Just plug in a random number into h(x)
#help-13
stuck gazelle
nvm its just something stupid with mathxl I just go up one and right one
for some reason it keeps marking it wrong if I dont randomly guess what it wants me to put
cosmic steppe
Well that's not always the case. That only works because the leading coefficient is 1
cedar kilnBOT
@stuck gazelle Has your question been resolved?
polar atlas
Given I have v and phi(N) how would I calculate s?
cedar kilnBOT
Given I have v and phi(N) how would I calculate s?
crystal raptor
Hope that v and φ(N) are comprime so that v has an inverse that you can find with euclids algorithm
polar atlas
so do I just do gcd(v,phi(N)) using euclids algo?
crystal raptor
Yeah and then if gcd is 1, run it back to bezout
polar atlas
whats bezout?
crystal raptor
Bezouts lemma says you can always find λ,μ such that λa+μb = gcd(a,b)
polar atlas
oh we never learned that
crystal raptor
Okay well if you have other ways to calculate modular inverses then do those
polar atlas
what does extended euclid algo do?
cedar kilnBOT
@polar atlas Has your question been resolved?
cosmic steppe
Do you know what the vector field is
I would start by identifying the vector field and seeing if it's conservative
Have you been dealing with 2D or 3D vector fields?
Alright so you've been dealing with rotary and not curl
Identify the field from the path integral
Yup but the example above is a 3D vector field
Yup
Now I'd start by finding rot(<x,0>)
well I wouldn't even parametrize the curve
Like curl but for 2D
Uh
If $F = \vecb{A,B}$ then $\text{rot}(F) = \pdv{B}{x} - \pdv{A}{y}$
wraith daggerBOT
Umbraleviathan
cosmic steppe
Yup so that tells you that the field is conservative and you can apply the gradient theorem
So now you need to find a function, f(x,y) such that the gradient of f is <x,0>
Yup
The information above tells you the path goes from (0,0) to (3,27) right
Hm
,w Integrate[t, {t,0,3}]
wraith daggerBOT
errant wolf
hello
cedar kilnBOT
cosmic steppe
Np
cedar kilnBOT
Available help channel!
rain vine
cedar kilnBOT
rain vine
is the expression $$ [(x+10)(x+6)-60]0.25= 27$$
wraith daggerBOT
JXHN
cosmic spindle
r u assuming x is the border width?
cedar kilnBOT
<@&286206848099549185>
Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
rain vine
yeah I get it the expression suppose like this
cosmic spindle
check if the total area is the first part of ur expression
rain vine
$$ [(2x+10)(2x+6)-60] * 0.25 = 27$$
cosmic spindle
yea
wraith daggerBOT
JXHN
cosmic spindle
thats right i think
rain vine
I also tried other way but it way off can u tell what long there
cosmic spindle
?
rain vine
bascially i find the difference of big volume - small volume = 27
$$ (2x+10)(2x+6)0.25 - 1060.25 = 27 $$
wraith daggerBOT
JXHN
rain vine
what's wrong with this?
cosmic spindle
those 2 are the same
cedar kilnBOT
cedar kilnBOT
Available help channel!
round nimbus
I was going through my notes, and I was practicing to rotate this conics.
However, I got confused when I started plugging it into desmos. xy = 1 shows a hyperbola with a transverse x axis rotated 45 degrees, and the solution is a hyperbola with a transverse x axis.
If you rotate xy = 1 45 degrees, shouldn't the final be a hyperbola with a transverse x axis?
cedar kilnBOT
I was going through my notes, and I was practicing to rotate this conics.
Howe...
@round nimbus Has your question been resolved?
cedar kilnBOT
@round nimbus Has your question been resolved?
cedar kilnBOT
@round nimbus Has your question been resolved?
round nimbus
ok i got it, basically its rotation of axis and not the rotation of the function itself 😭
.close
meager jungle
how do i approximate the y value of a local minima so that i can check if the value is larger than a specific number
dull oxide
wdym
meager jungle
how do i check if a local minima of a function is larger than a specific number if getting the root of the derivative is difficult
dull oxide
!show
cedar kilnBOT
Show your work, and if possible, explain where you are stuck.
dull oxide
For all x?
meager jungle
yes
dull oxide
I'm guessing you found the derivative
meager jungle
the roots are pretty hard to find
dull oxide
But you found the derivative, yeah?
meager jungle
yes
tame wraith
@meager jungle oh right
Just use iteration
Specifically the newton raphson method
For the derivative
gritty viper
Just use iteration
How does this make a proof?
