notice that this set can be expressed as the intersection of the null spaces of two linear maps
#help-19
green elm
twin wyvern
??
we are supposed to test this using if it is closed under addition or scalar multiplication
to see if it is a subspace
a1 +a2+3a4=0
b1+b2+3b4=0
(a1+a2+3a4)+(b1+b2+3b4)=0
idk whwat to do now
sharp oak
Way too difficult of an ask
But if you have a span for the space, then it becomes easy to check these
sharp oak
I mean we can check these still, but with a form that's easier to check
We can get a span by reducing this matrix:
[1 1 0 3 | 0]
[0 3 0 -2 | 0]
twin wyvern
I mean we can check these still, but with a form that's easier to check
we havent learnt matrix
sharp oak
Oh fam really? Yike awarded
I mean we can still do the same thing but without the matrix notation. That is, use equation (2) to remove x2 from equation (1)
3x1 + 3x2 + 9x4 = 0
- 3x2 - 2x4 = 0
Gives us 3x1 + 11x4 = 0
We can see the space as
Span{(11, 0, 0, 3), (0, -2, 0, 3)}
That interpretation makes it obvious. All of the subspace axioms are in there.
odd edgeBOT
@twin wyvern Has your question been resolved?
odd edgeBOT
@twin wyvern Has your question been resolved?
sand night
odd edgeBOT
sand night
Is this right
?
I forogt to label the 10 seconds at the 4th dash but after than that
Oops I cut off the most important part it says 3.5 ft from
green elm
looks fine to me, assuming you consider the midpoint of the buoy's height to be 0
sand night
Ye I’m not not given any other information so makes because waterline would be 0
Ty
.close
brittle galleon
What would the range of this function be and why?
odd edgeBOT
What would the range of this function be and why?
young moss
!status
odd edgeBOT
What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
mystic saffron
What would the range of this function be and why?
what are the biggest $$|n|$$ and smallest numbers the denominator can reach?
clever fjordBOT
What should I do
young moss
what are the biggest $$|n|$$ and smallest numbers the denominator can reach?
what if he has an answer but just didnt show it 👀 , anyways this channel is now urs :exit:
brittle galleon
I know that the domain is R^ - {(0,0,0)} since the function is underfined for (0,0,0)
In terms of the range
i'm not too sure where to begin...
mystic saffron
all your variables are in the denominator
brittle galleon
**What should I do**
well it's infinite no?
young moss
wouldn't it be faster to just answer the question <:NoOoOo:1080809826310955038>
Im having fun watching 
brittle galleon
This function returns the gravitational field strength given, x,y and z
So shouldn't the max g be 300000?
wait no
the max has to be infinity regardless of what g stands for right?
green elm
g will be 300000 if x^2 + y^2 + z^2 = 1, right? What happens if x^2 + y^2 + z^2 is smaller than 1?
brittle galleon
g will be 300000 if x^2 + y^2 + z^2 = 1, right? What happens if x^2 + y^2 + z^2 ...
yes g will be 300000 when the denominator = 1
green elm
what if the denominator is 1/2
brittle galleon
it will double
green elm
and if the denominator is 1/10000
brittle galleon
it get even larger
green elm
is there any maximum?
brittle galleon
no
green elm
right, we can make it as large as we want by making the denominator small
odd edgeBOT
@brittle galleon Has your question been resolved?
stark heart
@brittle galleon
Yeah correct
But there is only one number that is impossible to get even if you tried any possible number
brittle galleon
that number is 0
stark heart
Yes
Now that is the answer
R-{0}
Got it?
@brittle galleon ?
Do you have any more questions?
@brittle galleon
odd edgeBOT
odd edgeBOT
Available help channel!
tepid ledge
someone knows how to solve this
odd edgeBOT
@tepid ledge Has your question been resolved?
odd edgeBOT
odd edgeBOT
Available help channel!
valid condor
How would one solve this?
odd edgeBOT
How would one solve this?
valid condor
yea, believe so
quasi sparrow
Do you know a formula that relates two vectors and the angle between them
valid condor
yeah
which means i have u dot v = -21 i believe
but i dont see how to get 2v and 3w
quasi sparrow
Do you know how to expand ||a-b||^2 if a and b are vectors
quasi sparrow
Yea expand that using dot product rules
valid condor
uhhh
is that just foil….?
4 v dot v - 6 v dot w + 9w dot w?
and just substitute and square root?
I’m not sure about dot product rules
odd edgeBOT
@valid condor Has your question been resolved?
quasi sparrow
I’m not sure about dot product rules
You did it right
Use the given information and your dot product from before now
quasi sparrow
costheta = u * v / ||u|| ||v|\ right?
