the magnitude is 13
#help-38
quiet turret
quiet turret
and not -arctan
4th quadrant
marsh forum
this is in the third quadrant
quiet turret
this is in the third quadrant
when in third quadrant, dont we add 180 to theta'
marsh forum
I think so
quiet turret
,calc arctan
solid kilnBOT
The following error occured while calculating:
Error: Undefined symbol arctan
quiet turret
uh
round mango
when in third quadrant, dont we add 180 to theta'
Principal arguments range from (-pi,pi]
quiet turret
arctan(12/5) is 67
marsh forum
,w principal branch of arctan(x)
quiet turret
,calc 67+180
marsh forum
Principal arguments range from (-pi,pi]
isn't it (-pi/2,pi/2)?
round mango
isn't it (-pi/2,pi/2)?
No iirc for complex numbers the principals arguments were (-pi,pi]
quiet turret
uh
round mango
isn't it (-pi/2,pi/2)?
And this way we're missing two whole quadrants
quiet turret
so what am i doing wrong
marsh forum
No iirc for complex numbers the principals arguments were (-pi,pi]
ah, ok, got confused with inverse trig functions, sorry
quiet turret
-180+67
in my notes i wrote that if theta' is in 3rd quadrant, we do pi + theta'
my notes are wrong?
oh even 180-theta' is wrong
i need to do -pi
quiet turret
okay wait can u tell me the rules
for every quadrant
quadrant 1: it stays the same
quadrant two: pi - theta?
quadrant 3: -pi + theta
4th quadrant -theta'
round mango
Yes, but make sure theta is the positive one in all these cases
quiet turret
Yes, but make sure theta is the positive one in all these cases
wym
its gonna be negative when in quadrant 4
no?
round mango
Like we have in the fourth quadrant
The arctan gonna be negative
But you won't write (-(-60)) for example
That'll give you 60 which is just wrong
Just worry about the magnitude
Then deal with the signs and quadrants with logic
round mango
It's correct if theta is arctan(|y/x|)
quiet turret
yeah thats what i use
round mango
But incorrect if theta is arctan(y/x)
Good then
Always take the mod inside and then what you've written above is correct
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wise heart
if a limit has the argument of an 'unrelated' value relative to what the variable approaches, can it be said that the 'unrelated value' is equal to whatever the limit is?
wise heart
what i'm trying to ask is this
can we make this deduction?
please ping if you respond, thx very much
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fallen zealot
please ping if you respond, thx very much
it is correct
the thinking process behind is really cool and can you help you understand function way better.
i find it very amusing.
wise heart
the thinking process behind is really cool and can you help you understand funct...
what process are you referring to?
i'd like to know about it if you have the time to share, please
fallen zealot
what process are you referring to?
its more of an abstract concept in my mind. maybe you understood in a way that its much simpler for you.
wise heart
its more of an abstract concept in my mind. maybe you understood in a way that i...
it could be said that everything that is under pure math is abstract.. and even some in applied.. I didn't really imagine any process
I just thought they were disconnected, so changing p value wouldn't affect C, so C should be equal to the limit
fallen zealot
true true.
i kinda think the same way.
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wise heart
true true.
i kinda think the same way.
alright. I really think I understand why you had said it was amusing to think about. Maybe not specifically with this example, but with certain concepts and thoughts that may be quite simple, I also feel like they are so satisfying and nice to think about.
Have a good day
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frank merlin
why does the div of F need to be 0?
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why does the div of F need to be 0?
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coarse thicket
When I’m proving an inequality and the last line is a strict equality, does it mean I’m done?
