i dont understand the problem
#help-39
midnight haven
spring crystal
Oh wait I think I got it
sharp vigil
let's say that f(x) =1/(1-x) and g(x) = 1/(1-x)^2.
Then g(x) is the derivative of f(x)
Therefore, the power series of g(x) is the derivative of the power series of f(x)
spring crystal
let's say that f(x) =1/(1-x) and g(x) = 1/(1-x)^2.
Then g(x) is the derivative o...
So if the derivative of 1/(1-r) is equal to the oriignal function then it means the derivative of of 1/(1-r) is the power series representation of the original function? Is that what it’s supposed to mean
sharp vigil
the derivative of the power series or 1/(1-r) is equal to the power series of the original function
spring crystal
the derivative of the power series or 1/(1-r) is equal to the power series of th...
Is that same for integration
sharp vigil
yes
spring crystal
Integration of 1/(1-r) is equal to power series of original function
sharp vigil
the integral of 1/(1-r) is -ln(1-r). so the power series of -ln(1-r) the integral of the power series of 1/(1-r)
spring crystal
How am I suppose to know when to use derivative or integration
Or all integration always have ln
sharp vigil
that's just the integral of that particular power series
sharp vigil
How am I suppose to know when to use derivative or integration
if the function you are considering looks like the derivative or integral of a function with a known power series
pearl pondBOT
@spring crystal Has your question been resolved?
severe wadi
I have more of a conceptual question regarding series in calc 2
severe wadi
im trying to learn my lectures but I'm not quite sure I understand this lesson. So I know that a series is a summation of different values of the main term and I learned all the theorums and tests to tell weather it diverges or congerves
but know I'm the p-series lesson where my professor is talking about "radius of convergence" of a series
does anyone know how that is different that the interval of convergence?
versed mica
are you referring to power series
severe wadi
yeah
versed mica
an interval is not a radius
the interval of convergence is an interval containing values of x for which the series converges
leaden wadi
versed mica
the interval contains all points within the radius but it doesn’t necessarily contain the endpoints
consider a standard geometric series
leaden wadi
Always check the endpoints for convergence.
versed mica
$\sum_{n=1}^{\infty} x^n$
jolly parrotBOT
knief
severe wadi
does that mean that the series function is the function of a circle? like I dont get how it has a radius
versed mica
function of a circle?
severe wadi
like is the series the same as x^2+y^2 = 1?
versed mica
think of it like a number line, the power series is centered at some value x = c, and the radius of convergence tells us how far to the left and right we can go which guarantees convergence of the series
versed mica
like is the series the same as x^2+y^2 = 1?
i know what a circle is but no series are not circles, they’re sums
severe wadi
think of it like a number line, the power series is centered at some value x = c...
ok wait I think I get it but also, what does it mean for a power series to be centered at some values x=c, because my professor was saying that too but I didnt get it
like is that where it most converges? but also what does that even mean?
versed mica
ok wait I think I get it but also, what does it mean for a power series to be ce...
when the sequence inside the sum is zero
severe wadi
ohhhhhhhhh
versed mica
$\sum_{n = 1}^{\infty} (x-c)^n$
jolly parrotBOT
knief
versed mica
at x = c it’s all zeros
versed mica
like is that where it most converges? but also what does that even mean?
there’s no such thing as most converges, it does or it doesn’t
severe wadi
think of it like a number line, the power series is centered at some value x = c...
ok wait sorry, one more question. does the interval of convergence also tells us how far left and right we could go before we hit divergence?
severe wadi
there’s no such thing as most converges, it does or it doesn’t
got it
versed mica
yea it’s just a set tbh
as are all intervals
think of it as the set of x values for which the series converges
versed mica
**knief**
here for instance it would be (-1,1) note that the endpoints aren’t include despite the radius of convergence being 1
and the center being 0
c - R < x < c + R is always going to be convergent
versed mica
and we check the boundary or endpoints to see if we include those
versed mica
ok wait so the radius of convergence would be (-1,1)?
no radius is just a number like a length
interval is a set or collection of numbers
severe wadi
ok so (-1,1) is the interval of convergence?
severe wadi
ok thanks, so what would be the radius? if the center is at 0?
versed mica
ok thanks, so what would be the radius? if the center is at 0?
well the center is at 0
do you mean not at 0?
versed mica
ok thanks, so what would be the radius? if the center is at 0?
the radius in the example is 1
severe wadi
ohhhh ok
versed mica
c - R < x < c + R is always going to be convergent
^
0-1 < x < 0+1
center is 0
radius is 1
severe wadi
ok got ittt
versed mica
are you familiar with how to find the radius of convergence
severe wadi
um no, I didn't get to that part yet, I was just trying to understant how a series has a radius
severe wadi
ohhhh ok thank you so much! this rlly helped me undertand
versed mica
you’re welcome
severe wadi
.close
pearl pondBOT
pearl pondBOT
fathom mauve
yw
barren pivot
is there someone who knows how to do this question
feral sedge
how far does the ball roll before it hits the wall
barren pivot
270cm?
feral sedge
correct
barren pivot
how does that help with the question??
feral sedge
so the wheel will essentially turn a distance of 270cm
so you have to figure out where P is after you move it 270cm around the circle
barren pivot
120?
limber talon
If you could lay out the circle in a straight line, how long would it be?
first, what is the name of the part of a circle that I'm referring to?
