You can as long as you consider the region. If you do dx first, the bound would be different. By Fubinis theorem, the end result is the same.
#help-23
crisp minnow
feral finch
ok, and i forgot to mention that i also know that the bound would be different, i figured that it should be the same bc thats how nice math is, thank you
.close
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feral finch
You can as long as you consider the region. If you do dx first, the bound would ...
they showed that its the same on the next page, i just didnt look lmao
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warm rain
Don’t mind the goofiness on the sheet but how do u do b)
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Don’t mind the goofiness on the sheet but how do u do b)
quick iron
@warm rain
warm rain
What
quick iron
Do you remember a formula which is like
P(A U B)' = P(A' B')
Just put intersection symbol on rhs between A' and B'
warm rain
No
warm rain
I don’t get why it can’t be 1 - 0.6
warm rain
Yes but in this case why isn’t It 1 - (A upside down U B )
quick iron
U mean A intersection B ?
warm rain
Yes
warm rain
so doesn’t it mean not the intersection
quick iron
$A' = U-A$
flat frigateBOT
Akira
quick iron
$P (A' intersection B')$
flat frigateBOT
Akira
warm rain
Yes I know it’s the intersection but I’m confused with the ´
quick iron
Oh
warm rain
<@&286206848099549185> can someone draw it
quick iron
Do u know abt universal set ?
quick iron
Got it ?
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quick iron
🗿
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hard dock
can someone help me with ags2 trig? circles n stuff
safe radishBOT
can someone help me with ags2 trig? circles n stuff
hard dock
@raven vessel
versed wave
!15min
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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.
versed wave
can someone help me with ags2 trig? circles n stuff
!xy
safe radishBOT
can someone help me with ags2 trig? circles n stuff
Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.
@hard dock Has your question been resolved?
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karmic frost
how do you factor out 3x^2-11x>20 to solve for the inequality
safe radishBOT
how do you factor out 3x^2-11x>20 to solve for the inequality
compact wraith
Bring the 20 over to the other side first:
\
\
$3x^2-11x>20\Rightarrow 3x^2-11x-20>0$
\
\
Then plot the quadratic and deduce the inequality from there.
flat frigateBOT
Max
karmic frost
ohh
i forgot to move it ot the other side
so are the zeros 4 and -5
wait
i meant
nvm thats before zero
split ether
Bring the 20 over to the other side first:
\\
\\
$3x^2-11x>20\Rightarrow 3x^2-11...
Some text
[ 3x^2 - 11x > 20 \implies 3x^2 - 11x - 20 > 0 ]
Some other text
flat frigateBOT
A Lonely Bean
Some text
\[ 3x^2 - 11x > 20 \implies 3x^2 - 11x - 20 > 0 \]
Some other text
compact wraith
Ah okay makes sense, I know begin equation doesn't work with that bot, cheers
compact wraith
so are the zeros 4 and -5
Just find the zeros and plot the quadratic
Then you can read off the solution from the graph
split ether
Ah wait I'm not sure if \[ \] will work for you, it needs the package fleqn if I remember correctly
karmic frost
yeah i think -4 and 5 are the zeros
i just have to plot them now
thx guys :)
.close
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median vigil
Ah wait I'm not sure if `\[ \]` will work for you, it needs the package fleqn if...
\[ \] is native LaTeX syntax (which may be modified by those packages)
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stiff plank
can the angle of ABC in cases like this suggest anything about the angles on the other 3 faces?
safe radishBOT
can the angle of ABC in cases like this suggest anything about the angles on the...
lean otter
can the angle of ABC in cases like this suggest anything about the angles on the...
Is it based on coordinate geometry
stiff plank
im not trying to solve the problem
lean otter
I can use orthocentre and assuming a coordinate of a , find vector,then magnitude will give me AD
stiff plank
just want to know whether the angle of ABC is significant
since it's not on the three faces shown
lean otter
Find ABD
stiff plank
oh wait got it
lean otter
Angle
stiff plank
cosine rule
tepid nymph
cosine rule
yupp
stiff plank
Find ABD
you can?