cedar kilnBOT
@meager jungle Has your question been resolved?
cedar kilnBOT
@meager jungle Has your question been resolved?
echo sinew
Hey!
wicked vortex
What’s ur question
nova snow
crimson sedge
haha
cedar kilnBOT
@echo sinew Has your question been resolved?
royal loom
.close
orchid anchor
I can't get the surface area
cedar kilnBOT
I can't get the surface area
royal loom
Have you found the area of the sides?
orchid anchor
17 and 17
royal loom
There are more than 2 sides.
orchid anchor
you mean area of the base?
royal loom
What is stopping you from finding the area of the rest?
orchid anchor
idk how to
royal loom
Do you know how to find the area of a rectangle?
orchid anchor
base x height?
royal loom
850
this is meaningless to me, you have to be more specific. Say, the area of ( ) is 850, because .....
if you want help
orchid anchor
850 is rectangle area, 550 is the whole triangle area
and 616 is the area of the base
cursive ferry
can anyone help me about this questio“Find a special solution to a differential equation y''+y=e^x+cosx
royal loom
there are more than 1 rectangles on the shape, and more than 1 triangles
royal loom
can anyone help me about this questio“Find a special solution to a differential ...
Read #❓how-to-get-help , this channel is occupied.
@orchid anchor these are the areas you need to find
Also, the side opposite the slanted side
So, note that the black and red areas are repeated on the backside
so whatever they are, double them
orchid anchor
22 x 17, 17 x 50, 22 x 50/2, 22 x 22/2
royal loom
find the area of the base (the green)
orchid anchor
that?
royal loom
22 x 17, 17 x 50, 22 x 50/2, 22 x 22/2
this is just a list of numbers to me, be more specific if you want me to check anything for you
royal loom
Sorry but that doesn't mean you should just paste your question into here with really no effort on your part to describe what you need help with or what you are trying
I'm willing to help, I'm just not going to baby you through it either
royal loom
If you would show me your work I could try to tell you what went wrong
(just pasting random numbers in the chat doesn't count as showing your work)
orchid anchor
how do you want me to show my work
royal loom
Did you do it on paper?
royal loom
748 for the black
this is right
orchid anchor
1782 after we add the yellow
royal loom
1232 after we add in the red
this is also right
royal loom
1782 after we add the yellow
this is way off.. how are you finding the area of the yellow?
orchid anchor
50 x 22/2
royal loom
22/2 is not the length of that diagonal side
orchid anchor
what do I have to type in?
royal loom
find the length of it's base, (50)
multiply by the length of it's height
which is the diagonal
which you have to find
orchid anchor
ok I got 2787.63
royal loom
find the area of all the sides, and add them up. That will give you the surface area.
orchid anchor
is 2787.63 right?
royal loom
no clue
but, you're more than capable of finding the surface area. Just find the areas of all the sides and add them up
if you get it wrong, then double check that you found the areas correctly
As I said above, I'd be happy to help but you have some opposition to explaining/thoroughly showing your work. So I can't check for you
orchid anchor
1232 after we add in the red
So this is correct
From here I need to add yellow and blue right?
royal loom
As I said above, find the area of all the sides and add them up
royal loom
then you either didn't find all of the sides, or you found the area of some of them incorrectly
if you'd organize your work on paper it'd be easy for you to see what is going wrong
or easy for me
royal loom
No one is going to give answers here
orchid anchor
alr thanks for nothing
royal loom
you haven't tried showing your work coherently
orchid anchor
.close
cedar kilnBOT
royal loom
alr thanks for nothing
If "nothing" is volunteering 30 minutes of my time to you to try to help teach you this, despite you being unreceptive and ungrateful, then you are welcome.
cedar kilnBOT
Available help channel!
crimson sedge
which channel do i ask stochastic processes questions
cedar kilnBOT
which channel do i ask stochastic processes questions
tropic oxide
#probability-statistics , #advanced-probability or here
cedar kilnBOT
@crimson sedge Has your question been resolved?
deep plover
gm
olive helm
Kind of a shot in the dark, but how the heck do I even start a proof like this?
olive helm
We've touched a little on special divisibility rules; For example, numbers take a certain form when they are divisible by 101 or 7 or 3 or etc.
I have a feeling I'm supposed to use the fact that e is the modular mult. inverse of 10 mod n, but I'm not sure how... (Does that somehow guarantee that n' will be divisible by d?)
Gonna step away to work on other problems for a bit, please ping me if you respond!
finite raven
What is multiplicative inverse?
