you can
#help-13
slate lintel
cedar kilnBOT
@lavish stag Has your question been resolved?
slate lintel
it says gcf
idle sonnet
oh right
I read wrong
thought it had to be a polynomial gcf
I’ll delete my messages
can you find the gcf of 8 and 12
cedar kilnBOT
cedar kilnBOT
Available help channel!
frigid fjord
What?
tropic oxide
bot's having a mental breakdown
cedar kilnBOT
Available help channel!
frigid fjord
Ummm what???
cedar kilnBOT
Ummm what???
frigid fjord
I didn't even close my question..
What is wrong with the bot
<@&268886789983436800> sorry for the ping but the bot isn't working
It literally closed on me just now
I'm going to ask my question again (close this channel). But mods, please look into this mess lol :)
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
tacit mulch
how many different car plates can be made if each plate consists of two letters of the alphabet and five random digits?
tacit mulch
it's 26^2*10^5, no?
lunar lynx
What about permutations?
tacit mulch
that is 67600000, but book says 60840000
lunar lynx
Is it stated that first two are letters?
tacit mulch
yes, of the english alphabet
lunar lynx
Or can they be at any place?
lunar lynx
yes, of the english alphabet
Alright. Learn to give all information.
tacit mulch
first two letters, then five digits
lunar lynx
Cool
lunar lynx
it's 26^2*10^5, no?
Then it seems right to me.
tacit mulch
so book is wrong?
lunar lynx
Are you sure that you aren't missing anything in question?
tacit mulch
yes
lunar lynx
so book is wrong?
Seems so.
tacit mulch
"when the car plate should be two letters from the english alphabet and thereafter a five-digit number"
thank you for the confirmation then
lunar lynx
"when the car plate should be two letters from the english alphabet and thereaft...
Well, that is a little subjective to interpretation i think.
tacit mulch
how?
lunar lynx
A five digit number - is 04563 a five digit number?
tacit mulch
unless you mean some wacky stuff like digits from a 12-digit system
tacit mulch
A five digit number - is 04563 a five digit number?
yes
livid hound
,calc 60840000/26^2
wraith daggerBOT
Result:
90000
ah wording matters
5 digit number specifically,
not followed by 5 digits
so the first digit of that can't be 0
lunar lynx
yes
Lol. Book didn't consider that.
Anyway, not on you. They weren't exactly clear either.
tacit mulch
Result:
```
90000
```
so 26^2 times 9 times 10^4??
lunar lynx
Yes
tacit mulch
ooooh i get it
livid hound
always post the original unaltered/unparaphrased question
tacit mulch
always post the original unaltered/unparaphrased question
i'm not anglophone so i need to translate 😅
question was unintuitive, i've seen plenty of car plates with numbers starting with 0 i think
.close
crimson sedge
can someone help me? I kept getting fractions with large numbers.
versed fulcrum
!status
cedar kilnBOT
What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
!show
cedar kilnBOT
Show your work, and if possible, explain where you are stuck.
livid hound
where's your work that lead to that
mental trail
What did you find for the reason of your geometric sequence?
livid hound
*ratio, not reason
livid hound
how'd you get that
crimson sedge
uhm
would you mind my workings?
images
I substituted A in the first image...
I did it in another method too but I got the same answer
cedar kilnBOT
@crimson sedge Has your question been resolved?
crimson sedge
<@&286206848099549185>
sudden yoke
can someone help me? I kept getting fractions with large numbers.
first
a+ar+ar^2:ar^2+ar^3+ar^4 :: 4:9
first
a(1+r+r^2):ar^2(1+r+r^2)
cancel that out
a:ar^2 :: 4:9
1:r^2 :: 4:9
sudden yoke
find a using the 6th term thing
sudden yoke
I made a careless mistake
welcome
feral relic
I'm kinda lost on how to do this problem, not sure how to go about it. I think the mean of Y = (a + mean(X) + mean(U)) which would mean a is zero, if that assumption is true, this problem becomes easier but I'd still like some help putting me in the right direction
cedar kilnBOT
I'm kinda lost on how to do this problem, not sure how to go about it. I think t...
@feral relic Has your question been resolved?
feral relic
I think I worked it out and I got [a,b,c] = [0,.5,.5] can anyone confirm this?
crimson sedge
The height of two vertical pillars is 1.5 m and 3 m, respectively. Ropes are stretched from the top of one pole to the bottom of another pole (see drawing). At what height above the ground do these ropes cross?
lilac magnet
!status
cedar kilnBOT
What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
1
lilac magnet
Tbh I just need a lil help where to start, probally the rest I could finish
same… i also don’t know how to solve this…
crimson sedge
same… i also don’t know how to solve this…
Cool
<@&286206848099549185>
hi
Hello
crimson sedge
The height of two vertical pillars is 1.5 m and 3 m, respectively. Ropes are str...