.
odd edgeBOT
odd edgeBOT
Available help channel!
hybrid gyro
(4a² - 4a +1)½ + |a +4| = a + 7
odd edgeBOT
(4a² - 4a +1)½ + |a +4| = a + 7
hybrid gyro
Can anyone tell me why we won't just cancel the square root by (2a-1)^2
dry scarab
sqrt(a^2) = abs(a)
tall veldt
e.g. sqrt((-5)²) does not equal -5
hybrid gyro
Ah ic my theory was we were saving a root of the equation
So how will the question go from here
odd edgeBOT
Available help channel!
strange basin
How to convert a standard eqn of an ellipse to a gen eqn?
tall veldt
A gen eqn?
tall veldt
Yeah what is a general equation
strange basin
tacit wasp
You do the calculations and you're done
Let's say you start with $\frac{{\left(x - 1\right)}^2}{4} + \frac{y^2}{9} = 1$
clever fjordBOT
Alberto Z.
tacit wasp
Then what would you do?
strange basin
Square the binomials then distribute the denominator
tacit wasp
You don't need to distribute the denominator
strange basin
Yeah my bad, that's the process our instructor taught us. But yeah it's the same thing without distributing
tacit wasp
**Alberto Z.**
Then you have: $\frac{x^2 -2x + 1}{4} + \frac{y^2}{9} = 1$
clever fjordBOT
Alberto Z.
tacit wasp
**Alberto Z.**
And then: $\frac{1}{4}x^2 - \frac{1}{2}x + \frac{1}{4} + \frac{y^2}{9} = 1$
clever fjordBOT
Alberto Z.
tacit wasp
**Alberto Z.**
Then: $\frac{1}{4}x^2 + \frac{1}{9} y^2 - \frac{1}{2}x + \frac{1}{4} - 1 = 0$
clever fjordBOT
Alberto Z.
strange basin
Yeah
tacit wasp
**Alberto Z.**
Almost last step: $\frac{1}{4}x^2 + \frac{1}{9} y^2 - \frac{1}{2}x - \frac{3}{4} = 0$
clever fjordBOT
Alberto Z.
tacit wasp
**Alberto Z.**
And finally $x^2 + \frac{4}{9} y^2 - 2x - 3 = 0$
clever fjordBOT
Alberto Z.
tacit wasp
To reach this form, as you asked
strange basin
I mean from general equation to standard
strange basin
From this
tacit wasp
To reach this form, as you asked
And you can now say that a=1, b=4/9, c=-2, d=0, e=-3
strange basin
**Alberto Z.**
to this
tacit wasp
Ahnn the opposite way you mean
tacit wasp
Sorry, I totally misunderstood it then, my bad
I would do it by completing the square
strange basin
It's fine, can you still help me with it?
tacit wasp
It's fine, can you still help me with it?
Yep
strange basin
I would do it by completing the square
Can you show me an example?
tacit wasp
Can you show me an example?
Yeah
Suppose you have $$x^2 - 2x + 3$$ Do the first two terms ring you a bell?
clever fjordBOT
Alberto Z.
strange basin
Binomial expansion? Square of binomial?
tacit wasp
Yeah, it should remind you of (x - 1)², right?
strange basin
Yup
tacit wasp
Do you agree if I write that $x^2 - 2x + 3$ is the same as $x^2 - 2x +1 -1 +3$?
strange basin
Yeah, it should remind you of (x - 1)², right?
Wait, if this is the equation before squaring, shouldn't the last term be +1?
Yeah
clever fjordBOT
Alberto Z.
strange basin
Yeah I noticed
strange basin
But I believe you still agree
Yup
clever fjordBOT
Alberto Z.
tacit wasp
Which is ${\left(x - 1\right)}^2 + 2$
clever fjordBOT
Alberto Z.
tacit wasp
https://www.youtube.com/results?search_query=completing+the+square+method
If you want videos, you can pick one of these, they are all good in my opinion
strange basin
Thank you
Do you know the representation of A, B, C, D, and E in the general equation of an ellipse?
tacit wasp
No, I haven't studied that yet, I'm sorry
lucid pewter
How do I integrate (2x)^1/3
odd edgeBOT
How do I integrate (2x)^1/3
lucid pewter
true minnow
there is a straight forward formula to differentiate x^k where k is any number really
so we can do the reverse to integrate
true minnow
f(x)=x^k
f'(x)=kx^(k-1)
that means:
f(x)=x^k
F(x)=(1/k+1)x^(k+1) + C
lucid pewter
Can u show me on paper or sum
woeful ravine
1=2/2
Then 2^1/3 becomes 2^4/3 and 4 in denominator becomes 8
odd edgeBOT
@lucid pewter Has your question been resolved?
odd edgeBOT
odd edgeBOT
Available help channel!
eager cypress
odd edgeBOT
eager cypress
Hi there can someone teach me part (b) ?