yeah i was just wondering if you could use ABC to find ABD or DBC or ABD + DBC
lean otter
It's related with solutions of triangles
tepid nymph
yeah i was just wondering if you could use ABC to find ABD or DBC or ABD + DBC
yup u can
tepid nymph
yeah i was just wondering if you could use ABC to find ABD or DBC or ABD + DBC
im not sure for the last 2 angles
but ABD should be able to found
stiff plank
oh how do you do that
tepid nymph
i think we can just use sum of triangle to find ABD? BAD is given so
tepid nymph
yeah i was just wondering if you could use ABC to find ABD or DBC or ABD + DBC
i think u can also find other angles
after finding x value
and AD value
and BD value
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somber dust
how do I do B
stiff plank
are you stuck on the if or the only if part
somber dust
I just don't know what to do
stiff plank
to prove it is it's own inverse is pretty simple, just substitute a = -c and solve
stiff plank
do you know how to find the inverse
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somber dust
how do I do this
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how do I do this
mental abyss
because y(-x)=y(x)
somber dust
does even symmetry mean a function fails horzintal test?
mental abyss
yes
somber dust
does odd then mean it is a function?
mental abyss
in general yes
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young wyvern
My teacher didn't teach me this, but gave me the homework. Can anyone help please, thank you.
safe radishBOT
My teacher didn't teach me this, but gave me the homework. Can anyone help pleas...
young wyvern
Do you know how to do long division?
yes, I do.
young wyvern
I don't know how to do the long division with algebra 😭
meager merlin
Lets start with this
Then take the highest polynomial degree of a
so whats a^3 / a?
young wyvern
Wait, I found the answer, sorry for bothering you, it was a²+b²
Thanks for the help though.
.close
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frigid locust
is the feasible region for the following this ?
safe radishBOT
is the feasible region for the following this ?
cobalt saddle
frigid locust
$$6x - 8y \leq 12$$
$$3x+4y \geq 6$$
$$x \geq 0$$
$$ y \geq 0$$
flat frigateBOT
JustToPro
meager merlin
is the feasible region for the following this ?
Yeah, why not?
pine horizon
is the feasible region for the following this ?
yes
since feasible region is determined by all the constraints including x, y ≥ 0
safe radishBOT
frigid locust
since feasible region is determined by all the constraints including x, y ≥ 0
the little triangle is not included in feasible region , yes?
pine horizon
yeah its not
frigid locust
ok good
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slate elbow
find all (a,b) such taht a^2 - b! = 2024
safe radishBOT
find all (a,b) such taht a^2 - b! = 2024
pine horizon
but how to conclude this task
make perfect square inside the square root
that happens if u take b=1
a = sqrt(2024+b!) -> a = sqrt(2025) -> a = 45
now put values of a and b in the original equation and check if its true
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@slate elbow Has your question been resolved?
lilac sandal
How to decompose into partial fractions
safe radishBOT
How to decompose into partial fractions
compact wraith
Factorise the quadratic first
Does the question actually ask you to do partial fractions? This seems like a lot of work
compact wraith
Factorise the quadratic and do partial fractions as normal
tardy pivot
Why would I need to factorize it first?
in theory you dont have to
compact wraith
Because it's already in partial fractions form?
tardy pivot
could do Ax + B over the quadratics and each power up to 3
compact wraith
You'll just get back to the original thing
tardy pivot
but then whats the point of partial fractions
lilac sandal
So Ax+B over (x^2-6x+11) + Cx+B over (x^2-6x+11)^2 etc.?
tardy pivot
You'll just get back to the original thing
yeh ur right
lilac sandal
D i mean
neat fable
How to decompose into partial fractions
the quadratic cannot be factorised because the discriminant is negative and so the quadratic does not have real roots
just to take note
safe radishBOT
neat fable
can someone tell me if this is right or wrong approach???
it does seem like you are on the right track
lilac sandal
it does seem like you are on the right track
After following that I ended up with 2 known values and the other 4 unknown, however.
