#help-27
severe ermine
The width is two different numbers
As you can see in the bottom half it is wider
Than it is in the top half
I need to know what the average width is
If we look at the room, there are basically two rectangles
One larger one
And one small one
I know the dimensions of these
And the areas
But I do not know how to calculate the average width of the entire irregular polygon
Can someone please help?
I have been stuck in the office for the past 90 minutes
I really want to get home and I can't until this is sorted
<@&286206848099549185>
Please someone
supple knot
The width is two different numbers
do you know the proportion of width 1 and proportion of width 2?
supple knot
like 60/40, 70/30, 50/50
severe ermine
I just don't know how to get the average
supple knot
you just need the proportions
supple knot
that doesn't answer my question
supple knot
like 60/40, 70/30, 50/50
this is what i'm looking for
severe ermine
In square meters
8.788927335640139 for the smaller one
91.2110726644 for the bigger one
supple knot
do you know what a proportion is?
severe ermine
91.2110726644/8.7889273356
supple knot
the two proportions should add up to 1 or 100%
supple knot
like 60/40, 70/30, 50/50
like these numbers do
severe ermine
They do
supple knot
,calc 91.2110726644/8.788927335640139
woven radishBOT
Result:
10.37795275591
Why are you dividing it?!
severe ermine
If you want proportions why are you diving them!?
91.21107266435986/8.788927335640139
To the lowest place possible
supple knot
$avg_{width}=8.788927335640139/ 100 \cdot smaller_{width} + 91.2110726644/100 \cdot larger_{width}$
woven radishBOT
riemann
severe ermine
The width on the larger one is 2.863 meters, the width on the smaller one is 1.284 meters
Ok I am gonna give that a shot
$avg{width}=8.788927335640139/ 100 \cdot smaller{1.283} + 91.2110726644/100 \cdot larger_{2.863}$
woven radishBOT
V
severe ermine
Ah it does not calculate it for you
,calc avg{width}=8.788927335640139/ 100 \cdot smaller{1.283} + 91.2110726644/100 \cdot larger_{2.863}$
woven radishBOT
The following error occured while calculating:
Error: Unexpected operator { (char 4)
severe ermine
= ((8.78/100)*1.283) + ((91.21/100)*2.863)
Is it this?
,calc = ((8.78/100)*1.283) + ((91.21/100)*2.863)
woven radishBOT
The following error occured while calculating:
Error: Value expected (char 1)
severe ermine
,calc ((8.78/100)*1.283) + ((91.21/100)*2.863)
woven radishBOT
Result:
2.7239897
just an aside, your image doesn't look like it's 91% one width and 9% the other width. but probably the diagram isn't to scale?
severe ermine
Width?
Is it not the area?
The values I provided are for the square meters....
The area size
devout snowBOT
@severe ermine Has your question been resolved?
devout snowBOT
@severe ermine Has your question been resolved?
devout snowBOT
@severe ermine Has your question been resolved?
supple knot
The values I provided are for the square meters....
proportions of the room that is small_width and large_width, not proportion of the areas
Find the two lengths $L1 = A1 / W1$ and $L2=A2/W2$
woven radishBOT
riemann
supple knot
Now express the lengths in terms of proportions
supple knot
**riemann**
and replace 8.7... and 91.2... with the new length proportions
kindred bear
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hybrid snow
You didn't answer the question then
It says verbatim that the answer is in the form of A + Bkπ
Which means you need to account for all answers
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kindred bear
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sharp robin
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sharp robin
What’s does sin mean in this case
sin(165°)
What does it mean
<@&286206848099549185>
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<@&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.
mild prawn
Hi
sharp robin
Hi
mild prawn
Hm, let me check.
main gull
What’s does sin mean in this case
What exactly do mean?
sharp robin
What are sin and cos
main gull
$sin \theta = \frac{opp}{hyp}$
woven radishBOT
dldh06
sharp robin
I don’t understand it
main gull
Do you not know your trig ratios?
sharp robin
What does that mean
sharp robin
Yes
restive river
@sharp robin as a suggestion, make sure that others understand what information you're looking for. don't make them guess.
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fast helm
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fast helm
i just need help confirming my integrating
is the integration of sqrt(1-cos^2x)
(1-cos^2x)^3/2 over 3/2-2cosxsinx ?
supple knot
(1-cos^2x)^3/2 over 3/2-2cosxsinx ?
Differentiate it and see if it equals the integrand
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young cobalt
u got beaten bro other channel
pseudo basin
.close
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wooden veldt
You should use the divergence test
Find the limit of the power by rationalising the numerator yeah
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stable glen
Hello guys, i need your help, does anyone here knows how to solve for the area of the plane region(application of integration), such as solving for the vertical and horizontal strips?