^
crimson sedge
can you translate
The text above the image is translation
The height of two vertical pillars is 1.5 m and 3 m, respectively. Ropes are stretched from the top of one pole to the bottom of another pole (see drawing). At what height above the ground do these ropes cross?
its 1 meter
about 1 meter
About
Yeh ai
But how to solve it xd
I less care about the answer than how to solve it
cedar kilnBOT
@crimson sedge Has your question been resolved?
hallow vortex
I less care about the answer than how to solve it
do you know how to solve trigonometry?
like what is sin, cos and tan?
you know that, right?
hello!?
chrome vigil
Sin is opposite/hypotenuse
Cos is Adjacent/hypotenuse
Tan is opposite/adjacent
hallow vortex
Bro i asked Colney
hallow vortex
ohh
chrome vigil
My bad lol
hallow vortex
My bad lol
whatt? Why?
hallow vortex
Sin is opposite/hypotenuse
Cos is Adjacent/hypotenuse
Tan is opposite/adjacent
Not even this?
hallow vortex
so you basically don't know anything?
this is your start?
hallow vortex
alright so don't try solving this now
crimson sedge
It's homework
crimson sedge
alright so don't try solving this now
For tommorow :d
hallow vortex
what? Without teaching?
hallow vortex
ok so i'll help
crimson sedge
Tday
hallow vortex
Mean?
crimson sedge
Mean? Wym
hallow vortex
ok so first remember the Formulas
crimson sedge
What formulas
hallow vortex
Sin is opposite/hypotenuse
Cos is Adjacent/hypotenuse
Tan is opposite/adjacent
Do you understand what is this?
crimson sedge
alright so i'll send you a link please check that
So trigonometry gives me angles
How is that usefull
crimson sedge
Sin is opposite/hypotenuse
Cos is Adjacent/hypotenuse
Tan is opposite/adjacent
Ik how to calculate them
But how will that help me
hallow vortex
It is the only thing required
you can apply trigonometry in only right angled triangle
hallow vortex
first name each point in the diagram
you only got the opposites and you want to find the base so apply tan
hallow vortex
first name each point in the diagram
send a pic after naming
crimson sedge
Take what?
hallow vortex
BC/CE
hallow vortex
Take what?
angle
hallow vortex
ah no
AE/EC
you will take the small triangles afterward but first find the large ones which you got
hallow vortex
smth?
crimson sedge
Smth = something
crimson sedge
Ah oke
hallow vortex
did you get anything?
hallow vortex
and
crimson sedge
1.5m/EC
hallow vortex
Is tanx(bec)
put this as equation 1
crimson sedge
Wym
hallow vortex
now did you notice both have EC
crimson sedge
Yes
crimson sedge
put this as equation 1
What you mean by this
hallow vortex
Means that you should mark the first equation as eq1 and 2nd as eq2
this will save from confusion
crimson sedge
K
hallow vortex
now did you notice both have EC
i understand that you're not dumb in maths so do you have any idea how to solve EC
crimson sedge
:d
hallow vortex
wait a bit
hallow vortex
but you don't know that
crimson sedge
Yeh
hallow vortex
that's confusing me
hallow vortex
there are answers online did you check?
hallow vortex
no
we need EC
here it is in feet but is understandable
if you feel any doubt in that answer then ask i can help in that
crimson sedge
if you feel any doubt in that answer then ask i can help in that
I'm trying to apply that to my problem
hallow vortex
apply
and btw which chapter's question is it?
i don't think it's related to trigonometry
crimson sedge
and btw which chapter's question is it?
Ahm
A real-life use of the similarity of triangles
hallow vortex
broooo
you should have told already
and here i was applying trigonometry in this 
which grade are you in?
crimson sedge
which grade are you in?
I am in 10th but this is late 9th grade since we are behind like 1month
.close
quartz salmon
Need help with this
quartz salmon
Initially I thought we would need to use the Bertrand’s ballot theorem to get the probability of A being ahead at all times. And once we have the fraction (the probability (4/14)), we multiply by the number of permutations, which is 14!. But my teacher said:
If you have 14 votes and of them you should choose 5 of one kind, in how many ways can you do that? The first one you have 14 places, the second 13 and so on to the fifth when you have 10 place left. Using the multiplication principle that means \frac{14!}{9!} but then the order of the individual votes does not matter so you get…
cedar kilnBOT
@quartz salmon Has your question been resolved?
quartz salmon
Could someone explain why we use “multinomial coefficient”?
cedar kilnBOT
@quartz salmon Has your question been resolved?
cedar kilnBOT
@quartz salmon Has your question been resolved?
tribal kite
Could someone explain why we use “multinomial coefficient”?
You see, when u swap any of the votes allotted to each person, A or B, nothing is changed, thus you have to account for that non-change
quartz salmon
You see, when u swap any of the votes allotted to each person, A or B, nothing i...
The number of strings of 14 A's and B's that have exactly 5 Bs is \binom{14}{5}. ("14 choose 5") The way the question is written, it's not clear that you should ignore the voters' identities when counting the vote sequences, but that's what my teacher expects. The same approach with Bertrand's ballot theorem still works, because all \binom{14}{5} vote sequences are equally likely. I suspect they don't expect me to use Bertrand's ballot theorem, though. Maybe they just want me to write a program to enumerate the solutions and count them that way. To clarify, treating the voters as indistinguishable means counting AAAAAAAAABBBBB only once instead of 9!5! times for all the different ways the A voters and B voters could be reordered.
solemn quail
It says that A has to be leading at all times, but I guess that means except before any ballots have been chosen
So it has to start with AA....