Imagine you have a square that is 4cm on each side, that means the total distance that the square would traverse would be 4 + 4 + 4 + 4= 16.
barren pivot
first, what is the name of the part of a circle that I'm referring to?
i’m not too sure
the circumference??
limber talon
correct
now, try to see how you can use to concept of the circumference to help with figuring out how much length the point P traverses
barren pivot
wait i’m confused how will i know the height of P by this?
limber talon
wait i’m confused how will i know the height of P by this?
First, figure out the question above, and see if it helps
Once you've done that, post your working out here
pearl pondBOT
@barren pivot Has your question been resolved?
tepid current
pearl pondBOT
pearl pondBOT
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Available help channel!
lament parrot
How do i find a new solution using a old solution by using linear combination in the equation x^2 - 8y^2 = 1
By this i mean, if a old solution is (u,v), then the new solution is of the form (au + bv, xu + yv)
lament parrot
I kept trying values but there is probably a way without having to try it
Or a efficient way to try
I tried finding 2 solutions, say (a, b); (x, y)
And then tried writting x as ak + bj and same for y but there are so many options and most dont work
cursive wraith
that's how you find more solutions to pell's equation
n = 8 here
since x^2 - ny^2 = 1
cursive wraith
But can u give me a tip to find it by myself
not sure there's really a way to find this method yourself
cursive wraith
it was studied extensively by mathematicians
lament parrot
Yeah i can imagine
cursive wraith
even for n = 8 it's hard to find it yourself
cursive wraith
ik
pearl pondBOT
versed mica
<@&268886789983436800>
brazen lynx
help
pearl pondBOT
No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/
@brazen lynx Has your question been resolved?
dapper spear
Solve. 5) Jeff bought beads. 3/4of the beads are glass. - 1/6of the glass beads are pink, and the rest are green. Jeff packs the green glass beads equally into 10 jars. What fraction of the beads that Jeff bought is
in each jar?
@brazen lynx put ur question in chat
brazen lynx
oki
sorry
Solve. 5) Jeff bought beads. 3/4of the beads are glass. - 1/6of the glass beads are pink, and the rest are green. Jeff packs the green glass beads equally into 10 jars. What fraction of the beads that Jeff bought is
in each jar?
safe lance
Solve. 5) Jeff bought beads. 3/4of the beads are glass. - 1/6of the glass beads ...
just make a flow chart
brazen lynx
what have you tried/what r u stuck on?
i dont even know where to start
in sp confused
brazen lynx
just make a flow chart
whats thay
dapper spear
i dont even know where to start
well
start by making all fractions given have a common base
dapper spear
denominator!
yes
brazen lynx
oh okay
dapper spear
common denominator mb
dapper spear
so now we have 18/24 red, 4/24 pink right?
brazen lynx
oh i had somthing different i think
dapper spear
what did u have
brazen lynx
the denominator was 18
bc that was the lowest
for each
bcc that was the lowest common denominator
dapper spear
bcc that was the lowest common denominator
it's not though
brazen lynx
oh okay
dapper spear
3/4 = 13.5/18
brazen lynx
oh my bad
dapper spear
four doesn't go into 18 evenly
dapper spear
don't apologize it's ok 😭
brazen lynx
❤️❤️😭
dapper spear
Solve. 5) Jeff bought beads. 3/4of the beads are glass. - 1/6of the glass beads are pink, and the rest are green. Jeff packs the green glass beads equally into 10 jars. What fraction of the beads that Jeff bought is
in each jar?
so do u know how to find common denominator?
brazen lynx
yes
dapper spear
r u sure
brazen lynx
yes i was just confused mb
dapper spear
ok it's ok if you don't btw I would teach you
anyway
what r the fractions in common denominator?
brazen lynx
what r the fractions in common denominator?
wdym
brazen lynx
oh ues
dapper spear
what should we make them so that we can mess with them?
brazen lynx
yes
brazen lynx
right
dapper spear
so if the "rest" are green
and we know what 18/24 and 4/24 of them are
what must the last few be?
brazen lynx
2?
dapper spear
/24 yeah
dapper spear
no
brazen lynx
or we sinplify?
dapper spear
that's how many green beeds were originally there
brazen lynx
oh
dapper spear
but then it says the guy took those and split them into ten jars right?