I have try to solve using (6! × 5!)÷ 2 and my answer went wrong
mystic saffron
It doesn't say whether all the men are distinct and all the women are distinct or not
On second thought maybe it obviously is the case
mystic saffron
It doesn't say whether all the men are distinct and all the women are distinct o...
@eager cypress Can you show your working for question a so I can see whether you made this assumption or not?
eager cypress
<@792530063299444747> Can you show your working for question a so I can see whet...
(a) (10-1)! = 9! = 362880 by formula : (n-1)!
mystic saffron
(a) (10-1)! = 9! = 362880 by formula : (n-1)!
Why n-1?
eager cypress
<:thonk:406575732563902485> Why n-1?
the formula of permutation in the case of cirlce
mystic saffron
the formula of permutation in the case of cirlce
Ooooh I missed the "round table" part
eager cypress
yea
eager cypress
Ooooh I missed the "round table" part
i did my part (a) correctly and im trouble in part (b)
mystic saffron
@eager cypress So as with question a you can pick any person as the anchor and consider the rest
Were you even thinking of the n-1 formula this way?
Because that's sort of the logic behind it
Because it doesn't matter if you rotate the table around you can pick any person as the anchor and think of them as always being at the same seat no matter what
This way you can translate from a round table problem to a line problem
...Does that make sense?
I feel like I'm saying nonsense
Ping me once you get back
eager cypress
Ping me once you get back
i just cant figure it out how does the ans given is 14400
mystic saffron
i just cant figure it out how does the ans given is 14400
But did what I say make sense or was it nonsense?
I have a feeling I just gave a gibberish explanation which is kind of embarassing
eager cypress
This way you can translate from a round table problem to a line problem
how this happen ?
mystic saffron
Mhm
How you can do that translation by anchoring 1 person
Did that explanation make sense?
eager cypress
Did that explanation make sense?
okay yea?
mystic saffron
Oof good
Okay so you can do the same for question b
It doesn't matter who you pick
velvet egret
Are we considering the 5 men and 5 women to be distinct?
mystic saffron
Are we considering the 5 men and 5 women to be distinct?
I asked myself the same question and ended up with the conclusion that we are
And this is what Loi did in their calculations too
The question doesn't give more info
velvet egret
Then I’d say it should be 2(5!) multiplied by the number of ways which the groups can be seated around the table
Which should be 10?
mystic saffron
Then I’d say it should be 2(5!) multiplied by the number of ways which the group...
Are you talking about question a or b?
velvet egret
b
mystic saffron
Sounds like a !nosols moment
eager cypress
how if i grouped those men who are seated together counted as 1 ?
mystic saffron
Then I’d say it should be 2(5!) multiplied by the number of ways which the group...
multiplied by the number of ways which the groups can be seated around the table
The "round table" thing implies that you can rotate the table and it's still the same configuration
It's actually divided by 10
Dangit I think that might actually be an easier way to think about it than that anchor thing I was talking about
Actually maybe not
mystic saffron
how if i grouped those men who are seated together counted as 1 ?
I can't think of an easier method... Pick a man as your anchor and consider the cases where there's 0 men to their right, 1 man, etc... up to 5 men to their right
Or I just realised you could just think about how the men are ordered relative to the anchor
Yeah, that'd be much easier, my bad
@eager cypress Does that help?
eager cypress
<@792530063299444747> Does that help?
can you show your steps ? so that i can easily understood
mystic saffron
can you show your steps ? so that i can easily understood
First assume one man is your anchor
Then consider all the ways to order the 5 men relative to the anchor
Then consider all the ways to order the 5 women relative to the anchor- wait oh wow this is much easier than I thought
Yeah, come to think of it... It's not as hard as I thought
If the 5 men are seated together then the 5 women are also seated together
I don't know how I didn't realise this earlier
This makes the calculations easier
@eager cypress Looks like even I had a bit of a learning curve there... Does that help?
eager cypress
I don't know how I didn't realise this earlier
so is 5! x 5! x 5! ?
mystic saffron
so is 5! x 5! x 5! ?
Where does the third 5! come from?
eager cypress
5! (arranging the entities) * 5! (arranging the men within their group) * 5! (arranging the women within their group)
mystic saffron
"the entities"?
eager cypress
the men are seated together as i said (6-1)!
mystic saffron
Mhm
...I don't know where 6-1 comes from
It's just 5!
