,w 2√20
#help-33
merry terrace
elfin berryBOT
merry terrace
Don't forget to add the unit which is metre
And yeah your answer is correct but it would be 8.9443m
Cause we add one to the final decimal if the final digit of the decimal is greater than 5
It is approximation
woeful lantern
hmm weird doesnt accept it as correct
oh it finally went through
thanks for the help
.close
marsh citrusBOT
merry terrace
hmm weird doesnt accept it as correct
What did it accepted as an answer?
lament spruce
I set up a matrix for this and got
[1 0 0 0 0 0 0]
[1 2 4 8 16 32 2.9]
[1 4 16 64 256 1024 14.8]
[1 6 36 216 1296 7776 39.6]
[1 8 64 512 4096 32768 74.3]
did i do something wrong because a5 seems to be a free variable when solving this
gray shale
what's the difference between max(f(x)) and sup(f(x))?
marsh citrusBOT
what's the difference between max(f(x)) and sup(f(x))?
devout mauve
the max might not exist over a given set
gray shale
wdym?
devout mauve
for m to be the max, there needs to be a point y so that f(y)=m
such a y might not exist
think of the function f(x)=x on the interval (0,1)
this doesn't have a maximum
gray shale
it has a maximum but just for (0,1)
gray shale
ah ok u see it like that
then let's see :
f: R -> R
for all x€R, max(f(x)) = m
for all x€R, sup(f(x)) = s
are m and s equal
sharp mortar
Same question
devout mauve
you can't pick x and then do a maximum of the now fixed value f(x)
or well you can, but it's definitely not what you want
gray shale
i'm not talking about the maximum but the function max()
gray shale
in what case one can exist without the other?
sharp mortar
i'm not talking about the maximum but the function max()
What's the difference
sharp mortar
in what case one can exist without the other?
The max may not exist
An example was given above
gray shale
What's the difference
when we talk about maximum we have to precise if it's local or global
still temple
a maximum is just a special type of supremum; if s is a supremum, then its also a maximum if there is an x such that f(x) = s. If theres no such x however then its just a supremum and not a maximum
gray shale
if max exists then sup also exists
so sup can exist without the max
devout mauve
yes, like the example I gave above
gray shale
i don't really got your example
you said that there's no max in (0,1) but more me it's just 1
sharp mortar
I thought a guy called max would know more about maximuma
devout mauve
but 1 is not in the interval
still temple
take the function f(x) = x in the domain f: (0, 1) -> R
still temple
take the function f(x) = x in the domain f: (0, 1) -> R
whats the supremum of this function?
gray shale
1
still temple
but can the function ever take the value 1?
gaunt gulch
i graphed this out
marsh citrusBOT
i graphed this out
gaunt gulch
but im not sure which would be the best answer
marsh citrusBOT
Show your work, and if possible, explain where you are stuck.
gaunt gulch
Show your work, and if possible, explain where you are stuck.
just graphed it out
marsh citrusBOT
@gaunt gulch Has your question been resolved?
gaunt gulch
<@&286206848099549185>
marsh citrusBOT
@gaunt gulch Has your question been resolved?
noble ore
Hello I'm currently having trouble understand what data set would be good to analyze and create a cumulative distrubution function for
marsh citrusBOT
Hello I'm currently having trouble understand what data set would be good to ana...
@noble ore Has your question been resolved?
marsh citrusBOT
@noble ore Has your question been resolved?
main idol
Hello I'm currently having trouble understand what data set would be good to ana...
this is too vague. are you working on any specific problem
noble ore
Right now for a project
i need to find a data set to make a cdf for
And was wondering if theres any suggestions u may have
marsh citrusBOT
@noble ore Has your question been resolved?
waxen bridge
Kaggle.com
You can get dataset from here. Hope it helps.
wary wolf
wary wolf
idk whats the command
bright jay
<#903481101744484362> please close one
Too late
bright jay
whats the command
.close
carmine oyster
I cannot find a way to get my tangent lines right. Like how do I know where my second point for it is at? I only have like 1 or 2 tries left…
marsh citrusBOT
I cannot find a way to get my tangent lines right. Like how do I know where my s...