Like e*10 = 1 mod (d)?
If then you can do $10 n' = n-a_0 +10e a_0 \implies 10 n' \equiv n-a_0 +10e a_0\mod d \implies 10 n' \equiv n-a_0 +a_0 \equiv n \equiv 0 \mod d$
Since $\text{gcd}(10,d) = 1$, we have $n' \equiv 0 \mod( d)$
@olive helm seems correct to you?
Wait, I have to go back as well (d |n'->d |n)
(d |n'->d |n) is easy
wraith daggerBOT
tales
cedar kilnBOT
@olive helm Has your question been resolved?
olive helm
Oh, I see!! Huh, I guess I just needed to write the algebra out to avoid confusing myself.
Thanks a bunch! Seems correct to me
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
cold briar
!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
5
And 1
No this is not an exam
And no i havent learned this
I see that they just add and subtract the margin of error
Why?
And is it correct?
And no this is not my assignment
Ok I understand that there is points on the question
Idk how to prove the fact that this is not my assignment either
Why am i talking to myself
Ima just .close
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
bronze pivot
Is this more like
Rotating the loop about an axis lying on the plane of the page
or
Translating the loop in a direction perpendicular to the page.
?
cedar kilnBOT
Is this more like
**Rotating the loop about an axis lying on the plane of the p...
@bronze pivot Has your question been resolved?
cedar kilnBOT
@bronze pivot Has your question been resolved?
crude valley
What is your question?
bronze pivot
What is your question?
this ^
crude valley
You replied to my question
I don't think either answer you suggested describes what the picture looks like to me
This is clearly not a translation.
If the axis of rotation lied inside the plane the rotation would happen in space - i.e. it would "leave the plane"
To me the picture looks like
"Rotation about an axis orthogonal to the plane that passes through a point inside of the circle" (and based on how you drew the arrows i'd say it's pretty close to the center)
cedar kilnBOT
@bronze pivot Has your question been resolved?
cedar kilnBOT
@bronze pivot Has your question been resolved?
weak trail
I need help with this example
cedar kilnBOT
I need help with this example
weak trail
<@&286206848099549185>
dull oxide
What have you tried?
weak trail
So giving values to A, B and C of a triangle with what they give me
but I think I'm not putting them correctly
or at least Idk how to find what they are asking me
storm talon
cedar kilnBOT
@weak trail Has your question been resolved?
cedar kilnBOT
velvet mortar
<@&268886789983436800>
crimson sedge
$\forall x \in (0,3) \land (4,6)$
cedar kilnBOT
$\forall x \in (0,3) \land (4,6)$
wraith daggerBOT
MrTrim
crimson sedge
is this correct?
quartz frost
Wdym
dull oxide
Invalid syntax
dull oxide
what are you trying to say in english?
crimson sedge
for all x in (0;3) and (4;6)
quartz frost
$\forall x\in (0,3)\cap (4,8)$
wraith daggerBOT
~Martin
quartz frost
Although i find it more pretty to have an extra space behind the element symbol
crimson sedge
im trying to write on what intervals function has negative/positive values by quantifiires and i dunno if this is correct
dull oxide
well that intersection will result in the empty set
Did you mean union?
(0,3) or (4, 8)?
crimson sedge
i saw that you cannot use the union in indicating intervals in which function has positive/negative values and the intervals just being listed after a comma so i dont know what to use
cedar kilnBOT
@crimson sedge Has your question been resolved?
dull oxide
i saw that you cannot use the union in indicating intervals in which function ha...
what??
dull oxide
I see. Because each interval is a separate instance of when f is increasing
Taking union makes it all one set and it may not qualify as increasing in that whole single instance
Read the top answer
crimson sedge
yes yes so how can i represent those using quantifires?
cedar kilnBOT
cedar kilnBOT
Available help channel!
crisp dove
cedar kilnBOT
sinful geyser
mystic wren
Can someone guide me through this step by step?
cedar kilnBOT
Can someone guide me through this step by step?
mystic wren
Evaluating the integral
rain drift
ok so this might be a little bit nasty lol but I think I see a way to do it
what do you think the first thing we should try is?
mystic wren
trig substitution?
rain drift
not quite let's hold off on that
although yes that would my first through too
but there's something unique about this
hint: what is the deriviative of sqrt(x^2-9)?
rain drift
yep perfect!
so how about this
what if we did u-sub and let u = sqrt(x^2 - 9)?
