homie is not getting a break huh
#help-0
alpine sable
and don't feel obligated to help either
spare ocean
haha im messing w u
alpine sable
I'm broke asf I lost my job haha
But I would 100% pay him for this if I had the money haha
alpine sable
yeah I might be suing the company
reef pier
and don't feel obligated to help either
you'd be surprised, it's a strange combination of ego and insanity and being really bad at saying no
spare ocean
spit in a customers face?
reef pier
but i love helping
alpine sable
you'd be surprised, it's a strange combination of ego and insanity and being rea...
fair enough haha
alpine sable
No I was sick for 2 days with doctors notes and they fired me, which is illegal for 1, they also were working a 17 year old 80 hours a week without breaks which is also illegal. So I might be suing haha,
spare ocean
life's much better on the other side
reef pier
i'm not sure if i'll get a masters or if i'll go straight for the phd
i'm definitely looking at europe tho
alpine sable
oh?!
reef pier
i'm tryna get out of here 😭
alpine sable
fr
reef pier
all my friends are studying abroad
spare ocean
No I was sick for 2 days with doctors notes and they fired me, which is illegal ...
good idea
Netherlands is nice, but dont underestimate eastern europe
unless you fancy insanely well done infrastructure
reef pier
yeah especially for some of their math graduate programs
spare ocean
good night^^
reef pier
of course, good night!
spare ocean
npnp, didnt do much
reef pier
im probbaly also gonna head to sleep lol
reef pier
aight see you bro, i'll be on later
spare ocean
ait bet, gn
lone heartBOT
@alpine sable Has your question been resolved?
lone heartBOT
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Available help channel!
chrome tapir
are these both infinite solutions?
lone heartBOT
are these both infinite solutions?
hearty quartz
You can employ Gaussian Elimination
chrome tapir
You can employ Gaussian Elimination
whats that
modern sedge
if you don't know that, just use any method for solving system of equations
hearty quartz
whats that
oh line and plane. I missed that detail. Thought it was two planes
modern sedge
oh line and plane. I missed that detail. Thought it was two planes
Does it actually matter?
it can still be broken down to 3 equations
(x-2)/3 = y+5, y+5 = (z-6)/8, 5x+y-2z+2=0
chrome tapir
it makes sense tho 💀
hearty quartz
You can make y the subject in the equation (x-2)/3 = (y+5)/1
modern sedge
Do you know how to interpret this result?
modern sedge
You can make y the subject in the equation (x-2)/3 = (y+5)/1
parametrization is actually better here, its much quicker
modern sedge
it makes sense tho 💀
It does, coincidentally
do you know how to interpret the result
chrome tapir
yeah
infinte solutions
when you have 1 value it means one solution
when you no values
ie 4 =0
you have no solutions
since 4 can never equal zero
heres a harder question @modern sedge
idk how to do this
modern sedge
infinte solutions
You sure?
chrome tapir
what do you think then?
modern sedge
I think that you didn't even check if what chatgpt did is correct
hearty quartz
It seems correct
modern sedge
It seems correct
You sure?
chrome tapir
I think that you didn't even check if what chatgpt did is correct
i did
chrome tapir
no
modern sedge
then do it
chrome tapir
oh
modern sedge
modern sedge
do it yourself, simplify it yourself
chrome tapir
-5 = 0 💀
modern sedge
mhm
chrome tapir
no solutions
modern sedge
yeah
chrome tapir
ok ok
modern sedge
watch out for chatgpt
chrome tapir
lets try this dawg
modern sedge
it makes bullshit seem like it makes sense
modern sedge
alright so the line is parametrized with some parameter s
Can you read off expressions for x, y, and z from the parametrization of line?
modern sedge
<@951190447185874994> this is what i did so far
there should be -2bs
modern sedge
otherwise it seems correct
I'd further simplify it to (22-2b)s + (16-a) = 0
maybe you could also solve for s
and then think about when it has infinitely many solution, when it has no solutions, and when it has one solution
chrome tapir
why would 16-a be in brackets
modern sedge
why would 16-a be in brackets
its not necessary, it was just to better fit the linear function formula mx + c
modern sedge
how do you solve for x in 3x + 4 = 0?