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coarse thicket
<@&286206848099549185>
spark belfry
When I’m proving an inequality and the last line is a strict equality, does it m...
can u give an example as to what you mean?
spark belfry
that looks like a dead end..
coarse thicket
that looks like a dead end..
why tho...
spark belfry
cos the eqn comes back to being equal
coarse thicket
cos the eqn comes back to being equal
I got it tho
it's the same as a =< b and b=c
therefore a=< c
frozen sierra
Hey, so Iam working on some exercises for my exam and I need to examine some sequences regarding their monotony. Is it enough to write down some elements of the sequence and conclude that its ascending or decending?
brazen forge
Hey, so Iam working on some exercises for my exam and I need to examine some seq...
no
you need to prove for all in an interval you're considering
frozen sierra
for example, how would we show that an = n/(2n + 1) is ascending?
brazen forge
calculate a_(n+1)-a_n
and check for what n, a_(n+1)-a_n>0 or <0 or =0
if its >0 its ascending if <0 its desceding and for =0 its constant
frozen sierra
oh, ok, logical
one more thing
to determine monotony of an = 10^n/n!, I converted it to a retrospectively defined sequence and proved by induction that an+1 > an for every n
Is this a correct way to prove it?
brazen forge
yes
frozen sierra
okk, thanks a lot for your help!
brazen forge
np you're welcome
frozen sierra
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loud bobcat
which one is the incorrect answer?
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which one is the incorrect answer?
split chasm
what's your reasoning for each of those answers
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wraith hinge
Hello
wraith hinge
I'm having hard time with this proof, for n in {2,3,4,5} I did the proofs except for 11, how to do it?
Here's the def of a euler brick btw
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unborn lantern
I'm having hard time with this proof, for n in {2,3,4,5} I did the proofs except...
If you brute force it, you find that the squares of numbers mod 11 can only be 0, 1, 3, 4, 5, and 9. I think this is how you do it
'cus the only three way you can add these up (when all sides are not divisible by 11) and get another quadratic residue are 1 + 3, 1 + 4, and 4 + 5, but that's not compatible with an Euler brick
or uh maybe it is?
no, no i think this is right
u should think about this because i've never had a number theory lecture
wraith hinge
u should think about this because i've never had a number theory lecture
alr but appreciate the help anyways
thx
unborn lantern
lemme know if it works out
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unique plinth
Can I just say no directly since [2 -1 4] is a not a column matrix?
unique plinth
or am I supposed to treat it as a column matrix and check if its in the kernel
left oriole
i assume the latter.. is a distinction made between row and column depictions of R^3 vectors elsewhere in the same section of whatever you're reading?
unique plinth
yeah I'll assume the latter
ionic pendant
row and column vectors are or aren't interchangeable depending on if it's convenient for the author from my experience
unique plinth
alright
another question, how do I go about finding the basis for the kernel and range
oh wait nvm
I figured it out
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visual hollow
[212 W5 EXCL4 Q3]
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stark bison
Well, what made you choose e though?
visual hollow
i chose e coz (sigma tau) (sigma^2 tau) = sigma tau sigma^2 tau = sigma sigma^2 tau tau = sigma^3 tau^2 = e e = e
marble wharf
why did you just switch the middle two
marble wharf
why should it be commutative
visual hollow
ig idk
marble wharf
you know that $\tau\sigma=\sigma^{-1}\tau$. thats how to "switch" them. play around with that
solid kilnBOT
Denascite
visual hollow
idk how the inverses work here
"The inverse of a 'word' is given by writing the backwards and negating all the powers. e.g.: 'xyx^(-4)y^2'. (xyx^(-4)y^2)^(-1) = y^(-2)x^4y^(-1)x^(-1). "
e.g.: $'xyx^(-4)y^2'. (xyx^(-4)y^2)^(-1) = y^(-2)x^4y^(-1)x^(-1)$
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Ir3ne
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(You may edit your message to recompile.)
visual hollow
e.g.: $xyx^(-4)y^2. (xyx^(-4)y^2)^(-1) = y^(-2)x^4y^(-1)x^(-1)$
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Ir3ne
marble wharf
so sigma*sigma^2=e
marble wharf
so sigma*sigma^2=e
think about this
do not trust AI
you have no way to verify what it says
marble wharf
well thats notation you shouldnt use in a group
visual hollow
ik, just using shorthand
marble wharf
mhm, ik. i filter
you say that and still you post a wrong image
marble wharf
ik, just using shorthand
dont
visual hollow
it's not wrong ? it obeys the relations of D_3
marble wharf
well it claims (sigma tau)(sigma^2 tau)=e
visual hollow
i checked, but i checked by timesing-
visual hollow
well it claims (sigma tau)(sigma^2 tau)=e
that's also what i have
marble wharf
well and we already saw that it is false
visual hollow
yeee
visual hollow
ok
zinc wagon
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zinc wagon
Can someone explain the process to solve this?
