
= \frac{1 - 0}{1+0}$
wraith daggerBOT
Welf
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(You may edit your message to recompile.)
distant bridge
without the i
past crescent
oof
mellow loom
$\lim{\frac{f}g} = \frac{\lim{f}}{\lim{g}} \
\lim{fΒ±g} = \lim{f} Β± \lim{g}$
wraith daggerBOT
Welf
distant bridge
hm
im stuck here $\displaystyle\lim_{n\rightarrow\infty}\frac {1-\frac2n}{1+\frac 2n}$
hasty fulcrum
without the i
$\lim_{n\to\infty}\frac{1-\frac2n}{1+\frac2n}=\frac{\lim_{n\to\infty}(1-\frac2n)}{\lim_{n\to\infty}(1+\frac2n)}
hasty fulcrum
$\lim_{n\to\infty}\frac{1-\frac2n}{1+\frac2n}=\frac{\lim_{n\to\infty}(1-\frac2n)}{\lim_{n\to\infty}(1+\frac2n)}$
bru
hasty fulcrum
**blanket**
does this help @distant bridge ?
you can apply the limit to both numerator and denominator
when its a constant over infinity, it tends towards 0
so its essentially $\frac{1-0}{1+0}
distant bridge
does this help <@371611734777266176> ?
how does that help
hasty fulcrum
whats 2 over infinity
i know its not a good way to look at it, but what's 2 over a huge number
what does that converge to?
distant bridge
so i dont need to do smaller steps?
wraith daggerBOT
blanket
hasty fulcrum
np
distant bridge
**blanket**
this is 1
hasty fulcrum
ye
distant bridge
is it that n -> 0 makes it converge?
hasty fulcrum
it is convergent when it converges to a number
a limit is divergent when it doesnt diverge to a specific number
distant bridge
like $(-1)^n$
wraith daggerBOT
Sas
distant bridge
is diverge
hasty fulcrum
yes
hasty fulcrum
ye[p
distant bridge
if it reached a constant
hasty fulcrum
thats when we talk about summations of a series
distant bridge
okei
is this right $a_n = \frac {n^2-2}{n+2} =\displaystyle\lim_{n\rightarrow\infty} \frac {\frac {n^2}{n^2}-\frac {2}{n^2}}{\frac {n}{n^2}+\frac {2}{n^2}} =\displaystyle\lim_{n\rightarrow\infin} \frac {1-\frac {2}{n^2}}{\frac {1}{n}+ \frac {2}{n^2}}= \frac {1-0}{0+0} = 1$ ?
wraith daggerBOT
Sas
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)
distant bridge
maybe i did it wrong
clear berry
is it n-2 or n^2 - 2?
distant bridge
n^2
clear berry
So, this is a different question?
clear berry
maybe remove the gap in the end
distant bridge
this one is inf
wraith daggerBOT
Sas
clear berry
how are they same?
clear berry
nope
clear berry
For this the best way is to use partial fractions
Basically, separate the fraction out
like you know that, n^2 - 4 = (n+2)(n-2)
clear berry
$\frac{n^2-2}{n+2} = \frac{n^2 - 2 - 2 + 2}{n+2} = \frac{n^2 - 4 + 2}{n+2} = \frac{n^2 - 4}{n + 2} + \frac{2}{n+2}$
wraith daggerBOT
numbpy
clear berry
Do you understand this?
distant bridge
nop
distant bridge
kvotient rule?
clear berry
is this right $a_n = \frac {n^2-2}{n+2} =\displaystyle\lim_{n\rightarrow\infty} ...