We're not arranging 6 things around a round table
Also it sounds like you're arranging the men... twice
mystic saffron
thank you <@456226577798135808>
You can now .close this channel
eager cypress
.close
flint fog
Find the volume of the parallelepiped determined by (3, 1, 0),
(4, 2, 1), and (1, 2, −1)
flint fog
Don't know how to come up with the vectors to plug into the volume formula
This is linear algebra
north crow
use Pythagoras?
clever fjordBOT
TimK
north crow
,rotate
clever fjordBOT
flint fog
I did AC x BC for (b x c), ended up with volume = 0 after I dotted that with a
So that's incorrect
mystic saffron
Find the volume of the parallelepiped determined by (3, 1, 0),
(4, 2, 1), and (1...
yes construct a matrix and find the determinant
mystic saffron
I did AC x BC for (b x c), ended up with volume = 0 after I dotted that with a
do you know how to find the determinant of a 3x3 matrix
odd edgeBOT
@flint fog Has your question been resolved?
odd edgeBOT
odd edgeBOT
Available help channel!
chilly bane
hey I don't understand how my teacher went from this stage to the next.
dry scarab
notice there is $\pi^2$ missing
clever fjordBOT
ils
chilly bane
notice there is $\pi^2$ missing
where
dry scarab
under dl
dry scarab
cosa= d/r
chilly bane
yep
dry scarab
Cos^2a/d^2 = 1/r^2
chilly bane
don't understand how you do it... @dry scarab
odd edgeBOT
@chilly bane Has your question been resolved?
chilly bane
I don't understand why it's not d^2/cosa^2
odd edgeBOT
@chilly bane Has your question been resolved?
odd edgeBOT
@chilly bane Has your question been resolved?
odd edgeBOT
hardy belfry
odd edgeBOT
Available help channel!
junior storm
i need help with a question
odd edgeBOT
i need help with a question
junior storm
A projectile is broken into two pieces at the maximum height. Then its
(a) momentum increases. (b) momentum decreases.
(c) kinetic energy increases. (d) kinetic energy decreases.
whats the answer ?
i thought the KE would decrease as KE is directly proportional to mass (KE =1/2 mv^2) and the mass of the projectile is decreasing
but apparently, its wrong
odd edgeBOT
@junior storm Has your question been resolved?
true minnow
momentum p=mv
in other words p=dF/dt
so momentum is the derivative of the force
and the force here is gravitation which doesnt change with time
therefore momentum is constant
thats why we call it a conserved property
like energy
however, only because energy in total is conserved, does not mean kinetic energy specifically has to be preserved
energy can be converted into other energy types
think about kinetic and potential energy in this example
true minnow
ah no
junior storm
🥲
junior storm
how
true minnow
we just now look at two parts of the bullet
but they both still exist
well i guess it depends on if we look at one or both pieces
junior storm
but wont it be considered as 2 different objects now that it has been seperated
true minnow
ahh wait
i cant read i guess
"at max height"
if we throw a ball up
it will reach a maximum height
at that point, it will have a velocity of 0 right?
junior storm
yes
true minnow
and kinetic energy is 0.5mv^2
junior storm
yes
true minnow
so kinetic energy there is 0
junior storm
yes
true minnow
yes, if we only look at one piece, the mass does decrease
but at max height we had 0.5mv^2 where v is 0, so even then KE does increase
junior storm
they need to be more specific with the conditions
true minnow
if we have any mass and START to move, then our kinetic energy must increase
junior storm
imma just go with your answer lol
even tho i dont understand
not that i didnt undestand your explaination but i dont get the question to begin with
well
thanks
.close
elder wing
odd edgeBOT
dry scarab
,tex .exp rules
clever fjordBOT
ils
elder wing
is it fractional exponent
dry scarab
not only
elder wing
Its 2?
odd edgeBOT
@elder wing Has your question been resolved?
tepid yacht
Notice how the problem gives you a fraction but the answer it wants is not
tepid yacht
Yes you need to apply the fractional exponent rule
But you need to apply something else
elder wing
so square root of 27 and 1/5 as exponent
tepid yacht
Why 1/5?
elder wing
Cus one and five if its not that then im lost
tepid yacht
No
tepid yacht
Let's take it one step at a time, you want to represent $\frac{1}{(\sqrt{23})^5}$ as $a^{\frac{b}{c}}$
clever fjordBOT
dldh06
elder wing
Yes
tepid yacht
So let's convert the $(\sqrt{23})^5$ as a fractional exponent first
clever fjordBOT
dldh06
tepid yacht
What would that look like with a fractional exponent?
elder wing
would u add 5 exposnt of 23
elder wing
2
tepid yacht
No
elder wing
?
tepid yacht
What is $\sqrt{23}$ writtern as an exponent?