modern sedge
you shift 16-a to the right?
yeah, so (22-2b)s = a-16
modern sedge
Why 22-2b = 16+a?
infinite solutions is when it simplifies to 0 = 0
when does (22-2b)s + (16-a) = 0 simplify to 0 = 0?
chrome tapir
what would i need to do then
modern sedge
first of all, there can't be no s in the equation
meaning the coefficient of s has to be 0
or 22-2b = 0
then it simplifies to 16 - a = 0
and it can have either 0 or infinitely many solutions, depending on a
chrome tapir
its -16 + a since we put it on the other side
modern sedge
its -16 + a since we put it on the other side
yeah, its actually the same thing
-16 + a = 0 and 16 - a = 0 are the same equations
chrome tapir
true
modern sedge
Anyway, do you understand what happened?
chrome tapir
not really
modern sedge
(22-2b)s + (16-a) = 0 is a linear equation
chrome tapir
why is s zero
modern sedge
the solutions are intersections with y = 0
try varying a and b and see when you get no solutions (no intersections) and when you get infinitely many solutions (infinitely many intersection, basically the red line being same as the purple one)
modern sedge
if you had just ax + b = 0, do you know when this has 0, 1 and infinitely many solutions?
modern sedge
you're close
very close
if a = 0, then it simplfies to b = 0
now this can be either always false, or always true
depending on b
if b is e.g. 1, then it's 1 = 0, which if false
but if b is 0, then it's 0 = 0
chrome tapir
ye
modern sedge
meaning there are infinitely many solutions
modern sedge
and whenever a =/= 0, then
ax + b = 0
ax = -b
x = -b/a
Gives us exactly one, unique solution
modern sedge
infinite solutions when ax equals neg b
infinite solutions when ax = -b?
modern sedge
you shouldnt even be using x
the conditions should be based purely on a and b
no x
Standard way to solve ax + b = 0 is:
ax = -b
x = -b/a
However this works only if a =/= 0, because otherwise we would be dividing by 0. But at least we know that when a =/= 0, there is exactly 1 solution (-b/a)
Now consider the a = 0 case
then it simplifies to
a(0) + b = 0
or b = 0
which is true only if b = 0, otherwise it's false
if it's false, then the equation has no solutions
if it's true, then all x are solutions
meaning it has infinitely many solutions
so summing up:
a =/= 0: 1 solution
a = 0 and b =/= 0: no solutions
a = 0 and b = 0: infinitely many solutions
chrome tapir
i see i see
bro not going to lie, the test is in 3 hours
so right now, i kinda want to memorise how to do it
and then understand later
modern sedge
hmm interesting strategy
it's hard to memorize it unless you understand it
but good luck
lone heartBOT
@chrome tapir Has your question been resolved?
chrome tapir
so a equals 16? @modern sedge
modern sedge
so a equals 16? <@951190447185874994>
there are 3 questions
for a) it's when they intersect at single point
meaning when (22-2b)s + (16-a) = 0 has a single solution
that's when b =/= 11
for b) it's when (22-2b)s + (16-a) = 0 have infinitely many solutions
that's when a = 16 and b = 11
for c) its when (22-2b)s + (16-a) = 0 have no solutions
that's when b = 11 and a =/= 16
lone heartBOT
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Available help channel!
alpine sable
est ce que -1 est un nombre impaire
lone heartBOT
est ce que -1 est un nombre impaire
lethal belfry
english only please
no need of other languages
your native language and english will suffice
idle mantle
lethal belfry
,w parity of -1
ocean sealBOT
alpine sable
,w parity of -1
what means parity
lethal belfry
what means parity
odd or even
lone heartBOT
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Available help channel!
jaunty mulch
lone heartBOT
jaunty mulch
How do i work out this
what do the x values mean
I don't understand what im reading here
knotty garnet
jaunty mulch
why do they just give me
soft onyx
i did this question earlier haha
soft onyx
because there’s 2 outcomes
soft onyx
either -1 OR 0
jaunty mulch
oh cause
for x values
it says there are 2 ?
so for everything else there is also2
soft onyx
yeah :)
lone heartBOT
Available help channel!
