slim iron
so should i do log4782969/-log3 and use the absolute value of the answer as the exponent?
#help-0
alpine sable
In that case
n will be a complex number
Powers of negative number cannot be represent with real numbers unless their exponent is an integer
wanton nova
@daring reef
lone heartBOT
<@494183312026501122>
lone heartBOT
daring reef
thank you for the help
wanton nova
Np
lone heartBOT
Available help channel!
lone heartBOT
Available help channel!
terse smelt
lone heartBOT
lone heartBOT
@terse smelt Has your question been resolved?
terse smelt
<@&286206848099549185>
icy crane
wat is L
lime vine
lone heartBOT
@terse smelt Has your question been resolved?
ashen pulsar
alpine sable
$\ln (x+1) - \ln (x-2) = \ln x$
$e^{\ln (x+1) - \ln (x-2)} = e^{\ln x}$
$\frac{e^{\ln (x+1)}}{e^{\ln (x-2)}} = e^{\ln x}$
$\frac{x+1}{x-2} = x$
$x^2 -3x - 1 = 0$
ocean sealBOT
Yustina
alpine sable
,w x^2 - 3x - 1 = 0
ashen pulsar
it would be a right
neat sierra
Or you can similarly use ln(a) - ln(b) = ln(a/b). You'd get the same result
last ether
Wait
Isn't there an easier way
You can factor ln(x) out
I guess it works both ways
You would still get the quadratic
ashen pulsar
but would there be an extraneous solution
last ether
Well you can try plugging it in and see if it's true
last ether
but would there be an extraneous solution
there will be one yes
last ether
use log proprties
last ether
$$3\log\left(2a\right)-\log\left(2a\right)$$
$$\log\left(\left(2a\right)^{3}\right)-\log\left(2a\right)$$
$$\log\left(\frac{\left(2a\right)^{3}}{2a}\right)$$
$$\log\left(\left(2a\right)^{2}\right)$$
ocean sealBOT
Umbraleviathan
last ether
Yeah
ashen pulsar
ohhhhh
i looked at my notrs and i get it
but for some reason my answer isnt on there
last ether
lets see
$$3\log\left(2a\right)-\log\left(2a\right)=\log\left(11a+3\right)$$
$$\log\left(\left(2a\right)^{3}\right)-\log\left(2a\right)=\log\left(11a+3\right)$$
$$\log\left(\frac{\left(2a\right)^{3}}{2a}\right)=\log\left(11a+3\right)$$
$$\log\left(\left(2a\right)^{2}\right)=\log\left(11a+3\right)$$
$$4a^{2}=11a+3$$
$$4a^2-11a-3=0$$
Check extraneous solutions
ocean sealBOT
Umbraleviathan
last ether
Im not good with compounded stuff
ashen pulsar
shoot
last ether
Lemme see
If I can remember
$$A = I\left(1+\frac{r}{12}\right)^{12t}$$
$A$ is the amount, $I$ is the initial value (deposit), $r$ is the interest rate as a decimal, $t$ is time in years
ocean sealBOT
Umbraleviathan
last ether
@ashen pulsar
last ether
Plug in the information given to you
ashen pulsar
whats rate
would it be 1.085
or 0.0085
nvm
why is r divided by 12 there
@last ether
last ether
It's just the formula
ashen pulsar
whats the original formula
last ether
I don't know jackshit about finances lol
ashen pulsar
im so lost
last ether
$$A = I\left(1+\frac{r}{k}\right)^{kt}$$
$A$ is the amount, $I$ is the initial value (deposit), $r$ is the interest rate as a decimal, $t$ is time in years, $k$ is the frequency of compounding
ashen pulsar
this due in one hour
ocean sealBOT
Umbraleviathan
lone heartBOT
@ashen pulsar Has your question been resolved?
last ether
What was the initial deposit Carlos made
_ _
ashen pulsar
last ether
Uhh
I guess you can use logarithmic regression on your calculator
But I gotta sleep
ashen pulsar
oh ya
lone heartBOT
@ashen pulsar Has your question been resolved?
fervent timber
why do people even use such a confusing notation for angles?
can’t we just stick to good old decimals?
tacit arch
Boats, I think
lone heartBOT
@hushed ether Has your question been resolved?
swift shore
why do people even use such a confusing notation for angles?
can’t we just stic...
Because they need garbage to fill up the curriculum
median oar
why do people even use such a confusing notation for angles?
can’t we just stic...