clever fjordBOT
dldh06
tepid yacht
You can apply the fractional exponent logic here too
elder wing
Can u pull up the laws again
clever fjordBOT
dldh06
elder wing
i meant 23
tepid yacht
So you have $\sqrt{23}$, you look at the fractional exponent rule, you see how it has the $\sqrt[y]{a^x}$
clever fjordBOT
dldh06
tepid yacht
What would x and y be for $\sqrt{23}$?
clever fjordBOT
dldh06
elder wing
y would be on the left side
tepid yacht
Yes
elder wing
x would be exponent
elder wing
number?
tepid yacht
Yes a number
elder wing
5?
tepid yacht
No
elder wing
1?
tepid yacht
I'm just asking for $\sqrt{23}$
clever fjordBOT
dldh06
tepid yacht
Yes
elder wing
Uhm
tepid yacht
Basically what I am asking for you is to compare $$\sqrt{23}$$ and $$\sqrt[y]{a^x}$$
clever fjordBOT
dldh06
tepid yacht
You know a = 23
elder wing
Yea i just dont know
elder wing
Are they the two numbers that make 23
elder wing
There's no written exponent so that must mean what?
I dont know
tepid yacht
Are they the two numbers that make 23
No
elder wing
ok well idk
tepid yacht
Where is the -5 from
elder wing
Huh
elder wing
The x^1 = x?
dont u add a 1 if its by itself
tepid yacht
dont u add a 1 if its by itself
Yes, that's what I was indicating, if there is no exponent, that means there is an imaginary 1 as the exponent
elder wing
Ok
tepid yacht
So what is the exponent for $\sqrt{23}$ when you compare it with $\sqrt[y]{a^x}$, in other words what is x?
clever fjordBOT
dldh06
tepid yacht
Where is the 5 coming from
tepid yacht
That's not what I'm asking, I am trying to get you to do it one step at a time
First by writing $\sqrt{23}$ with a fractional exponent
elder wing
what r u asking cus i dont understand what u are asking i dont know how to do that i told u
clever fjordBOT
dldh06
tepid yacht
what r u asking cus i dont understand what u are asking i dont know how to do th...
I am trying to get you to do it one step at a time
elder wing
tepid yacht
First by writing $\sqrt{23}$ with a fractional exponent
clever fjordBOT
dldh06
tepid yacht
What is the exponent for $\sqrt{23}$ when you compare it with $\sqrt[y]{a^x}$, in other words what is x?
clever fjordBOT
dldh06
elder wing
1
tepid yacht
What would y be?
elder wing
past sandal
If this doesn't clear your doubts idk what will
elder wing
do i make it negative?
tepid yacht
What would y be?
You should know that if there is no y written, it's indicated with an imaginary 2, because it's the sqrt
tepid yacht
do i make it negative?
Stop trying to jump forward, as I mentioned, we are going one step at a time
tepid yacht
And the first step is writing $\sqrt{23}$ as a fractional exponent
clever fjordBOT
dldh06
tepid yacht
Do you see how $\sqrt{23}$ is very similar to example a here?
clever fjordBOT
dldh06
elder wing
sure
tepid yacht
Can you rewrite $\sqrt{23}$ with a fractional exponent?
clever fjordBOT
dldh06
elder wing
square root of 23 with a 2 on the left and 1 on right?
tepid yacht
Are you trying to say $\sqrt[2]{23^1}$?
clever fjordBOT
dldh06
tepid yacht
So now how would you rewrite that as an exponent?
tepid yacht
So how would that look like?
elder wing
Square root of 23^1/2
tepid yacht
What I mean is, if you look at example a, and went from right to left, because that's what you are doing with sqrt(23), if you notice there is no square root symbol with that 3 on the left, therefore why would you have one still, in your statement with Square root of 23^1/2?
elder wing
Cus i didnt know u wanted me to solve the square root of 23
tepid yacht
I didn't ask for you to solve for anything, all I asked was for you to rewrite $\sqrt{23}$ with a fractional exponent
clever fjordBOT
dldh06
elder wing
And i said i dont know how to and ive said it multiple times i dont understand so idk i just tried and when i think its right its wrong and im not even sure what i did earlier with the half is right cus u dont tel me
tepid yacht
That's why I'm trying to walk you through it with examples like above
elder wing
I dont see how its the same when it dosent have the 1/ on top
tepid yacht
Because we are going one step at a time, with $\frac{1}{(\sqrt{23})^5}$
clever fjordBOT
dldh06
elder wing
was the 1/2 right?
tepid yacht
So you want to start with the inner most part, in this case the $\sqrt{23}$
clever fjordBOT
dldh06
elder wing
Okay
tepid yacht
**dldh06**
So we are going to rewrite $\sqrt{23}$ with an exponent instead, then replace it here
clever fjordBOT
dldh06
elder wing
k
tepid yacht
So how can $\sqrt{23}$ be written with an exponent?
