how am i supposed to find x with what i have so far
#help-13
delicate atlas
crimson sedge
i tend to be a slow worker, however so far you have it right
delicate atlas
huh
zenith ridge
Combine them
zenith ridge
Into1 fraction
Bro uw make the thing into 1 fraction
Jst times the denominator to each
delicate atlas
when i multiply exponents, i add them right?
zenith ridge
Correct
delicate atlas
oh i see where i messed up
zenith ridge
Nice
delicate atlas
x^3/2 should be positive not negative in the denominator
zenith ridge
Yes ik
delicate atlas
so it becomes 2450/x^2
zenith ridge
The other one is half
delicate atlas
Bro u merge the denominator won't change the numerator?
no fucking clue
zenith ridge
It'll give u the ans
zenith ridge
Jst use photomath
It's a very useful app
zenith ridge
Because u prolly typed the -in denominator?
delicate atlas
no
zenith ridge
Wow
delicate atlas
what the fuck
bruh its bc i had +- together 💀
this app dumb as hell
ok but i still dont know how tf im supposed to do this w/o photomath @zenith ridge
delicate atlas
Bro u merge the denominator won't change the numerator?
wdym by this
delicate atlas
Wow
how do you simplify this w/o cheating
<@&286206848099549185> how to simplify this?
.close
crimson sedge
dense socket
Well, get on integratin
undone epoch
Do it separetly. What is $$\int_{0}^1(1-x^2)^{\frac{1}{3}};dx$$
wraith daggerBOT
Good
dense socket
Show Work
stiff totem
they're not integrable
you're supposed to spot that the two integrands have a relationship
||they're inverses over the interval of integration||
crimson sedge
yes
cedar kilnBOT
@crimson sedge Has your question been resolved?
cedar kilnBOT
cedar kilnBOT
Available help channel!
minor bear
hey uh
minor bear
can someone supervis me while i do this since it said i did it wrong
i dont need anyone to solve js supervise and tell me what i did wrong
ping me if anyone is here
minor bear
i did i saw you helping in other channels and thought id ask
cyan wren
Then why delete
minor bear
ion know i js do that lol
cyan wren
Now dis boi deciding how I should react to it
cyan wren
Now dis boi assuming my emotions
final meteor
sweet crest
!15min
cedar kilnBOT
Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
civic coral
Mickey
prisma ether
,w det {{1, 0, 2}, {1, -1, 1}, {0, 1, 1}}
cedar kilnBOT
,w det {{1, 0, 2}, {1, -1, 1}, {0, 1, 1}}
wraith daggerBOT
crystal raptor
Great thanks
cedar kilnBOT
@prisma ether Has your question been resolved?
torpid skiff
may i know how to do (b)
cedar kilnBOT
may i know how to do (b)
sweet crest
triangle - blue
torpid skiff
u mean i have to find the area of the blue triangle?
cedar kilnBOT
cedar kilnBOT
Available help channel!
barren badge
How do I find 2nd endpoint if I already have midpoint and 1st endpoint
livid hound
midpoint formula
barren badge
how if I only have 1 endpoint
dire geode
how if I only have 1 endpoint
Write down the formula using your endpoint and midpoint and use algebra to solve for other endpoint
dire geode
Can you show what midpoint formula you're using
cedar kilnBOT
@barren badge Has your question been resolved?
cedar kilnBOT
final meteor
do you know the derivative of logx?
Yeah, but for that you need to know the derivate of logx and the chain rule.
frigid crown
gilded hull
Need help answering and explaining 3a - 3c
cedar kilnBOT
Need help answering and explaining 3a - 3c
gritty viper
No, you're subtracting 5x from 3
cedar kilnBOT
@gilded hull Has your question been resolved?
gilded hull
<@&286206848099549185>
feral coyote
for b it's also positive
gilded hull
how come?
feral coyote
cause + * + = +
feral coyote
you mean 1st question?
gilded hull
how come
gilded hull
so negative
feral coyote
yes
gilded hull
so 3a would be we are subtracing a number, 5x, to 3 to get 7. Thus, 5x must be postive. Since 3 is positive, in order for the product 5x to be positive, then x must also be positive.
and c would be positive as well?