Oh nvm
It's impossible to decompose I guess
.solved
neat fable
i think it can't be decomposed yea
sleek sentinel
wolframalpha can solve it but uses complex numbers
also yeah you have to crunch a 6x6 matrix lol
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spring stirrup
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spring stirrup
could someone explain this to me i dont understand what it wants me to do
twilit moat
It looks like you need to figure out how to convert from metres to steps or vice versa using the graph
sleek sentinel
It looks like you need to figure out how to convert from metres to steps or vice...
not quite
spring stirrup
what is it then?
sleek sentinel
- how many meters away is the shop?
hint: area under the curve
- find the meters-to-steps ratio and convert
spring stirrup
i dont understand how to figure this out
sleek sentinel
wait my bad this isn't a calculus question
ok the distance to the shop is the highest point on the graph
spring stirrup
ok
sleek sentinel
and then the first part of the question tells you how many meters per step he takes
sleek sentinel
that sounds right yeah
spring stirrup
it was wrong
spring stirrup
wild mountain
so 2.5 steps per meter
spring stirrup
the question changes if i get it wrong twice
wild mountain
it's the same thing just different values
ok so
took 500 steps to walk 150 meters
wild mountain
so 3.33333 steps / meter
spring stirrup
ye
wild mountain
now it took 450 steps to walk to the shop
spring stirrup
ye
wild mountain
so to convert to meters
spring stirrup
you times it
wild mountain
450/3.33333
spring stirrup
ohh
wild mountain
now notice that the function goes downward when he walks to the shop
spring stirrup
ye
wild mountain
so he's coming back towards his house
wild mountain
so the answer will be distance from house to postbox - distance from postbox to shop
spring stirrup
oh
wild mountain
your displacement is final position - initial position
and since the final position is lower that the initial position
your displacement will be negative
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wild mountain
you needed to do 150-135 @spring stirrup
they wanted distance from house to shop not postbox to shop
spring stirrup
.reopen
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spring stirrup
ive tried doing it but nothing works could i just get the answer
<@&286206848099549185>
dim meteor
ive tried doing it but nothing works could i just get the answer
ok find the distance of the postbox from the home first
spring stirrup
250
dim meteor
250
why 250?
he kept waliking until he reached the postbox
which was until he reached 200m
spring stirrup
oh right i looked at it wrong mb
dim meteor
yeah and he took 500 steps to go there and come back
spring stirrup
yes
dim meteor
the amount of meters he travels per step is how much?
spring stirrup
2.5
dim meteor
yes
so if he walks for 450 steps, how many meters would that be
$\frac{d}{450}=0.8$
flat frigateBOT
The د
spring stirrup
360
dim meteor
there you go
spring stirrup
so is that the answer or is there more?
dim meteor
of course
spring stirrup
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brazen parrot
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brazen parrot
hi how i find the direction of the third force?
dim meteor
hi how i find the direction of the third force?
add the two force vectors you have now
brazen parrot
add the two force vectors you have now
550
dim meteor
the third force vector will be the negative of that
brazen parrot
oh
this is what i bave rn
idk how to do it? rn im thinking
oh down south so the vector go down
and then on a bearing of 50 degrees
dim meteor
ok so the south force has a magnitude of 300N
brazen parrot
yes
dim meteor
split the 250N force into its horizontal and vertical components
brazen parrot
ok so the south force has a magnitude of 300N
the 300N is just j right
dim meteor
the 300N is just j right
yeah
brazen parrot
-j?
dim meteor
it'll be -300j yeah
dim meteor
ehh, theres a simpler way
brazen parrot
oh?
dim meteor
the i component will be 250cos(theta)
and the j component will be 250sin(theta)
theta here is from the positive x-axis
so 40 degrees
brazen parrot
the i component will be 250cos(theta)
wait what
can u draw dis pls ):
i am sleepy
dim meteor
so the the 250N 50º vector equals $im\cos\theta + jm\sin\theta$
flat frigateBOT
The د
brazen parrot
i am dumb
dim meteor
makes sense?
dim meteor
yeah
dim meteor
so 160.69 is 161?
sure but its better to round to one more unit while calculating
dim meteor
hmm why are we using tan
dim meteor
use cos for the i component
brazen parrot
dim meteor
ok so thats your 250N force vector, now add to it the 300N vector (which we said was -300j) to get the net force vector
brazen parrot
dim meteor
yes excellent
now that the net force
we need to add another third force that cancels this net force
brazen parrot
-191.51i + 139.3j?
dim meteor
yup but you need an angle
brazen parrot
sin rule!!
dim meteor
that works but it'll be a bit painful
since youll have to do cos rule first
to get another side
what you can do instead is
tan(theta)= j component / i component
and arctan that to get theta
dim meteor
ahh thatll work then yes
dim meteor
the bearing is from due north and clockwise
to help you, think of the force coming from the center of the object
dim meteor
perfect
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viral venture
I agree with the 1/4 * 1/3 but I don't get the 1/4 on the left
Theres 6 outcomes and only one of them, 4, satisifies both A and B
@primal summit
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@primal summit Has your question been resolved?
viral venture
It should be 1/6
Its still not stochastically independent tho
So thats good
It's 1/6 because of 6 possible dice rolls only 1 of them is in both A and B
Honestly im not very sure on exactly why it isn't 1/6, you could probably tweak the contents of A and B to make it 1/6
The task to make two sets A and B stochastically independent?