we want how much is in one jar
if we take a number and split it in ten what math operation are we doing?
brazen lynx
division
brazen lynx
oh oki
dapper spear
dividing by ten is the same as multiplying by 1/10 right?
brazen lynx
oh yes
brazen lynx
ooo yess
dapper spear
1/12 times 1/10 is?
dapper spear
there u go
brazen lynx
that would be the answer?
dapper spear
it should be if I didn't missread something
brazen lynx
ill check the answer sheet brb
dapper spear
alr
dapper spear
it says this is the answer
dude what
brazen lynx
i know right
dapper spear
oh I'm dumb
brazen lynx
oh no ur not
brazen lynx
yes
dapper spear
i wonder hiw math in my furure will be if im strufgling
lmao
brazen lynx
do u thin u can help me again
dapper spear
i wonder that all the time been struggling a crap ton in my class so far
yeah lemme think
Solve. 5) Jeff bought beads. 3/4of the beads are glass. - 1/6of the glass beads are pink, and the rest are green. Jeff packs the green glass beads equally into 10 jars. What fraction of the beads that Jeff bought is
in each jar?
ok so
3/4 of the beads are glass
1/6 are pink
the rest of the glass beads are green?
is that what it's trying to say?
dapper spear
i think so
brazen lynx
yea
dapper spear
because it says... "green glass beads" later on
brazen lynx
oh then yes
brazen lynx
hmm
dapper spear
cuz you take the quantity and divide by six
brazen lynx
no 4:24
dapper spear
if the rest are green
thennnn
15/24 of the glass beads are green?
15/(24*10) = ....
3/(2*24)
3/48
brazen lynx
wow
dapper spear
alright lemme walk you through it now that I didn't missread "glass" as red smh
sorry for wasting the time the first time
anyway
brazen lynx
oh dw
brazen lynx
yes
dapper spear
and we're saying 1/6 of this 3/4 is pink glass right?
brazen lynx
yes
dapper spear
so we need to figure out what is 1/6 of 3/4
brazen lynx
oh i know how to do that
dapper spear
yeah it's multiplying the quantity we have (3/4) by the fraction that we want of it
essentially, it's just taking 3/4 and dividing by six (six of whatever you get added up will give you 3/4)
dapper spear
oh i know how to do that
alr show me
brazen lynx
so 1/6x4=4/24
dapper spear
no
brazen lynx
ou
brazen lynx
yes
brazen lynx
oh
brazen lynx
yes
dapper spear
we're trying to find 1/6 of three fourths
3/4 are glass
1/6 of those are pink glass
brazen lynx
yea
dapper spear
if 6 things are glass
and 1/6 of those are pink glass
we know that 1 is pink glass
in other words we take the 6 and divide by six
brazen lynx
alright
dapper spear
same thing here just with fractions
brazen lynx
oh so 18/24 divide by six?
brazen lynx
let me try that
brazen lynx
that goes back to 3/4
dapper spear
3/4 times 1/6
brazen lynx
oh i multiply?
dapper spear
that goes back to 3/4
18/24 divided by six is 3/24
brazen lynx
18/24 divided by six is 3/24
oh
dapper spear
you have 18, break it up into groups of six to get three
brazen lynx
i thought the denominator changes to mb
dapper spear
oh i multiply?
4/6 = 4 * (1/6)
brazen lynx
4/6 = 4 * (1/6)
oh yea
dapper spear
ur just multiplying them
brazen lynx
what do we do after we get 3/24
dapper spear
3/4 times 1/6 basically
ok
so we know that the rest of the glass beads are green right?
brazen lynx
yea
dapper spear
so if we have 18/24 beeds that are glass
(which is just 3/4 with a different denominator)
brazen lynx
yeso
dapper spear
and we know that 3/24 beads are pink
the rest are green
now it's substraction
so how many r green?
brazen lynx
oh yes
dapper spear
anyway 15/24 glass beads right
brazen lynx
yes
dapper spear
green glass beads*
brazen lynx
yea
brazen lynx
yes
dapper spear
15/24 times 1/10 isssssssssss
brazen lynx
uhhmm
dapper spear
haha nw
brazen lynx
oh so 15x1
dapper spear
over?
brazen lynx
24x10
dapper spear
yeah
brazen lynx
im so dumb sorry
dapper spear
what I originally did is multiply them all out then note all the factors, then see which factors cancel
then realize I didn't simplify as much as I should've b/c 15/24 is 5/8
one method of simplification is what I did above, where I (tried to) factor everything out as much as possible then cancel out what appears in both the numerator and denominator
the other method is to divide the numerator and denominator both by a common factor
that's what I did with the 3/48 when I realize I didn't do all the factors
3/3 = 1
48/3 = 16
brazen lynx
then 15 by 15
dapper spear
you can also do it in increments
like you know for a fact 240 is divisible by 5 right?