@feral coyote
wraith daggerBOT
TimK
gilded hull
oh so any postive number.
gilded hull
so 3a would be we are subtracing a number, 5x, to 3 to get 7. Thus, 5x must be p...
this reasoning ^
@feral coyote
feral coyote
i just cant do math at all
good luck, then
gilded hull
.close
crimson sedge
Prove that it is impossible for the equation Ax =b to have exactly two distinct solutions.
this is for my linear algebra class and i wrote: if a contains no zeros then it implies it is linearly independent and a unique solution will be the outcome for all values of x. Is this enough?
feral coyote
Prove that it is impossible for the equation Ax =b to have exactly two distinct ...
for any polynomial, the amount of roots is the highest degree
- line can be intersected with a line only once
(or infty)
crimson sedge
.close
cedar kilnBOT
Available help channel!
true beacon
cedar kilnBOT
true beacon
how do we know x^2 + y^2 = 1 in this scenario
livid hound
equation of unit circle
long arrow
unit circle
true beacon
then given this scenario would a^2 + b^2 be 1 correcyl?
long arrow
yes
barren badge
how can I I convert a number to radica
cedar kilnBOT
how can I I convert a number to radica
dire geode
$\sqrt{ab} = \sqrt{a}\sqrt{b}$ for any positive numbers a, b
wraith daggerBOT
riemann
dire geode
Do you know $\sqrt{100}=?$
wraith daggerBOT
riemann
barren badge
10
dire geode
**riemann**
Should probably memorize this
barren badge
**riemann**
wait so ✔️16 is equal to ✔️1✔️6
barren badge
or is ✔️16x2 equal to ✔️16✔️2
dire geode
Yes
barren badge
Ok
dire geode
,calc sqrt(32)
wraith daggerBOT
Result:
5.6568542494924
,calc 4sqrt(2)
wraith daggerBOT
Result:
5.6568542494924
But how do I get radical
dire geode
But how do I get radical
From what
barren badge
wait a sec
dire geode
$\sqrt{300} = 10\sqrt{3}$
wraith daggerBOT
riemann
dire geode
**riemann**
Find a and b such that ab=20
barren badge
So ✔️20 is equal to ✔️20✔️1
dire geode
That's true, but not useful
dire geode
Isn’t A = 20
No
barren badge
AB=20?
dire geode
Find a and b such that ab=20
Yes I said that here
dire geode
✔️300 = 10✔️3
You wouldn't say sqrt(300) = sqrt(300)*sqrt(1)
As most simplified form
You have to find all the factors of 20
barren badge
Yes I said that here
OHHHH
A and B are factors of AB
Wait if ✔️20 is AB
and 10 and 2 are factors
wouldn’t 2✔️10 be equal to it
dire geode
No
wraith daggerBOT
riemann
dire geode
**riemann**
Use this as a hint
dire geode
✔️300 = 10✔️3
From this problem
dire geode
Do you know 100 * 3 =?
barren badge
300
dire geode
Do you know 100 * 3 =?
Do you know how to simplify sqrt(300) using this
barren badge
30 right
dire geode
No
dire geode
**riemann**
Use this
barren badge
✔️100✔️3
dire geode
Right
barren badge
Oh man I just got it
10✔️3!!!
!!!
Ok so
✔️20 is equal to
✔️10✔️2
wait that won’t work
✔️5✔️4
2✔️5!!!!!!!
thanks 🙏 deadass I was cryin
.close
sweet hedge
How would I find a and b such that this is true?
cedar kilnBOT
How would I find a and b such that this is true?
sweet hedge
I tried this but idk what I’m doing it or if it’s even the right way
grand island
Wouldn't you need |a| >= a^2+b^2
sweet hedge
Why
grand island
If a divided by a^2+b^2 is an integer
sweet hedge
If a divided by a^2+b^2 is an integer
How do you get that absolute value of a is bigger than a^2+b^2 from that statement
Oh wait
I see what you are saying
kindred storm
No, |a| can be less than a² + b².
grand island
No, |a| can be less than a² + b².