Its good like this
You check if P(X and Y) is P(X)*P(Y)
Just like you did
If its true then they're independent
If its not they're dependent
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fresh tree
right/
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@fresh tree Has your question been resolved?
twilit solstice
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twilit solstice
how does one get this result
ive tried l' hoptial and im not sure what other methods there are
seems v complex
safe radishBOT
@twilit solstice Has your question been resolved?
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@twilit solstice Has your question been resolved?
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tardy crescent
is the answer 3
safe radishBOT
is the answer 3
tardy crescent
i got r=1,2 or 3
safe radishBOT
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tardy crescent
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wary kernel
"Given complex number z satisfying |z| = 1. Find the maximum value max M and the minimum value min M of the expression M = |z2 + z + 1| + |z3 + 1|."
No matter who I ask this question seems to be a foreign language. I thought the answer was 0 but apparently that's wrong too. Idk if its a me problem or the question is just bad, I think its me tho 😭
safe radishBOT
"Given complex number z satisfying |z| = 1. Find the maximum value max M and the...
stoic dune
Max is easy to get, keep in mind the triangle inequality
wary kernel
A friend asked if I was substituting z in that expression at all, but I dont think so right
stoic dune
Substituting z?
You'll definitely want to keep in mind that |z| = 1
And any rules that || obey are important
I think circle inequality can get the min, but I admit I'm weaker there
wary kernel
I see
muted nymph
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muted nymph
Im a little confused about part e and i think its about understanding what d is
im not sure if d is supposed to be the same as the d in the statement d = nx + my or if it is supposed to be ~d
and if so im not sure how I would show that d is in S
so far what I have attempted is I have stated that since S = k in Z st k = nu+mv for u,v in Z. then if d is in this set it will also be in this form
But I may be lost because my other intution is telling me it has something to do with the gcd(n,m)
I know in part c and d that ~d is in S and that ~d divides n and m
so I am assuming that 1 <= ~d <= gcd(n,m)
But im not sure where to go from here im very lost on trying to piece it all together
this is all the work i have so far but i dont think it is anything useful
<@&286206848099549185>
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@muted nymph Has your question been resolved?
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@muted nymph Has your question been resolved?
muted nymph
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atomic pike
hmm
atomic pike
huh
zinc crown
What is your doubt?
stoic fern
Oh and k is 8.99E9, i forgot to mention that
lean otter
What is your doubt?
🇮🇳
atomic pike
What is your doubt?
bro litteraly none i just msged here and this thing took over
lean otter
This isn’t a messaging channel
zinc crown
This guy isn’t even the owner of the help channel 💀
lean otter
Use it if you actually need help
atomic pike
.close
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zinc crown
🔠
zinc crown
Are u not Indian
Of course I am I got 102% on JEE
earnest olive
Real chad
lean otter
U keep saying doubt
Indians will always say doubt instead of question and I have no freaking clue why
earnest olive
Alr doorbell camera, nice conspiracy theory
zinc crown
Indians will always say doubt instead of question and I have no freaking clue wh...