Is this for a computer science class? Othersise, it's weird that you have to print the answers.
Do you know the interpretation of binomials as lattice paths?
With that method, you can calculate the answer here quite quickly and easily by hand.
cedar kilnBOT
@quartz salmon Has your question been resolved?
fair geyser
@quartz salmon it's not clear, there's no real indication
but it's like the right guess
damn i was 12 hours late
round ridge
hey
junior dome
<@&268886789983436800>
slate lintel
because the A and B change spots right
yes
cedar kilnBOT
@round ridge Has your question been resolved?
upbeat gorge
cedar kilnBOT
idle sonnet
im new to spanning sets
Do you know the definition of a spanning set
upbeat gorge
if every vector in the set can be written as a linear combination of the other vectors
my lecturer kind of glossed over how to check it
idle sonnet
if every vector in the set can be written as a linear combination of the other v...
so, what you need to check here is whether or not every vector in R^3 can be written as a linear combination of the 3 vectors in U
upbeat gorge
would this just be like gaussian reduction
idle sonnet
would this just be like gaussian reduction
You don’t have to do that
upbeat gorge
i havent really been taught how to write vectors as linear combinations which is my problem
idle sonnet
i havent really been taught how to write vectors as linear combinations which is...
it just means
can you add and subtract the vectors in U to each other to get every vector in R^3?
for example, you can get (2,2,4)
by adding (1,0,0) to (1,2,4)
which means
(2,2,4) is a linear combination of the vectors in U, and thus it is in the span of U
upbeat gorge
so do i need to get a combination of vectors such that every vector can be made
cause i dont see how the first and second vector can be combined to make the last one
idle sonnet
cause i dont see how the first and second vector can be combined to make the las...
You don’t need to do that
You are supposed to combine the first, second, and third vectors to make R^3
upbeat gorge
(3,4,4)
idle sonnet
cause i dont see how the first and second vector can be combined to make the las...
the last one is also in the span of U, because it can be made from itself
upbeat gorge
i just have no idea what im supposed to be doing
idle sonnet
notice that you can also get (1.5, 3, 2)
because it is (1,0,0) + (1,2,0) + 0.5(1,2,4)
which is a linear combination
upbeat gorge
(2.5, 3, 2)
idle sonnet
and you can also get (0,2,4)
upbeat gorge
wait so is determining if its a spanning set really just being able to add them?
idle sonnet
and you can also get (0,2,4)
because (0,2,4) = (-1)(1,0,0) + (1,2,4)
idle sonnet
wait so is determining if its a spanning set really just being able to add them?
And subtract, and add scalar multiples
idle sonnet
wait so is determining if its a spanning set really just being able to add them?
I think you're saying the right thing, could just be phrased better
upbeat gorge
is it because they're all in R^3
idle sonnet
is it because they're all in R^3
Is what because they’re all in R^3
upbeat gorge
that it spans
idle sonnet
I don’t understand
idle sonnet
that it spans
could you put it all together into a full sentence
idle sonnet
when does a set not span
consider the set {(1,0,0), (-1,1,0),(-1,-1,0)}
this does not span R^3, even though all vectors are in R^3
because there’s no way to make (0,0,1)
and even though there are 3 vectors
upbeat gorge
ohhhhhhh
ohhhhh
because the z for all of them is 0
its impossible to make any vector (x,y,z)
because z will always be 0
if i had {(1,0,0), (0,1,0),(0,0,1)}
it spans because i can make any vector i want out of those
idle sonnet
it spans because i can make any vector i want out of those
Exactly
For some sets, you can’t make any vector you want out of them
idle sonnet
Here, you have to prove that you can
idle sonnet
we may write v = x(1,0,0) + y(1,2,0) + z(1,2,4)
slight issue here, but you have the right idea
when you compute x(1,0,0) + y(1,2,0) + z(1,2,4), it isn’t equal to v
because
v = x(1,0,0) + y(0,1,0) + z(0,0,1)
because you already said x, y, and z were the components of v
idle sonnet
v =i(1,0,0) + j(1,2,0) + k(1,2,4)
i, j, and k are already used for unit vectors, but if we ignore that, you’re right
and you can continue
upbeat gorge
yeah lol i just thought of the first thing that came to mind
so they have to be linearly independant to be a basis right
idle sonnet
so they have to be linearly independant to be a basis right
could you finish proving that it spans R^3?
upbeat gorge
v =i(1,0,0) + j(1,2,0) + k(1,2,4)
is this not enough
idle sonnet
v =i(1,0,0) + j(1,2,0) + k(1,2,4)
there are still details to be filled, such as why i,j,k must exist, given that x,y,z are the components
you could derive formulas for i,j,k from x,y,z
and that would be enough
idle sonnet
i = x
j = x + 2y
k = x + 2y + 4z?