zinc wagon
find
dx/dt
dy/dt
apply chain rule ,
dy/dx = dy/dt * dt/dx
dt/dx would simplify to 2t right?
zinc wagon
dx/dt and dt/dx are different things btw
yea that's what i am confused about
i can just do such dy/dt/dx/dt and that would simplify to 2t^2/2t
t^2/t
vernal warren
dy/dt is not 2t^2
zinc wagon
dy/dt is not 2t^2
sorry 3t^2
vernal warren
yes that gives dy/dx
zinc wagon
yes that gives dy/dx
then how would i go by doing the second derivative?
vernal warren
$$\frac{d}{dx}(\frac{dy}{dx}) = \frac{d}{dx}(\frac{3t^2}{2t}) = \frac{d}{dx}(\frac{3t}{2})$$
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JustToPro
zinc wagon
**JustToPro**
but this doesn't yeild the correct answer?
vernal warren
why not?
zinc wagon
3/2t is the correct answer to this problem...
i don't see how d/dx(3t/2) leads to that
vernal warren
let me solve it again wait
zinc wagon
can you show me your working?
vernal warren
ill type it here
$$\frac{d}{dx}(\frac{dy}{dx}) = \frac{d}{dx}(\frac{3t^2}{2t}) = \frac{d}{dx}(\frac{3t}{2}) = \frac{3}{2}\frac{d}{dx}(t) = \frac{3}{2} \times \frac{1}{2t} = \frac{3}{4t}$$
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JustToPro
vernal warren
4th step is cuz
$$\frac{d}{dt}(x) = 2t$$
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JustToPro
zinc wagon
yea i think the answer book is wrong
vernal warren
maybe , ask the teacher about it
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foggy thistle
is there any shortcut methods to solve this?
,w y = (1-tan2x) / (1+tan2x)
foggy thistle
,w y = (1-tan2x) / (1+tan2x)
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foggy thistle
first derivative
worldly wing
You want $(\frac{1-\tan 2x}{1+\tan 2x})’$
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kheerii
worldly wing
Convert tan2x to terms of tanx only and then simplify
You should get something easier to work with
Long division and things
Quotient rule also shouldn’t be that bad though
That’s probably easier than converting
foggy thistle
im not quite used to quotient rule yet haha
worldly wing
Well then this can be a good practice
proven sluice
Isn't that tan(π/4 -2x)?
worldly wing
Isn't that tan(π/4 -2x)?
Yeah it is
proven sluice
And differentiation of tanx is sec²x ryt
foggy thistle
yep
worldly wing
Yeah
proven sluice
So it's done ryt
worldly wing
So you would get -2sec^2(pi/4-2x)
Then you could do some simplifying to get the answer given in wolframalpha
zinc wagon
first derivative
is the answer to this -2sec^2(2x)?
foggy thistle
still solving it rn but ill see
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cosmic meadow
Divided by what
foggy thistle
$(1+tan(2x))(-2sec^2(2x)-(1-tan(2x))(2sec^2(2x))/(1+tan2x)(1+tan2x)$
cosmic meadow
U are missing $ at the end
solid kilnBOT
shou
foggy thistle
i cancelled both 1+tan2x
cosmic meadow
No you cant
There is a minus in between the numerator
You didnt factor correctly
foggy thistle
oh this cant be cancelled?
$-1+tan2(2x)$
solid kilnBOT
shou
foggy thistle
yes
foggy thistle
v^2= (1+tan(2x))^2
foggy thistle
v^2= (1+tan(2x))^2
cant this be factored to two terms?
cosmic meadow
-(2sec^2(2x)(tan^2(2x)+1)-(2sec^2(2x))(1-ran^2(2x))/(1+tan^2(2x))^2
Correct? Check for any typo
foggy thistle
yep correct
cosmic meadow
Now simplify this first so i can see how you do
And show the while process cause u made a mistake in the sinolificati
Simplification
cosmic meadow
Correct
zinc wagon
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zinc wagon
can someone check if this is correct?