Do you have a doubt?
lean otter
Like that lmao
devout shale
Please keep the doubt channel on topic
zinc crown
^ what my sir said
lean otter
So many Indians lol
atomic pike
come to chill
zinc crown
come to chill
Maam you lose helper points for participating in chill
lean otter
Lmfao
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dapper tundra
I need help understanding radians in a concept, especially in relation to time compared to revolutions
safe radishBOT
I need help understanding radians in a concept, especially in relation to time c...
pure agate
Radians are a measure of an actual length while degrees are a measure of rotation.
buoyant coral
^
dapper tundra
Radians are a measure of an actual length while degrees are a measure of rotatio...
right but isnt one radian equal to pi?
buoyant coral
Yes
pure agate
Yes.
buoyant coral
Because you went 1 pi across the circle
Whats the formula for circumference of a circle
@pure agate
dapper tundra
2pi*r
dapper tundra
pi*r
buoyant coral
Look at that
dapper tundra
so a radian is basically the measure of half the circumference of a circle
pure agate
No.
dapper tundra
no?
pine horizon
radian is an unit of measurement of angles
dapper tundra
right
pure agate
radian is an unit of measurement of angles
No.
pine horizon
thats pi
pure agate
A degree is a measurement of an angle.
dapper tundra
I understand that
pure agate
A radian is the measure of an arc length.
pine horizon
oh yeah, forgot that
pure agate
Give me a moment to make a graph to demonstrate.
dapper tundra
so when you convert revolutions (circumference) to radians, you are essentially getting the circumference into terms of arc lengths?
dapper tundra
Give me a moment to make a graph to demonstrate.
thank you
frosty gorge
can someone help me with my math hw???
dapper tundra
can someone help me with my math hw???
dapper tundra
The orange arc is a measure of **1 pi**.
right
pure agate
What question did you have specifically in regard to time and revolutions?
pure agate
In that context, radians would be a measure of the periodicity of a trigonometric function.
rpm means rotations per minute, but I'm sure you already knew that.
dapper tundra
rpm means rotations per minute, but I'm sure you already knew that.
yes
im trying to understand what a radian actually is conceptually , since it seems like I've gotten completely different answers depending on who I ask
pure agate
Mathematically, 1 radian is the arc measure equivalent of a radius length.
edit : Correction.
dapper tundra
Mathematically, **1 radian** is the arc measure equivalent of a **radius** lengt...
s = rθ?
so when we convert it, the conversion factor is quite literally rθ, so we're getting circumference in terms of arc lengths when we convert
does that make sense or no?
dapper tundra
That would be 1 radian.
so it essentially is just the radius if it was an arc
pure agate
Yes.
dapper tundra
Yes.
is that why would the conversion factor for radians be rθ? since its getting the radius in terms of the sector length
or is there something im still not getting?
pure agate
is that why would the conversion factor for radians be rθ? since its getting th...
To the first part, yes.
dapper tundra
To the first part, yes.
what is wrong with the second part?
pure agate
Nothing.
1 radian has the equivalent rotation about a circle regardless of the radius, but it's actual arc length is dependent on the radius of the circle.
dapper tundra
1 radian has the equivalent rotation about a circle regardless of the radius, bu...
let me think about that for a second
pure agate
Reload that Geogebra link I posted.
dapper tundra
Reload that Geogebra link I posted.
I see that the arc length thats highlighted is (d) is pi no matter how much I change the radius length
pure agate
?
pure agate
Let me say this, the arc measure in radians around a circle will always be 2π rads.
dapper tundra
Let me say this, the arc measure in **radians** around a circle will always be *...
right
pure agate
And the conversion to an actual length would be 2πr.
The former is just a measure of rotation while the latter is an actual length.
dapper tundra
got it
so radians measures rotations in terms of pi
which acts like circumference but only for the measure of the angle
and not the length
pure agate
Radians are in terms of the radius. 1 radian is an arc length equivalent to the radius of the circle.
It just so happens that half of a circle as a measure of π radians = 3.14 radians.
dapper tundra
Radians are in terms of the radius. 1 radian is an arc length equivalent to the...
so the total amount of those arc lengths always equals ~2pi?
dapper tundra
It just so happens that half of a circle as a measure of **π radians = 3.14 radi...
got it
pure agate
Now an arc length of 2π on a circle with a radius of 2 would not be the same as an arc length of 2π radians on a circle with a radius of 2 though.