agile plinth
I do not know where I went wrong with question 3, the answer is supposed to be £68. Please help
lofty heart
basically
if you have the shopping before VAT is 100%
and then 20% of that is added onto the original 100%
so you have 120%
the way you worked it out is as if it is 100%
you need to treat the after VAT value as 120% and you should get the right answer
agile plinth
ohhh
thank you
got the right answer
@lofty heart wait wait you still there?
you see question 4 yeah
lofty heart
ya
lofty heart
think youve done the same mistake basically but reversed
at 100% its the original value right
then you lose 28% and now youre at 12960
lofty heart
yeah
agile plinth
lofty heart
You didnt use that it was 72%
Imagine you have value x let it be like 100 for ease
But pretend you dont know that x
and you know after 2 years it decreases by 28% and the new value is 72
So 72 is 72% and obviously you know 10% is 10 not 7.2
Can you use a calculator for this
If you can it can be done a lot easier
lofty heart
the easiest way is probably to just find 1% and then multiple by 100
so if 12960 is 72% divide by 72 to get 1%
then multiply by 100 to get 100%
lone heartBOT
@agile plinth Has your question been resolved?
alpine sable
How to solve question 19?
lone heartBOT
How to solve question 19?
merry depot
use the definition of absolute value. If the thing inside is positive or negative.
then do the algebra to factor it.
hard aspen
factorize the quadratic and make cases interval wise
livid sage
(in other words, the same way you would do most other problems on that page)
hard aspen
the polynomial is negative in the interval (-2,-1) no?
you'll need to multiply it with -1 then
alpine sable
So it will be-x 2. - 4x. -1?
hard aspen
it will be -x^2 -3x - 2 + x + 1
also arent you meant to solve for x not just state whether its real
alpine sable
I've found out the values in all 3 cases
hard aspen
it will be -x^2 -3x - 2 + x + 1
only the stuff inside the abs value is multiplied with -1
alpine sable
Taken the intersection to find value of x
alpine sable
only the stuff inside the abs value is multiplied with -1
Kk
Can u also tell how to solve questions like 18 and 20?
hard aspen
This right?
in the first case x will be -1,-3. not 1,3
alpine sable
in the first case x will be -1,-3. not 1,3
Yeah, sorry for that
hard aspen
Can u also tell how to solve questions like 18 and 20?
make cases when x > 0 and when x < 0 for 18
and 20 is the same thing
alpine sable
hard aspen
note that |x| = x if x >= 0 else |x| = -x
alpine sable
This correct?
hard aspen
This correct?
yep
lone heartBOT
lone heartBOT
Available help channel!
neon basalt
Help
ocean sealBOT
A brief description and guide on how to use me was sent to your DMs!
Please use ,list to see a list of all my commands, and ,help cmd to get detailed help on a command!
tribal field
Send your question
neon basalt
Send your question
tribal field
!status
lone heartBOT
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
This is my final problem on thr worksheet and i need help asap
I gottaturn this in
tribal field
Do you know the distance formula?
tribal field
Can I see what the other questions were? So I have a better idea what type of proof is being asked for?
tribal field
Are you sure you don't know the distance formula?
Like
The distance between (a,b) and (c,d) is sqrt((a-c)^2+(b-d)^2)
neon basalt
r =6 D= d_AB = sqrt( (4,5-0 )^2 + (4-0 ) ^ 2 ) = 6 the point lines on the circle.
this is what i wrote for this one
tribal field
So apply similar logic to Q3
It is sufficient to prove that the length of BP is the same as PD and CP is the same as PA
neon basalt
So apply similar logic to Q3
It is sufficient to prove that the length of BP is ...
wait is this the whole answer for that one problem i have
lone heartBOT
@neon basalt Has your question been resolved?
long axle
<@&268886789983436800>
lone heartBOT
long axle
bruh what
<@&268886789983436800>
automod keeps deleting the messages i think
THANK YOU
clever folio
They should be muted
steady roost
I got it
clever folio
Thanks for the help. Gonna delete the screenshot since it's also fairly inappropriate to be safe. Senior mods have perms to see deleted stuff iirc.