Like
Let $u = \sqrt{x^2 - 9}$. Then $du = \frac{1}{2}\frac{2x}{\sqrt{x^2 - 9}}dx = \frac{x}{\sqrt{x^2 - 9}}dx$.
$\\$ Then we see that$dx = \frac{\sqrt{x^2 - 9}}{x}dx$
wraith daggerBOT
MellowDramaLlama
rain drift
hmmm
wait
lol
oh yes okay that'll work
We can also see that since $u = \sqrt{x^2 - 9}$, then $u^2 = x^2 - 9$ which means $u^2 + 9 = x^2$
wraith daggerBOT
MellowDramaLlama
stable edge
Let $u = \sqrt{x^2 - 9}$. Then $du = \frac{1}{2}\frac{2x}{\sqrt{x^2 - 9}}dx = \f...
should that not be du
rain drift
yeah you're right thank you
stable edge
at thr enf
rain drift
see? we double check each other lmao
mystic wren
**MellowDramaLlama**
Sorry could you explain further after this?
rain drift
yeah of course
ok so let's start over
I'll number my steps up to that point
bear with me as I write this all out
mystic wren
Wait I’m really sorry, I just saw that I must use trig sub in my work in order to get credit 😭
But I would still like to see the other method if it’s alright
Since you’re already typing it too
If not it’s ok
rain drift
ooooh
no then I wont' bother lol
no worries
it was a cool way to solve it but let's use trig sub since that's your area of focus
rain drift
no worries
ok so yes trig sub
which trig method will we use for $\sqrt{x^2 - a^2}$?
wraith daggerBOT
MellowDramaLlama
mystic wren
a sec
mystic wren
dx = 3sec (theta) tan(theta)
rain drift
bingo!
so we have the following now: $\\-10 \int \frac{\sqrt{(3sec(\theta))^2 - 9}}{(3sec(\theta))^3}3sec(\theta)tan(\theta)d\theta$
wraith daggerBOT
MellowDramaLlama
rain drift
you agree so far?
mystic wren
Yes
mystic wren
3sec^2(theta)?
rain drift
not quite. Remember that $(ab)^3 = a^3b^3$
wraith daggerBOT
MellowDramaLlama
mystic wren
Oh so 27sec^3(theta)?
mystic wren
First square the 3sec(theta) so we get 9sec^2(theta) -9
mystic wren
The 9 to get sec^2 - 1
mystic wren
Tan^2
rain drift
I'm so proud of you
so we have sqrt(9tan^2)
which means we can get rid of that sqrt
so now we're left with this (which we'll clean up in a sec)
$\-10 \int \frac{3tan(\theta)}{27sec^3(\theta)}3sec(\theta)tan(\theta)d\theta$
wraith daggerBOT
MellowDramaLlama
rain drift
there's quite a lot we can combine and eliminate here
care to take a crack at it? ^_^
rain drift
yep exactly
so we can pull out that constant and we're left with
$\frac{-10}{3}\int \frac{tan^2(\theta)}{sec^2(\theta)}d\theta$
wraith daggerBOT
MellowDramaLlama
rain drift
now what does sec^2 equal?
rain drift
sorry to be more clear. what is sec relation to cos?
mystic wren
1/cos?
rain drift
bingo
so sec^2 is the same thing as 1/cos^2
and when you have 1/(anything) in the denominator, you can move that (anything) to the numerator
so then we have $\frac{-10}{3} \int tan^2(\theta)cos^2(\theta)d\theta$
wraith daggerBOT
MellowDramaLlama
mystic wren
Sin/cos?
mystic wren
The cos^2 cancels out
rain drift
yep!
so after ALL of that
we're left with $\frac{-10}{3} \int sin^2(\theta) d\theta$
wraith daggerBOT
MellowDramaLlama
rain drift
wow that was nasty. I don't like trig subs lol
there's a sub you can do as well now with sin^2. It's not 1 - cos^2.
rather it's sin^2 = 1/2 * (1 - cos(2theta))
have you ever seen that?
mystic wren
Ohh ye
rain drift
so we do that and we're left with
$-\frac{10}{3} \int \frac{1}{2}(1 - cos(2\theta)d\theta = -\frac{5}{3} \int 1 - cos(2\theta)d\theta$
wraith daggerBOT
MellowDramaLlama
rain drift
now just integrate that real quick
mystic wren
Is it this?
rain drift
yep exactly
don't forget your + C 🙂
now one last step is to convert everything from theta back to terms of x
drawing a triangle here will be super helpful
mystic wren
Okay I’ll try
rain drift
sounds good I'll be on standby
mystic wren
How do you convert the first theta?