so do 15/5
= 3
brazen lynx
yes
brazen lynx
yes
dapper spear
then you see 3/48 and divide by 3 again
brazen lynx
is there any way i can save these chats
brazen lynx
o
brazen lynx
you can save a chat link tho
how can i do that
dapper spear
lemme show you
brazen lynx
oki
dapper spear
ill try to do this question on my own tysm btw
nw I dm'd you the link as well
good luck
brazen lynx
nw I dm'd you the link as well
thanks so much
brazen lynx
remember it's 15/24 times 1/10 right
aorry to bug u why did we multiply by 1/10 again
dapper spear
aorry to bug u why did we multiply by 1/10 again
the ten jars
you're taking the fraction of green glass beads
and dividing it amongst ten jars
b/c we're solving for green glass beads per jar
rose sentinel
71 determine if it converges and if it does what does it converge to as n approaches infinity
rose sentinel
Naturally I see 0^0 and I mean I don’t remember if we call that undetermined or not but I’d say 1, the answer is e^-1 and I don’t see how
summer imp
$0^0 = 0$ or $0^0 = 1$ is a debate in itself.
However, in this case, when you have $f(n)^{g(n)}$ where both $f$ and $g$ tend to 0, you can't just take the limit of the inside and the limit of the exponent and call it a day. It's inderterminate
jolly parrotBOT
Azyrashacorki
rose sentinel
$0^0 = 0$ or $0^0 = 1$ is a debate in itself.
However, in this case, when you ha...
So then how do they conclude e^-1
?
summer imp
You could take log, then find the limit of log_(a_n) and then get a_n back
rose sentinel
I don’t see it still not sure how to carry that out
summer imp
Consider $\ln(a_n)$, compute the limit of that, say $L$, and then by continuity $$\lim_{n\to\infty} a_n = e^{\lim_{n\to\infty \ln(a_n)}} = e^L$$
jolly parrotBOT
Azyrashacorki
rose sentinel
Hmm okay
summer imp
Another way I think is to rewrite $\frac{1}{n} = e^{-\ln(n)}$
jolly parrotBOT
Azyrashacorki
pearl pondBOT
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Available help channel!
rose sentinel
Couldn’t figure out any of these could someone help?
pearl pondBOT
Couldn’t figure out any of these could someone help?
rose sentinel
Converge or not, if it does what to
pearl pondBOT
@rose sentinel Has your question been resolved?
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Available help channel!
quaint elm
Hey i know this is a dumb question me and my friend have different views, if you randomly sneeze 5 times everyday could you be able to find the average for that day or can you not because its random.
vestal tapir
the average what
quaint elm
time
foggy mason
like, the time you are more often to sneeze ?
quaint elm
like, the time you are more often to sneeze ?
yea
foggy mason
well sure it must be possible
but i dont think you need maths to know that 
And you need to sneeze like that for a lot of days
vestal tapir
like, the time you are more often to sneeze ?
what
vestal tapir
i just don't know what you meant
quaint elm
If i sneeze 5 times a day, at a random given time in the day. Could I possible find the average of the random sneezes before they happen? Or not because it’s going to be random
i wrote it dumb
foggy mason
i just don't know what you meant
the time he is likely to sneeze a lot
vestal tapir
If i sneeze 5 times a day, at a random given time in the day. Could I possible f...
that's more or les waht you wrote first time
it still doesn't make sense, average sneeze?
sly narwhal
Hi I’m his friend
acoustic sky
If i sneeze 5 times a day, at a random given time in the day. Could I possible f...
I feel like it's relatively random because I don't think much of us sneezes consistently throughout the day to definitively calculate per how many minutes or hours we will sneeze
sly narwhal
He’s basically asking , if he is aware he is going to sneeze 5 times in a day , at a random time. Could he find the average for the sneezes
😂😂
quaint elm
couldnt you use or not
sly narwhal
Before they happen
vestal tapir
you are trying to predict something about when the sneeze is going to happen
you;re going to fail
sly narwhal
Thank you
vestal tapir
it's random
sly narwhal
Thank you
quaint elm
crow is right
thanks
quaint elm
Bro what u agreed with me
noooo
vestal tapir
well the one who says you can't
quaint elm
Thank you
sly narwhal
Thank u goat
vestal tapir
you can make easy predictions for example "all 5 sneezes will happen between 1 AM and 11PM"
it will be right more often than not
very precise predictions will be wrong more often
pearl pondBOT
@quaint elm Has your question been resolved?
ionic loom
yall know how to do physics?
pearl pondBOT
yall know how to do physics?
pearl pondBOT
@ionic loom Has your question been resolved?
pearl pondBOT
@ionic loom Has your question been resolved?