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Available help channel!
tacit helm
I wanna know if this is a property that holds true for sigma, I can't think of a counterexample, and I don't know how else to prove or disprove this
hushed locust
consider ai = 1, bi = 1 for all i, and compute for some small number (e.g. up to 4)
charred summit
You can think of an easy counter example which is
a1 = 1, a2 = 1
b1 = 1, b2 = 1
Using the first expression on the left would yeild 2 as a result while the one on the right will yeild 1
wraith stratus
this is also just a case of $\frac{a}{b} + \frac{c}{d} \neq \frac{a+c}{b+d}$
ocean sealBOT
chebyshev's infinite pee norm
lone heartBOT
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Available help channel!
feral tundra
Hi guys i dont understand how to find the coordinates of $\begin{bmatrix} -5 & 6 \ -2 & 1 \end{bmatrix}$ when the basis is $\Bigl{ \begin{bmatrix} 3 & -3 \ 1 & 0 \end{bmatrix} , \begin{bmatrix} 1 & 0 \ 0 & 1 \end{bmatrix} \Bigr} $ i dont even know what a basis in $M_{2 \times 2} $ means, i just know how a basis works with vectors.
Do you have any advice or videos to understand this?
ocean sealBOT
mg
vale crag
well M_2x2 is a vector space right
so it has a basis
$$\left{ \begin{bmatrix} 1 &0\0&0 \end{bmatrix}, \begin{bmatrix} 0 &1\0&0 \end{bmatrix}, \begin{bmatrix} 0 &0\1&0 \end{bmatrix}, \begin{bmatrix} 0&0\0&1 \end{bmatrix} \right}$$
ocean sealBOT
aPlatypus
vale crag
you can write any matrix in M_2x2 as a linear combination of these 4
and they're linearly independent, you can't write any of these 4 matrices as a lin combo of the 3 others
still here @feral tundra
ocean hawk
is that even a basis then, it only has 2 elements
feral tundra
yes
but i tried to find the span of the subspace
and ended up with those matrices
vale crag
ok sure
you understand why talking about a basis of the space of matrices makes sense now ?
lone heartBOT
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Available help channel!
quartz lichen
Is this correct?
lone heartBOT
Is this correct?
ocean hawk
you shouldn't have any "x"s
native cloud
quartz lichen
you shouldn't have any "x"s
Can you explain why?
ocean hawk
you are evaluating the function at 0 + h
placid zinc
Is this correct?
Blue doesn't include x. Red highlights an x, I can't follow where it came from
quartz lichen
I am a little confused now because in the example question my Professor had x's in his.
This is from our lecture
placid zinc
From his limit onwards, there are no x's
quartz lichen
I had the wrong tab open lmao yes in this one he does not
I carried the x from my previous question
I am going to rework my problem and then we'll see from there
ocean hawk
looks good
lone heartBOT
@quartz lichen Has your question been resolved?
still vortex
yo can someone help me
lone heartBOT
yo can someone help me
still vortex
im doing unit circle rn but im kind of struggling and i dont really get how to find reference angle
This for example
How do I find the reference angle of this
narrow hedge
Draw it in terms of quadrants.
still vortex
i think its in the third quadrant
lost osprey
the definition of reference angle is the smallest acute angle between that angle and the x-axis
since the x axis is at every pi
or 180deg
digital hill
@still vortex it's in q2
still vortex
oh
digital hill
no
quartz lichen
Yes because reference angle is the smallest acute angle
still vortex
how did u get that
still vortex
u just subtracted 360 from 495?
quartz lichen
@still vortex I sent you a dm explaining
digital hill
and u get -360
still vortex
Is there a way to keep it in radians? or does every time i find the reference angle of an angle in radians, i have to convert it to degrees
quartz lichen
You can keep it in radians
digital hill
Is there a way to keep it in radians? or does every time i find the reference an...
it's easier to get degrees then convert to radians
quartz lichen
It's just easier converting imo
digital hill
bc deg is just pi/180
still vortex
my teacher added 8pi/4 to it
digital hill
your teacher is a little funny
still vortex
and got -3pi/4
still vortex
then idk but somehow the highlighted answer is pi/4
digital hill
or wrong
still vortex
no
quartz lichen
They are both technically reference angles
still vortex
but im so confused
quartz lichen
But without the actual question Idk what ur teacher wants
digital hill
They are both technically reference angles
i think teacher did it in account of only q2
digital hill
pure mathematical solutions are acc cancerous
if she had included a draw it would've been so much easier to understand
still vortex
yes the reference angle in Q1
DMs
Oh wait
so Is the easiest way to find the reference angle of an angle, by subtracting or adding 360 or 2pi until I get the smallest, positive acute degree?