Oh, I think that's what you did here
distant bridge
Oh, I think that's what you did here
yeah
clear berry
That should work just fine then
distant bridge
Oh, I think that's what you did here
did i do it rigght?
distant bridge
That should work just fine then
what would work fine+
clear berry
I mean what you did should work fine
You could also just divide by n and that'll also work
Just write things carefully
clear berry
Yes that works but dividing by just n makes a bit slicker
cause in what you wrote 1/0 which isn't defined
distant bridge
yeah
$a_n = \frac {n^2-2}{n+2} =\displaystyle\lim_{n\rightarrow\infin} \frac {\frac {n^2}{n^2}-\frac {2}{n^2}}{\frac {n}{n^2}+\frac {2}{n^2}} = \displaystyle\lim_{n\rightarrow\infin}\frac {1-\frac {2}{n^2}}{\frac {1}{n}+ \frac {2}{n^2}} = \frac {1-0}{0+0} = \frac 10$
wraith daggerBOT
Sas
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)
distant bridge
so this is diverge
clear berry
I was trying to write the latex but nvm, yes this diverges
In fact a good rule of thumb is that whenever the numerator has higher power, it will diverge
If the power of numerator is greater, it should converge to zero (not necessary)
If the highest powers are same it would be some non-zero number
distant bridge
$a_n = \frac {n-2}{n^2+2} =\displaystyle\lim_{n\rightarrow\infin} \frac {\frac {n}{n^2}-\frac {2}{n^2}}{\frac {n^2}{n^2}+\frac {2}{n^2}} = \displaystyle\lim_{n\rightarrow\infin}\frac {\frac {1}{n}- \frac {2}{n^2}}{1+\frac {2}{n^2}} =\frac {0- 0}{1+0} = \frac 01$
wraith daggerBOT
Sas
Compile Error! Click the reaction for more information.
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clear berry
yes
cedar kilnBOT
@distant bridge Has your question been resolved?
crimson sedge
can i get help on part a)
cedar kilnBOT
can i get help on part a)
random shale
what have u tried?
crimson sedge
i have like understood the b one i just dont get this that how should i find the value of p one
i do have the coordinates
sharp ore
You have a straight which should go through points A and B
crimson sedge
itβs like how to find p
dim mortar
You can imagine the x value as the "input" of a function and the y value as its "output".
If you put in a certain value of x
lyric narwhal
Point B has coordinates (p,0) and lies on the line 3y+4x=18
crimson sedge
i thought this equation 3y+4x=18, ill input the values of x and y given
dim mortar
you will get a specific value of y
in this case you have 0 as the y value and p as its input
all you need is to put them into the equation given
crimson sedge
im trying to understand this
crimson sedge
all you need is to put them into the equation given
this equation 3y+4x=18
dim mortar
the y value is its "height"
crimson sedge
is p is on the x axis
dim mortar
yep
crimson sedge
this whole is x axis meaning it should be p
p is basically im calculating
i have got it
thanc
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
mighty mortar
How does the ^2 in the first step (pointed with the green arrow) disappeared?
earnest socket
How does the ^2 in the first step (pointed with the green arrow) disappeared?
1/6 (k+1) is factored out of both terms in the first line
cedar kilnBOT
sonic thistle
Sirius Black
cedar kilnBOT
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leaden gyro
hello
tropic oxide
@leaden gyro http://nohello.net
leaden gyro
Sorry I'm uploading a picture and my question
tropic oxide
$\sum_{i=1}^3 4 = 4+4+4 = 3\cdot 4$
wraith daggerBOT
Ann
lavish prawn
anyone familiar with transitive closures? i'm having issues trying to understand part c, i already proved a and b
lavish prawn
what i have to prove on c is that, supposing M is the set of all transitive closures on A that contain R as a subset or $m \in M$, such that $\forall m \in M (R \subset m)$ what i have to prove here is that $\forall m \in M (\cap F \subset m)$ right?
wraith daggerBOT
beginner
cedar kilnBOT
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clever dune
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clever dune
I'm a bit confused on a few things
inland fossil
what are you confused on?