I am really confused with this figure, if what is the limits and the values i should input the formula of vertical and horizontal strips. I hope someone can help me with this.
devout snowBOT
Hello guys, i need your help, does anyone here knows how to solve for the area o...
torn wave
Hello guys, i need your help, does anyone here knows how to solve for the area o...
you mind sharing the problem itself?
regal torrent
Hello guys, i need your help, does anyone here knows how to solve for the area o...
What area r u tryna find
Area enclosed by what
stable glen
What area r u tryna find
by x=4, y=8, and y^2=x^3
regal torrent
by x=4, y=8, and y^2=x^3
Yea so what have u tried
Try drawing the boundaries
Like mark the region
torn wave
assuming youre tryna solve the area under y^3=x^2 (on the graph, you might have switched the exponents in ur text) from x=4 and y=8 individually, you can set up integrals in 2 ways
either you do both of them by hand, one with the y axis being the integral of the inverse of the function, or you do the area of the rectangle denoted by the lines x=4 and y=8 and subtract one of the areas
stable glen
Yea so what have u tried
what i have tried is this,
torn wave
,rotate
woven radishBOT
stable glen
either you do both of them by hand, one with the y axis being the integral of th...
like to separate definite integrals right?
torn wave
ooh youre just tryna find teh area under y^3=x^2 over the y axis
i thought you meant both
if youre going to do just that, i suggest you try and integrate the inverse
and switch the bounds of the integral to be the position of the y=8 function
or 8
literally the same thing
stable glen
ooh youre just tryna find teh area under y^3=x^2 over the y axis
yup just the top
torn wave
well what would the inverse of y^3=x^2 be
stable glen
well what would the inverse of y^3=x^2 be
does that mean that ill gonna sub a number to a certain variable?
torn wave
do you know integration?
stable glen
yupp
torn wave
cause from your work i saw you using only the limit definition of an integral
stable glen
cause from your work i saw you using only the limit definition of an integral
for the vertical strip? yeah, i havent finished it yett
torn wave
well lets just compute the inverse first
the inverse of y^3=x^2 is x^2=y^3 right?
now we have to make y the subject so we can integrate
torn wave
yes that is correct
now integrate that function from 0 to 8
since we figured out the inverse, you can think of it as interchanging the x and y lines
stable glen
now integrate that function from 0 to 8
96/5
torn wave
i havent actually done it 1 second
stable glen
thenn what am i gonna do next?
torn wave
does the problem ask you to do anything else?
stable glen
just find the area of the plane using vertical and horizontal strip
so thus our answer 96/5 sq. units is the area of the shaded region already?
torn wave
yes thats it
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pulsar bone
If t = tan(θ/2), express the following in terms of t.
a) tanθ
b) sinθ
c) cosθ
pulsar bone
can someone walk me through this
crisp mauve
what have u tried
uve gotta use formulas and just solve for the trig funcs
also tan x = sin x / cos x thats all u need to know pretty much
pulsar bone
how do you get from t = tan(x/2)
to
i understand how you use this to find cos x and sin x
pulsar bone
how do you get from t = tan(x/2)
but i dont get this
crisp mauve
$\tan x = \frac{\sin x}{\cos x} = \frac{2\sin \frac{x}{2} \cos\frac{x}{2}}{\cos \left(\frac{x}{2}\right)^2 - \sin \left(\frac{x}{2}\right)^2}$
woven radishBOT
ta
crisp mauve
then we divide by cos(x/2)^2 and get that
$\frac{2\sin \frac{x}{2} \cos\frac{x}{2}}{\cos \left(\frac{x}{2}\right)^2 - \sin \left(\frac{x}{2}\right)^2} = \
\frac{2\sin \frac{x}{2} \cos\frac{x}{2}}{\cos \left(\frac{x}{2}\right)^2 - \sin \left(\frac{x}{2}\right)^2} \cdot \frac{\frac{1}{\cos \left(\frac{x}{2}\right)^2}}{\frac{1}{\cos \left(\frac{x}{2}\right)^2}} = \
\frac{2\cdot \frac{\sin\left(\frac{x}{2}\right)}{\cos\left(\frac{x}{2}\right)}}{1 - \left(\frac{\sin\left(\frac{x}{2}\right)}{\cos\left(\frac{x}{2}\right)}\right)^2}=\
\frac{2\tan\left(\frac{x}{2}\right)}{1 - \left(\tan\left(\frac{x}{2}\right)\right)^2}$
woven radishBOT
ta
green walrus
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green walrus
how is $\lim_{x \to 0} (x + 1) = 1$ possible?