still vortex
if she had included a draw it would've been so much easier to understand
im still so confused
lone heartBOT
@still vortex Has your question been resolved?
still vortex
What does it mean evaluate?
like cosine, sine, tangent, cosecant, secant, and cotangent?
<@&286206848099549185>
junior vigil
junior vigil
like cosine, sine, tangent, cosecant, secant, and cotangent?
Yes
junior vigil
Unit circle should have angles/radians labeled.
still vortex
nah its geometry
soft pawn
still vortex
but how do i find x and y
junior vigil
soft pawn
yeeah
junior vigil
????
still vortex
for real!
junior vigil
It literally says use the unit circle.
junior vigil
,tex .unit circle
ocean sealBOT
🫎MooseyMooseMooser 🫎
junior vigil
Yes
still vortex
bro ive been doing math all day and im getting a massive headache 💀
still vortex
I thought what I was doing was hard
what grade r u in
alpine sable
10
still vortex
dam
still vortex
oh thats not too bad
alpine sable
I’ve gotta learn all that in a day
With circles
Uhm , I think , but I was sick for 3 weeks
still vortex
,tex .negative unit circle
bro i cant
i have to finish like so much crap this week
this is what its like every week
until school is over
digital hill
learn mathematics for the sake of improving your analytical thinking skills
it's greately beneficial
still vortex
HELP
still vortex
learn mathematics for the sake of improving your analytical thinking skills
i need help again
how do i evaluate tan(-105) without a calculator
.close
lone heartBOT
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Available help channel!
stray light
lone heartBOT
stray light
does anyone know how -cot(pi/2)= 0 and how -cot(pi/6)= -sqrt(3)
I understand it has to do with something regarding the unit circle but I cant figure it out
long axle
tan(pi/2) = 1/0 therefore
-cot(pi/2) = -1/tan(pi/2)
= -1/ (1/0)
= (-1 * 0)/1
=0
@stray light got it?
stray light
did u do tan bcuz its the inverse?
pine tundra
Cotangent is the reciprocal of tangent
long axle
not inverse, but reciprocal of cot
stray light
yea that
long axle
tan(pi/2) = 1/0 therefore
-cot(pi/2) = -1/tan(pi/2)
= -1/ (1/0)
= (-1 * 0)/1
=...
U understand this? @stray light
pine tundra
$cot(x)=\frac{1}{tanx}=\frac{1}{\frac{sin(x)}{cos(x)}}=\frac{cos(x)}{sin(x)}$
jolly yoke
but I'll likely not remember it
How well do you remember your unit circle?
stray light
Like very vividly
I understand the sin, cos, tan, but if its sec, csc, or cot I'll get cooked
long axle
I understand the sin, cos, tan, but if its sec, csc, or cot I'll get cooked
Just remember that sin = 1/csc and cos = 1/sec and tan = 1/cot
ocean sealBOT
Bishop
stray light
Just remember that sin = 1/csc and cos = 1/sec and tan = 1/cot
ok
stray light
Just remember that sin = 1/csc and cos = 1/sec and tan = 1/cot
so would csc= 1/sin, sec= 1/cos, and cot=1/tan
long axle
Yes
stray light
one more question
when Im plugging in 1/tan(pi/2) I get undefinied
the video states its 0
if we get an undefinied expression does it mean its always 0?
long axle
tan(pi/2) = 1/0 therefore
-cot(pi/2) = -1/tan(pi/2)
= -1/ (1/0)
= (-1 * 0)/1
=...