clever dune
How can I show P(A) + P(B) β₯ $P(A \cup B)$
wraith daggerBOT
arrow891
wraith daggerBOT
arrow891
inland fossil
only if they are disjoint
clever dune
what is meant by "max"
rose rose
max{a, b} = a if a is the bigger of the two
clever dune
but how could i show that one is bigger than the other
inland fossil
you dont need to, you can assume that without loss of generality
inland fossil
yea its safe
wraith daggerBOT
clever dune
i saw that
inland fossil
clever dune
okay if that's the case
clever dune
How can I show P(A) + P(B) β₯ $P(A \cup B)$
then what about this
inland fossil
okay so first off, the question doesnt say anything about A and B being disjoint
rose rose
As said that only holds if A and B are mutually exclusive
There is a more general formula for P(A \cup B)
wraith daggerBOT
clever dune
but doesn't the intersection account for over counting or whatever
so by subtracting that
wouldnt P(A) and P(B) be equal to the rhs
inland fossil
but doesn't the intersection account for over counting or whatever
well yeah thats why we subtract by the intersection
P(A) + P(B) - P(A and B) = P(A union B)
inland fossil
P(A) + P(B) = P(A union B) + P(A and B)
clever dune
not both
clever dune
oh
because of that I'm taking out a and b
and the sum of a+b should always be >= a-b
right?
rose rose
You are veering a little off course. The formula for the probability of union holds forall A, B. You just substitute in and evaluate the inequality to see under what condition it holds
clever dune
okay
says nervously
then I get P(A)+P(B) β₯ P(A)+P(B) - $P(A \cap B)$ β₯ max{P(A),P(B)}$
right?
wraith daggerBOT
arrow891
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)
clever dune
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crimson sedge
y=a(x-d)^3+c this is a cubic function can u give me an example of an absolute value function using the same variables?
hollow nebula
y= a|x-h| + k
cedar kilnBOT
@crimson sedge Has your question been resolved?
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short blade
what is giving you trouble
lyric narwhal
the slope of any particular line is gonna be the money per hour yes?
short blade
the slope of any particular line is gonna be the money per hour yes?
look at the axis
they change
short blade
it doesnβt really matter where diego is specifically, what youβre looking at is the relative positions between the names
the question is asking you to select all the graphs
letβs start with A
as you go further right, the money earned increases
as you go further up, the time worked increases
so if we have a very steep line, it means that they worked a lot of hours, but didnβt earn a lot of money
so they earn less money per hour
make sense?
similarly
a nearly horizontal line
will mean that after working a few hours, you earned a lot of money
(youβre not going too high up, but youβre going further right)
indeed
but thereβs more graphs that are correct
in particular, look at D (i canβt see C here)
actually D is not correct for similar reasons
but i assume C would be
i see
thorn tusk
Sooo, I gotta help my lil cousin with his homework but he goes to an international school and idk if my english is good enough to understand whats going on. Basically I just need an answer to this question.
grand forge
,rotate
wraith daggerBOT
grand forge
to get gradient of a perp line, get the negative recipricol
aka flip the fraction and stick a minus sign on it
WOAH THATS NOT IT THO THERE IS MORE
once you have the gradient
and the 2 points it passes through
in our case (3,1)
put them into the equation y = mx + c, and find c
after u done that
Than re-arrange to putted into the desired formt ax + by = c
little pumice
cedar kilnBOT
crimson sedge
Hey I have an idea
We can use the property like
All squares are rhombus
So
Diagonals are given
So we can use them
Though I haven't tried the question but this might be the right attempt to it
Also these two are similar triangles
cedar kilnBOT
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grand adder
if 2^x is convex and 0<x<1 demonstrate that 2^x>x+1
cedar kilnBOT
if 2^x is convex and 0<x<1 demonstrate that 2^x>x+1
gritty viper
comparing to the definition of convex will be useful here
think about the endpoints of the interval, 0 and 1
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@grand adder Has your question been resolved?