I recall it has something to do with arcsin or one of them
rain drift
so x = 3sec(theta). We can use the arcsec
but if your teacher doesn't like that then convert with: $arcsec(x) = arccos(\frac{1}{x})$
wraith daggerBOT
MellowDramaLlama
rain drift
so solve for theta in x = 3sec(x) then we can convert by taking the arcsec of each side
rain drift
there's an identity there
what does sin(2x) equal?
once you see it that's where the drawn triangle will come into play
mystic wren
I’m not sure
rain drift
2sin(x)cos(x)
crimson obsidian
$$\sin{2x}=2\sin{x}\cos{x}$$
wraith daggerBOT
Calamity
mystic wren
I see
rain drift
so then all in all we have: $-\frac{5}{3}(\theta - sin(\theta)cos(\theta))$
wraith daggerBOT
MellowDramaLlama
mystic wren
Ok I think I got it
rain drift
kk sounds good
I got the final answer if you want to double check with me when you are done 🙂
rain drift
,rotate
wraith daggerBOT
rain drift
looks good to me!
if you wanted to change arcsec to arccos, the equivalent would be arccos(3/x)
but otherwise it all looks great!
dense kelp
Hi, could I get some help on an easy statistics question?
cedar kilnBOT
Hi, could I get some help on an easy statistics question?
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
rain drift
do you have to do this by hand or can you use like excel?
dense kelp
I could use an excel
rain drift
oh okay
yeah there's a function for that
so I would make a table for your points, like so
dense kelp
Yeah that seems about right
rain drift
so you can either just use a built in function (I'm forgetting what it is right now)
or you could use the following formula
rain drift
ah okay yeah
so then I would just make cells for each of the following
sorry one moment
rain drift
ok so normally I would not recommend opening any files on discord on here lol
but here's the excel file
the cells should have each formula
I gotta head to dinner so hopefully it'll make sense
but you'll notice that the trend line that was automatically created in the graph matches the b_1 and b_0 cells 🙂
kk best of luck!
crimson sedge
this is a simple question but when exactly do I know when i should be using radiants vs degrees
crimson sedge
do i just use radiants the moment im dealing with sin/cos and other trigonometric functions
smoky idol
use radians because they're cooler ;)
opal laurel
use radians because they're cooler ;)
ong
smoky idol
there's no real moment to use them, I just think they're easier to work with. You won't see many degrees in trig and calculus though, so getting used to them is a good thing
opal laurel
if there is pi in the problem use radians
you could kind of like see it in that
radians is the basic language of degrees for computers, so they are more common on accounting apps such as excel, google sheets, etc
But i gues you could just use degrees unless it asks you for radians?
smoky idol
how do i know which one to use
kinda depends. But yes as Lighter said, if there's pi, there's a very low chance of it being pi degrees lol
crimson sedge
alr in this case the question had a pi
this was the start of the question
so if its evident like this i assume its safe to say that the teacher expects an answer in radiants
crimson sedge
cedar kilnBOT
crimson sedge
is this proof complete?
i feel like somewhere in here, our professor shouldve included
a<c<b?
cedar kilnBOT
@crimson sedge Has your question been resolved?
cedar kilnBOT
@crimson sedge Has your question been resolved?
fringe mauve
six problems (numbered 1 to 6) are set for a test. Students can score a 0,1,2 or 3 marks for the problem. Find the number of ways a total of 15marks can be scored for the six problems
fringe mauve
idk where to start
wraith daggerBOT
fäf
fringe mauve
yeah
radiant topaz
any combinatorics method that you know to tackle this?
radiant topaz
In a way you can think that there are atleast three questions where you get 3 marks
radiant topaz
if you get 2 marks for all question then you get total marks of 12 which is less than 15
fringe mauve
cause thats the minimum
radiant topaz
cause thats the minimum
yes that's the minimal case
fringe mauve
so three questions with three marks are assumed pretty much
so for that
is it?