the other way round
upbeat gorge
x = i
y = j-x/2
z = (k-x-2y)/4
(x,y,z) = i(1,0,0) + j-x/2(1,2,0) + (k-x-2y)/4(1,2,4)
perhaps
idle sonnet
x = i
y = j-x/2
z = (k-x-2y)/4
I think so
That should complete the proof
Or, another way to do it is
idle sonnet
Show that you can get (1,0,0), (0,1,0), and (0,0,1) from U
idle sonnet
Show that you can get (1,0,0), (0,1,0), and (0,0,1) from U
Then, you can get all of R^3
This way should involve less algebra in the proof to check
idle sonnet
i cant find any examlpes of this online
does your textbook have any examples
upbeat gorge
dont have a textbook
every example in the lecture notes is a 2d set
and every number in r^3 is either 1, 0 or -1
not very helpful lmao
this is basically all i get
idle sonnet
dont have a textbook
you could ask in #book-recommendations for a linear algebra textbook, or look in #books-old
upbeat gorge
my course doesnt need a textbook
idle sonnet
you could ask in <#716264872018706443> for a linear algebra textbook, or look in...
these help self-learners
upbeat gorge
i literally cannot find a single video/example on how to prove that its a spanning set
idle sonnet
What about asking your teacher
upbeat gorge
ill ask tomorrow
sturdy steeple
can someone explain me how we went from the thrid line to the 4th
cedar kilnBOT
can someone explain me how we went from the thrid line to the 4th
@sturdy steeple Has your question been resolved?
raw wren
for the 1st year both will be same but if the compounding happend every 6month then it wont work?
raw wren
has to have compound annually just like here for them to be equal for 1st year
and to get only the interest p(1+r/n) ^(n*Y) we have to subtract p from this equation??
drifting marlin
They have to compound at the same frequency for them to accumulate the same amount after 1 year yes
And yes, interest = accumulated value - initial value (or principal if you want)
raw wren
They have to compound at the same frequency for them to accumulate the same amou...
so for simple interest its always annually ?
drifting marlin
No
drifting marlin
There's nothing wrong with having simple interest stated in months
Because simple interest is a linear accumulation, saying 6% annual means the same as 0.5% monthly, for example
raw wren
so if it was like SI after every 6 month and same for compound then how they can become equal?
the 1 yr period can be achived by
raw wren
Because simple interest is a linear accumulation, saying 6% annual means the sam...
ohh okay
raw wren
so if it was like SI after every 6 month and same for compound then how they can...
@drifting marlin but in such case how to manage
drifting marlin
Manage what?
raw wren
Manage what?
for the year
for themto be equal
i mean how they can become equal in non annual case
drifting marlin
If the rate is the same and they accumulate at the same frequency, they'll be equal after 1 period
Be it yearly, monthly, whatever
raw wren
If the rate is the same and they accumulate at the same frequency, they'll be eq...
ok so after the first period is the key given same period for both
@drifting marlin here does if value equal to mean is added then it won't change the mean always?
drifting marlin
For a normal distribution yes
raw wren
For a normal distribution yes
for regular list?
drifting marlin
You don't have to ping me twice per minute
raw wren
You don't have to ping me twice per minute
sorry i thought you forgot thats why
pls don't mind
thanks!
.close
swift furnace
hey what is the value of √2+i√2
cedar kilnBOT
hey what is the value of √2+i√2
livid hound
the intentions of the question are unclear
livid hound
the value of $\red{\sqrt{2} + i\sqrt{2}}$ is $\red{\sqrt{2} + i\sqrt{2}}$
swift furnace
umm
wraith daggerBOT
ℝam()n()v
swift furnace
so it like is not any answer?
livid hound
the intentions of the question are unclear
feral coyote
or it can be expressed as ae^ib
livid hound
like what is the value of 5
swift furnace
5
livid hound
yeh, exactly
swift furnace
is it like a equation or anything
livid hound
technically it is a question
just a REALLY bad one
as per my example in the same form
swift furnace
actually the whole thingy is this √2+i√2 / 10
livid hound
same issue
livid hound
if the expression is already simplified
there isn't anything that needs to be done with it
cedar kilnBOT
@swift furnace Has your question been resolved?
orchid summit
cedar kilnBOT
orchid summit
Hi this is my homework and I don’t know what it’s asking me
I’m on status 1
I know the product of [f(x)][g(x)] is (f(g(x)))
crystal raptor
I know the product of [f(x)][g(x)] is (f(g(x)))
no the latter is the composition, here they literally just want you to put the green dots at the product of the outputs of each function
orchid summit
What does that mean?
crystal raptor
i.e. the green dot at 1 should be at y = f(1)*g(1)
orchid summit
i.e. the green dot at 1 should be at y = f(1)*g(1)
So it should be on 1,0?
crystal raptor
what is f(1)?
orchid summit
3
crystal raptor
and g(1)?
orchid summit
0
crystal raptor
are you sure
orchid summit
Yeah?