Because you use that for maps, degrees minutes seconds
It also separates things better for a human mind to grasp
swift shore
It’s such a niche specific mechanic skill
Surely any person using maps in navigation will learn this again at their job, or more likely, have a computer perform it
lone heartBOT
@hushed ether Has your question been resolved?
swift shore
@hushed ether do you know how to convert from stupid DMS to decimal
median oar
There are 60 minutes in a degree and 60 seconds in a minute
median oar
Yeah he understands that
swift shore
Oh
swift shore
Ah that’s so weird
median oar
Because you need to borrow from before
swift shore
I would just convert to decimal, subtract, then convert back
median oar
Like 100- 12 is not quite 198
First you do 1 degree minus 22 minutes and 13 seconds
That should equal 37 minutes and 47 seconds
Because when u add them
13 seconds + 47 seconds is 1 minute 0 seconds
Then 22 minutes + 37 minutes is 59 minutes, plus the 1 minute from before it’s 1 degree 0 minutes
They are like digits of a number
Normally in decimal you go to 10 and it shifts the digit
Here it goes to 60 then shifts
Instead of ones, tens, hundreds
You have seconds, minutes, degrees
10 ones make a ten, 10 tens make a hundred
60 seconds make a minute, 60 minutes make a degree
median oar
Like base 60, in a way
Wait you you hear about decimal seconds
No it’s more like 90.00.00 - 48.22.13
And u need 60 to shift a “digit” or a dot here
swift shore
Wait you you hear about decimal seconds
Huh
lone heartBOT
@hushed ether Has your question been resolved?
signal pecan
lone heartBOT
signal pecan
i dont know how to create this equation i am stuck
the rate is not the same
so what would be the b value
a value would be 49 since its the starting value
but what about the b and x value
sudden hinge
either do as instructed and approximate the parameters using desmos or plug in 2 arbitrary rows into the equation y = ab^x to solve for the parameters
lone heartBOT
@signal pecan Has your question been resolved?
signal pecan
either do as instructed and approximate the parameters using desmos or plug in 2...
i am but its not working
i get like the first 2 points right and then others wont work
one point is right but others wont work
stiff surge
Help
flat ore
what have you tried
stiff surge
I know how to solve quadratic equation but I don't know how to solve these types of questions
stiff surge
what have you tried
Just tried manually solving them but it is too complicated due to there is usually a different way
flat ore
do you know the quadratic formula?
stiff surge
yep
stiff surge
Sorry I don't know how to use this bot
flat ore
i dont think there are other ways
flat ore
Can you teach me how to use this bot?
#resources scroll all the way to the top
stiff surge
okay
flat ore
ocean sealBOT
realhuman
flat ore
yes use this
stiff surge
a=3, b=-5 and c= 1
stiff surge
ye
ocean sealBOT
realhuman
tight locust
Lol
stiff surge
I will just tell the answer.. Also the above answer is wrong it is supposed to be 5 instead of negative 5
The answer is option b
@flat ore The answer for that question is option b
stiff surge
you wrote that wrong
no?
stiff surge
oops ye
flat ore
not -5
alpine sable
Damn
alpine sable
Nothin
Yall just 100988× smarter than me
Thats all
🥲
I been failing math bro
Ong
lone heartBOT
tight locust
,calc 1 + 12/(2 + 12/(2+12))
ocean sealBOT
Result:
5.2
,calc 100 × 2
ocean sealBOT
The following error occured while calculating:
Error: Undefined symbol ×
tight locust
,calc sqrt(13)
ocean sealBOT
Result:
3.605551275464
Damn
lone heartBOT
Available help channel!
alpine sable
,calc 100 x 2
ocean sealBOT
The following error occured while calculating:
Error: Undefined symbol x
lone heartBOT
,calc 100 x 2
wanton nova
,calc 100*2
ocean sealBOT
Result:
200
@alpine sable Has your question been resolved?
tired shard
lone heartBOT
honest wren
What have you tried
honest wren
Yea
tired shard
and idk how to convert -1.1547 into exact values
honest wren
Do you know what sin60 is?
honest wren
Do you know what sin300 is in terms of sin60
tired shard
no
honest wren
Do you know how the relationship between angles of the 4 quadrants?
tired shard
Do you know how the relationship between angles of the 4 quadrants?
sorta not really
ik which is positive for which
and negative for which
honest wren
Do you know how to draw a diagram to represent it in terms of a triangle?
tired shard
Do you know how to draw a diagram to represent it in terms of a triangle?
i can draw a unit circle
honest wren
yea
tired shard
so how do you get the exact value?
honest wren
So sine is opposite/hypotenuse
Say the hypotenuse is 1
What's the length of the opposite?
tired shard
sqrt3/2?
honest wren
Yeah but since it's pointing down we take it as negative
tired shard
right
honest wren
So sine300 is
honest wren
Yeah so you can find cosec300
tired shard
could you explain how thats cosec i dont really understand that aspect
since its cosec shouldnt its be -(2/sqrt3)?