cosmic saffron
assume I have a number like
1234.567
what is the 1234 part called as?
cosmic saffron
like the part of fraction that is on the left side of the .
sharp vigil
the integer part
cosmic saffron
ah... thx
pearl pondBOT
@cosmic saffron Has your question been resolved?
short orchid
Guys im back with different question. How to continue 6b? 😇
pearl pondBOT
Guys im back with different question. How to continue 6b? 😇
short orchid
i've been thinking about this question for one day now
pearl pondBOT
@short orchid Has your question been resolved?
blissful salmon
Guys im back with different question. How to continue 6b? 😇
wait, first actually picking the three children is fixed. then you have 6 people remaining and have to pick 2 out of the 6 people. how many ways are there of choosing the 2 people?
short orchid
wait, first actually picking the three children is fixed. then you have 6 people...
6P2?
torn lake
Yes
Cuz the first 3 calcs u did were for the chances of getting the bakers so the rest is basically just asking how many different combos u can have after getting all bakers kids
short orchid
Cuz the first 3 calcs u did were for the chances of getting the bakers so the re...
oooh
but the first three are already in form of probability right
torn lake
Yes
short orchid
meanwhile 6P2 are not yet in form of probability
blissful salmon
Cuz the first 3 calcs u did were for the chances of getting the bakers so the re...
yeah which should be 6P2
blissful salmon
Guys im back with different question. How to continue 6b? 😇
the idea is that it would be * 2/6 * 1/5 after your calculation (in probability form)
short orchid
the idea is that it would be * 2/6 * 1/5 after your calculation (in probability ...
ohhhh okok i'll try
thank you so much cindy and adin
blissful salmon
ohhhh okok i'll try
wait a min, wouldnt it be combinations though, not permutations?
blissful salmon
Huh???
because we are asking to select from a group of people, wouldnt it be (6C2)/(9C5) ?
blissful salmon
No replacements mean combos right
combinations mean all permutations of the same string are considered as one
like AB and BA are considered as 1 altogether
blissful salmon
Guys im back with different question. How to continue 6b? 😇
because we are selecting a group of people it is meant to be combinations. so picking person A and then person B is the same as picking person B and then person A.
short orchid
because we are selecting a group of people it is meant to be combinations. so pi...
yes!
blissful salmon
yes!
so then after the three children are selected, we have 6C2 ways of picking the two other people. and the total number of ways of picking 5 people out of 9 is 9C5, therefore the probability is just (6C2)/(9C5)
blissful salmon
so then after the three children are selected, we have 6C2 ways of picking the t...
ignore what i previously said, this should be it
short orchid
so then after the three children are selected, we have 6C2 ways of picking the t...
OHH this makes sense
okay okay thankuuu smmm
blissful salmon
okay okay thankuuu smmm
no prob, sorry for the confusion!!
short orchid
.close
pearl pondBOT
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Available help channel!
urban sun
pearl pondBOT
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 was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
nimble osprey
just counts the number of blue lines with respect to n ...and do the same thing for red lines... then solve the euquation in n that you get
pearl pondBOT
@urban sun Has your question been resolved?
urban sun
just counts the number of blue lines with respect to n ...and do the same thing ...
nc2 - n?
sry for late reply I was the in bus
blissful salmon
nc2 - n?
yes, this is the number of red segments
now how about the number of blue segments?
now you just equate them together and solve for n
pearl pondBOT
@urban sun Has your question been resolved?
urban sun
now how about the number of blue segments?
wont it be same
blissful salmon
wont it be same
no, it wont. the number of blue segments is n
urban sun
then how did you get this?
by formula
number of diagonals - side
bcz sides arent diagonals
blissful salmon
number of diagonals - side
yes the side ones happen to be the number of blue segments
urban sun
ohh
urban sun
n!/n-2! 2! = 2n
how to solve this
quickly
thanks @blissful salmon for helping
Have a great day
.close
magic olive
pearl pondBOT
magic olive
Stuck on part c😔
pearl pondBOT
@magic olive Has your question been resolved?
magic olive
.close
wispy meadow
can someone help me with this? idk where to start
pearl pondBOT
can someone help me with this? idk where to start
broken fossil
I don't really get it but it looks like you plug in -3x for the X's then square what you get
feral leaf
can someone help me with this? idk where to start
Do you know what f(-3x) means?
wispy meadow
Do you know what f(-3x) means?
yes
feral leaf
What does it mean?
wispy meadow
function of -3x
pseudo oxide
function at -3x
feral leaf
Do you know what to do with the -3x?
wispy meadow
I sub it in f(x)?
there's another bracket outside it and squared which is confusing me
feral leaf
I sub it in f(x)?