woven radishBOT
Willow
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kindred bear
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ancient furnace
You can use the identity that sin^2(x) = 1 - cos^2(x)
kindred bear
You can use the identity that sin^2(x) = 1 - cos^2(x)
ty
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vernal anvil
how would i prove 3, just started doing proofs but am finding the ways to prove these obvious statements challenging
devout snowBOT
how would i prove 3, just started doing proofs but am finding the ways to prove ...
graceful cosmos
Using ring axioms?
vernal anvil
this is our axiom
i was thinking something to do with distributivity but not sure
graceful cosmos
-a is the additive inverse of a
vernal anvil
or maybe an additive inverse
graceful cosmos
A notation they're using
vernal anvil
ah
so can i essentially state
if -a is the additive inverse of a
-(-a) is the additive
?
or something
graceful cosmos
-(-a) is the additive inverse of -a yeah
graceful cosmos
That means
-(-a) + (-a) = 0
wooden veldt
You still have to prove it
graceful cosmos
Yeah we're still proving 3
vernal anvil
but not how to show it
graceful cosmos
That's a definition
vernal anvil
oh right
graceful cosmos
It's what makes -a what it is
graceful cosmos
Btw if I showed you this equation:
-(-a) + (-a) = 0
What would you say the inverse of (-a) is?
vernal anvil
-(-a)
graceful cosmos
But -a is the inverse of a
vernal anvil
could i say something like;
a+(-a) the additive inverse =0
and then
subtract -a from both sides?
graceful cosmos
What is "subtract"?
graceful cosmos
That doesn't exist yet haha
vernal anvil
now what if i were to say like
the normal additive inverse property
and just replace a with -a
graceful cosmos
Wait, have you proved that inverses are unique yet?
vernal anvil
havent gone over the proof but i know the statement yes
my prof has covid so only slides are being posted
no actual explainations
graceful cosmos
Okay. So using the two equations above, it's easy to spot two inverses of -a
a is an inverse.
-(-a) is an inverse.
vernal anvil
and so is -a
graceful cosmos
But inverses are unique. So:
strange cloak
devout snowBOT
strange cloak
Can anyone see what I did wrong?
solar kelp
I need help me with my homework
strange cloak
But I still did something wrong
small raptor
Why’d you put Y** = -10
strange cloak
I assumed gravity to be so
vast rain
Can anyone see what I did wrong?
do you know if the walls have zero thickness?
strange cloak
I think that's that the question assumes - the wall has 0 thickness
small raptor
I assumed gravity to be so
WHAT IN THE ENGINEER
vast rain
hmm so I see you did the whole kinematics thing to figure it out
small raptor
U round pi to 3 too?
strange cloak
So when X =6, y = 6, when X=12, y also = 6
vast rain
but perhaps an easier thing to do here is fit a quadratic to it lol
strange cloak
Nope
small raptor
but perhaps an easier thing to do here is fit a quadratic to it lol
Yea this would be easier
strange cloak
Ya, probably find the equation, and hence to solve for it's maximum, and it would be way easier
Found the equation
vast rain
then the slope of the tangent line at x = 0 is also tan alpha (I think that's where the name "tan" actually comes from)
solemn fossil
So Im doing this math project thru desmos creating a roller coaster; specifics dont really matter. Trying to figure out possible ways I can make that transition look a little nicer
devout snowBOT
So Im doing this math project thru desmos creating a roller coaster; specifics d...
solemn fossil
Oh sorry lol
twin stump
Do you know calculus
solemn fossil
Sadly no
solemn fossil
Ik the beginning of calculus you learn how to calc slope of a curve or whatever, this is my 10th grade summative tho lol
twin stump
If you knew calculus, what you would do is take the derivative of your function ont he left and try to get it to be the derivative of the function on the right
Do you know how to take derivatives?