.close
mossy tusk
(x+3)+4 (x+4)+4
lone heartBOT
(x+3)+4 (x+4)+4
amber heart
what?
could you clarify further
are you trying to solve an equation?
@mossy tusk
gray isle
no
alpine sable
it’s an unnecessary bracket
gray isle
if
(x+3)(+4) was written, multiplication between the (x+3) and 4 would be implied,
yeh, the parentheses around the x+3 are useless
and its presence or absence won't affect the value of the expression
alpine sable
so u remove them, and sum x + 3 + 4 = x + 7
alpine sable
oh yeah mb
turbid phoenix
if you are trying to simplify (x+3)+4 (x+4)+4
expand the middle term
collect x terms
add constants
lost dirge
yes^
gray isle
if it was just (x+3)+4, that'd simplify to x+7,
but isn't what you're starting with
torpid chasm
lone heartBOT
torpid chasm
is this false, right?
lone heartBOT
@torpid chasm Has your question been resolved?
torpid chasm
yes
small wave
lone heartBOT
@torpid chasm Has your question been resolved?
lone heartBOT
lone heartBOT
Available help channel!
sudden pasture
I know I already have a channel open, but this one is simpler. Is it true that:
sudden pasture
I couldn’t find this anywhere as a rule, but think it’s true
hushed tinsel
yes it is true
hushed tinsel
I couldn’t find this anywhere as a rule, but think it’s true
there is no rule
you can verify by putting the values of x
wary stream
FYI, @sudden pasture as the bot stated, don't open multiple channels, so close the other channels you have open
sudden pasture
This is just a smaller question I needed for the other one. I already said that in the opening
thank you for the confirmation @hushed tinsel
sudden pasture
yea ill try
hushed tinsel
thank you for the confirmation <@768035976269398026>
np
sudden pasture
.close
lone heartBOT
lone heartBOT
Available help channel!
rose sable
alright so
lone heartBOT
alright so
rose sable
Im working on indices
And stuck on this small part
how can I know that sqr root of 8 is 2^3/2
keen bear
well, what is the prime factorization of 8?
rose sable
2x2x2
keen bear
so what is that in power notation?
rose sable
well thats the part im confused on why its 3/2
keen bear
2x2x2 is 2^3, right?
rose sable
yes
keen bear
so now we can take the square root of it. We need two important facts to get to why it's 3/2
$\sqrt{x}=x^{\frac{1}{2}}$
ocean sealBOT
GoldenPhoenix
rose sable
yes i understand that
keen bear
$(x^{a})^{b}=x^{ab}$
ocean sealBOT
GoldenPhoenix
keen bear
$(2^{3})^{\frac{1}{2}}=2^{3*\frac{1}{2}}$
ocean sealBOT
GoldenPhoenix
keen bear
which gets your result
keen bear
yeah, this leads to the nice property that a root of a power is the same as the power of a root
rose sable
so if its for example cube root of 8 it would be
give me a sec
8/3
i think i did it wrong
ocean sealBOT
GoldenPhoenix
keen bear
now you substitute in the prime factorization of 8, and that gives you $(2^3)^{\frac{1}{3}}=2^{\frac{3}{3}}=2^1=2$
ocean sealBOT
GoldenPhoenix
vagrant rover
I don't even understand where to start answering this
lone heartBOT
I don't even understand where to start answering this
vagrant rover
If anyone could help me get started that would be very appreciated
lone heartBOT
@vagrant rover Has your question been resolved?
vagrant rover
This is the information that I have gathered so far.
My current misunderstanding is that I’ve never seen a rational function in the form of (ac+b)/(cx+d). I’ve only seen rational functions in factored form.
<@&286206848099549185>
abstract fractal
What makes you think the horizontal asymptote is 0?
lone heartBOT
@vagrant rover Has your question been resolved?
vagrant rover
What makes you think the horizontal asymptote is 0?
Yeah you’re right it could be something else
I thought so cause it looked like 0.2 approached y=0
abstract fractal
It says that, standing really far away from the magnet, the measurement is 0.2
vagrant rover
But we don’t have anything to compare it to
abstract fractal
I think the implication is that you're standing arbitrarily far
vagrant rover
It says that, standing really far away from the magnet, the measurement is 0.2
Yeah so I put 10 feet back as an approximation
abstract fractal
In other words, the asymptote, I would say, is 0.2
vagrant rover
I think the implication is that you're standing arbitrarily far
Wait wait wait actually
The magnet doesn’t go forever
So eventually it will tend toward 0
abstract fractal
But there are magnets everywhere, plus the earth's magnetic field. I think 0.2 is just the "ambient" magnetic field
vagrant rover
But there are magnets everywhere, plus the earth's magnetic field. I think 0.2 i...