clever fjordBOT
dldh06
elder wing
2 and 1?
tepid yacht
How can you make it look like $a^\frac{x}{y}$?
clever fjordBOT
dldh06
tepid yacht
What would a, x, and y be?
elder wing
27 A
23*
And idk x and y
u wont anwser me on 1/2 so😭
This is giving me a headache i feel like im over thinking it
tepid yacht
It is 1/2, all the other times you were saying 1/2, you included extra words that was not needed
tepid yacht
Square root of 23^1/2
Like here, you do not need the square root of part at all
It is just 23^(1/2)
elder wing
but i thought i needed to find the square root of 23?
tepid yacht
You're not finding a value
elder wing
Ok
tepid yacht
You're converting from one form to another
elder wing
So i just put 23 no square root ^ 1/2
tepid yacht
The form is a square root, you want it to be an exponent
tepid yacht
So i just put 23 no square root ^ 1/2
Why are you throwing extra words in there?
tepid yacht
It is just 23^(1/2)
.
elder wing
OKAY SO ITS 23^1/2
tepid yacht
Now with $\frac{1}{(\sqrt{23})^5}$ the $\sqrt{23}$ gets replaced with $23^\frac{1}{2}$
clever fjordBOT
dldh06
tepid yacht
Which is just $\frac{1}{(23^\frac{1}{2})^5}$
clever fjordBOT
dldh06
tepid yacht
Now how can you simplify $(23^\frac{1}{2})^5$ into one exponent?
tepid yacht
You use power of a power rule there
clever fjordBOT
dldh06
elder wing
1?
tepid yacht
Why are you saying one?
elder wing
1/2 x 5
elder wing
I thought it was 1
tepid yacht
Do you know how to multiply fractions?
$\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}$
clever fjordBOT
dldh06
elder wing
i have to do that 5 times?
tepid yacht
No
elder wing
do i do it once and x by 5
tepid yacht
When you multiply fractions, you mulitply across the numerator and across the denominator
$$5 = \frac{5}{1}$$
$$\frac{1}{2} \times \frac{5}{1}$$
elder wing
this is taking way longer than i thought it would
tepid yacht
What does that equal to?
clever fjordBOT
dldh06
elder wing
5/2
clever fjordBOT
dldh06
elder wing
okay
tepid yacht
Now you replace the $(23^\frac{1}{2})^5 $ in $\frac{1}{(23^\frac{1}{2})^5}$ with $23^{\frac{5}{2}}$
clever fjordBOT
dldh06
elder wing
Ok
tepid yacht
And you get $\frac{1}{23^{\frac{5}{2}}}$
clever fjordBOT
dldh06
tepid yacht
Now you need to transform so it's not a fraction anymore
Which applies the negative exponent rule
elder wing
23 ^ -5/2
tepid yacht
Yes
tepid yacht
Yes
tepid yacht
tepid yacht
Do u know which button i need to put to make the - exponent fraction
The negative exponent is you putting a minus sign in front
elder wing
tepid yacht
Tbh I don't know how that site works, what if you delete all that again, type in 23 then push that button?
tepid yacht
23 ^ -5/2
In that blue square, type in the exponent, what you have here
You might have to press the minus button first then the fraction button
tepid yacht
Clear all that
Type in 23 then push that exponent button
Then press the minus button first then the fraction button
Then type in the fraction
elder wing
tepid yacht
You are suppose to type that -5/2 inside the blue box
tepid yacht
It's negative 5/2
tepid yacht
Yes that's better
elder wing
so should i just send it like that
tepid yacht
That's the form that it wants
bitter ether
how can I do this?
odd edgeBOT
how can I do this?
bitter ether
that’s polynomial function right?
spice fiber
take log both sides ig
tribal ingot
@bitter ether use logarithms
reef sandal
It's not a polynomial
odd edgeBOT
@bitter ether Has your question been resolved?
drowsy gulch
odd edgeBOT
drowsy gulch
Now whats DBC
57?
sand night
Alright
drowsy gulch
DCB=48
sand night
yes
drowsy gulch
ye
drowsy gulch
ye
odd edgeBOT
odd edgeBOT
Available help channel!
primal summit
odd edgeBOT
primal summit
what is the question trying ot tell and how to solve ?
please ping me if i dont respond right away
viscid flint
please ping me if i dont respond right away
it's saying that 44m of distance along the track gets you 28° of circle
west merlin
so like an arc then?
upbeat drum
If you have a full circle with an angle of 360° at the center, 44m of track only goes 28° across.
an arc
you got a formula for calculating arc length?
primal summit
you got a formula for calculating arc length?