solemn fossil
No clue lol, bit advanced. I could try to learn but not an expectation for the assignment
If there's no easy method, not the end of the world 🤣 just my inner perfectionist wants to get rid of the nasty decimals
twin stump
Can you tell me what the functions are
twin stump
So i'll quickly walk through this with you. So this is the function on the left
We want to find it's derivative when x is 25
It's derivative is -3.2(x - 21)
So, when x is 25 we have the slope is -12.8
solemn fossil
It's derivative is -3.2(x - 21)
How do you get this
twin stump
Power rule: the derivative of x^n is nx^(n-1)
So that 2 went in front and multiplied with the -1.6
and the power decreased by 1
The constant disappeared because that is what happens when you take the derivative
So now we have a function f(x) = a(x - b)^2 + c, and we want it to go through (25, 22.4)
(this is the function on the right, and we're going to figure out what a, b, and c could be)
Plugging in the point gives the equation 22.4 = a(25 - b)^2 + c
Now we take the derivative and set it ot the slope that we calculated. The derivative of f(x) is f'(x) = 2a(x - b)
So we have the equation 2a(25 - b) = -12.8
Notice that is 2 equations and 3 variables, so one will be change-able and we'll be able to find different parabolas that smoothly connect with the other one
solemn fossil
I see
This is going to take me a bit to comprehend lol, will ask if I have any questions 🤣
@twin stump can i reopen this channel if it automatically closes? i have to go eat dinner rn
twin stump
Sure
vast rain
I see
you could also look at smoothing splines
which basically do a soft enforcement of the smoothness condition
twin stump
Solving the two equations gives you these (I found it easiest to make b the free variable)
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heady trail
hello may I ask for with the blue circle statement why the orange one wont be zero?
devout snowBOT
hello may I ask for with the blue circle statement why the orange one wont be z...
@heady trail Has your question been resolved?
torn vessel
it would be 0 at t_0
heady trail
it would be 0 at t_0
yes but tan^-1(0) not equal to 0?
torn vessel
yeah it is
heady trail
it would be 0 at t_0
but now the tan^-1 still remains at the end
torn vessel
because it's being evaluated at v(t), not v(t_0)
heady trail
but they are the same
heady trail
because it's being evaluated at v(t), not v(t_0)
why the first can be t0 but second cannot?
heady trail
if they're the same
ya I know, but how can two same unknown, one can change to other things and one do not?
torn vessel
around x=0, |ln(x^2+1)| < |arctan(x)|. They're both close to 0 there, but the log is closer
so letting it just be approximately 0 is a better approximation
heady trail
around x=0, |ln(x^2+1)| < |arctan(x)|. They're both close to 0 there, but the l...
ohhhhh I see
I understand now thank you
.close
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bright burrow
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bright burrow
can anyone explain the question or the numerator the answer is D
also for this
This process is valid?
💀 hopefully this helps, if anyone understands 19 hint pls explain
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@bright burrow Has your question been resolved?
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@bright burrow Has your question been resolved?
bright burrow
<@&286206848099549185>
So i was thinking of using the tree diagram for this
And i think my unequal side is okay
But for the equal side im pretty sure the 1/6 is okay
But then the child throws two more dice
So basically like equal,equal,x,y
Now what ive found is 1,1 (the equals) only work with (1,3),(2,2),(3,1)
And (2,2) works with (1,1)
If the equals are 3,3 or 4,4 or more it never works
So i have 4 cases where it works
But would the denominator be 36
Anyway the answer i get this way is 1/9+1/54
Which is 7/54 and very off from the answer key
bright burrow
You mean after simplification?
bright burrow
Sometimes the options are left unsimplified
red sierra
hm ok
i don't think you need to multiply 5/6 on the unequal side
you just need to calculate the probability of getting (1,5)(2,4)(4,2)(5,1) out of a total 36
bright burrow
that is still 1/9
red sierra
wouldnt it just be 1/9?
bright burrow
what 5/6.2/15 represents is p(unequal numbers intersection sum of those unequal numbers is 6)
direct 1/9 is better but it didnt strike me when i was first doing it
red sierra
oh i got the answer
so for the unequal side, 1/9 is right
ill rewrite my process again since mine is too messy
bright burrow
Cool
red sierra
my phone camera broke so it's bad quality srry
tell me if you don't understand somthing
bright burrow
I get it
bright burrow
my phone camera broke so it's bad quality srry
I do think that there is a better way of drawing the tree
But i only realized that after seeing this
red sierra
I do think that there is a better way of drawing the tree
what way is that?
red sierra
ohh yeah that looks better
bright burrow
Thanks tho theres still two other questions here
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red sierra
hi again
bright burrow
Theres still 2 more questions before this
red sierra
so the second card has to be 0 or 2 or 4 or 6 or 8
bright burrow
Yea
red sierra
and the first card has can be any number excluding the second card
bright burrow
I think its easiest to just take cases
red sierra
so if we assume we choose the second card first, bc it doesnt matter which order u draw the cards
it would be 5*8=40
bright burrow
so if we assume we choose the second card first, bc it doesnt matter which order...