Yeah but I wouldn’t image that’s part of this question
vagrant rover
But there are magnets everywhere, plus the earth's magnetic field. I think 0.2 i...
Hmmm
abstract fractal
When it says that the measurement is 0.2 standing really far from the magnet, plus the fact it doesn't tell us how far, I can't see many other ways to interpret it
vagrant rover
You don’t think it could be tending toward 0 though?
I can see what you mean
Well regardless of the HA for now, wouldn’t we need more information to actually construct a function
abstract fractal
I don't think so, honestly. Otherwise you can't really use the 0.2 number
You'd need how far away you are. The only way it can be of use is if it's the asymptote
abstract fractal
Plus, 0.2 is a nice fraction. Makes for nice coefficients of a and c
vagrant rover
Plus, 0.2 is a nice fraction. Makes for nice coefficients of a and c
Ah okay
true
Oh yeah that makes a lot of sense now
@abstract fractalI don't know what to do next
I need a vertical asymptote or a vertical intercept to find the equation, right?
Idk how I would find the vertical intercept, so I would assume that the vertical asymptote is what I need to find
But idk how
abstract fractal
You know a and c, or at least what they could be
vagrant rover
yeah 2 and 10
abstract fractal
I would have gone with 1 and 5, but 2 and 10 works too
vagrant rover
yeah
abstract fractal
With the two points, you'll have two equations. Two equations, two unknowns
vagrant rover
And you have two points
right
abstract fractal
Like what do they represent
Dunno. Numbers. I'm not sure what they physically represent, if anything
abstract fractal
By plugging them in
vagrant rover
do you mean like two linear equations?
OHHHHHHH
okay okay sec lemme try
@abstract fractalWait no I still don't get it
2.3 = (2(6)+b)/(10(6)+d)
That's what I wrote
and after that idk
abstract fractal
That's one equation
Woah, that shouldn't be 60(6).
That should either be 10(6) or just 60
vagrant rover
4.4= (2(8)+b)/(10(8)+d)
abstract fractal
Yep
Now to solve with your favorite systems of equations method.
Substitution, elimination, whatever you want
vagrant rover
I would have gone with 1 and 5, but 2 and 10 works too
Hey so I got the answer I think
but just one quick quesiton
shouldn't it be 2 and 10 and not 1 and 5 since we're multiplying
by x
like wouldn't simplifying here result in different functions
abstract fractal
Let's say it's supposed to be 2 and 10 but we guess 1 and 5
Then b and c will be fractions
They'll be /2
To get rid of the fraction, we'd multiply the top and bottom by 2, turning 1 and 5 to 2 and 10
Similarly, the other way around, if we guess 2 and 10 and it's supposed to be 1 and 5, then b and c will be even, and we can divide out a factor of 2 from the top and bottom
Either way, we'll get the same answer
vagrant rover
abstract fractal
Yep. Notice you have the case where you can factor out a 2 from the top and bottom
That'll just simplify the fraction
vagrant rover
Should I rewrite as
abstract fractal
That's fine
vagrant rover
Wait which one is fine
vagrant rover
Yep. Notice you have the case where you can factor out a 2 from the top and bott...
yeah yeah I see what you mean
abstract fractal
Either one, really. The latter is most simplified
vagrant rover
Should I rewrite as
Ah okay, I'll go with this
abstract fractal
Now you have the function, and you can answer the next parts
vagrant rover
Now you have the function, and you can answer the next parts
Oh actually one question
It's okay the this function shows on both sides, right?
like
what i mena
Because that doesn't make intutive sense to me
abstract fractal
Yeah, that's fine. That's how rational functions work. Though, in order to physically make sense with what the function actually means, we would probably take the absolute value, but that's unnecessary and doesn't affect the answer to any of the problems
vagrant rover
But if we get to like say, 11, feet near it
it would switch up?
that makes no sense to me
OHH
THat's the answer for one of the other question parts
it's 10 feet into the room
abstract fractal
Yep
abstract fractal
Thus, standing at x = 9 and x = 11 should give the same result. It's the wrong sign in practice, which is why one may use the absolute value, however I wouldn't suggest putting the function in absolute values as it unnecessarily complicates things
vagrant rover
Right right right
Wait uh
yeah okay
wait
how would I put it in absolute value if I did want to?