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wraith hinge
you could have simply applied DL hospitals rule
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zinc wagon
you could have simply applied DL hospitals rule
That's not permitted in my course
<@&286206848099549185>
wraith hinge
oh sad that would have made this very easy
zinc wagon
oh sad that would have made this very easy
yea i know
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raw gate
why y(t) = T{x(t)} = x(-t) is non-causal?
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why y(t) = T{x(t)} = x(-t) is non-causal?
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sudden basalt
i found the vertex but how to i find the x intercepts?
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i found the vertex but how to i find the x intercepts?
sudden basalt
since the vertex is the y intercept
heady lava
The x-intercepts are where the y- coordinate is 0, so set m(x)=0 and solve
sudden basalt
what equation do i input the 0s into?
heady lava
You can think of how a function takes in an x value and spits out a y value. In this case you're trying to do find what x value gives you a y value of 0.
When I said set m(x)=0 I meant solving -2x²+4=0
sudden basalt
You can think of how a function takes in an x value and spits out a y value. In ...
i got + or - 1 but its wrong
heady lava
How did you get to ±1?
sudden basalt
i solved it with first i turned it into -2x^2=-4
then divided by -1
then sqre rooted each side and got 2x=2
then x= 1
@heady lava
heady lava
After dividing by -1 you get 2x²=4, which you should divide both sides by 2 again before taking the square root
heady lava
What do you mean by even
sudden basalt
I need to graph it
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sudden basalt
Maybe you could just choose the integer points to graph it then
Wdym❓
heady lava
from what I can tell, that just graphs it for you automatically if you choose a few points right
sudden basalt
I need to have a vertex and then another point
sudden basalt
from what I can tell, that just graphs it for you automatically if you choose a ...
How do i find a point that makes it so the x intercept is 1.4142135623733095❓
heady lava
you don’t have to do it at the x intercept right
sudden basalt
No
heady lava
anywhere else as long as it’s on the curve is fine right
sudden basalt
I need to graph the equation and now i know the vertex and the x intercepts
heady lava
but you don’t have to graph it at those points specifically right
sudden basalt
No
I just dont know how to make the graph intersect the x intercepts where i want them to
heady lava
all I did was evaluate m at 0, 1 and 2
if you have 3 points then you can draw a unique quadratic for those 3 points
m(x) is the only quadratic that can pass through these points so naturally what you get after graphing must be m(x)
sudden basalt
i dont understand
heady lava
hmm
I don’t really know how to explain without involving copious amounts of algebra
because a quadratic polynomial is ax^2+bx+c where a,b,c are parameters, you can think of how you need 3 conditions to constrain those 3 parameters
those 3 conditions are basically just a system of 3 equations with 3 unknowns which is usually solvable
sudden basalt
i found the vertex but how to i find the x intercepts?
Can i also have help with the questions
@heady lava
sudden basalt
yeah
heady lava
So the range would be from -inf to 1 because the graph is going up when x is between -inf and 1
I shouldn’t be using the word range
interval
heady lava
oh my god I’m braindead
im so sorry
m(x) is increasing on (-inf, 0], decreasing on [0,+inf)
I personally wouldn’t say there is a minimum but i would put -inf at x= + or - inf
sudden basalt
m(x) is increasing on (-inf, 0], decreasing on [0,+inf)
It says this is wrong
heady lava
try (-inf, 0) and (0, +inf) maybe
heady lava
what if you put does not exist
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fringe marsh
whats an example of a function with 2 left inverses
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whats an example of a function with 2 left inverses
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scarlet kite
whats the answer
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whats the answer
prime sierra
Find x with e.g. (10x-1) - (7x+2) = (7x+2) - (8x-7)
scarlet kite
x=3?
prime sierra
yep!
scarlet kite
thats all?
prime sierra
continue the patern 17, 23, ...
scarlet kite
29
prime sierra
and for AD ...