crystal raptor
why 0
crystal raptor
y = 3 yeah
rinse and repeat
you should soon realise this is alot easier than you thought because of the nature of g
orchid summit
Oh Alr
Yeah
I was thinking about how to find the product but the dot wasn’t moving across the x axis
But now I realize
Thx
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
south cobalt
can someone draw for me
cedar kilnBOT
can someone draw for me
south cobalt
i cant
warm bone
desmos
livid hound
what's your issue with drawing
livid hound
have you been introduced to the xy-plane before
south cobalt
have you been introduced to the xy-plane before
yes
livid hound
the point (5,9) is the point with an x-coordinate of 5
and a y-coordinate of 9
do you have any issues with plotting single points
cedar kilnBOT
@south cobalt Has your question been resolved?
waxen egret
2x^2+x-6 over x^2-1 how can i factore this
cedar kilnBOT
2x^2+x-6 over x^2-1 how can i factore this
south tundra
You can factor quadratics using Vieta's theorem, it states that ax^2 + bx + c = a(x - x1)(x - x2) where x1 and x2 are the roots to ax^2 + bx + c = 0
So you can start by finding the roots
Are you told to factorize those polynomials or you just want to simplify the fraction?
waxen egret
Are you told to factorize those polynomials or you just want to simplify the fra...
simplify
south tundra
According to root factor theorem, a polynomial is divisible by (x - a) iff a is one of its roots, so, if any terms were shared in factorisations of 2x^2 + x - 6 and x^2 - 1 (so that we would cancel them out), it would also mean that they share a root
Makes sense?
waxen egret
wait i dont get it 😭 im sorry
south tundra
Let's assume after we factorize 2x^2 + x - 6 and x^2 - 1, some linear factor gets cancelled out
Say it's some (x - a)
It would mean that (x - a) both divides 2x^2 + x - 6 and x^2 - 1, right?
south tundra
Some number that we are about to find out
Assuming it exists of course
Okay I can explain this without introducing variables
Can you factor x^2 - 1?
waxen egret
(x + 1)(x - 1)
south tundra
We would be able to simplify if either (x + 1) or (x - 1) were present in the factorisation of 2x^2 + x - 6, right?
So that one of them cancels out
waxen egret
We would be able to simplify if either (x + 1) or (x - 1) were present in the fa...
it's not present right?
south tundra
Yes, because it would imply that -1 or 1 is a root of 2x^2 + x - 6
But that's not true
So nothing will get cancelled out when we factor those polynomials
waxen egret
so it's just stay 2x^2+x-6 over x^2 - 1
so i dont need to factor it. it's the simpliest form
south tundra
Right
red oak
cedar kilnBOT
red oak
How would I work this out
cedar kilnBOT
@red oak Has your question been resolved?
red oak
<@&286206848099549185>
remote rock
<@&286206848099549185>
bro read it few times you will figure out ..
red oak
bro read it few times you will figure out ..
I have
I’ve been reading it for 30mins
I asked for help for a reason
remote rock
ans is 513 isn't it ??
remote rock
I asked for help for a reason
.
remote rock
i think soo
red oak
Can u tell me how u calculated it?
remote rock
she marked bee with paint and the when she collect new bees she found out that 11 of them are already marked which means they are from first batch now substract 11 from 415 and then add it with 1st batch thats the total bee .
remote rock
<@&286206848099549185>
ahhh
crimson sedge
hi
dire geode
1 hour later lovely
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cedar kilnBOT
1 hour later lovely
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red oak
Interesting that every other helper is helping someone else out
regal pewter
lmao i would help you but shit attitude
cedar kilnBOT
@red oak Has your question been resolved?
crimson sedge
Great service
wym its free lmao
sonic cradle
Great service
if you want better service you can pay me 15 quid an hour and ill happily oblige 😁
cedar kilnBOT
cedar kilnBOT
Available help channel!
red lion
Can someone explain this to me? I don't understand how long division works, I do understand what are we trying to do but I don't understand the method.
obsidian coral
Do you understand normal long division?
red lion
Do you understand normal long division?
No not really.
obsidian coral
red lion
So you are dividing 7527 by 13
obsidian coral
No not really.
You should have a strong fundamental in regular long division because polynomial long division is the same logic
obsidian coral
So you are dividing 7527 by 13
In that example, yes
red lion
You should have a strong fundamental in regular long division because polynomial...
I will take a look, or try to find a youtube video
cedar kilnBOT
@red lion Has your question been resolved?
tame juniper
a
humble karma
Inspiring
humble karma
First letter of the alphabet
old lotus
r
tame juniper
tame juniper
The parabolic part of the lower edge line of the longitudinal section of the bridge can be calculated using the graph of a function defined in R
x=0.8-a*x^2
can be described with a © R+.
f) In Figure 1, the length of one of the two bottom surfaces of the middle component is labeled s.
Determine all values of a that yield at least 0.1 dm for this length.
(4 BE)
(s) In the context of the facts, explain that arbitrarily large values of a are out of the question for the description of the lower edge line.
old lotus
Who calls a bot zaza
tame juniper
I need help with f) cause i dont know what i am supposed to do
Jay bro
if u dont help me
please leave the channel
old lotus
Bro idk what even 18 x 23 is..
tame juniper
U'll learn it eventually
humble karma
Ok so you want s >= 0.1dm
old lotus
I hope
humble karma
What you should do is find the zeroes of the parabola you're given.