Just absolute everything?
abstract fractal
Yep, since physically we only care about the magnitude, not the sign
abstract fractal
Np 
vagrant rover
.close
polar solar
the marscheme says that "it should be 33/100" i got 33/100. is my answer right
polar solar
because the marchscheme also says use 2 comparable figures, 33 and 100
lone heartBOT
@polar solar Has your question been resolved?
polar solar
<@&286206848099549185>
shut socket
Gcse fella
polar solar
what?
zenith carbon
Yes you’re correct
You don’t really need to do that really long addition you did of pi
polar solar
Yes you’re correct
thanks
i was just tryna make sure because i thought the mark scheme said i was wrong
polar solar
oh you have the same test
zenith carbon
Yh I did it at some point
real sparrow
lone heartBOT
real sparrow
Hi, I need help with question 4 (ii)
ocean sealBOT
illuminator3
karmic rapids
read #❓how-to-get-help pls
real sparrow
I know but the radius is 5/pie
karmic rapids
pi not pie lol
wanton nova
haha
karmic rapids
<@&268886789983436800>
wanton nova
🥧
real sparrow
hold on
sly mantle
@alpine sable pls use a free channel
karmic rapids
$$\left(\frac{a}{b}\right)^2 = \frac{a^2}{b^2}$$
real sparrow
And then what do i do with the pie squared at the bottom
ocean sealBOT
illuminator3
real sparrow
damn auto correct
wanton nova
And then what do i do with the pie squared at the bottom
🥧 squared?
wanton nova
haha
karmic rapids
And then what do i do with the pie squared at the bottom
cancel out with the other pie
wanton nova
🥧
real sparrow
so will i get pi? at the bottom
wanton nova
yes
real sparrow
ah okok
karmic rapids
indeed
lone heartBOT
lone heartBOT
Available help channel!
alpine sable
Hi! How would you do this problem?
lone heartBOT
Hi! How would you do this problem?
alpine sable
so the person would travel around the circumference 6 times
how would you find the circumference?
2 pi r
yeah so instead of r
its t
so 2pi t
*6
so 12pi t
Oh, because they would travel around it 6 times
yeah
you got it?
thank you
yes
np
.close
.close
.close
tawdry jolt
What am I doing wrong here?
lone heartBOT
What am I doing wrong here?
tawdry jolt
I also said it was 0 and that was wrong too
Desmos shows that both are kind of correct
dusty fox
And that's why neither are correct
safe lark
how can i prove here that ADC is congruent to ACM and that DBC is congruent to BNC
safe lark
wanton nova
you're only given the pic?
safe lark
ABC is a right triangle "around" it is a circle distances of points A and B to the tangent which passes throught point C are m and n. What are lenghts of legs?
safe lark
you're only given the pic?
i just gotta know how to prove those triangles are congruent
safe lark
you're only given the pic?
and the picture isnt givent its part of the solution
safe lark
<:hmmCat:831508801646755850>
wait i think i might know
wanton nova
both triangles have a right angle
safe lark
yea
safe lark
<@&286206848099549185>
lone heartBOT
@safe lark Has your question been resolved?
safe lark
<@&286206848099549185>
lone heartBOT
@safe lark Has your question been resolved?
frigid hatch
you could say that angle ACB is alfa and angle CAD is beta so 90 + alfa + beta = 180, alfa + beta = 90.
now if you look at the triangle ACB the angle CAB is alfa and si the angle CBD must be beta, you can use the same logic to complete triangle MCA and triangle NCB so that you can prove that, for example, ACD is congruent to MCA because they have one length in common and two angles
safe lark
you could say that angle ACB is alfa and angle CAD is beta so 90 + alfa + beta =...
you mean ABC is alfa?
ACB is 90
safe lark
you could say that angle ACB is alfa and angle CAD is beta so 90 + alfa + beta =...
i know all of that, but you just say ACD is congruent to MCA because they have one length in common and two angles, how do i prove for the second angle, idk how to apply what you said to that
frigid hatch
safe lark
yea thats what u get in the end
frigid hatch
yes so where's the problem
frigid hatch
MCA is congruent to ACD because AC is in common and alfa and beta are adjacent to AC
safe lark
how do u know that MCA is same as DCA
the angle
frigid hatch
you need at least two angles and a length to prove two triangles congruent
safe lark
i understand that
but how do i prove that angles MAC is same as DAC, MCA is same as CDA...
we cant just say it is we have to prove it
safe lark
you need at least two angles and a length to prove two triangles congruent
also you said that CAD is beta and later on that CBD must be beta, that would mean that ABC is an isosceles triangle
frigid hatch
do you know the external angle theorem?
safe lark
do you know the external angle theorem?
tell me what it is, idk the names on english
if what u mean is like when a side is continued as a line the internal angle + external equal 180deg
safe lark
oh yes
safe lark
and what then?
frigid hatch
forget the last thing I said
you could probably work this out knowing that two angles subtending the same arc are congruent
MCA and CBA for example
have you done that theorem?
safe lark
nope
safe lark
have you done that theorem?