6C3
radiant topaz
yes
fringe mauve
for which questions get three marks
radiant topaz
but think about more cases
case 1 : 3 questions get 3 marks
case 2 : 4 questions get 3 marks
case 3 : 5 questions get 3 marks
radiant topaz
what other?
fringe mauve
and they add up
radiant topaz
and others get 1
no need to go fot that
fringe mauve
why not?
radiant topaz
we know we want atleast 3 three marks answers, so you can find how to use 0,1,2 when there are 4 questions that give three marks
fringe mauve
ohhhh
radiant topaz
we decide number of three marks questions and then we find how many 0,1,2 marks questions fix in remaining sum
when there are three 3's
they add to 9
so remaining sum is 15-9 = 6
we have to get three numbers from the set of {0,1,2} to get sum of 6
which happens only when all three of them are equal to 2
so our case gives us 3+3+3+2+2+2=15 which can be arranged in 6C3 ways
radiant topaz
fringe mauve
dont u need to choose which questions get 2 marks
radiant topaz
dont u need to choose which questions get 2 marks
yes
radiant topaz
that's what is done in 6C3 ways
radiant topaz
so it would be 6C3*6C3
nope
fringe mauve
ohhhhhhh
ok ok
that meks sense
so the 6C3
is to decide which questions get 3 marks
then there are 3 qs left
out of those 3
we decide which questions get 2 marks which is 3C3
which is just 1
radiant topaz
okay
fringe mauve
so for the other cases
for the 4 questions
with 3 marks
its 6C4 to decide which questions get the three marks
3+3+3+3+2+1=15
radiant topaz
its 6C4 to decide which questions get the three marks
no
fringe mauve
oh
fringe mauve
then i need to decide qhich questions get the 2 marks and 1 mark
is that just 2C1 * 2C1
uhm so no?
so i have 2 questions from which 1 gets 2 marks and the other gets 1 mark
lets start with just the two marks
i dont understand
isnt it just 2C1 to see which gets 2 marks
and then 1C1 for the last question which gets 1 makr
is that yes?
cool col
finally
for the case 3
is 6C5 to see which questions get 3 marks
and then 1C1 for the last question qhich gets 0
kk
thanks then
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cedar kilnBOT
cedar kilnBOT
Available help channel!
crimson sedge
Help me
crimson sedge
Alright
So
What's the probability that 6 dice will roll out for a total of 6 points?
craggy oriole
There's only one combination of 6 rolls totaling 6 (each one rolls a 1), what's the total number of outcomes?
rain drift
I feel like this problem was solved/requested earlier.
The only way to get a total of 6 points from 6 die is to roll 6 1's
the probability of rolling a 1 is 1/6 with a fair die
in order to do that 6 times you would do (1/6)^6
tropic oxide
hold on
as in, you are rolling 6 standard six-sided dice and looking at the total, and you wish to know the probability that this total also equals 6
is that what you're saying?
crimson sedge
Yes
tropic oxide
Oh. Ok so like .214337?
in this case 0.214337 is definitely quite far from the answer.
cerulean vigil
hello
crimson sedge
Hi?
craggy oriole
Should be 1/6^6
rain drift
Oh, then how did I get that?
I have no idea how you got that lol. Can you show how you got that?
(1/6)^6 = 0.00002143347
it's extremely unlikely you'd get that
crimson sedge
oh
rain drift
hence why the probability is so small.
crimson sedge
Oh that makes sense
craggy oriole
Only 4 orders of magnitude off lol
rain drift
in other words, the chance of rolling 6 1's from 6 die is 0.002143347 %.
Fun fact, according to a Google search, the probability of being struck by lightning is 1/15300, which is 0.00006535947
in other words, you have a better chance of being struck by lightning than rolling that on the dice lol
rain drift
crimson sedge
OK in all seriousness, ty
I understand now
Good bye!
Ty
hang on how do I close
uh
Oh
.close
tranquil citrus
I need help with maths
The question is
**
If the geometric mean of (3x+1)/2x and (2x+2)/3x is sqrt(195)/15, find the positive value of x.
**The answer in book is
Value of x is 4.
But I can't solve it.
Please help
tranquil citrus
please help
crimson sedge
Don't worries
It is handy to use log with base 2 here, so 2 = 2 1 and 8 = 2 3. The arithmetic mean of the exponents (1 and 3) is 2, so the geometric mean is 2 2 = 4. This can be verified by our geometric average
Factor 2x^2-3x+1. 2x2 − 3x + 1 2 x 2 - 3 x + 1. For a polynomial of the form ax2 +bx+ c a x 2 + b x + c, rewrite the middle term as a sum of two terms whose product is a⋅c = 2⋅1 = 2 a ⋅ c = 2 ⋅ 1 = 2
Understand..?
tranquil citrus
.close
tired inlet
hey guys could someone help me out with solving quadratics by completing the square
tired inlet
but why can't I divide everything by 2?
violet flume
because you change the expression
like if you just have the number 6 or something
you cant divide that by 2
no different here
tired inlet
but I mean the equation is equivalent right?