You draw both cards same time, but then you arrange in successive order is what i got
bright burrow
so if we assume we choose the second card first, bc it doesnt matter which order...
The only way to ensure that you choose the second card first
Is ensuring the value of the first card is lesser than that of the second
bright burrow
it would be 5*8=40
5/9 or 40/c(9,2) is what the solution key says but i think its wrong
Because their logic is just c(5,1)c(8,1)
red sierra
yeah i got 5/9
bright burrow
yeah i got 5/9
I know but it shouldn't work
red sierra
bright burrow
Like show me where this is wrong, the idea is that i fix one card and see what possibilities i have, like i picked 0, so i can use 2,4,6,8 hence 4
red sierra
ignore the first line
red sierra
lol congrats
warped relic
!help
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Please read #❓how-to-get-help
rain marlin
i said sorry
bright burrow
.close
bronze vessel
Find the differential
$d^3f\left(x,y\right)hh'h'' for :f\left(x,:y\right):=:x^3:+:y^3:−:3xy\left(x:−:y\right)$
h-es are vectors
woven radishBOT
Git commit
devout snowBOT
@bronze vessel Has your question been resolved?
wooden veldt
hh'h''?
bronze vessel
Yes
wooden veldt
what is h?
bronze vessel
what is h?
"h-es are vectors"
wooden veldt
yeah, what vectors?
bronze vessel
[x,y]
Original description of this exercise didn't even mention what h-es are vectors
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devout snowBOT
bronze vessel
Find the differential
$d^3f\left(x,y\right) for f\left(x,:y\right):=:x^3:+:y^3:−:3xy\left(x:−:y\right)$
woven radishBOT
Git commit
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bronze vessel
Find the differential
$d^3f\left(x,y\right) for :f\left(x,:y\right)=:x^3+y^3−:3xy\left(x:−:y\right)$
woven radishBOT
Git commit
devout snowBOT
@bronze vessel Has your question been resolved?
devout snowBOT
@bronze vessel Has your question been resolved?
devout snowBOT
@bronze vessel Has your question been resolved?
frail canopy
recall that $df(x,y)=f_x(x,y)dx+f_y(x,y)dy$
woven radishBOT
please request a new nickname
frail canopy
@bronze vessel use this to help you out
devout snowBOT
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bronze vessel
<@246710022568935424> use this to help you out
It supposed to be 3d matrix
devout snowBOT
@bronze vessel Has your question been resolved?
frail canopy
It supposed to be 3d matrix
oh rly? I've never seen this before
kindred bear
devout snowBOT
hybrid snow
do you know your cos(a+b) and cos(a-b) identity
hybrid snow
so just plug values
hybrid elk
couldnt you just arccos the two values?
kindred bear
wait but there is not sin
autumn sparrow
wait but there is not sin
Create a triangle and use the cosine values as an aid for constructing the values of the sides
glossy dew
sin^2 + cos^2 = 1
winter patrol
both angles are acute
glossy dew
._.
autumn sparrow
then use the pythagorean theorem to find any missing sides, and then plug in the appropriate values
glossy dew
$sin = \sqrt{1-cos^2}$
woven radishBOT
GameSwitch
kindred bear
Create a triangle and use the cosine values as an aid for constructing the value...
alr ty got it now
.close
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autumn sparrow
np!
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fast helm
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fast helm
what rule is used to find this?
jovial mauve
Do you know the derivative of a^x wrt x?
fast helm
wrt?
fast helm
alna^x?
jovial mauve
No
fast helm
a^xlna?
fast helm
3^(2x)ln3?
woven radishBOT
Stephen
jovial mauve
Right
fast helm
3^2x*ln9
arctic field
same thing 
woven radishBOT
Stephen
devout snowBOT
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devout snowBOT
how do i do this
quaint citrus
Just break it up into separate shapes
Then add the areas above the x and subtract from it the area below the x
U understand?
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outer stirrup
Hello, which of these solutions is correct?
devout snowBOT
Hello, which of these solutions is correct?
restive river
first
outer stirrup
Following this
So first one is definitely correct? Maybe they are both wrong idk 😄
restive river
also if you look at the second answer logically
the hypotenuse is 15 km
and the answer says the height is 14.95 km
outer stirrup
Yeah I thought about that, angle would have to be 45 degrees in that case right
restive river
no
the angle would be very close to 90 degrees
the hiker would be walking up a wall almost
logically, it doesn't make sense
restive river
a 14 slope and a 14 degree slope has some difference i think
but im confused with the wording "hiking up 14 slope"
ashen vault
I wanna parameterize equation
$x^3+y^3=x^2+y$
I have change it to
$x^3-x^2+y^3-y=0$
and created 2 functions
$x(t) = t^3-t^2 \ y(t) = t^3-t$
However, when i've plotted the graph, i got something completely different than starting equation. What am i doing wrong?