maybe we have in primary school but not here in hs, and we dont usually need something we didnt go over in hs
frigid hatch
safe lark
yea i know what it is
frigid hatch
lol
safe lark
but idk if i can use the theorem if we didnt learn it
frigid hatch
what have you learnt
safe lark
what have you learnt
i cant list everything we learned xd
safe lark
what have you learnt
this is a chapter with congruency and similarity of triangles if thats what its called in english
frigid hatch
where are you from?
safe lark
croatia
frigid hatch
ok
safe lark
where are you from?
you?
frigid hatch
italy
safe lark
oh nice
frigid hatch
you would still need some other knowledge other than congruency and similarity, especially if you're asked to prove something
but anyway, I'll let you know if I find another way of proving it
safe lark
this is on electronic book, like "compexer tasks" (literal translation), we usually dont have that hard on test but i saw the teacher gave us one of these questions when we were revising for a test so im doing it
safe lark
but anyway, I'll let you know if I find another way of proving it
maybe this can help you
same color - same angle
<@&286206848099549185>
safe lark
i tried extending this to get a rectangle
safe lark
if you didn't do it yet
sure
lone heartBOT
@safe lark Has your question been resolved?
alpine sable
i need to do 2 slides on 2 roman operations
lone heartBOT
i need to do 2 slides on 2 roman operations
alpine sable
like division and fractions or something like that
Something short like this
Thats multiplication i already done that
<@&286206848099549185>
lone heartBOT
@alpine sable Has your question been resolved?
alpine sable
<@&286206848099549185>
ashen sage
The hell they teaching these days
strong wedge
hello
strong wedge
when is u subsitution not required? when should i know if its nessesary to use or not
rigid smelt
Intuition, sometimes it works and doesnt work, and there is not really a time that it is unnecessary
For example in exercise 6, you can either substitute or algebraically manipulate the integrand
tight gulch
You can also just play around with setting u= to parts of the equation and find du (the derivative) and see if anything will cancel out nicely
near hollow
If two functions seem to have no relation and are products for instance 12... then parts is the way
lone heartBOT
@strong wedge Has your question been resolved?
sterile nimbus
Hi, I'm trying to solve this recurrence:
but I'm unsure about how to transform $2^n$ into the proper form of $n^klog_p\left(n\right)$
ocean sealBOT
Dr Xionel
lone heartBOT
@sterile nimbus Has your question been resolved?
frail rivet
hello, if a function f_n is uniformly convergent (which means f is continuous) does it imply that its continuous?
frail rivet
LMAO
stone glen
I don't understand 
stone glen
Refer to Google before here
frail rivet
yea i did
to prove for continuity on [0,2]->R,
I plug in 1/n for n^2*(1/n) = n and 1/n for 2n - n^2*(1/n) = n. is approaching it like this enough or do i need lim?
merry depot
you probably don't need to do a limit, but you should at least mention why you only check those points.
frail rivet
because they are different functions?
merry depot
how do you know there's not a discontinuity somewhere else
dawn birch
you can individually prove continuity on [0, 1/n), (1/n, 2/n), and (2/n, inf) then verify x = 1/n and x = 2/n
to thus prove continuity on [0, inf)
frail rivet
individually prove continuity?
frail rivet
oh with the delta epsilon criteria?
dawn birch
if they’re being really strict yeah
you might just get away with asserting the limit equals the value of the function at the points on the interval so it converges
depending on level of required rigorousness
merry depot
you can probably just note that each of those are polynomials
dawn birch
yes
frail rivet
Oh true
novel night
Is the question simply whether f_n defined above is continuous? Or was the question something about uniform convergence?
frail rivet
to prove for continuity on [0,2]->R,
I plug in 1/n for n^2*(1/n) = n and 1/n for...
but i dont get why lim isnt necessary here
novel night
If a sequence of functions f_n converges uniformly to a function f, and each f_n is continuous, then the limit function f is continuous as well. That doesn't really apply here to showing that f_n itself is continuous.
It's a general fact that if a function is defined piece-wise like f_n above, the function will be continuous if each of the pieces are continuous, and they agree on the overlaps.
slim steppe
can i get some help with this?
slim steppe
<@&286206848099549185>
tacit arch
can i get some help with this?
Are we supposed to know Q6
slim steppe
Are we supposed to know Q6
no, what im confused on is what recursive rule any of those are i can't figure it out
tacit arch
no, what im confused on is what recursive rule any of those are i can't figure i...
Knowing Q6 would probably help
slim steppe
tacit arch
Yup does help
Write your sequence as arithmetic operations of the two previous terms
a_n =f(a_(n-1 ), a_(n-2))
slim steppe
Write your sequence as arithmetic operations of the two previous terms
is this for q6 or q7?
slim steppe
`a_n =f(a_(n-1 ), a_(n-2))`
could you explain this in words, it would be a lot easier to understand
tacit arch
Write your sequence as arithmetic operations of the two previous terms
.