That would contradict the 3rd condition
grand island
Ah true
kindred storm
Try a = 0 and find what b is allowed to be. Try a = 1 and find what b is allowed to be. Then, see if a = 2 is possible.
grand island
Indeed
sweet hedge
Wouldn't you need |a| >= a^2+b^2
Since this is false, what’s a counter example?
Cuz I can’t see why it’s not tru
grand island
a = 0 b = 1
cedar kilnBOT
@sweet hedge Has your question been resolved?
sweet hedge
a = 0 b = 1
Would this be valid,
sweet hedge
Try a = 0 and find what b is allowed to be. Try a = 1 and find what b is allowed...
Yeah a = 2 isn’t possible
Or -2
a is either -1, 0 or 1
kindred storm
Would this be valid,
Yes, that looks fine.
cedar kilnBOT
Available help channel!
clear igloo
yo
clear igloo
if im dividing a polynomial degree 4
by
a linear
and i have 2 of its factors
first divide by factor #1
then divide quotient by factor #2
right
tropic oxide
well yeah that's how you break off the known factors to factorize the rest
clear igloo
well yeah that's how you break off the known factors to factorize the rest
whats the logic behind this?
that'd be the question
tropic oxide
do you know how factoring works for natural numbers
clear igloo
?
tropic oxide
prime factorization?
clear igloo
yeah no
tropic oxide
clear igloo
ig my question is
tropic oxide
okay abandon that idea
tropic oxide
why cant i divide bybthe same factor twice
cause your thing might not be divisible by (that factor)^2 lol
tropic oxide
why do i have to use bothp
your polynomial is (factor 1) * (factor 2) * (some more shit)
to get to the other shit
you divide out by each known factor
so that they are out of your way
cedar kilnBOT
@clear igloo Has your question been resolved?
clear igloo
i see
clear igloo
so that they are out of your way
that makes sense
craggy sentinel
cedar kilnBOT
craggy sentinel
am i multiplying by the conjugate right?
do i only change the sign between the +1 and sqrt x
wraith daggerBOT
MrFancy
craggy sentinel
-x-1 right
surreal cave
that'll make multiplying by the conjugate easier :)
cedar kilnBOT
@craggy sentinel Has your question been resolved?
inner quest
Let (picture), show that the generator of J equals the borel sigma algebra
flint plinth
i assume you mean, J generates the borel sigma algebra?
inner quest
Yeah so sigma(J)=B(R)
flint plinth
one direction is easy, the members of J are borel sets, so sigma(J) ⊆ B(R)
to go the other direction, it suffices to show that any open interval is a countable union of members of J
inner quest
I am not completely sure on how I would show that for any open interval
i know that the borel sigma algebra is generated by any of the following systems:
inner quest
to go the other direction, it suffices to show that any open interval is a count...
but basically show that (b,c)=U[a,a+1) for a,b,c in R ?
flint plinth
ah wait, sorry, i forgot the intervals in J all have length 1
in general you'll have to do intersections as well
inner quest
im following an example for the sets with intervals including infinity*:
but i cant see to make it make sense here
flint plinth
hmm well first, observe that you can get any interval of the form [a,b) where a < b < a+1, by taking the following intersection:
[a,a+1) ∩ [b-1,b)
so every interval of the form [a,b), with 0 < b-a <=1, is in J
then you can get longer intervals of the form [a,b) by taking countable unions of the shorter ones we just showed are in J
for example:
if n is the smallest integer in [a,b) and m is the largest in terval in [a,b), then you can get [a,b) as the following union:
[a,n) U [n,n+1) U ... U [m-1,m) U [m, b)
so that shows that any interval of the form [a,b) is in J
now you can show that any (a,b) is in J by taking unions:
(a,b) = union of [a+1/n, b) for n=1 to infinity
the above is a sketch, you'll want to fill in the details
inner quest
the above is a sketch, you'll want to fill in the details
I think i get the general idea now. We show as in the proof above that the intervals of the form given in J is in the borel sigma algebra and that the interval (whichever one i pick that generate the borel sigma algebra) is a element in the sigma algebra generated by J?
flint plinth
I think i get the general idea now. We show as in the proof above that the inter...