prime sierra
I don't know the name of the theorem in English, but it might be proportionality theorem
prime sierra
With that trapezoid EKHG , the equation would be 7x+2 = 1/2*(8x-7 + 10x-1) => x=3
Continue with trapezoid ADJF to get AD = 35
scarlet kite
ok
wraith hinge
ho
kindred pier
whats the Derivative of this and how
Do you know power rule and chain rule?
wraith hinge
yeah il but theres the 3 where did it go
ik the answer is: 1+(1-x)^-2/3 x (-1)
i just dont understand where the 3 dissapered
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viral oasis
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wraith hinge
Hi! Could someone please help me setup this question, I have no idea how to.
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jaunty jolt
So I think I’m on the right track but I’m not exactly sure how the interval would affect my answer.
jaunty jolt
I was thinking since the interval is between 2nd and 3rd quadrant. Sin and tan are positive and then cos would be negative but I’m not too sure about that
heady lava
since sin a is positive, a should be within the second quadrant
Then cos and tan are negative
jaunty jolt
right that makes sense I didn't think about that. so it would be -4/5 and -3/4
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winged epoch
i need help to verify if my answer is correct
At the same moment, a motorcycle leaves city A and another leaves city B, with the intention of meeting on the 80-kilometer straight road that connects both cities.
Knowing that the speeds of the motorcycles are 75km/h and 55km/h, calculate how long it will take them to meet.
so i got 23.4 minutes. that's the time it will take for them to find each other but the work they gave me shows results that doesn't make any sense. (btw on "ninguna de las anteriores" it means none of the above)
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i need help to verify if my answer is correct
At the same moment, a motorcycle ...
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proven sluice
i need help to verify if my answer is correct
At the same moment, a motorcycle ...
I am getting 0.62
winged epoch
how did you got that answer?
proven sluice
Let's assume the time taken is t..alright?
By both vehicles
So distance travelled by A and B will be what?
Wait is my ans correct tho?
winged epoch
no sure about it thats why i'm asking
proven sluice
So distance travelled by A and B will be what?
Nvm can u tell me this? Since speed is given what's the distance
winged epoch
i got my answer because at least the formula that i use here is distance / speed and that by each motorcycle so it will be 80/75 and 80/55 these will give me 1.06 and 1.45 hours
i just subtracted them and it gave me 0.39
winged epoch
Nvm can u tell me this? Since speed is given what's the distance
the distance is 80 km
proven sluice
What will be distance covered by A in t hours?
proven sluice
i got my answer because at least the formula that i use here is distance / speed...
I doubt that's not what we are supposed to do
winged epoch
I doubt that's not what we are supposed to do
proven sluice
What will be distance covered by A in t hours?
@winged epoch can u tell me this?
winged epoch
<@723751210661707838> can u tell me this?
i don't understand your question :(
wdym?
proven sluice
See if A takes 't' hours to meet B and speed of A is 75, what will be the distance covered?
It will be 75t right
proven sluice
Distance = speed×time
winged epoch
i know but why do we have to take the distance of it if
ohhhh
now i get it
the distance it takes to see the other bike
proven sluice
So distance by A is 75t and by b 55t this should sum up to 80
winged epoch
not the distance in total right?
proven sluice
U will get t as opt a then
proven sluice
not the distance in total right?
Correct
winged epoch
ok let me try to do it again
yeah 0.62
didn't knew that thank you so much!
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woven geode
Hi
delicate belfry
Note, cm = 0.01m
woven geode
Wdym
woven geode
not sure about the numbers
This is what I got on my phone calculator so it shld be right… hopefully
delicate belfry
Wdym
Might be that I am still dizzy, but cm is 0.01 m. So if you squared it, you'll have 0.01^2 m^2.
delicate belfry
For your unit.
woven geode
I actually got
I got that as the answer but they wanted it to 2 decimal places
So I added a 0 is that right?
delicate belfry
Someone else should help you.