Maybe you should do 6 before 7
slim steppe
Okay
silver drum
slim steppe
.close
vocal fulcrum
lone heartBOT
oak perch
Can you choose one of them and ask it
Whatever I answer 1
- left hand side is log_2(2020)
- that is a linear fractional transformation, or simply solve it by definition, very easy
3)t^2+at+b=0 has exactly one real root t
- is too easy, omit
- seems interesting let me think about it
Use $Z[x]/((x-1)x^{2}) \cong Z[x]/(x-1) \oplus Z[x]/(x^2)$
Find the inverse image of $(2,2x+3)$
ocean sealBOT
Cogwheels of the mind
oak perch
Now since the inverse image of (0,1) and (1,0) are 1-x^2 and x^2 respectively, so answer is (2)x^2+(2x+3)(1-x^2)=-3x^2+2x+3 mod (x-1)x^2
So (-3,2,3)
Can’t do you homework for you, 2,3 left to yourself
lone heartBOT
@vocal fulcrum Has your question been resolved?
vocal fulcrum
Can’t do you homework for you, 2,3 left to yourself
This is for a study in japan scholarship
Filled out the form and there will be a written test
No syllabus is given and only past year papers are avilable online
vocal fulcrum
Open questions?
oak perch
In fact they are too simple
I don’t see anything you can research about those questions
vocal fulcrum
Didn't read let me check them out forst then 
Parametric equations
Some terms I don't understand
And then the probability question
Should be doable
Had read some reviews of maths b being very difficult and in a video a guy went as far as saying you can't prepare for it in 2-3 months
Might have gotten influenced by him
Wtever thnxx
.close
red timber
I will make a presentation to show a visit to the water park with friends or family. Through the work on this, i will show practical use of mathematics. It is important that i include more of the topics in the subject. I will have to make a plan that includes prices, size, room, volume. I decide myself what i want to present at my presentation. A visit to a water park can be very varied from time to time. In the presentation I must also explain how i worked and delimit the topic, what sources i have used and how i have worked with it. Im not really an expert at math and not sure where or how to start, so help would be appreciated. Thank you.
nimble fern
Oh, I like maths project! Do you mind tell us what grade is this project for?
red timber
Oh, I like maths project! Do you mind tell us what grade is this project for?
10th grade
nimble fern
I think you are list out the possible uses of those criteria,
- prices
- size
- room
- volume
What can you think of from these topics?
red timber
regarding room, volume, size, would i search the average size of a waterpark or would i search up a waterpark nearby that i can use as an example?
nimble fern
Of course! That would be a brilliant idea! Also, you can get the price of tickets and meals inside the park
nimble fern
You can also compare size of different pool, depths and volume of water, capacity for each facility
Or even time for queuing
There are so many things to do in this project!
red timber
You can also compare size of different pool, depths and volume of water, capacit...
thanks for the ideas! Could u help me doing so?
nimble fern
thanks for the ideas! Could u help me doing so?
I don't think I have enough time to going through all of them, but you can try draw the blueprints for your imaginary water park, and plan the whole thing.
I always think that drawing out ideas would help a lot!
red timber
I don't think I have enough time to going through all of them, but you can try d...
Alright, thank you!!
oak perch
Parametric equations
Some terms I don't understand
And then the probability q...
1 is solved, 2 you said you can do it yourself, so only 3 right?
3(1), dy/dx=(dy/dθ)/(dx/dθ)
2)y(t)d(x(t))=y(t)x’(t)dt
3)πy(t)^2d(x(t))=πy(t)^2x’(t)dt
Sorry to interrupt
nimble fern
Alright, thank you!!
Something like this
And draw each pool with an extra sheet, and prices with table, etc.
Good luck with your project! @red timber
red timber
Good luck with your project! <@402578021212749826>
thank u so much! I appreciate it lots
lone heartBOT
@red timber Has your question been resolved?
chrome shore
Why is the answer 0?
lone heartBOT
Why is the answer 0?
north adder
Why is the answer 0?
try finidng the derivative of this
chrome shore
The derivative...
north adder
differentiate F(x) = f(x)/g(x)
gray ingot
quotient rule
chrome shore
Then yeah quotient
north adder
sure product or quotietn
if your question has been answered please close the channel
lone heartBOT
lone heartBOT
Available help channel!
tough orbit
Can any1 explain how to do 6b? I did a and got the answer as 13.5 cm2
median oar
so that's the cross section right?
tough orbit
so that's the cross section right?