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cedar kilnBOT
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dusky scarab
can somone tutor me?
cedar kilnBOT
can somone tutor me?
slow thicket
can somone tutor me?
no
crystal raptor
Ask questions in here for free tutoring
slow thicket
if you have a speciific question ask it
timid owl
i like this place
slow thicket
but not an hour tutor session if thats what youre asking
timid owl
it helps u without gibing u the answer
timid owl
but not an hour tutor session if thats what youre asking
this dude guided me 2 hours π
he had patience.
dusky scarab
oh alright,thank you
timid owl
depends on the person
cedar kilnBOT
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livid hound
you'd also need to consider the position of Z for the first type
cedar kilnBOT
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plain quail
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wispy marten
This is wrong, and also 1-6 is not -7
wispy marten
e is power n too, did you notice that?
plain quail
yeah but i didnt know what to do with the n so i just hoped the way i did it would work
wispy marten
Haha, that's like trying to enter in a country with drugs hidden and hoping you're not being caught π Unfortunately you got caught
plain quail
i did indeed get caught
wispy marten
What can you say about a^n / b^n ?
plain quail
i am unsure
wispy marten
Please look at power rules in general
plain quail
would it just become a/b
wispy marten
You will have to use an identity about $\frac{a^n}{b^n}$
wraith daggerBOT
FΞliΟ
wispy marten
would it just become a/b
Math isn't about guessing, it's already been twice that you guess
plain quail
(a/b)^n?
wispy marten
Much better
Unfortunately you have 6^(n-1)
But you can use another power rule
In order to have what you want
plain quail
6^n - 6?
wispy marten
Not quite...
plain quail
oh divde instead of subtract
wispy marten
$\frac{e^n}{6^{n-1}} = \frac{e^n}{6^n/6}$ is good
wraith daggerBOT
FΞliΟ
wispy marten
But this is not (e/1)^n. Where are all the 6s going in that?
plain quail
take the reciprocal and multiply
wispy marten
6^n and 6 aren't cancelling each other
plain quail
6e^n/6^n
wraith daggerBOT
FΞliΟ
wispy marten
Then you finally have some a^n / b^n that you can use
plain quail
(6e/6)^n
wispy marten
$\frac{e^n}{6^{n-1}} = \frac{e^n}{6^n/6} = \frac{6e^n}{6^n} = 6\left(\frac{e}{6}\right)^n$
wraith daggerBOT
FΞliΟ
wispy marten
You have to be able to use these rules, eyes closed
I won't be behind you in your test
plain quail
you see i learned these rules a while ago but havent seen them in the past like 5 years or something π
wispy marten
Math is like building a castle, it is useless to be able to build the tower of the castle [using the geometric series properties], if you cannot build the base [solving basic algebras that will lead you on using the geometric series stuffs]
wispy marten
Did you get the question right?
plain quail
so then a = 6 and then r = e/6?
wispy marten
Not quite for a
plain quail
i havent tried yet
wispy marten
a is the first term. What happens when you replace n by 1?
plain quail
makes it to the power of 1
wispy marten
6e/6 = e, not 6
wispy marten
The first term is 6e/6 = ...
wispy marten
Yes
wispy marten
Good job!
plain quail
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cedar kilnBOT
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marsh pond
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marsh pond
If I multiply by (-1) I need to do that to both sides, correct?
marsh pond
If I multiply by (-1) I need to do that to both sides, correct?
Iβm not sure if that will help .. but worth a tryβ¦
gilded elm
maybe ur thinking of factorizing it
marsh pond
It works
What a shit show
Do you deal with these trig identities all the time?