What do you mean by this?
wispy meadow
like I rewrite it as f(-3x) = 2(-3x)^2 + 2(-3x)
pseudo oxide
simplify and square it
wispy meadow
Now simplify that
f(-3x) = 18x^2 -6x
pseudo oxide
square that
feral leaf
Now you square it
pseudo oxide
and you're done
wispy meadow
is it 324x^4 - 36x?
wispy meadow
324x^4-108x^3-108x^3+36x^2
=324^4 - 216x^3 + 36x^2
feral leaf
Yes
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vestal pelican
got the answer which was
(0.2)(0.8)^x-1 but why, isnt the formula P(X=x) = (q^x-1)*p where q is the probability of an event failing, how is 0.8 failing?
vestal tapir
that formula is when you fail until you suceed
in this problem it's reversed
you succeed multiple times and fail once
vestal pelican
so whats the formula for that then
vestal tapir
jsut swap q and p
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neon jolt
hello
neon jolt
I got this reduction of order question
and in my teacher''s solution marked in yellow I divided the whole equatio by x^3 and I got different results
is what I did valid in this type of questions ?
pearl pondBOT
@neon jolt Has your question been resolved?
neon jolt
<@&286206848099549185>
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midnight haven
Hello, is it right? I always get lost when it comes to roots
midnight haven
Hello, is it right? I always get lost when it comes to roots
try doing this step again
Did I do deletion wrong? Is it gonna be like
√3*1
2*√3?
oh sorry will write it normally xD
midnight haven
try doing this step again
is this the correct way of thinking?
midnight haven
try doing this step again
1/(1/a) = a
midnight haven
is this the correct way of thinking?
i dont understand what you are doing here
thats fair neither do I
sorry for late response I spilled whole cup of water over my desk
midnight haven
1/(1/a) = a
sorry, still can't really understand it :( could you explain? Does a equal 2 since there's root 3 two times?
and they cancel out?
its just a silly mistake
i think writing out the correct answer will help you figure out where you went wrong
midnight haven
try doing this step again
it should become 3/2 and not 2/3
midnight haven
its just a silly mistake
i think writing out the correct answer will help you fi...
I would be thankful, I need to repeat working on both roots and fractions but don't really have time till tommorow
midnight haven
it should become 3/2 and not 2/3
huh ok gimme a minute to think about it
Yup, still nothing xD we need to switch places of numerator and numeral? Also I noticed I lost minuses on the way but let's not worry about that
oh root 3 and root 3 they become just 3?
midnight haven
Simplifying means to delete two numbers that are the same, right?
feral leaf
Close, remember your signs
midnight haven
the result becomes on plus since there are two minuses? Do two minuses become a plus in division as well?
oih wait
it becomes multiplauying
makes sense now minus multiplied by minus
so it's 3/2 ?
feral leaf
Yes
midnight haven
OMG I get it now!!! Thank You very much for clarifying :)
I forgot the basics hahah
.close
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bitter wolf
Question: Given that the length of the segment BC is equal to the sum of the lengths of the segments AC and AD (picture 1) find the value of α
The second picture shows what I have come up with so far. I think the fact that the triangle BCE is isosceles might lead somewhere, but I don't see how.
pearl pondBOT
Question: *Given that the length of the segment BC is equal to the sum of the le...
@bitter wolf Has your question been resolved?
bitter wolf
<@&286206848099549185>
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@bitter wolf Has your question been resolved?
acoustic path
Question: *Given that the length of the segment BC is equal to the sum of the le...
you have already found it
EDA = BDC = 110, so CED = alpha = 40
sick shadow
Assume that we want to crate a box with a square base. We have a 10m² of material to contrust the box. Assuming that we use all of the material, find the dimensions of the box (in meters) that will give the maximum volume.
I want to stress, this is not an open box problem (Google kept only giving me open-box links)
sick shadow
I found this link
https://brainly.com/question/54634022
I got pretty close to this but I am struggling to understand why the surface area is that
Website says:
$SA = x^2 +4xh$
jolly parrotBOT
Xbye
summer imp
That one is open
summer imp
The answer looks like peak AI
sick shadow
I understand how x^2 = the base, but idk where we're getting hte 4xh.
sick shadow
Yeah, from the formula I literally could not make heads or tails of where they got the dimensions
summer imp
The box is a square base prism
jolly parrotBOT
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summer imp
Indeed
sick shadow
$2x^2 + 4xh = SA$
jolly parrotBOT
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jolly parrotBOT
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sick shadow
and our volume I guess is... let me see the volume formulas
Wait, isn't SA the same as volume?
summer imp
No
summer imp
The volume of a prism is area of base * height
sick shadow
Yes
summer imp
You found the area of a base and you know the height
jolly parrotBOT
Xbye
sick shadow
Wait what
sick shadow
I'm not going to assume it's a cube
summer imp
**Xbye**
Issue is that it has two variables, but your equation here allows you to solve for say h and make the volume into a formula of just x
sick shadow
Yes
I can use the SA equation to solve for h
and then plug that into volume formula right?
summer imp
Yep
That's like how every problem of this type goes.