woven geode
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Need help w that someone 🙏🏽🙏🏽🙏🏽
orchid wagon
what have you tried
woven geode
what have you tried
Im only brain dead at this question
orchid wagon
pretty sure its wrong
woven geode
Yea but how do I solve it
orchid wagon
you are going to use cm as your unit
the radius is 4cm
now heres my question, what is the distance do you think the tip of the clock hand travel for 1 cycle?
rough goblet
also keep in mind that hour clocks complete 2 revs in one day
because it's a 12 hour clock
oops... sorry fung
orchid wagon
yes, but we'll get to that later
orchid wagon
now heres my question, what is the distance do you think the tip of the clock ha...
answer this first
woven geode
It needs to travel 12 twice so 2 times to get to 24
woven geode
12
orchid wagon
given the length of the clock hand is 4
rough goblet
no as in the circumference
like what is one circumference is i think what fung's asking
orchid wagon
to cut to the chase, the distance traveled in 1 cycle is the circumference of the hand tip revolution
the clock hand length is 4, aka the radius is 4
woven geode
Yes
orchid wagon
so, whats the circumference?
woven geode
25.13?
woven geode
It wants the answer in 2 decimal places tho
orchid wagon
i know
woven geode
And I don’t have my calculator w my rn
orchid wagon
but if you use 2 decimal places everywhere the final result will be wrong
orchid wagon
this doesnt require calc??
orchid wagon
correct
and stay that way
now the circumference is 8pi
which means in 1 revolution, the tip travels 8pi cm
orchid wagon
now heres my next question, how many revolution does the clock hand travel in 2x1/2 days
woven geode
2 and a half
orchid wagon
16 x 2 1/2
do not jump the gun
orchid wagon
2 and a half
wrong
woven geode
One and a half?
orchid wagon
also keep in mind that hour clocks complete 2 revs in one day
i should remind you this
orchid wagon
1 day = 2 rev therefore 1/2 day = ... rev?
woven geode
1
woven geode
5
orchid wagon
correct
rough goblet
fungus
orchid wagon
hi
rough goblet
just a question
hi
2x1/2 is mixed fraction notation right
bc i've only ever seen it as 2 1/2
orchid wagon
yes
rough goblet
ohk
woven geode
Uhm
orchid wagon
anyway, 5 rev is correct
now, 8pi is the length of 1 rev
so after 5 rev then the distance is...?
zinc dove
2.5 makes it so much easier
woven geode
5x 8pi?
rough goblet
yes
woven geode
40 pi
zinc dove
Gg
orchid wagon
2.5 makes it so much easier
for the sake of simplicity im helping using his region's notation
rough goblet
2.5 makes it so much easier
this method is perfectly fine too
rough goblet
in fact i think it's better
woven geode
and theres your result
And this is for one day or 5 days?
orchid wagon
now only then, you convert this to decimal
rough goblet
since it appears that he's just learning algebra/geo
rough goblet
And this is for one day or 5 days?
5
zinc dove
It’s fine but if you scroll up both of us asked the same question
orchid wagon
And this is for one day or 5 days?
2 1/2 day
zinc dove
Cause it’s uncommon notation
woven geode
What
zinc dove
wtf you need five days for anyway 😭
orchid wagon
Oh so how will I solve for 5
find the amount of revs achieved in 5 days
orchid wagon
and use the same method
woven geode
Mbmb
rough goblet
@zinc dove if you're not gonna help, just occupy the channel... then please don't say anything
woven geode
I mean 5 hours
woven geode
How will I solve that
rough goblet
okay let's see
orchid wagon
I mean 5 hours
again, find the amount of rev achieved in 5 hours
zinc dove
<@271505491287343106> if you're not gonna help, just occupy the channel... then ...
Both these mfs thought it was 5 days not horus
What are you doing in this channel
woven geode
oh the second part?