yes
inner quest
yes
one small clarification: i say that "...is a element in the sigma algebra generated by J?" by this i mean that i should show that the interval that generates the borel sigma algebra through some set operations is an element of [a,a+1)*
flint plinth
one small clarification: i say that "...is a element in the sigma algebra genera...
you should show that the elements that generate B(R), for example, the intervals of the form (a,b), can be expressed as countable unions and intersections of intervals of the form [a,a+1)
inner quest
you should show that the elements that generate B(R), for example, the intervals...
yes and the other way around and im exactly done
flint plinth
yes
inner quest
.close
cedar kilnBOT
inner quest
ty
cedar kilnBOT
Available help channel!
visual tartan
.open
The equation (3×5²)÷5−20×4+75 is confusing me.
Using BIDMAS why does the subtraction come before the addition in this case?
sweet crest
from left to right
rain drift
BIDMAS/PEMDAS, you treat add/sub and mult/div as the same priority, since they're inverse operations of one another
so you do whatever comes first
DM first, and left to right, then AS, left to right
zenith sail
(B)(I)(DM)(AS)
mortal patrol
How do I reduce 124! mod 5^24?
cedar kilnBOT
How do I reduce 124! mod 5^24?
mortal patrol
Got told that 124 factorial has at least 24 factors of 5 in it, and hence it is a multple of 5^24
don't understand how 124 "has at least 24 factors of 5 in it"
zenith sail
well 124! is 1x2x3x4x5x6x7x8x9x10x...
there's already two 5's in the part I wrote out
since 10 is 2x5
and 5 is, well, 5
flint plinth
5 is definitely 5
mortal patrol
can this be generalised?
how many factors of m would n! have?
more precisely, how could I always know whether $a^m$ is a factor of n!?
wraith daggerBOT
Kalgar
zenith sail
how many factors of m would n! have?
every multiple of m less than or equal to n provides 1 factor of m
unless it's a multiple of m^2, in which case it provides 2
unless it's a multiple of m^3, in which case it provides 3
etc
like for 100!, if we wanted to know how many 5's are in its factorization?
well there are 20 multiples of 5 less than or equal to 100
so that's 20 5's
but 25, 50, 75, and 100 are actually divisible by 5^2
so that's four more 5's
so 100! is divisible by 5^24
livid hound
don't forget about 100 also being divisible by 5^2
zenith sail
don't forget about 100 also being divisible by 5^2
oops, i completely did lol
fixed now
cedar kilnBOT
@mortal patrol Has your question been resolved?
gleaming osprey
I need help solving this, and I tried with a calculator, but it comes back with a confusing answer
livid hound
show what you tried
gleaming osprey
kk
Tldr im trying to derive an equation given to me
it's:
y=e^(rx)
y'=re^(rx)
y''=r^(2)e^(rx)
but I have y''=e^(rx)+r^(2)e^(rx)
I'll make it pretty one sec
livid hound
it's also more efficient to apply constant multiple rule
gleaming osprey
What's that one?
livid hound
(af(x))' = a(f(x))'
gleaming osprey
So this might sound stupid but, how can you be sure that r is a constant?
livid hound
in this context, from the first derivative
if it r were related to x, you'd have something more complicated
gleaming osprey
It's given when you start learning how to solve second order differential equations
and this tutorial is kind of just giving it, saying "When you have ay''+by'+cy=0, the answer typically looks like y=e^rx"
and that's where it starts
then they show y' and then y'', and I didn't want to just take those equations and run, so I wanted to make sure I could derive them myself
cedar kilnBOT
Available help channel!
crimson sedge
hi i have some webwork questions i need help with, i don't understand any of it since i haven't taken math in a year and didn't take calc either
cedar kilnBOT
hi i have some webwork questions i need help with, i don't understand any of it ...
@crimson sedge Has your question been resolved?
cedar kilnBOT
@pallid orchid Has your question been resolved?
eager locust
hi i have some webwork questions i need help with, i don't understand any of it ...