violet flume
you can divide both sides of an equation by 2
you cant just divide some random expression by 2
starting by setting it equal to 0 
tired inlet
oh I see
tired inlet
yeah I meant to do that
so basically x^2 +11x/2 + 6 = 0
(x+11/4)^2 - 121/16 + 6 = 0
(x+11/4)^2 = -217/16 = 0
violet flume
this video is giving you a crutch thats not helpful
tired inlet
is this correct?
violet flume
the first step is to factor
tired inlet
but I mean if I don't want to factor
violet flume
$2x^2+11x+12 = 2(x^2+\frac{11}{2}x+6)$
tired inlet
since It is a non-monic quadratic
wraith daggerBOT
jan Niku
tired inlet
but I mean where does the 5 in the first term go in the video?
tired inlet
yeah
wraith daggerBOT
jan Niku
wraith daggerBOT
jan Niku
violet flume
usual technique is to totally isolate the terms with the x
$x^2+\frac{11}{2}x = -6$
wraith daggerBOT
jan Niku
violet flume
then you take half the coef attached to x, square it, and add it to both sides
$x^2 + \frac{11}{2}x + \frac{121}{16} = -6 + \frac{121}{16}$
wraith daggerBOT
jan Niku
tired inlet
yeah
violet flume
oh, you got the same thing 
thanks for waiting for me to catch up haha
alright, so all you have to do is take the root and move the constant over
$x = \pm \sqrt{-6+\frac{121}{16} } - \frac{11}{4}$
wraith daggerBOT
jan Niku
tired inlet
wait
wraith daggerBOT
Result:
1.5625
hmm well it seems we are using different methods of completing the square
tired inlet
https://www.youtube.com/watch?v=9k579cVrmyA
both methods produce the same results but I think I find this one easier for me to understand
violet flume
hmm? they do the same thing in the video
you end up with a perfect square on one side, and a number on the other
then you take the root, and move the coefficient
tired inlet
do you mind starting again?
tired inlet
well this is where I feel good up to: (x + 11/4)^2 - 121/16 + 6 = 0
tired inlet
so basically I can simplify to get (x+11/4)^2 - 217/16 = 0
violet flume
okay
violet flume
sure
tired inlet
then take the square root of both sides
violet flume
yup
tired inlet
then subtract 11/4 from both sides of the equation
violet flume
yes
tired inlet
so x = +/-sqrt(217/16) - 11/4
I don't get the correct roots when I simplify this
violet flume
,w 2x^2+11x+12=0
wraith daggerBOT
violet flume
👀
tired inlet
do you see what I mean
violet flume
ah, youve added incorrectly
violet flume
well this is where I feel good up to: (x + 11/4)^2 - 121/16 + 6 = 0
here
121/16 + 6 = 121/16 + 96/16
,calc 121+96
wraith daggerBOT
Result:
217
sorry, its negative
-121/16 + 6 = -121/16 + 96/16
you lost the negative somewhere
violet flume
well this is where I feel good up to: (x + 11/4)^2 - 121/16 + 6 = 0
so start here
but re-add those numbers
dont forget its negative: -121/16
tired inlet
Oh true so -25/16
tired inlet
ok so x = -4, x = -3/2
violet flume
tired inlet
thanks for helping out
violet flume
no problem
tired inlet
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
ionic thistle
cedar kilnBOT
ionic thistle
Put a number in x
u mean x= like 2
glossy shoal
Yes
tropic oxide
Put a number in x
this method prioritizes speed.
glossy shoal
Why
brittle axle
Sounds like hella brute forcing
Looks like you can try expanding the left hand side, then likewise expanding the right hand side and comparing coefficients for the terms
ionic thistle
Looks like you can try expanding the left hand side, then likewise expanding the...
what can i do on the left side
brittle axle
Rewrite the first term as (x^2 + 3x)*(x^2 +3x) and distribute that
Then add the result from the second term
It should be x^4 + 2*3*x^3 + 9x^2
Then add the second term when you distribhte the -2 throughout
Distribute right side afterwards(it will get nasty)
gritty galleon
Another method:
Let u = x^2 + 3x
wind hearth
At first I used the formula sqrt(A² + B² + 2ABCosθ), but im pretty sure that's not how it's supposed to be solved. I don't understand what "due east" and "due 60° north of west" mean.
tropic oxide
do you know what a compass looks like
pulsar fox
Its a pretty easy question
tropic oxide
wait do we have to visualise a compass to find theta?
you don't have to do anything.