Ye
oak perch
30 times what you got for a)
tough orbit
so if it were 30cm long
Pi r square h
median oar
how do you find the volume of a prism
tough orbit
how do you find the volume of a prism
Prism?
median oar
ok prism isn't the right word
tough orbit
30 times what you got for a)
But could you explain why?
median oar
Well
u can integrate a straight line from 0 to 30
but like i doubt that's what you're looking for
rustic stirrup
length will be height in the case and plug in the forumla ( pi times r^2 times height) , where height is 30 and radius is 7
tough orbit
from part a
Is it given? No
median oar
that's what u calculated right?
tough orbit
But I think I’ll be able to calculate it
median oar
the area of the shaded region
tough orbit
that's what u calculated right?
Oh yh sorry idk why I assumed you said volume
Yes ik the area
median oar
so the volume should be that * the length of the pipe
which u could prove via integration i suppose
tough orbit
so the volume should be that * the length of the pipe
Ohh ok thanks
median oar
but even with a triangular prism
the volume is the area of the cross section * height
a cube is also the cross section * height
tough orbit
Yh
median oar
a cylinder would be also πr^2 * h
rustic stirrup
A cylinder of volume V has height (5 * pi)/2, and radius r. f(x) = [2 * sin(2 * x - 4 * pi) + 184]^(1/2). This function makes a solid when revolved around the x axis. The volume of this function is the same as V in the domain pi/2 to (3 * pi)/6. Find the radius of the cylinder.
lone heartBOT
A cylinder of volume V has height (5 * pi)/2, and radius r. f(x) = [2 * sin(2 * ...
@rustic stirrup Has your question been resolved?
lone heartBOT
@rustic stirrup Has your question been resolved?
nimble fern
Hello, do you still need help with your question?@rustic stirrup
tough orbit
Hello, do you still need help with your question?<@759482147018113104>
I assume he does cuz he said his question hasn’t been resolved but I’m not sure he migh5ve solved it alr
lone heartBOT
@rustic stirrup Has your question been resolved?
abstract oriole
hi
nimble fern
A cylinder of volume V has height (5 * pi)/2, and radius r. f(x) = [2 * sin(2 * ...
Do you know what to do with f(x)? It says revolve around x-axis
Hint: integration
rustic stirrup
Do you know what to do with f(x)? It says revolve around x-axis
yup ! I know how to solve , but the volume is coming out to be 0 , and if that is the case the radius is 0 too , which is not possible
Maybe I am applying the limits of integration wrong
nimble fern
Can you show your work, maybe we can go through it and see if there is any mistake
stone glen
A cylinder of volume V has height (5 * pi)/2, and radius r. f(x) = [2 * sin(2 * ...
$\sqrt{2sin(2x)+184}$
ocean sealBOT
Lelouch
stone glen
,w integrate sqrt(2sin(2x)+184)
ocean sealBOT
stone glen
A cylinder of volume V has height (5 * pi)/2, and radius r. f(x) = [2 * sin(2 * ...
It's essentially says from $\frac{\pi}{2}$ to $\frac{\pi}{2}$
ocean sealBOT
Lelouch
stone glen
Recheck the question
lone heartBOT
stone glen
Lmao w?
lone heartBOT
Available help channel!
sage locust
lone heartBOT
sage locust
any hints?
stone glen
Yeah
Newton's method
This is clearly a JEE main question
They are tryna trap you, from the $p_{n+2}$ thing, make sure you have that right
@sage locust
sage locust
This is clearly a JEE main question
aye i am in 10th now
preparing for ioqm
wait two is not in subscript?
vale wigeon
$p_{n+2}$
ocean sealBOT
Ann
vale wigeon
this is how you latex it
ocean sealBOT
Lelouch
stone glen
Do you know the Newton's method?
sage locust
Do you know the Newton's method?
no
stone glen
Well then...
sage locust
what is that about
stone glen
Its about quadratics
It would take me ages to explain it here
So i assume u speak Hindi?
sage locust
So i assume u speak Hindi?
haa
stone glen
Ok
So just google 'Unacademy Atoms Quadratic Equations One shot' on YouTube , and there will be a lecture from Nishant Vora ( The Mozart of Math Teachers)
It's a lecture on quadratic equations
Just skip to the Newton's method section if you only want to learn that, but i suggest u watch the whole thing tbh
stone glen
Yeah correct
sage locust
Just skip to the Newton's method section if you only want to learn that, but i s...
ya i dont want to learn half the thing and get confused
tysm
stone glen
I suggest watch all the One Shots of this #BounceBack series, it's all Free , and this guy ( Nishant Vora ) is arguably the best math teacher for high school math
@sage locust
sage locust
I suggest watch all the One Shots of this #BounceBack series, it's all Free , an...
he has a playlist?
stone glen
Google #BounceBack