@carmine oyster Has your question been resolved?
carmine oyster
<@&286206848099549185>
outer ember
Find the equation of the tangent line by using the derivative to find the slope
Then choose a point other than the one on the curve that satisfies the equation
marsh citrusBOT
@carmine oyster Has your question been resolved?
carmine oyster
When I plug -2 in I get -12
So I now have (-2,-12)
So I use slope formula for that point?
Then I can plug in something to satisfy that?
Is that what needs to go down
marsh citrusBOT
@carmine oyster Has your question been resolved?
daring oracle
@carmine oyster you have (-2, -12) as the point, and the slope of the tangent line is given by the value of the derivative at that point (which you've already found)
carmine oyster
Tysm
marsh citrusBOT
Available help channel!
still temple
marsh citrusBOT
elfin berryBOT
Plob_lonst
still temple
It's the sum of all a
whole patrol
well is there any restriction to x or y ?
still temple
Not that i would know of
still temple
well is there any restriction to x or y ?
.^
whole patrol
Since there's no restrictions for the values of x, there's a line of possible values
To verify, make x = 0
then you get that y must be equal to 16/5
from a6 you have 16 = 3x + 5y = 0 + 5 * 16/5 = 16
so it checks out, and then the Sa7 is just 336/5
still temple
I mean no
The answer is 66 so it can't be 67.2
I know i said there's no restrictions for the value of x, but why would x=0, x can be anything as long as the equation stays true right.
I'm going to ask my teacher tomorrow about this, but thx for the help man.
.close
smoky marsh
can someone push me in the right direction for this? im not sure what step to make
marsh citrusBOT
can someone push me in the right direction for this? im not sure what step to ma...
smoky marsh
i feel like im forgetting/not understanding somehting?
keen plover
can someone push me in the right direction for this? im not sure what step to ma...
you could perform a u-sub here
u= g(x)
du=g'(x) dx
keen plover
no you're awesome
smoky marsh
so i've gotten 1/(g(x)^2-4) du, when taking the anti derivative, isn't that just ln(g(x)^2-4)? but that would make it difficult to find the answer without a calculator
keen plover
so i've gotten 1/(g(x)^2-4) du, when taking the anti derivative, isn't that just...
don't you mean 1/(u^2-4) du?
also do not forget the bounds 0 and 1 change
smoky marsh
yea i got that but then changed it back to g(x)^2
why would the bounds change in this instance?
keen plover
when you perform a u sub on a definite integral, the bounds must change
how do they change you might ask?
well you have to perform the function you substituted on the bounds
smoky marsh
so put in the 0 and 1
keen plover
can someone push me in the right direction for this? im not sure what step to ma...
for example, the lower bound 0 will change to 6, because we have to perform g(x) on 0, since we let u = g(x)
and the upper bound 1 will change to...
smoky marsh
5
smoky marsh
yea
keen plover
we can make the integral look more proper by multiplying it by negative one
doing this will flip the bounds
smoky marsh
so no will we get - intergral from 6 to 5 of 1/(u^2-4) DU
keen plover
- intergral from 5 to 6 of 1/(u^2-4) DU
the bounds before were 6 to 5, multiplying by negative one flipped them
smoky marsh
damn
alright, im gonna give it another try then
wait, so when you say 5 to 6, do you mean it like this?
isn't that read as from 6 to 5
smoky marsh
reading math is a bit confusing at times
keen plover
anyways do not forget the negative sign
originally it was 6 to 5
but that negative sign we added changed it to 5 to 6
smoky marsh
yup
keen plover
no because of the exponential
you have to use partial fractions to solve this
also since 4 is a perfect square there is a neat formula i would use
if you are stuck you can refer to this
dont forget the minus sign
smoky marsh
yea im just reviewing partial fractions in my textbook, thanks be being helpful and patient
keen plover
ok well once you find the antiderivative, subtract the antiderivative at u=5 from the antiderivative at u=6 and you should get your answer
smoky marsh
ok well once you find the antiderivative, subtract the antiderivative at u=5 fro...