Note the use of radians in the latter measurement.
dapper tundra
Note the use of **radians** in the latter measurement.
let me think about it for a second
pure agate
The orange arc has an arc length of 2pi while its radian measure would be pi radians.
dapper tundra
Oh! so the 2 pi radians of radius 2 is saying that given a radius of two and an angle of 2pi, the resulting arc would be the product of the two
pure agate
dapper tundra
in this case its 4*pi/2
pure agate
With a radius of 4, the radian measure of the arc would be π/2 radians but the actual arc length would still be 2π units.
dapper tundra
With a radius of **4**, the radian measure of the arc would be **π/2 radians** b...
what do you mean by actual arc length? as in circumference or?
pure agate
If you were to lay that arc flat on the x-axis, it's length would be 2π.
dapper tundra
If you were to lay that arc flat on the x-axis, it's length would be **2π**.
right
so the radius times the radian measure gives us the arc length, s = r θ
pure agate
It's weird, but actually explaining this to you made me realize I've been thinking about radians incorrectly my whole life. 
dapper tundra
It's weird, but actually explaining this to you made me realize I've been thinki...
usually its like, heres the conversion factor, why it works or what it does, only god knows lol
pure agate
so the radius times the radian measure gives us the arc length, s = r θ
Spot on.
dapper tundra
so im going to try interpreting it in context now
so if a turntable has the reading of 33rpm, we know that it is going 2pi around itself, which means that every second there are .55 revolutions per second . since ω = v/r , we know that when we apply the conversion factor of rθ, the radius cancels out and only leaves us with the angle measure. so we multiply the .55 RPS by the radian angle measure of 2pi radians, which we then get our converted factor of 3.4557..... rad/sec
pure agate
it is going 2 pi radians around itself.
dapper tundra
it is going **2 pi radians** around itself.
mb
thank you for helping me today Kookie!
pure agate
yw
dapper tundra
.close
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tranquil ore
The triangles are similar
The ratios of the heights and the bases are the same
Parallel bases and vertical angles
You don’t even need the vertical angles tbh
You do know how to find the ratio
I’ll save you the mindless calculation and let you in on the industry secret
If two shapes are dilated by a factor of x, their properties are scaled by x^(dimension of the property)
e.g. lengths scaled by x, area by x^2, volume by x^3
Yup
Make a horizontal line at the intersection
And try to figure out the areas of the resulting rectangles
Hi
What’s the area of the bottom rectangle
@lean otter
The calculation is very simple
Try to think of what the relationship would be
||it’s twice the triangle||
Now try to figure out top
Make variables
For base and height
Yes
dude i cant hold your hand through every step
just try
have you made variables
what is the area of the rectangle in terms of them
and what is the area of the triangle
whoa whoa
wut
what are the variables here
you only need two
no no
dont make variables for area
make for lengths
tranquil ore
For base and height
^
near cave
nice question
tranquil ore
yes but what is it in terms of xy
trapezoids
and no, use this
^
yes but look at the full pictures
my hands are gonna be sticky with weed for the next few minutes so ask me any questions now
near cave
lol
tranquil ore
what is the ratio of bases
yes
if the rectangle is width w, what is the top triangle base
yup\
close but *.5 cause triangle
but yea
yep
gotchu
gl with everything else
im out fo rthe night
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frigid locust
if a line has equal intecepts on both axes , does it mean its slope is 1?
sleek sentinel
i think so? draw diagram ideally
pine horizon
if a line has equal intecepts on both axes , does it mean its slope is 1?
if absolute values of intercepts are same then it'd be +- 1
sleek sentinel
(-a, 0) to (0, a) has a slope of a/a = 1
pine horizon
and if values of intercepts are same then slope would be -1
dull sequoia
if a line has equal intecepts on both axes , does it mean its slope is 1?
x^3 intercepts both axis
sleek sentinel
x^3 is not a line but yes
dull sequoia
well x/2 is a line then
frigid locust
and if values of intercepts are same then slope would be -1
how would it be -1 tho?
shouldnt it be just 1?
sleek sentinel
go on desmos and plot (1, 0) and (0, 1)
one is above and the other is to the right
frigid locust
yeah wouldnt its slope be 1?
sleek sentinel
pine horizon
how would it be -1 tho?
tan(135 degrees) = -1
or use the points (1,0) and (0,1) to find slope
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frigid locust
so its only 1 or -1 ? the slope
sleek sentinel
what else could it be
frigid locust
just asking :d
sleek sentinel
mb :d
but yeah (a, 0) and (0, a) are always going to be the same distance from (0, 0)
you might say the relationship is always 1-to-1
same for (a, 0) and (0, -a) which is the case for slope = positive 1
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frigid locust
ok another question , while solving a question i got a 3rd degree polynomial
4x^3 +2x - 36 = 0
i found out that x = 2 is a root
cuz 4(2^3) + 2(2) -36 = 0
4(8) + 4 - 36
32+4-36
36-36
0
so i did synthetic division on this to get a depressed quadratic that i could solve for the rest 2 roots
i get 4x^2 +10x -16 by using synthetic division
but (x-2)(4x^2+10x - 16) is not equal to 4x^3 + 2x - 36 , what did i do wrong?