I'm not really sure about how you can do it, but you can evaluate the functions with x = 1
coral charm
cedar kilnBOT
coral charm
<@&286206848099549185>
cyan turtle
After 15 minutes, feel free to ping Helpers.
read the instructions btw
cedar kilnBOT
What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
So u gonna help
cedar kilnBOT
What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
4
cedar kilnBOT
Show your work, and if possible, explain where you are stuck.
cedar kilnBOT
@coral charm Has your question been resolved?
coral charm
@nimble veldt
Us ur words lil bro don’t communicate through reactions
It was wrong btw
cedar kilnBOT
@coral charm Has your question been resolved?
gloomy prism
please help
cedar kilnBOT
please help
strange mauve
!status
cedar kilnBOT
What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
No
gloomy prism
cross multiply?
strange mauve
Yes
solid trout
cross multiply?
works
nimble veldt
yes, then sort x to the left and y to the right
gloomy prism
6x=25y?
nimble veldt
now divide by 6 and y.
random shore
subject of x
cedar kilnBOT
subject of x
strange mauve
!status
cedar kilnBOT
What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
vague rapids
subject of x
are you supposed to make x the subject?
sweet hedge
subject of x
What do you mean
cedar kilnBOT
@random shore Has your question been resolved?
pearl thorn
cedar kilnBOT
pearl thorn
ok
sudden yoke
the sum of two sides of a triangle is always greater than the remaining side
as for ii
sudden yoke
as for ii
Well I don't think there's a theorem for that you sort of just have to apply common sense ._.
pearl thorn
but how
sudden yoke
but how
Well I'm not sure, but let's say we have a triangle a b c such that c>a,b
a+b>c, but a+b<2c because well, the triangle would be flattened
flint flower
What is the component of the gravitational force acting on the block, along the direction of the inclined plane surface?
flint flower
not sure where to start, kinda bad at this topic
crystal raptor
It's already on the screen for you
flint flower
It's already on the screen for you
is it 16.79?
crystal raptor
No I mean, the expression for what you want is on the screen for you
crimson sedge
,calc 5*9.81
wraith daggerBOT
Result:
49.05
how are you getting 16.79 
crystal raptor
Fnet
flint flower
i thought it was fnet
crimson sedge
ah along the direction of the incline, okay
crystal raptor
There are two arrows pointing in the direction you want, only one of them involves gravity
flint flower
wait so if they want direction of incline then is it downwards
or the gravity kinda downwards
crystal raptor
Parallel to the slope
flint flower
so fnet 16.76?
crystal raptor
If you had friction is would be opposing the force of gravity down the slope so fnet would be less than gravity down the slope
flint flower
what about when the weight of the block changes
inner belfry
,calc x=(y+2)y=1.6729
wraith daggerBOT
The following error occured while calculating:
Error: Invalid left hand side of assignment operator = (char 9)
inner belfry
,calc x=y+2y=6.2827292778
wraith daggerBOT
The following error occured while calculating:
Error: Invalid left hand side of assignment operator = (char 7)
crystal raptor
,calc x=y+2y=6.2827292778
What are you doing stop interrupting this channel
crystal raptor
what about when the weight of the block changes
Well what do you think happens
flint flower
Well what do you think happens
well the simulation doesnt change the timing
its still the same time
but for the reason im not quite sure
is it cause its same gpe?
or acceleration is the same
cedar kilnBOT
@flint flower Has your question been resolved?
flint flower
.close
summer cradle
I am wanting to CLEP Calculus 1, however I have no experience with it whatsoever. In addition, i'm pretty bad at college algebra at the moment. How long will it take for me study for this CLEP if I put in 2 hours a day?
tropic oxide
if you're bad with algebra? probably a month minimum
nova snow
I would use y - y1 = m(x - x1) right
so x1 = p
and y1 = cln(p) ?
nova snow
and to find m is just product rule
nova snow
Oh yeah because c is a constant
twilit knot
I think i recognise you from seeing the channel name so many times haha
nova snow
well it's just derivative of lnx
At x = p so 1/p?
wintry pier
You can also simplify the equation of the tangent they give you
onyx dove
yeah so m=c/p
nova snow
I think i recognise you from seeing the channel name so many times haha
oh haha
nova snow
yeah so m=c/p
Wait why c/p and not 1/p?