but it might help if you do.
when something is facing exactly along one of the four principal compass points, we say it is facing "due north", "due south" etc.
tropic oxide
!nosols
cedar kilnBOT
As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.
tropic oxide
also i have not calculated the answer so i can't tell anyway
pulsar fox
also i have not calculated the answer so i can't tell anyway
OOOF, can you just do it quickly and let me know
wind hearth
The answer is said to be sqrt(13) in the answer key
tropic oxide
when something is facing exactly along one of the four principal compass points,...
while "60° north of west" means this: face due west, then rotate yourself 60° towards north. that's the direction you end up facing.
wind hearth
ah ok
pulsar fox
wind hearth
i think i can solve this myself now that i understand whats was meant by 60 ° north of west
thanks for da help
.close
cedar kilnBOT
floral prawn
.reopen
cedar kilnBOT
✅
floral prawn
help me with this question <@&286206848099549185>
pulsar fox
What question ?_?
wraith daggerBOT
1796
floral prawn
help pls
pulsar fox
Alright
So can you show me your progress, on how much were you able to solve till now ?_?
floral prawn
0%
floral prawn
i stupid at integral
pulsar fox
i stupid at integral
Its alright, you will get hang to it with some practice
pulsar fox
So what exactly do you know regarding this concept ?_?
....
floral prawn
where to practice?
tropic oxide
@floral prawn next time open a help channel that does not have somebody else's name on it
pulsar fox
:V
cedar kilnBOT
Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
floral prawn
<@1085862271399493732> next time open a help channel that does not have somebody...
what?
floral prawn
<@1085862271399493732> next time open a help channel that does not have somebody...
i dont know how to change the name of the channel
tropic oxide
you should go to a channel in the Math help (AVAILABLE) category and post your question there.
NOT reopen somebody else's channel like you did.
pulsar fox
where to practice?
Well, you can practice integration questions online. There are many problems available online from which you can practice.
floral prawn
oh
tropic oxide
post in an open channel and it'll get your name put on it.
floral prawn
sorry
earnest socket
people can reopen someone else’s channel?
pulsar fox
you should go to a channel in the **Math help (AVAILABLE)** category and post yo...
LMAO I was thinking, you were going to answer or help this person, thats why I said NO ANN
pulsar fox
people can reopen someone else’s channel?
I guess they can
@floral prawn Open a new channel and lets get to your problem over there
.close
cedar kilnBOT
floral prawn
i maked new channel
cedar kilnBOT
Available help channel!
orchid oriole
I keep getting these type of questions wrong, can someone help me
vague rapids
I keep getting these type of questions wrong, can someone help me
do you know value of sin(90+x)
and same for cos and tan
vague rapids
no
there are different identities
sin(90+x) is cosx due to the fact that sin is positive in 2nd quadrant
sacred grail
surely you'd go for 180-... for these
sacred grail
it's called like the reference angle or something
find the reference angle for 140 in the first quadrant
orchid oriole
The answer they got was sin40
orchid oriole
But for tan they got tan-90
sacred grail
-90?
orchid oriole
Yes
sacred grail
that is not the same as tan(140)
orchid oriole
And for cos it was cos-40
wraith daggerBOT
sacred grail
these are not equal
sacred grail
-cos(40) is not the same as cos(-40)
orchid oriole
How should I do it
sacred grail
are you familiar with the term reference angle
orchid oriole
No
sacred grail
is there another term that is used by your book
orchid oriole
I don’t think so, explain it, I’ll learn it ur way
livid hound
related acute angle is the alternate name
orchid oriole
No I haven’t learn it
sacred grail
you might want to look through your book to find where this is covered
sacred grail
sacred grail
you could use the three equations in the blue box here
you want to rewrite $\sin({\c b 140\degrees})$ as $\sin({\c b 180\degrees - \theta})$
wraith daggerBOT
sacred grail
what is the value of θ?
orchid oriole
40
sacred grail
no the point of rewriting 140 as 180 - 40 is so that you can apply this equation
because now with θ=40, you have an acute angle
orchid oriole
I’m lost again, I thought doing 180-140 was the only step
sacred grail
\begin{align*}
\sin({\c b 180\degrees - {\c r \theta}}) & = \sin({\c r \theta}) \\
\sin({\c b 180\degrees - {\c r 40\degrees}}) & = \sin({\c r 40\degrees})
\end{align*}
wraith daggerBOT
sacred grail
but because 140 = 180 - 40, we now also know that sin(140) = sin(40)
orchid oriole
Ahh alrr