thanks! I'll close the channel to not take up much time. should be good from here, thanks
.close
marsh citrusBOT
keen plover
no problem!
marsh citrusBOT
Available help channel!
gusty flower
marsh citrusBOT
gusty flower
need a little bit of help on this
twilit arrow
this function is only continuous if the pieces agree where they meet (that is, they agree at x = c)
so you want to find for what values of x the functions are equal
gusty flower
Yea so I tried setting them equal to each other
twilit arrow
and what happened then
twilit arrow
what is 5
gusty flower
C that makes it continuous everywhere right?
twilit arrow
yes
gusty flower
So what do I do if I have to different answers once I factor
twilit arrow
then there's 2 possible values for c
scarlet orbit
Prove 1+1 = 2
marsh citrusBOT
Prove 1+1 = 2
marsh citrusBOT
iron meadow
Prove 1+1 = 2
marsh citrusBOT
Available help channel!
still temple
Hi please help me
marsh citrusBOT
Hi please help me
still temple
How do i do thiss
I failed my exam 😂
I used google translate to translate it
It wasnt on english
This is original
$binomial
Idkkk
@tight lance
<@&286206848099549185>
Do you know Pascal's triangle?
Ummm i saw it before
dawn mango
what is the question ?
still temple
But didnt learn it
still temple
Here
Ooooooo
What do i do with it?
Do you you see how it is calculated and that the entries are just the binomial coefficients?
Mhm
e.g. $(a+b)^2= 1a^2 + 2a^1b^2+1b^2$ from the second row
elfin berryBOT
Landau08
elfin berryBOT
Landau08
still temple
Ohhhhhhhhhh
So i use that one
can you tell what i must be?
Hmmm
No 😭 im so bad
Do you understand why binomial coefficients come into play?
Uhhhh no
I know to do
(N
K
And
Tk+1
But not this
The binomial coefficient tells you how many ways there are to pick k from n elements.
Ohhh
when you multiply out the n brackets (a+b) in (a+b)^n and want to count many times you get $a^k b^{n-k}$ you pick k times a an (n-k)times b
Yea
elfin berryBOT
Landau08
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
still temple
so the the number in front of $a^kb^{n-k}$ is just $\begin{pmatrix}n\k\end{pmatrix}$
elfin berryBOT
Landau08
still temple
So its (21)
3
?
21 * 20 * 19
3 * 2 * 1
you want to find i such that $21 = \begin{pmatrix}i \2\end{pmatrix}$
elfin berryBOT
Landau08
still temple
Oooooooooo
have you found the 21 in Pascal's triangle that is an alternative way to compute binomials?
15+6?
can you read off what i is in that row?
Whole row?
Where is i there
Sorry im dumb im taking ur time 😭
Wait I'll draw something...
Kk thc
Ohh
So its 5?
(5
3
in which row does the 21 appear
Ohhh
So its 7 - 1v
?
right 7-1=6
(6
3
right
6 * 5 * 4
3 * 2 * 1
6 * 5 * 2
3
indeed $(a+b)^7=a^6 +7a^5b + 21 a^4b^2 + \cdots$
Ohhhhh
So thats the result?
sorry I meant 7
elfin berryBOT
Landau08
still temple
Oooooo
it's in the eighth row and because you start counting wich i=0 that corresponds to i=7
you can check:
Ohhhhh
So (7 )
0
$\begin{pmatrix}7\2\end{pmatrix}=\frac{7\cdot 6}{2\cdot 1}$
Im so baddddd 😭
elfin berryBOT
Landau08
still temple
$\begin{pmatrix}21\end{pmatrix}=\frac{7\cdot 6}{2\cdot 1}$
elfin berryBOT
zizela
still temple
Oh
so what is i?
Hmmmmm its 7?
That's right.
Ohhhhhh 😮
So i just write this and its correct?
Or i need to show how i got it
indeed and $(a+b)^7= a^7 + 7a^6b + 21 a^5b^2 + \dots$ has at its third coefficient a 21
elfin berryBOT
Landau08
still temple
Thats results?
the row in the triangle was not finished, I was just lazy, it continues as follows:
Ohhh
But on exam i would need to write this?
still temple
.
there was also a typo...