I need to memorize these
obsidian coral
Fyi, I'm pretty sure that where you are proving trig equivalencies, you only use only side and manipulate it in a way where it looks like the other side
obsidian coral
No you didn't, you multiplied by -1 on both sides, meaning you manipulated both sides
marsh pond
There is no other way to solve it
obsidian coral
you only use only side and manipulate it in a way where it looks like the other side
So multiplying by -1 manipulated both sides
gilded elm
er u just need to know sin + cos
the squared
i wouldnt bother memorizing the other ones
marsh pond
So multiplying by -1 manipulated both sides
How would you solve it without -1 to both sides?
obsidian coral
LHS, denominator, factor out -1
gilded elm
i wouldnt bother memorizing the other ones
well unless ur slow at algebra
marsh pond
Oh I see
obsidian coral
Things cancel, and then it simplifies to look like cos(x) - sin(x)
marsh pond
maybe ur thinking of factorizing it
Thatβs what you meant here
Alright I will try that instead.. that way the RHS remains pristine
obsidian coral
I need to memorize these
To answer this, what was stated above, just know the first one
The others are derived from the first one
gilded elm
yeah to get (2) divide by cos^2
on both sides
ill leave that as an exercise for the reader
to obtain (3) divide by sin^2
(also an exercise 
)
marsh pond
marsh pond
LHS, denominator, factor out -1
That is better. Thanks for the clarification on that!
marsh pond
To answer this, what was stated above, just know the first one
Is the first one a^2 + b^2 = c^2?
Just a different way of writing it?
As per the unit circle
Therefor hypotenuse is always 1
Legs are thetas
obsidian coral
Just know this identity
marsh pond
That one yeah
obsidian coral
The rest are derived from that
marsh pond
x^2 + y^2 = r^2
marsh pond
Just know this identity
Exact same identity as x^2 + y^2 = r^2 just written using trig functions?
obsidian coral
The rest meaning 2 and 3
If you just know identity 1, you can derive 2 and 3 based on that
obsidian coral
yeah to get (2) divide by cos^2
If you read this
gilded elm
Exact same identity as x^2 + y^2 = r^2 just written using trig functions?
ok if you want to see how the sin^2 identity is derived
draw a right triangle with sides a b c
marsh pond
I donβt get how divide both sides by cos for first identity gets the second identity?
gilded elm
I donβt get how divide both sides by cos for first identity gets the second iden...
exercise for you
recall tanx = sinx/cosx
marsh pond
Even if they are squared?
marsh pond
OK
gilded elm
draw a right triangle with sides a b c
and then consider any angle theta which is not the right angle, take sin theta and cos theta
obsidian coral
OK
Well $sin^2 = sin * sin, cos^2 = cos * cos$
$\\frac{sin^2}{cos^2} = \frac{sin * sin}{cos * cos} = \frac{sin}{cos} * \frac{sin}{cos} = tan * tan = tan^2$
wraith daggerBOT
dldh06
obsidian coral
to obtain (3) divide by sin^2
gilded elm
Well $sin^2 = sin * sin, cos^2 = cos * cos$
$\\\frac{sin^2}{cos^2} = \frac{sin *...
nooo u weren't supposed to do the exercise
marsh pond
First identity: Pythagorean theorem
Second identity: Divide Pythagorean theorem by cos
Third identity: Divide Pythagorean theorem by sin
obsidian coral
You got that backwards
marsh pond
Oh it matters which order? When you say second identity ppl know exactly which one?
Also, are there more than 3?
obsidian coral
Second identity based off your list
obsidian coral
Oh it matters which order? When you say second identity ppl know exactly which o...
No
I'm basing it off what you wrote
cedar kilnBOT
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snow condor
The i is an index that specifies the position of an element right?? But position 0 doesnβt make sense π
snow condor
Or like the first element is 0??
tropic oxide
the rightmost digit is the 0th
there's nothing wrong inherently with starting your numbering from 0 instead of 1
snow condor
is there a difference between 0 and 1
or is it the same
Can first position just mean the same as first number I guess
Or first thing
cedar kilnBOT
@snow condor Has your question been resolved?
snow condor
<@&286206848099549185>
tropic oxide
your question feels a little odd
snow condor
Can I use 0 or 1 and they both mean the 1st element
jagged charm
Hello, I was given this figure in math class and was asked to determine the equations of the trajectory at the center of point O.