Use the constraint to find an equation, then make the function you want to maximize/minimize into a function of a single variable so you can maximize/minimize it with Calc methods.
sick shadow
$2x^2 + 4xh = 10
4xh = 10 - 2x^2
h = \tfrac{10-2x^2}{4x}$
jolly parrotBOT
Xbye
summer imp
Yeah it's good
sick shadow
$h = \tfrac{10-2x^2}{4x}$
jolly parrotBOT
Xbye
jolly parrotBOT
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jolly parrotBOT
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sick shadow
Can't I simplify this by removing an x from the numerator and denominator?
or should I just leave it in
because I have to find the derivative
True, can't be 0 for length
$\tfrac{10x - 2x^3}{4}$
jolly parrotBOT
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jolly parrotBOT
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sick shadow
but I think I can simplify
Factor 8 out of the equation after distributing
Could have factored out the 4 earlier though
$V' = \tfrac{5-3x^2}{2}$
jolly parrotBOT
Xbye
sick shadow
Now I think I need to find where the numerator equals 0
Idk how to make the plus/minus symbol:
$x = +-\sqrt{\tfrac{5}{3}}$
jolly parrotBOT
Xbye
sick shadow
but we're dealing with length, so ignore the negative
Okay now I forgot what to do with this x.
Do I plug it into the SA formula now to solve for h? The volume formula has V X H and I only solved for V but SA I know is 10, and we solved for x just now and only have h left
Alright well I plugged it back into the surface area formula
$h = \tfrac{10-2(\sqrt{\tfrac{5}{2}})^2}{4*\sqrt{\tfrac{5}{2}}}$
jolly parrotBOT
Xbye
sick shadow
$h = \tfrac{\sqrt{15}}{3}$
jolly parrotBOT
Xbye
sick shadow
So plugging back into volume formula:
$V = x^2 * h$
jolly parrotBOT
Xbye
sick shadow
$V = (\sqrt{\tfrac{5}{3}})^2 \cdot \tfrac{\sqrt{15}}{3}$
jolly parrotBOT
Xbye
sick shadow
So the answer is...?
$ANSWER:
\tfrac{5\sqrt{15}}{9}$
Xbye
sick shadow
Can someone help me confirm?
pearl pondBOT
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supple hinge
would someone be able to help me out please
pearl pondBOT
would someone be able to help me out please
supple hinge
i have no idea how to go about this i would really appreciate any help thanks
tacit pond
So basically the maximum you can determine it as it has given you root
tacit pond
I think yes, but there’s some repeated roots though
supple hinge
ah so i have to take the points from the first statement so x = -4 x = 1 x = 2
haughty timber
determine which intervals the first equation is greater than 0
supple hinge
this is what im getting so far x < -4, -4 < x < 1, 1 < x < 2
haughty timber
-4<x<1 is wrong and you are missing 1 interval
supple hinge
is it x > 2?
supple hinge
i have to solve the second equation next right?
haughty timber
yeah
supple hinge
so x = -1 x = -2 x = 1
haughty timber
those are the roots which intervals is it >= 0
supple hinge
x < -2, -2 < x < -1, -1 < x < 1, and x >1
haughty timber
its >= 0 so the roots are included
haughty timber
well your intervals arent correct yet
supple hinge
ah
haughty timber
you determined at x = -1 and x = -2 and x = 1 it is equal to 0
so those values should be included as well because thats >= 0
supple hinge
ah so all those x values are bigger than or equal to zero right
haughty timber
im saying that it should be x <= -2 ... etc because -2 is part of the solution as well
right now you have x < -2 but not x = -2 which is also a solution
supple hinge
ohhh ok
haughty timber
tell me when you got the solution for the second equation
supple hinge
what i can think of so far is (-infinity, -1] [1, infinity)
haughty timber
thats right
supple hinge
wait that right?
haughty timber
now you find the intersection of this solution with the solutions to the first equation
supple hinge
ive forgotten how to find the intersections between the two
haughty timber
for example if A = [3, 8] and B = [5, 12] the intersection of A and B is [5,8]
its the interval that is included in both A and B
supple hinge
ohhhhhh i remeber thank you
(−∞,−4)∪(1,2)∪(2,∞)
applying that logic from earlier
thats what i got
haughty timber
there thats the solution
supple hinge
ohhhh thank you so much
haughty timber
youre welcome
supple hinge
.close
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midnight bloom
Anyone even understand how they would get 1/2C here?
pearl pondBOT
Anyone even understand how they would get 1/2C here?
sharp vigil
completing the square
pearl pondBOT
@midnight bloom Has your question been resolved?
eager dove
I really feel like I should know how to get the reference angle of a negative angle
dusty flame
-239 + 360 = 121
eager dove
-239 + 360 = 121
Ohh
and then we get the reference angle of the positive?