Oh
$(a+b)^7= a^7 + 7a^6b +\underline{21} a^5b^2 + 35a^4b^3+35a^3b^4+21a^2b^5+7ab^6+b^7$
elfin berryBOT
Landau08
still temple
Oooooo
as I just asked wolfram alpha so I don't commit any more typos
make sure you read the wiki article on the pascal's triangle: https://en.wikipedia.org/wiki/Pascal's_triangle
Will do thx so much
that graphic contains all you need
Thxxp
marsh citrusBOT
@still temple Has your question been resolved?
Available help channel!
Available help channel!
sweet pagoda
marsh citrusBOT
sweet pagoda
I’m not sure how to do this
sweet pagoda
angle chasing?
bright jay
Basically you need to find the angle to find the area of that sector
sweet pagoda
thats what im stuck on
I dont know how to find the angle with the information given
still temple
draw a line in the middle of the sector
so you get hypothenus + r = 40
actually just do arcsin on it
sweet pagoda
if I drew a line through the middle, wont the line also be 40
still temple
like draw it first and send
sweet pagoda
still temple
what is the length from the origin to the origin
sweet pagoda
40
still temple
no origin to origin
sweet pagoda
if you are talking about endpoints on the line
still temple
between the centers of the circles
sweet pagoda
oh
28
wait
16
no its 28
ok so I did ((sin90)/28) = ((sinx)/12), 12((sin90)/28)) = sinx, sin^-1(12((sin90)/28))) = x
then multiplied x by 2, found the area of the sector, then subtracted by area of circle
but its not correct
still temple
how much did u get as an angle of the sector
sweet pagoda
.786 radians
still temple
huh i got 0.886 radians
sweet pagoda
let me try again
i got the same thing again
i did it in degrees and got the right answer
sage gate
I'm stuck Rational exponents: Negative exponents and fractional bases in Aleks. Essentially my question is how do I know to answer either whole number or faction
marsh citrusBOT
I'm stuck Rational exponents: Negative exponents and fractional bases in Aleks. ...
@sage gate Has your question been resolved?
sage gate
I got passed the section but I'm still a bit puzzled not a big deal to get it answered tho
.close
quick willow
marsh citrusBOT
quick willow
can someone help me on how to do this?
marsh citrusBOT
@quick willow Has your question been resolved?
static quarry
,rotate
elfin berryBOT
static quarry
can someone help me on how to do this?
any thoughts or attempts so far?
stable path
marsh citrusBOT
stable path
i dont get it
its basic physics
but i cant get -14
i tried adding, even tried multiplying the 6
what am i doing wrong
leaden solstice
You should be fine. 1.5x6=9
marsh citrusBOT
@stable path Has your question been resolved?
marsh citrusBOT
marsh citrusBOT
Available help channel!
sage gale
Can someone help me with this?
marsh citrusBOT
Can someone help me with this?
main idol
try contradiction
mystic heath
Just want to confirm that this is true
marsh citrusBOT
Just want to confirm that this is true
ornate ginkgo
it is true
violet herald
marsh citrusBOT
violet herald
I got all the possible angles
And called ? X and ths other angle y
X+y =140
Also tried to construct another equation through the triangle in the right corner but I ended up everytime with the same equation
quasi osprey
I suspect Pythagorean theorem somewhere, cuz since it’s a square you can Pythagoras to equate the sides of the square and that’s how you can form a relationship between a lot of the sides
violet herald
I didnt Try anything related to sides but will give it a shot
Also if u solved it plz consider telling me the answer ASAP
quasi osprey
Sorry but I did not solve it.
But I also suggest doing the angle to side ratio stuff. Like tan(80) = A/B, that kind of stuff. Maybe something cool will happen when you isolate A from all the equations and equate them?
violet herald
130 if I’m not wrong
Idk the answer
celest sandal
Idk the answer
It should be 130
violet herald
How did u solve it
celest sandal
How did u solve it
I just took all angles of a square to be 90
So if you calculate each unknown angle using that you can get it
marsh citrusBOT
@violet herald Has your question been resolved?
celest sandal
50+unknown=180
marsh citrusBOT
50+unknown=180
long cargo
law of cosines
twin pike
Hi guyz
nocturne fiber
wolframalpha easily answers your query
twin pike
Can you tell me how to do it tho?