Then you'll know where they're placed at
old lotus
How do u get that blue diamond behind ur user
humble karma
It's pronouns I reckon
tame juniper
What you should do is find the zeroes of the parabola you're given.
How do i do that with the parameter
0,8-ax^2
humble karma
You can start by isolating x^2, then take the square root on both sides.
humble karma
You also need to take the square root of a
humble karma
Yeah
tame juniper
okay and now im supposed to find different numbers so that s is atleast 0,1
humble karma
Now this is the positive solution, so to express s, notice that 1 - x_0 = s yeah?
Where x_0 = 0.89/sqrt(a)
tame juniper
what do you mean by x_0
humble karma
That's the zero you found
tame juniper
Oh yeah
humble karma
$x_0 = \frac{0.89}{\sqrt{a}}$
wraith daggerBOT
Azyrashacorki
tame juniper
Oh yeahhh hahah ur right
humble karma
Ok
So yeah we express s as the distance between 1 (as in the figure you're given) and that intercept
$s = 1 - x_0 = 1 - \frac{0.89}{\sqrt{a}}$
wraith daggerBOT
Azyrashacorki
humble karma
Makes sense?
tame juniper
I'll explain and u say if its right or not
So if i understood it right the value of 1-0.89/sr*a must be atleast 0.1
and 1 is the distance from the left side of the s
and we want to find out how big the distance is of the whole S
so i just have to write it correctly down
humble karma
So s is just that small distance
tame juniper
1-08,9/sr*a=>0.1
humble karma
Yes
tame juniper
and thats it?
tame juniper
i just switch a with x than
humble karma
This will give you your range of values such that s>= 1
If it helps you, but you can just leave it as a and isolate like normally
humble karma
No you don't need an x here
0.89/sqrt(a) >= 0.1
You can multiply both sides by sqrt(a) right?
humble karma
Yes
tame juniper
Okay
tame juniper
Yeah
humble karma
And do remember that a is positive to begin with
So what would be the possible values of a as an interval?
tame juniper
+infinity
right?
ohhhh because its on the left site of the coordinate system
on the negative site
and i cant get a result of a negative squareroot
@humble karma
humble karma
a must be less than or equal to 79.21
humble karma
So 79.21 >= a
From this
tame juniper
Oh yeah ur right
humble karma
And you know that a>0 otherwise it wouldn't be a parabola yeah?
tame juniper
Yea
humble karma
So what's the interval?
tame juniper
a must be less than or equal to 79.21
this
tame juniper
Because if 0 is bigger than a it wouldnt be a parabola and wouldnt be equal to 79.21
right
humble karma
Yeah
tame juniper
so the interval must be between 0 and a
humble karma
Plus a was defined in R+ to begin with
tame juniper
so it cant be a negative number
humble karma
Yeah
tame juniper
so it must be 0.1-0.9 atleast
humble karma
What do you mean?
tame juniper
the values
the question is f) In Figure 1, the length of one of the two bottom surfaces of the middle component is labeled s.
Determine all values of a that yield at least 0.1 dm for this length.
humble karma
Which we have found
tame juniper
0<a<=79.21
humble karma
Yes
tame juniper
Because if 0 is bigger than a it wouldnt be a parabola and wouldnt be equal to 7...
so that is like the final sintence
sentence
@humble karma u there bro?
humble karma
Yeah
Well actually
If a is <0 the parabola would go upward
If it's 0 it's just a line
tame juniper
Okay
could u also help me for g)?
In the context of the facts, explain that arbitrarily large values for a are out of the question for the description of the lower edge line
humble karma
Well as a gets larger, the parabola gets skinnier and skinnier
More squished
And so for arbitrarily large a it would be arbitrarily skinny, so much so that your bridge would barely have an arch
cedar kilnBOT
@tame juniper Has your question been resolved?
crimson sedge
In how many different ways can five couples of husband and wife arrange themselves around a bonfire, if the men and women alternate?
I think it should be (5-1)! x (5-1)! = 576
slender mango
did you consider $$2*5!*5!$$ ?
wraith daggerBOT
Totalani
crimson sedge
mm no, because first 5! wouldn't be correct for a circular permutation where you need to eliminate 1, and idk if multiplying by 2 is appropriate here
slender mango
You have 2 groups, each group of 5
crimson sedge
mm is more like you have 5 women and 5 men, but now I think they don't need to be in fixed pairs, but they need to be alternate, so you can't do 9!, so you first need to figure it out for men = 24 and women = 24, and then multiply them to know all the possible ways
slender mango
yea
so if first place is taken by 1 man, the next 9 places can be filled by 9!
same with if 1 woman is first place
so you divide by 2
crimson sedge
so if first place is taken by 1 man, the next 9 places can be filled by 9!
mm you can't use factorials like that here, bc men and women need to be alternate
so the options aren't 9, are 4
and also you need to eliminate one (n - 1)! to take into account circular permutations
slender mango
ok i missed that
around the bonfire meaning circular permutation I assume
I think 24 is right what you said
but you divide it by 2
$$5*4!*4!=2880$$
wraith daggerBOT
Totalani
slender mango
with (n-1)!
crimson sedge
I think 24 is right what you said
24 is for men and women, so 24 and 24 ways to arrange it so 24 x 24 = 576
mm maybe idk if you would need to divide it by 2
but not multiply it by 5
or even add them like 24 + 24 ??