devout snowBOT
I wanna parameterize equation
$x^3+y^3=x^2+y$
I have change it to
$x^3-x^2+y^3-y...
woven radishBOT
redve
ashen vault
I should get something like this
but i got this
it doesn't seems even close about right
the second graph is on range [-2, 2] with dt=0.1
devout snowBOT
@ashen vault Has your question been resolved?
ashen vault
how would look like function x(t), and y(t), so i will get the upper graph? <@&286206848099549185>
ashen vault
.close
umbral roost
so I did everything till the circled part, but how do I get to the basis of the eigenspace?
devout snowBOT
so I did everything till the circled part, but how do I get to the basis of the ...
sick marsh
Well notice then that if we take the first column as x_1, second as x_2 and third as x_3 that we get x_1 = -x_3 and x_2 = -x_3. If you now take x_3=t with t a variable then we have together the vector
(-t, -t, t) or in other words t(-1, -1, 1) so we see that any multiple of (-1, -1, 1) is it's eigenvector and from there you can conclude that the basis has the vector (-1, -1, 1)
@umbral roost you follow?
umbral roost
yes im trying it out one second
i know what you mean but i dnt know how to write the equations times t.
I understand the steps you said and I can find the right answer, but i want to write it down the right way and I dont know how
rare pelican
how do i do this
devout snowBOT
@umbral roost Has your question been resolved?
signal mountain
formal fjord
Hello I have 23 devices and 13 work all right. If I pick 5 on random how big is the chance to get at least 1 faulty device.
devout snowBOT
Hello I have 23 devices and 13 work all right. If I pick 5 on random how big is ...
restive river
It is 1 - (probability that all the 5 picked devices are working fine)
Can you try to find (probability that all the 5 picked devices are working fine)?
restive river
Yup, that's correct 🙂
keen lodge
Please help me with this
devout snowBOT
Please help me with this
alpine idol
the task is to write a formula to calculate it's determinante ( but not ad - cb)
alpine idol
and then proof that the formula is true
i don't know how to write this
like with gauß i would have eliminate the c first to get a 0
how tf do i do this here lol
also no idea how laplace works in a 2x2 matrix
only used ad - cb so far
stone stump
if you were to apply gauß, with what constant would you have to multiply the first row so that c-const*a=0
alpine idol
if you were to apply gauß, with what constant would you have to multiply the fi...
my math is kinda weak
i mean my equation solving
sec
idk tbh
alpine idol
if you were to apply gauß, with what constant would you have to multiply the fi...
can you just show me the answer
c - (a* x) = 0
a*x = c
no idea dude i am a novice just tell me the answer lol@stone stump
i don't even think it exists
@stone stumpdude
i tried everything
i just need to know how to use it in the future
just tell me how to get the 0 there and i can finish this task
stone stump
x=c/a but I don't think you will get far in linear algebra if you are lacking basics like this
alpine idol
x=c/a but I don't think you will get far in linear algebra if you are lacking ba...
this means i need to multiply first row by c/a ?
and then subtract it from 2nd row?
also yeah i will need to revise some basics
alpine idol
but this interaction helped me a lot
there were some gaußes where i couldn't advance further cuz of this reason
now that i know this technique i will be able to solve it easily
@stone stump ok
c - ax = 0
c = a x
c/a = x
i multiply first line with c/a
c bc/a
c d
then i subtract it from the second one
c bc/a
0 d- bc/a
now i use (c * (d- bc/a) ) divide by c/a for determinante
it becomes * a/c
ok that makes the thing even uglier
stone stump
you don't change the first row
you multiply it with c/a and then immediately subtract it from the second
but the first row stays a b
alpine idol
oh its like -3 first row
but in this case
- c/a first row?
a b
0 d- b * c/a
a * ( d- b *c/a) is the determinant ?