yeah i do
thank for the help
.close
odd edgeBOT
odd edgeBOT
Available help channel!
dreamy yacht
Just a quick question: Is there is a difference between the order topology on N and the discrete topology?
raven grotto
nah, the open interval (n - 1, n + 1) = {n} is open in the order topology, so all point sets are open
so then all sets are open
dreamy yacht
Ok, thanks. Then I understood it correctly. GTP has been talking bs then
Thank you for answering that quickly 🙂
.close
raven grotto
strong jewel
I'm not sure how to do 11iv
odd edgeBOT
@strong jewel Has your question been resolved?
strong jewel
<@&286206848099549185>
strong jewel
anyone?
strong jewel
yea
gilded panther
What jc
strong jewel
dhs
gilded panther
ya
strong jewel
Oo which
strong jewel
Yea
light burrow
odd edgeBOT
light burrow
replace A_n with A_k, since n is already used for R^n
need hints for the second part
I have to show that
for all e>0 there exists N, for all v in C(C is a compact in R^m) such that k>N implies |A_n(v)-A(v)|<e
idk how to make use of the control that we are working on a compact subset
odd edgeBOT
@light burrow Has your question been resolved?
lost stirrup
can someone tell me if this is an accurate description of the cauchy sequence?
lost stirrup
has the notation: for all variables greater than 0, there exists a varaible N of the group of naturals, where all n and m are a distance apart determined like so: |Xn-Xm|, such that the variable is less than those members.
was from this
ive only just read up about the cauchy sequence
raven cliff
Not quite
It's 'For all variables greater than 0 (i.e. all positive epsilon), there exists a natural N such that for all naturals n, m at least N, the x_n and x_m are less than epsilon apart.'
Such a sequence would be Cauchy
lost stirrup
ok thank you
raven cliff
ok thank you
np
lost stirrup
np
sorry i dont quite understand it
i understansd the distance part and that there is some variable that will always be greater than the distance between each point n, m
but how does N come into play here
as far as i know its just a natural number
oh these numbers have to be equal or more to N
i completed mistsed that
.close
vivid magnet
odd edgeBOT
vivid magnet
we need a subset that doesn't have any rotational or reflective symmetry
would something like a spiral work?
like this?
or this maybe
<@&286206848099549185>
odd edgeBOT
@vivid magnet Has your question been resolved?
vivid magnet
or is there something much simpler lmfao
odd edgeBOT
@vivid magnet Has your question been resolved?
native agate
Trying to relearn some old stuff, bit stuck on this tho.
native agate
L_1 and L_2 are parallell
red thorn
You're trying to solve for x right?
native agate
yea, sorry
native agate
yea
I know the 95 and below is will equal 180
same with above it
so the 2x/3 should be 85
red thorn
so the 2x/3 should be 85
Yes
native agate
and I know the angle inside 4 side is 440 right?
or was it +90 each corner?
its 360
red thorn
So it basically boil downs to solving 2/3*x=85
native agate
yea
alright one sec
ok got it
Get rid of numerator by multiplying it on the right side, divide by 2 and get answer
thank you for the nudge 🙂
.close
robust moat
I have a problem that asks to integrate ln(1-x^2) without parts, I've tried some weird u / trig subs but I keep getting stuck, I just need a starting point to go from.
manic sleet
I have a problem that asks to integrate ln(1-x^2) without parts, I've tried some...
why not let $u=\ln(1-x^2)$ and $\dd v=1$?
clever fjordBOT
MrFancy
manic sleet
then simply use $\int u\dd v=uv-\int v\dd u$
clever fjordBOT
MrFancy
robust moat
I can't use integration by parts, I've tried trig sub with x=sin(theta) but I'm not sure where to go from there, this might not be the right approach anyway thoguh
manic sleet
**MrFancy**
^
robust moat
isn't that integration by parts?
manic sleet
isn't that integration by parts?
robust moat
I'm not allowed to use integration by parts
clever fjordBOT
MrFancy
robust moat
but then du=-2x dx, what do I do with the -2x?
manic sleet
solve for x, in terms of u
robust moat
yeah so I've tried that, I get to $\frac{-1}{2}\int \frac{\ln(u)}{\sqrt{1-u}} \dd u$
clever fjordBOT
Jason 지환
manic sleet
I'm not seeing a whole lot that doesn't involve IBP
robust moat
hmm yeah ikr I've already solved it by IBP so I have an idea of what I'm working towards, just seems hard to avoid IBP
I've tried a trig sub with $x=\sin{\theta}$ then it becomes $2\int(\ln(\cos{\theta}))\cos{\theta} \dd \theta$
clever fjordBOT
Jason 지환
manic sleet
then you're just gonna end up using IBP 
manic sleet
I'll keep playing with it, thanks anway!