Read this
tan(pi/2) = 1/0, which we call undefined as convention
stray light
yea
long axle
But we can also see that 1/tan(pi/2) = 1/(1/0) = 1(0)/1 = 0/1 = 0
stray light
ok but is it safe to assume that if we get undefined we can just say its 0 or nah?
long axle
Undefined doesn’t mean 0, it means 1/0 (for this sort of context)
For example, if the question was cos(pi) / tan(pi/2)
What would u put
stray light
well it would -1/(1/0)
long axle
And what does that evaluate to
stray light
undefined
long axle
Can you explain why
stray light
Cuz my calculator says so loolll
stray light
Ight
long axle
$\frac {-1}{\frac 10} = \frac {-1}{1} \div \frac 10$
ocean sealBOT
lone heartBOT
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Available help channel!
raw jetty
$$\frac{1}{1}C^{20}{0}+\frac{1}{2}C^{20}{1}+\frac{1}{3}C^{20}{2}+.....+\frac{1}{21}C^{20}{20}$$
ocean sealBOT
Skill_Issue
tardy stag
raw jetty
1+3/2+1+1/4
slender gull
**Skill\_Issue**
Looks like an integral.
raw jetty
i cant do integration
slender gull
i cant do integration
I see.
[\sum_{k=0}^n \binom{n}{k} \frac{1}{k+1}] is what you have
ocean sealBOT
! What the hell am I doing here?
ocean sealBOT
! What the hell am I doing here?
raw jetty
\[\sum_{k=0}^n \binom{n}{k} \frac{1}{k+1}\] is what you have
if it was this cant i do hockeystick
slender gull
if it was this cant i do hockeystick
It IS this, wdym if it was
raw jetty
**! What the hell am I doing here?**
can you explain how you get this
slender gull
**! What the hell am I doing here?**
Do you understand this
raw jetty
yea
slender gull
$\frac{1}{k+1} \cdot \frac{n!}{k!(n-k)!} \cdot \frac{n+1}{n+1} = \f{1}{n+1} \pl \frac{(n+1)!}{(k+1)!((n+1)-(k+1))!} \pr$
ocean sealBOT
! What the hell am I doing here?
raw jetty
oo
n is like a constant right so i can take it out of the sun
sorry, but what do i do with $$\frac{1}{21}\sum^{20}_{k=1} \binom{21}{k+1}$$
ocean sealBOT
Skill_Issue
raw jetty
cause afaik hockey stick is for the terms above that are increasing, not the terms below
slender gull
The sum started from k = 0
slender gull
cause afaik hockey stick is for the terms above that are increasing, not the ter...
yes, but this is even simpler lol.
Do you know what $\sum_{k=0}^n \binom{n}{k}$ is?
ocean sealBOT
! What the hell am I doing here?
raw jetty
no?
slender gull
I see.
raw jetty
oh is it 2^n?
slender gull
It is.
raw jetty
oh
raw jetty
so $\frac{2^{21}-1}{21}$?
ocean sealBOT
Skill_Issue
slender gull
Yep.
raw jetty
it is known that point O is at (0,0), point A, B, C is at (4,0) (0,3) (2,3) respectively, what is the ratio of the overlap from triangle OAB and OCB and the overlap of triangle OAB to OCB if triangle OCB is moved 2 to the right
lemme make a diagram
hot hatch
it is known that point O is at (0,0), point A, B, C is at (4,0) (0,3) (2,3) resp...
Is this done?
raw jetty
nope
ocean sealBOT
Monarch of Eternal Night
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
raw jetty
${n+1}_C _{k+1}=\frac{n+1}{k+1}\times n_C_k$
no that one is finished
hot hatch
Ohh, then which one
raw jetty
it is known that point O is at (0,0), point A, B, C is at (4,0) (0,3) (2,3) resp...
this one, the one you replied to?
raw jetty
i know this is abit scuffed but this is the diagram
raw jetty
one thing i noticed is that they are simmilar
actually nvm lol this is trivial
if EK=3, LH=6, EG=9, what is the area of ABCD
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alpine sable
uhh
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spiral yacht
if EK=3, LH=6, EG=9, what is the area of ABCD
Is the answer 45?