Yes yes
orchid wagon
then apply area of a fan formula
woven geode
Ji
woven geode
Wait so since the clock will be on 5 o’clock it’s using 5/12 of the area
woven geode
5/12 in decmixas would be: 0.47
orchid wagon
fine the area of the circle then find the ratio of hour 12-5 area to full circlr
woven geode
First of all for 2 1/2 days we got 40 pi
orchid wagon
which is yes, 5/12
woven geode
So I would have to do that in decimal
orchid wagon
tf is fan shape formula
1/2 r^2theta
rough goblet
i... don't know what that is but ok
woven geode
First of all for 2 1/2 days we got 40 pi
125.66?
orchid wagon
rough goblet
okay wait wait wait
why ru using 40pi
orchid wagon
this is fan shape
rough goblet
where does that cm from
rough goblet
this is fan shape
will check it out
woven geode
Uhm can we solve my issues first guys!!
rough goblet
yes yes sorry
rough goblet
okay wait wait wait
why ru using 40pi
.
woven geode
So for 2 1/2 days we got 40pi bc 5x 8 pi = 40 pi
rough goblet
why do u need that?
woven geode
@orchid wagon
zinc dove
So for 2 1/2 days we got 40pi bc 5x 8 pi = 40 pi
Do you remember why 5 and why 8 pi
Just out of curiosity
woven geode
Yea I’m writing stuff down
zinc dove
But do you know tho
woven geode
Swt
rough goblet
okay wait
are we doing the first question
or the second one/?
the first one, rihgt?
woven geode
@rough goblet @orchid wagon for b) what is the area swept by the our hand in five hours?
The answer would be 5/12 and convert it into decimal = 0.47
Is that right?
rough goblet
no-
5/12 in decimal is 0.4166666
find the total area
then multiply by 5/12
USE FRACTIONS FOR NOW please
rough goblet
you mean 16pi
woven geode
Unless u want the answer in decimals?
woven geode
Alrr
rough goblet
5/12 times 16pi = ??
rough goblet
yes
woven geode
Can I use decimals
rough goblet
no 16pi x 5/12
rough goblet
Can I use decimals
why u such a hurry?
woven geode
Yes but then I wld js add pi to the end yh?
rough goblet
that just complicates things
woven geode
why u such a hurry?
Coz I need to like hurry up n solve this
rough goblet
bro
using 2 or 3 will just mess ur calcs up
if u want to use decimalls
ur gonna need to use 4-5
for noww
woven geode
Oh
woven geode
solid kilnBOT
Result:
20.943951023932
yep
woven geode
So where do I go from here
rough goblet
idk
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tawny sundial
Prove that product of four consecutive natural numbers is not a square number.
tawny sundial
Any process except factorisation.
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acoustic osprey
help pls T_T
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help pls T_T
brisk tapir
Hi let me give this a shot
acoustic osprey
suree
acoustic osprey
i tried solving it and i got 9, i wanna make sure my answer is right
acoustic osprey
wait can u still help me, this is my homework T_T
brisk tapir
You can just continue posting questions and someone will reply
brisk tapir
!status @acoustic osprey
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fickle helm
Why is x^2 lebesgue integrable in R? Isn’t it by definition for it to be integrable the integral of abs( x^2 ) can’t be inf. doesn’t x^2 fail here
supple copper
Where does it say it’s lebesgue integrable
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left oriole
well its integral is defined but is infinite
if you're working in the extended reals, that's allowable as long as the integrals of its positive and negative parts are not both infinite
red jolt
what i need to do here?
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what i need to do here?
hallow cliff
what i need to do here?
T is some point in the hexagon and they want you to find x+y+z
red jolt
T is some point in the hexagon and they want you to find x+y+z
if i’m not wrong for triangle there is a property like this for x + y + z being equal to height
but idk what to do for this one
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hallow cliff
if i’m not wrong for triangle there is a property like this for x + y + z being ...
For equilateral triangles yes
hallow cliff
but idk what to do for this one
Just pick a nice point
For example the center of the regular hexagon
Or one of the corners
gilded ibex
been stuck on this question and every attempt i made is wrong
proven hound
Part b is for 3 marks? Damn.
gilded ibex
for a)
first i tried multiplying 2 so its left as 1-x=2*3
then 1-x=6
then added 1 both sides so final answer was left as x=7 (which i realised was wrong because if i solved the equation as x=7, the final answer wouldn't be 3)
then second attempt, i multplied x both sides (so it would be 1-2=3x)
devout drift
$1 - \f2x = 3$
solid kilnBOT
ColdTee
devout drift
You can do this couple of ways but I suggest take the lcm first.