lime dust
Show your long dividion
narrow ridge
Try regular long divison
frigid locust
i just do synthetic cuz im used to it more
oh wait nvm , i found my mistake
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forest maple
Which one is correct? (Or neither)
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Which one is correct? (Or neither)
@forest maple Has your question been resolved?
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forest maple
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lone arch
Sorry for the tag, I know its annoying
Can you send a larger screenshot of the problem?
remote lintel
Hello.
forest maple
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forest maple
Why's the x axis displacement even given
remote lintel
Why's the x axis displacement even given
I'm calculating. I'll explain when I'm done.
forest maple
Oh ok thanks
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forest maple
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forest maple
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frosty granite
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frosty granite
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flat frigateBOT
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frosty granite
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And also what would the stationary solution be?
When i try and work it out i get 8B/1+B
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tranquil glen
hello, can someone help me with this problem? i am trying to solve it for long but i cant do it 😦
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hello, can someone help me with this problem? i am trying to solve it for long b...
pure vector
hello, can someone help me with this problem? i am trying to solve it for long b...
solve a out?
tranquil glen
solve a out?
i have this
but i do not know if its correct
its rhombus so it should be 3 each side
tranquil glen
oh yes
I didn't read in the assignment that it is a rhombus and so I tried different sine and cosine theorems that didn't work out.. then I found out that it is a rhombus and wrote 3 on all sides but I still didn't see the Pythagorean theorem there.. thanks!
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gaunt inlet
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gaunt inlet
cansomeone explain what they mean by inflection point where the tangent lines switch sides?
does this drawing show that?
weak nimbus
inflection point = a point which changes the side where the function looks at
gaunt inlet
wdym by side
weak nimbus
x<0, it looks below, x>0 it looks above
btw to find a inflection point you need to evaluate the second derivative
of the starting function
gaunt inlet
oh wait really
this is what i did
it was increasing in that area for the first derivative, in the second derivative its concave down then concave up
weak nimbus
Ok. + means the function looks up, . it looks down, like a parabola if you think about it
weak nimbus
yes
stoic dune
"concave up" like, the curvature of the function is facing upward
gaunt inlet
ooh
tawdry sinew
can someone help me out?
what language is this or what does it mean? any help would be appreciated.
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calm gale
Just quick question if anyone has time
For part b, I did 10^-1/10 to find the value of b but it was wrong. Since the y coordinate is not base 10 do I have to use the base 4 relaltionship to find b?
Hence if I got this in an exam and it had not a base 10 do I always use the base to the power of the other value to find constant terms?
Thank you in advance!
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coarse geode
Can someone help me visualize this problem?
It clearly states that the midpoint of AB is at 14m why is the length not 14*2?
spice grove
If the midpoint is M
Then they mean OM is 14.
While you're thinking something like AM?
coarse geode
OH okay yeah that makes more sense thanks!
Do you know why that could be?
or like what theyre doing
spice grove
I do. (But don't ping me like that when I've already left)
Do you have a clear image of this in mind?
coarse geode
ive attempted to draw it so i hope i do
coarse geode
Yes
spice grove
And the arc AB subtends an angle less than 2pi at the centre
coarse geode
It completes 2pi radians in 16 seconds as per the previous part hence the pi/8
yes that's true
spice grove
Not sure where you mentioned those 16 seconds but alright.
coarse geode
Not sure where you mentioned those 16 seconds but alright.
given ("The sprinkler makes one full revolution in 16 seconds."
spice grove
yes that's true
The angle AB subtends is actually AOB
coarse geode
Yes i can visualize that
coarse geode
so just 2 * aom
okay yeah
ahh im seeing it now so they wanted the angle AÔM
cos of AÔm is adj/hyp
alright that makes sense
multiply it by 2 then
and thatll give us the entire angle AÔB
then angle/b = T
where b = pi/8
honestly im struggling on this entire questions so i might as well put it all in, ill try solving it though
major thing is ab visualization
spice grove
then angle/b = T
That's right.