I am not here for answer
nocturne fiber
,w graph 1/(sinxcosx)
elfin berryBOT
tacit bear
I need help with question 14
marsh citrusBOT
I need help with question 14
@tacit bear Has your question been resolved?
Available help channel!
raw mulch
I am stuck on how to do the working out for XxX^1/4. The textbook answer is X^5/4
marsh citrusBOT
I am stuck on how to do the working out for XxX^1/4. The textbook answer is X^5/...
nocturne fiber
,tex \factoid original
elfin berryBOT
raw mulch
I’m sorry this is the first time I’m using this
Write in index form
And simplify
I’m stuck on the process from this to the answer
<@&286206848099549185>
limber elk
raw mulch
? I will try
knotty trellis
raw mulch
I got to there and then got stuck because the answer has 5 over 4
knotty trellis
Ig you will have to memorize this one
raw mulch
Probably a good thing
I’m still so confused because the answer is x to the power of 5 over 1
knotty trellis
raw mulch
OOOOH
knotty trellis
I’m still so confused because the answer is x to the power of 5 over 1
Thats incorrect. It should be 5/4
knotty trellis
These are 2 properties you have to memorize
there are few more such as negative exponent, but you probably know them
raw mulch
I just haven’t done this for like a year and there wasn’t an example in the textbook
knotty trellis
I just haven’t done this for like a year and there wasn’t an example in the text...
It's ok. Nobody remembers all identities.
marsh citrusBOT
marsh citrusBOT
Available help channel!
flat bear
i have a pdf given as in the picture by f(y)
marsh citrusBOT
i have a pdf given as in the picture by f(y)
flat bear
where does the constant 0.2 come from when they integrate it to get the cdf
marsh citrusBOT
@flat bear Has your question been resolved?
sturdy mason
utilising f=ma formula, rearranging for for f/m =a , how can i apply the forceS?
sturdy mason
as they are two
what should i do with them ?
currently got f/15 =a
but idk what to sub into gf
f
thorny galleon
utilising f=ma formula, rearranging for for f/m =a , how can i apply the forceS?
!physics
novel fjord
mechanics is a part of physics lmao
nonetheless it gives you what the forces are
sum them and divide
sturdy mason
mechanics is a part of physics lmao
and im learning mechanics part of UK A Level mathematics, divided into Pure,Stats and mechanics, therefore its pretty normal to ask this sort of question here. Dont know that guy is sending that command
.close
marsh citrusBOT
safe vector
marsh citrusBOT
Available help channel!
still temple
Let $H$ be a normed space in which the norm satisfies the parallelogram law:
[
\norm{u+v}^2 + \norm{u-v}^2 = 2\parens{\norm u^2 + \norm v^2}\quad \forall u, v \in H
]
Show that the norm comes from a positive definite sesquilinear inner product
marsh citrusBOT
Let $H$ be a normed space in which the norm satisfies the parallelogram law:
\[
...
still temple
Any first ideas?
elfin berryBOT
devout mauve
something something polarization identities maybe which I always forgot what they are
still temple
something something polarization identities maybe which I always forgot what the...
from what i did
the parallelogram law does show that (u,v) is an Hermitian inner product
just took the complex conjugates
but now, we need to check for the linearity don't we
this seems a bit difficult
wtf
how in the hell do you show full linearity in the first variable
devout mauve
maybe first just additivity
then scalars in Z, Q and then by continuity in R
not sure about the jump to C
marsh citrusBOT
@still temple Has your question been resolved?
still temple
not sure about the jump to C
yeah one second i actually have something in mind maybe
marsh citrusBOT
@still temple Has your question been resolved?
light lynx
marsh citrusBOT
light lynx
Just need it to be solved wanna see if I got the right answer
still temple
what did u get?
light lynx
2 8
still temple
huh fr?
light lynx
Bro I would be surprised if I got it right the way I did it
still temple
how did u do it
leaden trout
Wanna show your work? Maybe we can fix it
light lynx
Well I got loge (4x-3) to equal loge x+1
I was able to solve it to 4/3
Then I put 4/3 into loge x+1
Then I got 7/3
Now that’s where I am stuck
leaden trout
You so want to calculate the intersection point C, right?