@stone stump
alpine idol
and that is equal to?
ad - bc
mindblown
WOW
@stone stumpbtw the thing i wrote earlier works as well
but yours is more efficient in the long run
but thx dude
this helped me alot
lunar harbor
.close
lavish wind
devout snowBOT
supple knot
Would be worth putting in #real-complex-analysis as well
devout snowBOT
@lavish wind Has your question been resolved?
devout snowBOT
@lavish wind Has your question been resolved?
devout snowBOT
@lavish wind Has your question been resolved?
devout snowBOT
devout snowBOT
Available help channel!
restive river
How can I find all positive integers a, b, and c such that a + b + c + 7 = a * b * c holds?
devout snowBOT
How can I find all positive integers a, b, and c such that a + b + c + 7 = a * b...
keen nacelle
testing
small raptor
Mhm I can’t think of a way to solve an equation with 3 variables with just 1 equation
hollow pollen
its a bit of work but its doable
sick marsh
I am guessing that because a*b*c grows much harder than a+b+c+7 there is some kind of upper bound to how many integers are possible?
hollow pollen
solve for some variable and check when its in integer
for example b = (a+c+7)/(ac-1)
and check when that is an integer
which requires ac-1 | a+c+7 of course
hollow pollen
I am guessing that because a\*b\*c grows much harder than a+b+c+7 there is some ...
correct theres not many solutions
restive river
b=1?
hollow pollen
so you only have to find a and b such that a + b + 8 = ab
restive river
ab ≤ a+b+8 , b ≤ (a+8)/(a−1) , a≤b gives a(a−1) ≤ a+8 i.e. a ≤ 4. If a=1 the condition ab−1|a+b+7 becomes b−1|(b−1)+9
that should be right
If a>1 i.e. a≥2 , the condition b≤(a+8)/(a−1) helps restricting the possibilities for the pairs (a,b) .
Finally, there are two possible solutions (a,b,c)= (1, 2, 10), (1, 4, 4) and their permutations.
omg thanks
could you maybe help me with the final explanation
could you write me a full final explanation
hollow pollen
oh wow that looks good yes
you will need to justify why you can choose one variable to equal 1
which tbh ive not done myself
restive river
could you do it please
could you finish the job and write a good explanation please since I have done so much
true nova
hey
true nova
can you evaluate the inner integral?
how would I do that
one min
ye how do I do that
<@&286206848099549185>
devout snowBOT
@true nova Has your question been resolved?
true nova
treat x like a constant
oh
restive river
so integrate wrt y then wrt x
Yes
This is more or less the same as the $\int \f{1}{1+u^2} \dd{u}$ integral
woven radishBOT
♡A(lex)♡
restive river
With respect to y
true nova
With respect to y
ok so that’s arctany + C right
restive river
No
true nova
wait what
restive river
Don't just forget about the x^2 coefficient there
restive river
Factor out x^2 from the denominator and apply the same formula
restive river
**♡A(lex)♡**
Sorry $\f{1}{a^2 + x^2}\dd{x}$ integral I mean
woven radishBOT
♡A(lex)♡
hybrid snow
**♡A(lex)♡**
mfw u sub
true nova
Sorry $\f{1}{a^2 + x^2}\dd{x}$ integral I mean
so $\frac{1}{x^2}\int{\frac{1}{(\frac{1}{x})^2 + y^2}$dy ?
dy
woven radishBOT
Lunars
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
restive river
Okay yeah
true nova
$\frac{1}{x^2} \cdot x \arctan{xy} + C$?
woven radishBOT
Lunars
true nova
so $\frac{1}{x}\arctan{xy} + C$?
woven radishBOT
Lunars
restive river
Yeah seems right
restive river
wait
restive river
**Lunars**
Compile Error! Click the <:errors:504266556054962196> reaction for mo...
Because like from this step what u r done is this
$\f{1}{x^2} \int \f{x}{(\f{1}{x})^2 + y^2)} \dd{y} = \f{1}{x^2} \cdot x \cdot \f{1}{\f{1}{x}} \arctan(xy)$
woven radishBOT
♡A(lex)♡
true nova
wait but don’t I have to sub y=1 and y=0 and subtract
true nova
ah ok
restive river
You will end up with arctan(x) anyways
true nova
yepp
restive river
Same story integrate by parts
true nova
,w integrate arctan(x)
woven radishBOT
restive river
Lmao or do that I suppose
true nova
and sub in
restive river
Yeah
restive river
Nw
true nova
.close
radiant drift
devout snowBOT
radiant drift
U want people to check ur 5 pages of solving that weird quartic <:xd:10636912312...
nooo this is a seperate one tho
its independent
vast rain
wait is this the depressed cubic
mellow panther
wait is this the depressed cubic
Yes it is
radiant drift
wait lemme try subing in first
vast rain
wow and not the derivation given on wikipedia
mellow panther
@radiant drift avoid tagging others
vast rain
a strange one
wooden pier
Hi
radiant drift
ok wait im getting it
radiant drift
wow and not the derivation given on wikipedia
my teacher is strange
he wrote all these on the spot lol
vast rain
the quadratic looks correct
radiant drift
he said he already proved @supple knot hypothesis, and is ongoing in the process of publishing it
vast rain
he said he already proved <@261933205387477002> hypothesis, and is ongoing in th...