for sure! Good luck with it, and it might be impossible without IBP but gl anyways
robust moat
.close
gentle lagoon
At registration for fall semester, 100 students signed up for English, 80 for math, 60 for science. 40 signed up for math and English but not science. 10 signed up for science and English but not math. 35 signed up for math and science but not English. If a special class is to be formed made of all those students taking English, with no math or science, what are the most and least numbers of students that the class may have?
gentle lagoon
How do I solve this
I know the most
Since it’s just students for science and English and math and English so the most is 50
But what’s the least
.close
zealous obsidian
odd edgeBOT
odd edgeBOT
@zealous obsidian Has your question been resolved?
zealous obsidian
.close
tiny pike
How is the same???
odd edgeBOT
How is the same???
tiny pike
If it even is
brave flint
0.5 in denominator written as 1/2
tiny blade
Can i say that this is true by the completeness axiom as all the subsets of bounded sets should have a sup ?
tiny blade
at least for addition and multiplication
odd edgeBOT
@tiny blade Has your question been resolved?
untold igloo
Can i say that this is true by the completeness axiom as all the subsets of boun...
I'm more concerned about your teacher typing "Bounded"
tiny blade
why?
untold igloo
idk, never heard it being used, bound is already the past tense of bind
tiny blade
have you done real analysis?
untold igloo
?
tiny blade
in mathematics
untold igloo
Can i say that this is true by the completeness axiom as all the subsets of boun...
but yes its true:)
tiny blade
bruh its not tho lol
untold igloo
ok i didnt look at the last 2
novel gyro
I understand that tan(x) is continous between pi/2 and negative pi/2, but I don't know how to use the properties of continuous functions to find the inverals in which make tan(x) continous
tribal ingot
I understand that tan(x) is continous between pi/2 and negative pi/2, but I don'...
well how is continuity defined at a point
novel gyro
well how is continuity defined at a point
tribal ingot
well yeah
f(a) should exist
lim x->a f(x) should exist
and the lim should be equal to f(a)
you can use it to see where the continuity breaks off
and then use it to prove that the function isnt continuous at that point
and if the function isnt continuous at a point then it cant be continuous past that point
but your answer is correct
novel gyro
and the lim should be equal to f(a)
well I have 2 question about that what if f(a) doesn't make sense, what do we do then?
novel gyro
if we are given some random f(a) that doesn't make any sense for example of arctanx pi or -pi
do we just say it doesn't exist, but how i prove that it doesn't exist beyond the points of pi/2 and -pi/2
.close
frozen hamlet
i need help. i cant figure out this code.
frozen hamlet
tepid yacht
i need help. i cant figure out this code.
Closed your other channel
And second this is a math server, not programming
You should ask in a programming one, check #old-network
odd edgeBOT
@frozen hamlet Has your question been resolved?
odd edgeBOT
odd edgeBOT
Available help channel!
frozen oyster
i don't get what this problem is asking about. what does it mean by "Region S consists of all the points that lie inside exactly one of the four circles."? by "exactly one", doesn't it mean region S only include points from one circle?
frozen oyster
link to the solution: https://artofproblemsolving.com/wiki/index.php/2021_AMC_10B_Problems/Problem_7
worn shore
How do i get the vector c that sits on the bisector of the angle defined by two other vectors, a and b. c should always be normalised, or in other words of length one. This also has to work for edge cases such as a 180 degree angle (for example vectors define (0, 1), (0 -1)).
I tried solving this with the dot product but got stuck, i also tried using
worn shore
that doesn't satisfy the property that it is always of length one. For vectors that sit on the same line it produces the null vector
tall veldt
I would just rotate one vector by half the angle between and then scale down to unit vector
worn shore
I would just rotate one vector by half the angle between and then scale down to ...
that works yeah
.close
mystic saffron
Can someone help me understand the reasoning behind this proof?
tall veldt
You need to pick the parts of the proof you don't understand
mystic saffron
oh ok
this part
why do we need to find n=1
and how did the author derive $b_k(n)\le b_k(n-1)$?
clever fjordBOT
KidneyDamage47
tall veldt
What do you mean why do we need to find n = 1?
odd edgeBOT
@mystic saffron Has your question been resolved?
mystic saffron
n-1 sorry
tall veldt
Still don't understand your question
odd edgeBOT
@mystic saffron Has your question been resolved?
clever fjordBOT
B3251
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
odd edgeBOT
@grim turret Has your question been resolved?
obtuse rivet
I’m working on e. How do I do it?
odd edgeBOT
I’m working on e. How do I do it?
odd edgeBOT
Available help channel!
light zodiac