spiral yacht
Oh ok
Oh it’s may be 180
I used pythagorus
6 times
R is radius of semi circle and GD=CH=x
Then first in triangle EKD for DK, then in EKA for AK and then in DKA to get DK^2 + AK^2 = AD^2
And similarly in LCB
I got 2 equations in x and R
Then it is a square of 2R side, so area = 4R^2
spiral lily
how do you know they both have R as radius
spiral yacht
I just guessed from the figure if ABCD is square and both are semi circle
And I think that they wanted us to guess it from figure and it seems on point figure
spiral lily
yeah so
radius=3sqrt(5)
area=4r²=180
ASSUMING all the lines given are parallel
3²+x²=(9-x)²+6²
x=6 if you work that out
and if x=6, then r=3sqrt(5), sides are 6sqrt(5) and the area is side²
36.5=180
i dont think using the pythagorean theorem 6 times is efficient
spiral yacht
i dont think using the pythagorean theorem 6 times is efficient
I know that it’s not efficient but I didn’t had any other idea in my brain that time
Thank you for it, I really don’t had that on my mind tbh
raw jetty
and if x=6, then r=3sqrt(5), sides are 6sqrt(5) and the area is side²
36.5=180
ah ok ty
ill close this then
.close
alpine sable
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viscid cave
thats easy
alpine sable
Nice
spiral lily
try multiplying the fraction by $\cbrt{x+2}$
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haygiya
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alpine sable
X+2?
spiral lily
well cuberoot of x+2
alpine sable
Ok let me try
spiral lily
actually
alpine sable
Ye?
spiral lily
how about cuberoot of x+1
since that 2nd part of numerator looks like the 2nd half of (x³+y³)=(x+y)(x²-xy+y²)
alpine sable
...
spiral lily
do you see it
alpine sable
No
spiral lily
the x²-x+1
alpine sable
Yes?
spiral lily
(x³+1)=(x+1)(x²-x+1)
alpine sable
Ok
spiral lily
cuberoot(x³+1)=cuberoot(x+1).cuberoot(x²-x+1)
spiral lily
1-x²=(1-x)(1+x)=(1-x).cuberoot(1+x)³ is what pops in my mind
but i'm not sure
let me try few things before i give feedback
spiral lily
two sided limit does not exist
spiral lily
i wouldn't call it wrong
problems like this does exist and it's good to know anyways
alpine sable
I see
Ok
I am currently finishing an other exercise 🙃
Just wait a bit i want you to check when i am done
spiral lily
sure
spiral lily
what's the first step
alpine sable
L hospital 🏥
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crude gull
hello
crude gull
forget the italian text,just consider the matrix and the PA=LU decomposition, why does the solution(the one circled in red) considers swapping between row 2 and 3 and not for example row 1 with 3?
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crude gull
.close
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sharp gust
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sharp gust
doesn’t that mean the density would be like a crazy tiny number
idk, it just doesn’t seem right
and for volume, if 59g is 23562, if i wanted to find the volume for 1000kg of feathers then i’d need a huge scale factor
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quartz lichen
Can somebody check my answer? Thank you!
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Can somebody check my answer? Thank you!
fleet crown
quartz lichen
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shut whale
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shut whale
Hello. I am starting Algebra 2 and I need assistance with this problem.
autumn condor
!status
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What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
5
I do not understand the textbook, step 3 has a -2 but becomes a 2 in step 4. I do not understand why.
autumn condor
(-2)^12 = (-1)^12 * 2^12 = 1 * 2^12
shut whale
Where does the (-1)^12 come from?
shut whale
Any number that is negative like -2 becomes a positive?
shut whale
And when the raised power is an odd number, it is negative?
autumn condor
yes
shut whale
7., thanks!