so you have a nutjob
of a prof
radiant drift
vast rain
so basically I only know the derivation wikipedia gives
but you can just assume that they're equal to zero
since you get one more degree of freedom through the substitution
vast rain
okay honestly whatever's written there is a mess so I'm just going to go off the one I read off wikipedia a while back
but it's essentially the same idea
you have $t^3 + pt + q = 0$, and you substitute $u+v=t$. Note that we're substituting two variables in the place of one
woven radishBOT
Saccharine
vast rain
so we have room to add an extra condition
and we're just going to say that $3uv + p = 0$. there exist numbers u and v such that both of these are true
woven radishBOT
Saccharine
vast rain
the proof of that fact is just by assertion and the fact that it's obvious
anyway
(okay no, but you can actually solve for u and v in terms of t and p)
and then you get $u^3 + v^3 + (3uv + p)(u+v) + q = 0$ and that's where the second assumption comes in
woven radishBOT
Saccharine
vast rain
nonono that's afterward
vast rain
you basically get a system of equations $u^3+v^3 = -q$ and $uv = -\frac{p}{3}$ and then it's the quadratic
woven radishBOT
Saccharine
vast rain
anyway
the gist of it is that you introduce two variables to replace one of them
but that gives you room to add an extra constraint that you can pick so you cancel a problematic term out
radiant drift
this is a result from a quartic equation
vast rain
the quartic equation relies on a reduction to cubic
what you have there is a derivation of the cubic formula
radiant drift
what you have there is a derivation of the cubic formula
yeh but there is not ^2 term
its a result from the reductino
vast rain
yeah you can reduce the normal cubic to a depressed cubic
something t = x- b/3a or that
agile zinc
is this right?
devout snowBOT
is this right?
agile zinc
I tried the method my teacher gave me
agile zinc
no..this is wrong
how do I move it?
earnest trellis
first take reciprocal of both sides
then multiply 6 on both side
then subtract 2
agile zinc
both sides?
earnest trellis
yeah
earnest trellis
on left and right side of =
agile zinc
why are you changing x and y in first step
my teacher told us to change it-
earnest trellis
so write everything in terms of x
winter patrol
and although a little sketchy, its generally accepted
earnest trellis
if u want to change
agile zinc
is the answer right?
winter patrol
using f^-1(1)x instead of y in the work would be better, when switching
but its fine
agile zinc
alr
earnest trellis
is the answer right?
just one or 2 more steps
agile zinc
as in?
winter patrol
whether you swap x,y at the start or end makes no difference to the end result
agile zinc
one of the reasons I was confused was bcs the textbook said the answer is (6-2x)/2
was wondering why there's 2 x(s)
is it an error?
restive river
same thing as your answer
agile zinc
but where did the other x come from
restive river
$(6-2x)/x = 6/x - 2x/x$
woven radishBOT
starlight
winter patrol
from combining fractions
common denominator etc
same principle that'd be applied to simplify
2 - 1/2
agile zinc
so my answer is also acceptable?
winter patrol
yes
agile zinc
alr ty
so for a question I got f^-1(x)=(x-8)²+3 but the answer says f^-1(x)=(8-x)²+3. Is my answer acceptable?
<@&286206848099549185>
earnest trellis
yes
cloud marlin
At 7 years old, Mark stands at 1.18m. Their mother noticed that each year, his height increases by 0.04m during the next 8 years. How tall will Mark be when he is 14 years old? Answer in meters.
devout snowBOT
At 7 years old, Mark stands at 1.18m. Their mother noticed that each year, his h...
sage burrow
what have you tried so far?
cloud marlin
1.18m + (7*0.04m) = 1.18m + 0.28m = 1.46m
sage burrow
so, what is your question then?
cloud marlin
is it right?
sage burrow
yes
sage burrow
i would say so.
sage burrow
if today is wednesday then also in 14 days. -> 15 is thursday, 16 is friday 17 is saturday. so i would say yes.
cloud marlin
okay okay thanks!
The length of a rectangle is five more than its width. The area of the rectangle is 52 square meters. Find the dimensions of the rectangle.
mortal sky
The length of a rectangle is five more than its width. The area of the rectangle...
Just put the info given in variable form and solve by equating to area
mortal sky
Now just put the value of x in terms of y
sage burrow
cloud marlin
wait i don't get it