I think I should add, because you don't count the rotations
slender mango
#help-13 message is this wrong?
do you have the asnwer?
because when you do 24 its not in a circle right
its in a row
crimson sedge
I think I should add, because you don't count the rotations
mm no, I think 24 x 24
crimson sedge
https://discord.com/channels/268882317391429632/903430334681608232/1151625835053...
Idk why x 5
crimson sedge
its in a row
mm wdym
slender mango
in a circular permutation you have 4! ways to arrange the people within each couple
crimson sedge
yes
slender mango
and 5 ways to arrange the couple
crimson sedge
in a circular permutation you have 4! ways to arrange the people within each cou...
mm each group (women or men)
crimson sedge
women = 24
men = 24
crimson sedge
and 5 ways to arrange the couple
mm 4!?
slender mango
i just said it, you have 4! ways to arrange the people within each group, 5 ways to arrange the couples, adn they can alternate
crimson sedge
"In how many different ways can five couples of husband and wife arrange themselves around a bonfire, if the men and women alternate?"
- Order matters
- The only condition is that men and women alternate
- 5 men and 5 women
crimson sedge
i just said it, you have 4! ways to arrange the people within each group, 5 ways...
you said 5
I am saying 4! ways to arrange the couples
but idk
slender mango
can yuo find out the answer there? now im just curious
crimson sedge
can yuo find out the answer there? now im just curious
I can't
I can just post it again
slender mango
do you need to add an answer?
crimson sedge
and see if another person knows it
crimson sedge
do you need to add an answer?
Yes
slender mango
try 2880
crimson sedge
thanks for the help
slender mango
I tried 😄
crimson sedge
.close
fervent hill
Hey my names Nate. I’m new to this server and joined because recently I started taking advanced Pre-Calc for my senior year in high school, and it’s been really giving me some problems honestly. At the moment, we are covering non-linear rational inequalities using Sign Charts. It hasn’t been too bad for the part, but I’ve been stuck on this one problem in particular.
fervent hill
If you can help me solve this, I would greatly appreciate it
rare vault
If you can help me solve this, I would greatly appreciate it
Is a sign chart finding the places where it crosses the x axis and then marking the signs within the ragnes?
rare vault
sure, so whats tripping you up with number 6?
wait a minute
what are you doing with that abs(x)
fervent hill
Well I understand the Absolute value part, but I'm stuck on trying to figure out what to do with the SQRT of x + 8. Does that mean that -8 is a part of the numbers that would make the equation undefined (which you mark on the numberline when solving with a sign chart)? and if so, how do I plug in numbers with it
Ill show you what I did
rare vault
yeah -8 is undefined (at it makes division by 0)
fervent hill
rare vault
and all numbers less than -8 are also undefined, because sqrt negative numbers rule
fervent hill
yeah -8 is undefined (at it makes division by 0)
ok nice i was thinking that, thanks
what do you mean?
OHH
right cause then it'd be imaginary
rare vault
yea
fervent hill
So then would I just avoid plugging in numbers that are equal to or less than -8?
rare vault
yeah
x <= -8 is all undefined
(also 9 of course)
what is the point of this part
not sure what this set of zeroes is doing at all
fervent hill
Im making the sign chart there
basically making borders
dotted lines are undef and solid are zeros
rare vault
there isnt a root/zero at -2 in the original function though
fervent hill
theres a zero at -2 because since it includes an absolute value, you have to write the inequality two times. One where (x-2) is negative (which would make x+2, and also flip the > to a <) and the original where it remains just (x-2)
If you look at the picture that I sent that shows my full work up to the point where I'm stuck at, you can see both branches
I think that's how you're supposed to do it anyways
rare vault
That doesnt seem right to me, but I suppose you will only get too many roots and not too few
you do need to double check if it asks for roots though, because -2 is NOT a root
fervent hill
Wait is a root the same as a zero?
fervent hill
I see
rare vault
and f(-2) is not zero
fervent hill
do you mean -2 can never be a zero
fervent hill
What about for something like (x+2)(x-4) = 0
wouldnt the answer be x = -2, and x = 4
rare vault
yes
fervent hill
thats what its asking for
rare vault
yes
(abs(x - 2) (x + 3))/(sqrt(x + 8) (x - 9)^2) = 0
the "answer" is x = -3, and x = 2
fervent hill
I see
rare vault
you can simply find zeroes by setting the top of the equation equal to 0
|x-2| (x+3) = 0 only at 2 and -3
fervent hill
I see, but what about the ABS
I thought then when you have an ABS, you have to make two equations
that mirror eachother essentially
like if you had |2x-2| = 6. You would make it into two equations, one being 2x - 2 = 6, and one being 2x - 2 = -6
rare vault
yeah thats right
why did you do |x-2| = 0 as (x-2) > 0 and (x+2) < 0
notice in your example you made the other side switch signs
you could do either side
but you distributed your negative sign wrong
okay wait im explaining this poorly
rare vault
you should have done (x-2) < 0 and (x-2) > 0
fervent hill
that makes more sense yeah
rare vault
okay I think you get the idea and I think I also answered your original question
sorry my explanations are lacking today
fervent hill
and it aligns with a practice problem i did earlier (albeit a lot less complex)
rare vault
yeah you got the splitting idea right, you just executed it wrong
fervent hill
okay now i get that part, thanks i appreciate it. But what about for the square root of the equation. It's being multiplied by (x-9)^2 right?