I was just adding 360 and not doing the last step
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short orchid
guys, for b, the mark scheme says it is 0<f(x)<1 ?
how do we know when to put the 1?
rough forge
guys, for b, the mark scheme says it is 0<f(x)<1 ?
how do we know when to put th...
Well f(x) = 1 - 8/(x^2+4) will never be 1 because 8/(x^2+4) will always be positive varying between 0 and 1 leaving a difference that is always between 0 and 1 but never 0 or 1
short orchid
Well f(x) = 1 - 8/(x^2+4) will never be 1 because 8/(x^2+4) will always be posit...
how do you know that it will always be 1
rough forge
it won't
in order for f(x) = 1 you would need to get 8/(x^2+4) = 0 which is impossible
another way to look at it is to consider the monotony in x > 2
it is strictly increasing in x > 2
if you consider the derivative
so the lowest value (that is never attained) is x-> 2 then f(x) -> 0 and the greatest x -> oo f(x) -> 1 so between 0 < f(x) < 1
short orchid
i did that 
short orchid
in order for f(x) = 1 you would need to get 8/(x^2+4) = 0 which is impossible
ohhh ure right
so how to do it
hardy basin
if ur not gonna be helpful stop trying to pick fights with people
shes asking for help on b 😭 😭 😭
rough forge
shes asking for help on b 😭 😭 😭
He is trying to deduce the inverse function
short orchid
so the lowest value (that is never attained) is x-> 2 then f(x) -> 0 and the gre...
wait i don't understand this
rough forge
and get by that the range by finding the domain of the inverse function
but you would have to know it is bijective first in x > 2
short orchid
ohhhh
my teacher told us to try on values like that
yes
yes
okayy i'll try your way
this one
i'll be back after i try it!
rough forge
wait i don't understand this
The interval is (2,oo). Since I can derive it's strictly increasing on that interval, I can consider the limits at the endpoints meaning, as x approaches 2 and x approaches infinity. The limits of these will be my bounds for f(x).
short orchid
The interval is (2,oo). Since I can derive it's strictly increasing on that inte...
do i have to know the shape of the graph to understand this?
rough forge
no
short orchid
how do you know that it is increasing in x = 2
rough forge
how do you know that it is increasing in x = 2
If you know that it is increasing then you can imagine it will have to look something like this
so by that what can deduce next is that the lower bound will be the limit as x->2 not the actual value at x = 2 because it's x > 2
next thing since it's always increasing for an upper bound you wanna see how the functions behaves as x->inf
short orchid
so by that what can deduce next is that the lower bound will be the *limit* as x...
ohhhh okay okay thank you so much
wait so i have to do derivative?
ohhhh
okay okay
rough forge
you can also do the method Revita suggested with the inverse, also neat
short orchid
wait how do we write x in terms of y? is it like making y as the subject?
yes
ohhh okok
short orchid
rough forge
think so
short orchid
guys i found x in terms of y already
rough forge
ok you can simplify it more
short orchid
ohhhh
jolly parrotBOT
𝔸dωn𝓲²s
rough forge
for y
short orchid
**𝔸dωn𝓲²s**
is 0 correct? 😅
short orchid
**𝔸dωn𝓲²s**
wait we solve for y right
short orchid
yes i did it
rough forge
,, \frac{-4-4y}{y-1} > 4
jolly parrotBOT
𝔸dωn𝓲²s
short orchid
then i multiply the whole equation by y-1 right
rough forge
not quiet
you gotta make two caes
when y-1>0 then yes
else if y-1<0 then the sign flips
short orchid
ohhhh
short orchid
,, \frac{-4-4y}{y-1} > 4
i got 0 for both if y-1>0 and if y-1<0
rough forge
you are supposed to get an interval
short orchid
jolly parrotBOT
𝔸dωn𝓲²s
short orchid
**𝔸dωn𝓲²s**
why can't i get the interval 😭
rough forge
the left is supposed to be y < 0 after you multiply by -1/8 the sign flips
same for the right
short orchid
the left is supposed to be y < 0 after you multiply by -1/8 the sign flips
which one is -1/8
i got 0/8
rough forge
🦖
Now you check what the common interval is
on the left you have the condition y > 1 and got as solution y < 0
which contradicts
you cannot have a number that is bigger than 1 and smaller than 0
on the right side same procedure
condition is y < 1
and you got as solution y > 0
so the common interval is
0 < y < 1
short orchid
you cannot have a number that is bigger than 1 **and** smaller than 0
what does it mean if it contradicts
like how will it affect my answer of the range
rough forge
it just means the first case didnt work out