cedar kilnBOT
sick patrol
Hi
cedar kilnBOT
Available help channel!
summer cradle
Is Khan Academy's Calculus 1 course a good test prep for the Calculus 1 CLEP test?
summer cradle
.close
scenic juniper
cedar kilnBOT
scenic juniper
idk what it means
tropic oxide
,rccw
wraith daggerBOT
cedar kilnBOT
cedar kilnBOT
Available help channel!
upbeat elm
I tried chat gpt and it said 83??
cedar kilnBOT
I tried chat gpt and it said 83??
jaunty pumice
!status
cedar kilnBOT
What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
1
gilded sonnet
lunar lynx
1
Hint: You can find (x+1/x).
You don't need to solve for $x$ fully. Just $\left(x + \frac 1 x\right)$ should suffice.
wraith daggerBOT
Enemagneto
lunar lynx
How did you get that?
Also, you probably don't need to.
Hint: || Try squaring (x + 1/x)||
jaunty pumice
Hint: (x+1/x)² = x²+1/x² + 2
onyx dove
nice
gilded pewter
this is an olympiad question isnt it
(x + 1/x)^2 = x^2 + 1/x^2 + 2
anagh is right
if x^2 + 1/x^2 + 2 = 83, make one constant term
upbeat elm
idk what to do exactly 😕
onyx dove
specifically what
upbeat elm
if x^2 + 1/x^2 + 2 = 83, make one constant term
with this
onyx dove
that's not written correctly
from the question, x^2+1/x^2=83
so using the hint, (x+1/x)^2=85
onyx dove
and why is that
gilded pewter
so (x - 1/x)^3 = 729
onyx dove
i've literally done the question
gilded pewter
i mean
crimson sedge
This can't be valid right?
cedar kilnBOT
This can't be valid right?
crimson sedge
The second one says that, for every person x, there is at least one person for which it's the case that, if the person is both a parent and a female, then she's a mother
Which means that here can be people which are both a female and a parent, that are not mothers
That's invalid right? Or am I wrong
digital cliff
the second one says for every person x, there exists a person y such that if x is a female and a parent then x is the mother of y
regal steeple
cedar kilnBOT
opaque orbit
derive
gritty galleon
not necessary i think
cedar kilnBOT
What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
might be some algebraic manipulation
dont blindly apply L'Hop
nope, wont work
bright karma
does the numerator factor
gritty galleon
does the numerator factor
not really
gritty galleon
hmm if u sub u = sqrt(x)..that might lead somewhere..lemme try
@regal steeple u can do L'Hop till then if u want
wraith daggerBOT
gritty galleon
hmm if u sub u = sqrt(x)..that might lead somewhere..lemme try
doesnt work
regal steeple
doesnt work
So only l'hopital?
bright karma
||i get how x^4 turns into 4x^3 but how does sqrtx turn into 1/2sqrtx||
gritty galleon
||i get how x^4 turns into 4x^3 but how does sqrtx turn into 1/2sqrtx||
power rule
bright karma
o
gritty galleon
So only l'hopital?
yes
regal steeple
Aight thanks dude
I mean I could do it with l hop
But wanted to know if there was another way
gritty galleon
u forgot the minus sign at the bottom i think
should be $(4x^3 \cdot -2 \sqrt{x}) + 1$
-7 instead of 7
regal steeple
Uhh
wraith daggerBOT
ItzKraken
regal steeple
Eh?
regal steeple
I think I'm correct
gritty galleon
$\frac{d(\sqrt{x})}{dx} = \frac{-1]{2x}$
wraith daggerBOT
ItzKraken
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
regal steeple
oh fudge
Hey if there is nothing there is 1. I multiplied 2x^(1/2) on both the numerator and denominator, which makes it {4x³ • 2x^(1/2)}/{2x^(1/2)}
And there was -1/{2x^(1/2)}
So it should be {4x³ • 2x^(1/2) - 1}/{2x^(1/2)}
gritty galleon
it should 4x^3 + 1/(2x^1/2)/... = ...