The only method I have in mind is to use the tools in physics.
Except that we are in math.
So it's not clear to me.
If someone could help me.
dire geode
,rotate
wraith daggerBOT
dire geode
Just gravity?
jagged charm
It is a ladder cloistered on a wall. It is falling.
jagged charm
Just gravity?
Yeah I think, but we're on math.
cedar kilnBOT
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crystal raptor
.test
viral tundra
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viral tundra
show with the differential quotient that f(x) is differential able at x0 with fΒ΄(x0)=-23
cedar kilnBOT
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viral tundra
<@&286206848099549185>
tame wraith
@viral tundra have you learnt quotient rule?
viral tundra
no
tame wraith
do you have to solve from first principles?
tame wraith
why did you cancel out the 5
teal grotto
cedar kilnBOT
mighty drift
Yes
mighty drift
Yes
cedar kilnBOT
clear berry
-e^(-x) + c
dusk finch
-e^(-x) + c
+C π
fallen moat
π
hollow nebula
π
fallow anchor
The prism and pyramid have the same bases and equal heights. determine the volume of the pyramid if the volume of the prism is 120 cm3
fallow anchor
<@&286206848099549185>
dusk finch
The prism and pyramid have the same bases and equal heights. determine the volum...
Do you know formula for volume of pyramid?
fallow anchor
V = b2h / 3
fallow anchor
yes
dusk finch
Great. Formula for prism is b^2*h, right?
fallow anchor
yeah
dusk finch
And you know that the volume of prism=120. So b^2*h=120
And volume of pyramid is b^2*h/3
And you already know what b^2*h is
fallow anchor
so 120/3 ?
dusk finch
Exactly
fallow anchor
thanks
dusk finch
You are welcome. If you're done you can close the channel with .close so other people can ask questions
fallow anchor
.close
odd badger
Hi, can someone explain to me what is happening in this step?
mighty drift
They multiply by 1
wispy marten
They multiplied by 1
crystal raptor
They multiplied by 1
wispy marten
They mutiply by 1
mighty drift
It's a known limit
cedar kilnBOT
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mortal bone
is this a linear ode
cedar kilnBOT
is this a linear ode
mortal bone
bcs i can't solve it
i tired findin A(x) which is the primitive of 3
which results into 3t
gritty viper
there should be a linear polynomial solution
for y_p
then the homogenous equation is separable
mortal bone
so this is the kind of separable ode right
gritty viper
the original isn't separable
you have to find a particular solution
which in this case, there's a y=mt+b type that does the trick
then solve the homogenous version
gritty viper
probably idk
mortal bone
but that's what i was searching bcs i don't know what approach to follow to solve it
dapper sonnet
Hi, I'm looking for a way to find the coordinates of a number based off of this square spiral
dapper sonnet
Basically say that there's a function to get the x
Like xcoord(14) would return 0, and ycoord(14) would return 2
I know how to do this if i make a loop that will go and make the spiral until the n number, but I wanna do it with a formula
long swan
This is not the typical spiral
dapper sonnet
I know, I'm looking for a square spiral
Doesn't matter which direction
But it has to go like thst
long swan
No I mean the grid doesn't usually contain 0
mighty drift
You can find how many numbers are in each square and then invert it to find the square in which it is. Then on each square do some thinking to figure out each coordinate more precisely
mighty drift
Can't help you all the way through up to an answer though
dapper sonnet
My math knowledge equals the math knowledge of a 5 grader
mighty drift
Ok then not like that
dapper sonnet
Ok maybe like 10th grade
But it can't be that complicated surely
Like I've seen many games do thst
To create like islands or plots etc
mighty drift
Game makers have much more math education than you think
dapper sonnet
I found out how to create it but like
With a loop
And if you have like 20k players
Or islands
20k loops every time someone makes it is like huge
Which is why I wanna just store the number and get the coords
I mean I could preload like many thousands and store in a list but