autumn condor
so (-2)^13 = -2^13
shut whale
🙂
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wintry ridge
ignore the circled A
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ignore the circled A
wintry ridge
I plugged in the number and none of the asnwers relate to what I got
Unless the rounding= .5040
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wintry ridge
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fervent berry
why is the last part equal to ♾️
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why is the last part equal to ♾️
royal grail
i know it has something to do with 3/2 being bigger than 2/3
you can also combine the powers to convince yourself
n^(3/2) / n^(2/3) = n^(3/2 - 2/3) = n^(5/6)
which tends to infinity
royal grail
i know it has something to do with 3/2 being bigger than 2/3
but yh the other way to think about it, is just that even though both n^(3/2) and n^(2/3) tends to infinity, n^(3/2) does it quicker
so the numerator gets much larger than the denominator much faster
and thus tends towards infinity
royal grail
np
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fervent berry
how do logs work in limits and why is -2n^2 bigger than e^-n 😞😞
fervent berry
i’m sorry to whoever is dealing w me all day i have no idea what am i doing
empty moth
how do logs work in limits and why is -2n^2 bigger than e^-n 😞😞
oh e^-n goes to 0
as n -> inf
fervent berry
oh okay makes sense
empty moth
3n^2 groes faster than both ln(n) and \sqrt(n)
empty moth
could u please elaborate what exactly does ln(n) mean 😞
oh inverse function of e^x
like ln(e^3) = 3
fervent berry
so ln(n) is just infinity??
in my case
and also if the power of e wasn’t negative
like e^n
would it be bigger
just imagining a scenario 😭
fervent berry
bigger than the numerator?
than the other n we have in denominator
fervent berry
okayaya ty 🙏🏻
fervent berry
so ln(n) is just infinity??
wait or is it 1^♾️
which is an indeterminate form
😦😦
buoyant saddle
could u please elaborate what exactly does ln(n) mean 😞
ln(n) is just a function
it’s the inverse function of e^x
you’re not familiar with logarithmic functions?
fervent berry
you’re not familiar with logarithmic functions?
no i missed half the semester 😭🙏🏻
buoyant saddle
wait or is it 1^♾️
what is 1^inf
oh maybe you should do some review on logarithms then
fervent berry
oh wait
buoyant saddle
you’re familiar with exponential functions yes
fervent berry
okay basically i know what logarithms are
but ln(n)
means 1/n
right
which makes it 0
when using in limits??
okay i think i got it ty 😭😭
.close
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buoyant saddle
nooo
don’t do that
ln(x)≠1/x
those are two entirely different functions
,w graph ln(x)
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buoyant saddle
it’s the inverse function of e^x
the reason it "disappears" in the limit
is because the x^2 dominates
it’s larger at infinity
same with sqrt(x)
fervent berry
is because the x^2 dominates
can i be real with u
buoyant saddle
go ahead
fervent berry
i’m still clueless 😭
buoyant saddle
no
no
it doesn’t go to zero
at all
it goes to infinity
but the x^2 is larger
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formal latch
How do I simplify this (please explain in detail, I'm really lost)
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How do I simplify this (please explain in detail, I'm really lost)
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formal latch
Try to use (a-b)^2 formula
can you elaborate?
solar pebble
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amber atlas
Find, using double integrals, the volume of the solid region $S$ bounded by the planes $x+z=6$, $y=0$, $y-x=0$, $z=0$ in the first octant.
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Halex
amber atlas
Not sure how to get the region where the integral is defined
amber atlas
Get all the bounds in terms of z
z=6-x, z=0 and solve for x?
solar pebble
Now you know for each x,y you have an expression for the heigh of the solid
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amber atlas
Now you know for each x,y you have an expression for the heigh of the solid
$\int_{0}^{6} \int_{0}^{x} (6 - x) , dy , dx$
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Halex
amber atlas
is that true?
solar pebble
does it mean perfect? haha
indeed
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ebon heath
hi
rose sigil
where?
fervent kestrel
Cause there may be an unknown constant that might have replaced 'a'
ebon heath
would I be able to detect that through long division?
rose sigil
you don't know what the factorization is at that point yet
if you knew it was (z-4)(z^2+z+1) then you'd already be done lol
ebon heath
oh so my long division was correct?
rose sigil
yea you can long divide
ebon heath
Ok another question
Why can’t I factorise z^2 + Z + 1? Is that because it would give an imaginary solution?
ebon heath
they did (pretty much) factor it in the solution
how do I express it in like 2 brackets form
like (Z+1)(Z-1)
like this form
rose sigil
ebon heath
like (Z+1)(Z-1)
ik this wouldn’t be the actual factorisation bracket thingy
rose sigil
so it would be uhh
$(z-4)\left(z - \frac{-1+i\sqrt{3}}{2}\right)\left(z - \frac{-1-i\sqrt{3}}{2}\right)$
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slayla