rare vault
divided by that?
fervent hill
Now i mean for the denominator
rare vault
it is in the demonimator
oh i see
yes (x-9)^2 is multiplied to sqrt(x+8) in the denominator
fervent hill
because part of solving sign charts is you have to essientally combine all negative and positive numbers, and use that information to determine if a section in the sign chart is negative or positive. (this is important because for instance if the inequality is stating that the equation is less than 0, then I have to only include negative sections for my answer
sorry if explain that badly
rare vault
I think the method they are using to teach you is unnecessarily confusing
fervent hill
I KNOW RIGHT
rare vault
I would just find the roots by looking at the numerator, then plug in some number between them and see if its positive or negative, then since we know it doesnt change in that range the entire range is what we tested
fervent hill
my old algebra 2 teacher warned me that this teacher that I have for advanced pre calc makes thing unnecessarily complex
and i really get it now
fervent hill
I would just find the roots by looking at the numerator, then plug in some numbe...
Yeah exactly, i'd do that too
but we have to use a sign chart
which makes the whole process a lot lengthier and more confusing in some cases
So do you have any clue on how I can go about solving this with a sign chart? I get now that the zeros are set and I only apply the negative to the 0 (which just remains as 0). But this square root is really tripping me out because I don't know how to apply it when doing the process of plugging in numbers for the sign chart
fervent hill
Honestly, not really when it comes to things like multiplying it by another equation
rare vault
f(x) = sqrt(x+8), what is f(-4)?
fervent hill
like what happens if take f(-4)
okay one sec
oh 2
right?
-4 + 8 = 4. and the sqrt of 4 is 2
rare vault
yeah
fervent hill
one sec brb
rare vault
okay I have to go anyways
just plug in a number for all the x's and solve it with algebra/basic operations
mossy pivot
help pls just want to make sure the top portion is right and i need a little guidance on the second part
digital cliff
whats up with the second part?
digital cliff
it basically wants formulae for the cost in those brackets
digital cliff
if 0<60<20?
this wouldnt be right but for the first box it would indeed just be 60
digital cliff
60+4(x-20)
this is good for the second one
mossy pivot
so the first one is just saying 20 gigabytes would be 60 dollars
second is asking for the amount over 20 up to 50
digital cliff
exactly
digital cliff
yup
mossy pivot
so 60+120+6?
digital cliff
nearly, youre still missing the x
mossy pivot
180+6(x-50)
cedar kilnBOT
cedar kilnBOT
Available help channel!
elder elm
Could someone help me understand
cedar kilnBOT
Could someone help me understand
elder elm
1A would be true, correct?
cedar kilnBOT
@elder elm Has your question been resolved?
cedar kilnBOT
cedar kilnBOT
✅
slate lintel
1a is true, but how can you prove it?
elder elm
1a is true, but how can you prove it?
This is what I have thusfar, does it seem to work? "Solving for y, we get y = root(12-x^2).
Since x and y must be positive integers,and x^2<y^2+x^2=12…the possible values for x are 1,2 and 3.
Substituting those values in, we get root(11), root(8), and root(3). None of which are integers. No value of x leads to y, therefore we have a contradiction. Our initial assumption that there exist positive integers x and y such that x^2+y^2=12 is thus false, making our original statement true."
slate lintel
sure that'll work
elder elm
sure that'll work
But what about 1B? I haven't gotten that, do I also just isolate for x, and try to find the integer solutions?
mental trail
you only have to find 1 solution
and a nice trick to do that (or prove the opposite)... have you tried maybe factoring?
elder elm
and a nice trick to do that (or prove the opposite)... have you tried maybe fact...
factoring b?
elder elm
Could someone help me understand
<@&286206848099549185> Could someone help me with 1B?
crimson sedge
Could someone help me understand
it’s asking you to do the same thing you did for 1a
bust seeing if the two integers equal 10
marble turtle
@elder elm please wait. I am looking into this
elder elm
it’s asking you to do the same thing you did for 1a
Yes, but how can I check.
marble turtle
If you take any integer from 0 to 9 the difference between the squares of these numbers increase as the digit value increases and the difference never becomes 10. It is 9 when x = 5 and y = 4 after that the difference between these values increases.
cedar kilnBOT
@elder elm Has your question been resolved?
odd sierra
cedar kilnBOT
odd sierra
Solve and get exact value they want
keen bluff
-x and factor it out
odd sierra
O
keen bluff
odd sierra
.close thnx
surreal ember
hey
dense relic
Send question
dense relic
I’ll give it a go
surreal ember
thanks bro
cedar kilnBOT
Please stick to your channel.
surreal ember
so I wanted to see if im deriving the right formula
cedar kilnBOT
dense relic
Go to that channel