coarse geode
I was able solve the rest of it except this last part
Again so they want us to model the change in the angle?
spice grove
I do. (But don't ping me like that when I've already left)
Also this.
spice grove
if you're doing i after you've already done h, it'd be rather quick
coarse geode
I mean I guessed h to be πt/8
because it would make sense as a function of time
and its substituted into the i part so i thought that's what it was coming from but im not exactly confident
for the i part i assume they did d/sin(α)=20/pi-α-β
spice grove
sin()
coarse geode
we are given β and we know pi in radians and subtracting those gives us 2.37 which is what is desired
and it seems like they substitute π𝑡/8 for alpha
which is why i assumed it was the answer to i
i hope my reasoning makes sense
coarse geode
yeah thats my only problem i dont like assumptions
spice grove
alpha is just the angle the sprinkler covers over time.
So it's just b * t
where b = pi/8
coarse geode
ah i see
which is why at t=0 alpha is at point A
okay that makes sense i wont take up any more of your time thank you!
and sorry once again ^^
little mountain
If I am given the Corner Coordinates of the Orange and Blue Parallelograms, how can I calculate what percentage of the Orange Parallelogram overlaps with the Blue Parallelogram?
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If I am given the Corner Coordinates of the Orange and Blue Parallelograms, how ...
river field
You are given all corner coordinates?
little mountain
To my knowledge, only three would be needed, but all four corner coordinates are known
river field
A dirty and inefficient way would be to calculate the coordinates of points where lines intersect, calculate the area of the new shape (by seperating it in triangles for example) and then comparing that area to the other 2 shapes accordingly...
In the case that no intersect points exists check if they overlap or aren't close to each other at all
And if they do overlap check which is bigger, as in, which is on top of which
I feel like there's a more efficient solution though
earnest olive
For 100% overlapping, you have to use the condition that the corner points of the inner parallelogram are on the same sides of the adjacent sides
and another case, when the area of both rectangles are both equal and they overlap with all vertices being the same
little mountain
A dirty and inefficient way would be to calculate the coordinates of points wher...
Alright, that does make sense to divide things into triangles
earnest olive
Oh yeah ofc it does
river field
I assume you're programing some kind of algorithm for this?
earnest olive
Do you know the area of a 4 sided figure? Those will help but it is really time taking
river field
In the general case the resulting overlap shape could be some polygon, so it's faster to just break it down into triangles than to check what kind it is
earnest olive
But for the sake of knowledge, it is $\sqrt{(s-a)(s-b)(s-c)(s-d)}$
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penguin
little mountain
I assume you're programing some kind of algorithm for this?
Yes, I am programming an algorithm for this.
earnest olive
then you should use all the formulas you can
river field
I'd start by writing a function that checks if the lines of the polygons intersect and calculate the coordinates of the points of intersection
If there are no points of intersection I'd check whether the polygons are within each other or seperated completely
If within each other check which is bigger to see if it's 100% or if it needs to be calculated
If separated then it's 0%
and then do the calculations for the general case intersection
wind echo
I’m being offered linear alg or DEQ next year which should I take?
wind echo
I’m currently taking multi
median vigil
linear algebra is usually a prerequisite for differential equations, at least from what i can tell
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river field
Take both :kappa:
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placid onyx
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sly needle
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sly needle
Can someone please help me with this
icy lance
,rcw
flat frigateBOT
icy lance
a fine
do you know the conditional probability formula
icy lance
yeah P( snowed given won ) ie P(snow | won) but there is a formula for P(A|B)
icy lance
yeah so (snowed and won)/(won)
icy lance
yeah
sly needle
I was a little bit confused
Can you help me with another
Number 3
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Nvm I got it
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timid escarp
Hello
timid escarp
i need help finding the following
I can determine the amplitude is 4
and I believe period would be 2pi
I need to find the equation
4cos(x)
timid escarp
I believe cos because sin goes through 0,0
I don’t have my graphic calculator with me so I can put that in and check
coral blaze
yeah thats good
timid escarp
alright thanks
lean otter
I don’t have my graphic calculator with me so I can put that in and check
Use desmos
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loud osprey
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