regal steeple
Why (+)
regal steeple
derivative of sqrt(x) is {1/2x^(1/2)} not negative
{1/2x^(1/2)}
gritty galleon
derivative of sqrt(x) is {1/2x^(1/2)} not negative
{1/2x^(1/2)}
ah yes..sorry 😅
yes then its correct
cedar kilnBOT
cedar kilnBOT
Available help channel!
prisma gull
Does that set ${\frac{n+1}{5n}\ : n\in \mathbb{N} }$ has a supremum ?
crimson delta
that set notation is incomplete
prisma gull
please wait
crimson delta
the parts in the set notation are thr wrong way around
wraith daggerBOT
.doc
crimson delta
👍
ok, what do you think about it having a supremum
sry my inet is dying
try computing a few elements in the set
then you see that 1/5 is in fact not the supremum
prisma gull
it's getting little bit bigger than 1/5 each time
I think 3 maybe an upper bound
but I don't knowthe sup here
@crimson delta
?
since a1<a2<a3<....<an<..
can I just say it's not bounded above?
<@&286206848099549185>
.close
wary storm
is there a way to find the area of triangle ODC?
cedar kilnBOT
is there a way to find the area of triangle ODC?
wary storm
i already calculated that area of CDOE is 43 if that helps
idek if it is possible to solve area of ODC or any other triangle in the larger triangle
but if anyone finds a way can you tell me
wary storm
i think the perpendicular bisector of AC is a straight line so you can use symmetery for that
cyan turtle
that means OA=OB=OC
cyan turtle
hmm
wary storm
so i found area od CDOE
*of
is 43 with some algebra
is that any help?
and area of total triangle ABC is 116
lemme send the pic again
wraith daggerBOT
Result:
10.440306508911
so basically what i did was
triangle FOB is same as triangle FOA so thats basically the same rule for the other 2 sets of triangles
wary storm
so basically what i did was
triangle FOB is same as triangle FOA so thats basica...
continuing from this, we can use algebra so consider FOB as x and AOE is y and ODC is z
so 2x + 2y + 2z = 116
x is already 15, so 30 + 2y + 2z =116
so y+z = 43 which is area of ODC + OCE
but can u find ODC
@cyan turtle did i lose you?
cyan turtle
im here
my geometry skills are gone tho and im trying to figure it out
what ive seen so far makes sense
cyan turtle
the thing is i dont think we have enough info to find odc
wary storm
yh thats what i thought
cyan turtle
because we lack angles
wary storm
but i was think using trig we could solve it somehow
cyan turtle
with angles we can do some trig to get exact values
but without that we have no references
wary storm
yh
i got close to figuring out the angles and using the trig formula but i didnt write it down and i lost my trail of thought
but im sure i was on the right track
k im back you still there?
cyan turtle
whats up?
well also now that i think about it
you can rule of cosines brute force ur way into this
wary storm
mhm
cyan turtle
if you know AB,AC and angle FAE
wary storm
yh
we could us a circle theorem to get FAE i think
the cyclic quadrilateral one, so angle FAE = half of angle BOC
cyan turtle
or take arctan (b/a) to get angleFAO
idr exactly what else you know
but you probably can find OAE
wary storm
yh
i was thinking in an algebra perspective but i dont think that will work
i'll figure it out later thx for the help tho
.close
tacit mulch
stupid question but how do i convert m/s^2 to km/h^2?
cedar kilnBOT
stupid question but how do i convert m/s^2 to km/h^2?
tacit mulch
so if the acceleration is 3 metres per second squared, how much is that in kilometres
is that the same as with velocity? so just time it with 3.6?
sweet crest
h=60^2s
foggy merlin
1 km/h²= 1000m/3600s^2
wait a sec
1h = 3600s
so its 3600^2 s^2
🤔
$\frac{1 km}{1 h^2} = \frac{1000 m}{3600^2 s^2} = \frac{1 m}{36 \times 360 s²}$
wraith daggerBOT
Herels
foggy merlin
,w 36 x 360
wraith daggerBOT
sweet crest
^-1
wraith daggerBOT
Herels
tacit mulch
so... we have an answer or what? 😅
mental trail
3.6
You're changing another s to h so × 3600 that
You do get that 1m/s² = 12960 km/h², but really no one uses the latter unit
foggy merlin
I know, Ive never used that unit
crimson sedge
cedar kilnBOT
primal socket
!status
cedar kilnBOT
What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
blazing dune
It isn't even 1 ?