Or you can subtract 1 both sides
Multiply x both sides
gilded ibex
lcm?
devout drift
Least Common Multiple
gilded ibex
mhm
devout drift
Or you can subtract 1 both sides
You can do this if you don't know how to do lcm yet.
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muted field
I've googled the solution, but I don't understand why I needed to subtract the digits from each other and then their GCD is suddenly the answer
surreal halo
can you elaborate?
surreal halo
,rccw
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proven hound
Do you know the modulo concept(taught in number theory ig)?
Basically if a number x is divided by y and leaves a remainder r, then the number x+ny when divided by y also leaves the same remainder r(n is a whole number)
muted field
uh no?
muted field
Basically if a number x is divided by y and leaves a remainder r, then the numbe...
gimme a min
Yeah, then?
proven hound
So if you take the difference between two numbers that leave the same remainder, you get a number which is a multiple of y
i.e., the divisor
Assume the numbers to be x1=r+n1 y and x2=r+n2 y and verify
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muted field
Assume the numbers to be x1=r+n1 y and x2=r+n2 y and verify
veriy what?
the divisor thing?
I did it's true
oh wait makes sense
,close
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merry zodiac
9^9^9 mod 100
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9^9^9 mod 100
rough goblet
...?
where did u get that from lol
it's been so long since i've done mod, one sec.
fathom ivy
euler's theorem go brr
merry zodiac
I tried to read about it on math exchange
fallen zealot
9^9^9 mod 100
from what book are you finding these mod by 100
merry zodiac
I got this from someone i guess she is reading dumit foote number theory
fallen zealot
i think you can break it into 25 and 4
then solve them seperately
then merge them
i dont know any direct way for mod by 100
rough goblet
ok darkskull i havent done advanced mod
fathom ivy
oh maybe it's not euler's theorem
rough goblet
but how does that work
fallen zealot
you break it apart into prime factors.
then you can use this theorem :
a = b mod by x
a = b mod by y
=> a = b mod by [x,y]
we did it so [x,y] would be xy
rough goblet
?
fallen zealot
? ?
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lusty delta
9^9^9 mod 100
easy way out that is obvious but not mathematically motivated: ||consider 9^1 (mod 100), 9^2 (mod 100), 9^3 (mod 100)… until 9^10 (mod 100)… you will very quickly see what happens||
better way to do this problem: ||consider application of Binomial Theorem||
vernal fern
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vernal fern
where do i go from here?
this is where my knowledge ends unfortunately
ive solved for x but there are c ouple more steps to find the domain if im correct
earnest briar
earnest briar
yes
vernal fern
oh
earnest briar
x >= -4
vernal fern
no to what?
earnest briar
because x >= -4
earnest briar
when you're solving inequalities, you need to move everything to 1 side
vernal fern
oh does my work look wrong
earnest briar
vernal fern
i got to the same conclusion tho
earnest briar
yeah but you will get the wrong answer when you're dealing with more difficult inequalities
vernal fern
mmm
crud
so wait it has to go like
x*1/2= 1x/2
hold on actually
whats going on in step 2
earnest briar
we need to know when the lhs equals 0, so we can forget about the 2 and solve it as x+4 => 0
vernal fern
we can just drop the 2 like that?
earnest briar
how do you cancel out 3^x?
vernal fern
oh does that not work here
earnest briar
no
you can't just cancel it out like that
I will give you a hint
you need to replace 3^x with a variable
so you have this now
earnest briar
try solving it now
vernal fern
-6t >= -66
4t <= 60
t <= 15
vernal fern
oh
ok my extrapolation did not track
i tried to put them over a common denominator
earnest briar
i tried to put them over a common denominator
first move them to one side and solve it that way
earnest briar
you can do that w these?
it's how you're supposed to solve them
earnest briar
also remember that if the denominator equals 0, then the inequality is undefined
you can't divide by 0
vernal fern
do u want int notation
earnest briar
sure
vernal fern
t ∈ (-∞,0) U [1,∞)