primal socket
What do you have to do?
crimson sedge
What do you mean by solving for this
idk its written in my book like that
i have no idea
blazing dune
It doesn't say simplify this in the head of the question?
blazing dune
Can I order from you to just capture the whole page
primal socket
I mean, there's not much you can do here
blazing dune
I am sure that there is something like this
For the above questions
But maybe in the previous page
crimson sedge
lemme see
Disassemble on factors by pulling out the common factor before parenthesis
The next polynomial
this is the text on previous page
it doesnt makes sense kinda
cedar kilnBOT
primal socket
I am guessing that's what you have to do
blazing dune
It is yes
cedar kilnBOT
Available help channel!
crimson sedge
cedar kilnBOT
crimson sedge
So I have made x = (x1 , x2 , x3) and taken lambda and mu both in F and have satisfied x in V as vector space over F.
I have satisfied them accordingly to the 8 axioms defining a vector space.
Now I feel a bit useless as I am trying to figure out what to do with x1 + x2 + x3 = 0
My intuition says get a dot-product such that <v,x> = o
basically multiplying vector x in V with orthogonal vector v in V
foggy merlin
My intuition says get a dot-product such that <v,x> = o
there are not talking about dot product or hilbert space or anything like that
you need to use the conditions x1 + x2 + x3 = 0 to show that V is a vector space
crimson sedge
Yea...
foggy merlin
thats it
crimson sedge
you need to use the conditions x1 + x2 + x3 = 0 to show that V is a vector space
Not sure what that means.
foggy merlin
let take two vectors from V : (x1, x2, x3) and (y1, y2, y3) and two scalars a,b from K = R or C
a(x1, x2, x3) + b(y1, y2, y3) = (ax1 + by1, ax2 + by2, ax3 + by3)
now we need to show that this result respect the condition of V
crimson sedge
The condition being x1 + x2 + x3 = 0 right?
foggy merlin
(ax1 + by1) + (ax2 + by2) + (ax3 + by3) = a(x1 + x2 + x3) + b(y1 + y2 + y3)
now since we take both vectors from V, they both respect the condition of V
x1 + x2 + x3 = 0
y1 + y2 + y3 = 0
therefore
(ax1 + by1) + (ax2 + by2) + (ax3 + by3) = 0
it means that (ax1 + by1, ax2 + by2, ax3 + by3) € V
we just show that V is stable by linear combination and we know the vector 0 respects the condition of V
therefore its a vector space
crimson sedge
:flushBlush:
you know wyim
Can we assume that 0 is the ''zero-vector'' ?
or does that have nothing to do with it?
i think it doesnt...
foggy merlin
Can we assume that 0 is the ''zero-vector'' ?
hmm wdym ?
crimson sedge
well
''...we know the vector 0 respects the condition of V'' could you explain this to me?
wraith daggerBOT
Herels
foggy merlin
so the zero vector of R^(3)
yes
crimson sedge
Oh yeah
Usually they write the zero element as zero indexed with V
just as how you indexed R^(3)
in zero
foggy merlin
Well, this zero is from R^3 so its the 0 of R^3
not only of V
it just happens that this zero is also in V
V is a subspace of R^3
crimson sedge
Right, zero can also imply a distinguished zero element in R^(infinity) or of a magic square because in both instances, adding the zero element to any element within V does nothing to another nonzero element.
IF I am right.
foggy merlin
R^{infinity} ?????
foggy merlin
Just write $$\mathbb{R}^n$$
wraith daggerBOT
Herels
crimson sedge
Just give me one moment
So back to what I said in the beginning I made x = (x1 , x2 , x3) in V which in turn is in R^3. By defining the eight axioms over an element in x,y,z in V I proved (to my belief) that V is a vector space over F. Which combination of axioms, if there are any, could lead me to the same steps as you took to prove it was a vectorspace over F?