The question you posted was about A and B
light lynx
No find a and b
leaden trout
Ok so then you have to set the equations equal to 0
light lynx
Yes I noticed when I was doing it I was finding c
light lynx
Oh ok
leaden trout
For the point C you set them equal to each other:
log_e(x) + 1 = log_e(4x-3) and solve it
still temple
For log_e (x+1) I am getting x = 0
is it not ln(x) + 1?
light lynx
Log turns to in
still temple
i think so since the answer you get better matches the picture
leaden trout
For log_e (x+1) I am getting x = 0
Yeah so, that's true, but a different function
leaden trout
log_e(x+1) is different from log_e(x) + 1
leaden trout
What do I do after I solve them
From the picture you know that the y-coordinates from A and B are 0.
leaden trout
So if you get the correct solutions, the points will be (x,0)
Yeah
Try to solve the equation for A again. You'll need to use this property in the calculation: e^(a+b) = e^a * e^b for some a and b.
light lynx
Try to solve the equation for A again. You'll need to use this property in the c...
So i need to use this?
leaden trout
So i need to use this?
I don't think you need it for B
Just for A
So we have
log_e(x) + 1 = 0
How can we get rid of log_e(...) ?
leaden trout
We need to apply the inverse operation of log_(...)
Which is e^(...)
So we apply e^(...) to both sides of the equation
Then we get e^(log_e(x) + 1) = e^0
light lynx
Ok
leaden trout
Then we use e^(a+b) = e^a * e^b
To get e^log(x) * e^1 = e^0
e^(...) and log_e(...) cancel
So we have x * e = 1
And x = 1/e
light lynx
To get e^log(x) * e^1 = e^0
How would this part look like on paper the ^ are kinda throwing me off
leaden trout
The log part is in the exponent of e
e raised to the power log(x)
Because " e to the power of x" and "log_e(x)" are inverse operations, when you combine them, you get the identity operation
So e raised to the power of log_e(x) is actually just x
stark wind
marsh citrusBOT
stark wind
how do i do this
sharp mortar
If z is a root then so is z*
stark wind
what is z*
knotty trellis
conjugate. if z=a+bi then z*=a-bi
brittle sun
what are the restrictions for inverse tanx
marsh citrusBOT
what are the restrictions for inverse tanx
brittle sun
like vertical asys
main idol
,w plot arctan(x)
elfin berryBOT
main idol
No vertical asymptotes
main idol
Inverse tangent is not the same as cotangent
brittle sun
isnt cos pi
i mean sin *
brittle sun
Inverse tangent is not the same as cotangent
wut
my whole life was a lie if this is true
main idol
,w define inverse tangent
elfin berryBOT
main idol
brittle sun
tan and inverse tan
brittle sun
https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:trig/x9e81a4f9838...
so both of them are sin/cos ?
ok lets say cos
my book says tan x is continitous
doesnt cos have a limit
pi/2
main idol
so both of them are sin/cos ?
No. Watch the video
marsh citrusBOT
@brittle sun Has your question been resolved?
brittle sun
No. Watch the video
i did and it didnt answer my questio
marsh citrusBOT
i did and it didnt answer my questio
main idol
Yes
brittle sun
i still dont know whats the difference lol
how their domains/ranges differ
@main idol
main idol
brittle sun
k thx
marsh citrusBOT
@brittle sun Has your question been resolved?
nimble kayak
can someone help with this question?
marsh citrusBOT
can someone help with this question?
stoic saddle
!status
marsh citrusBOT
What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
I'm pretty sure my method is wrong;
If someone could guide me through the whole thing that would be great
marsh citrusBOT
@nimble kayak Has your question been resolved?
marsh citrusBOT
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subtle glen
Hello
marsh citrusBOT
@subtle glen Has your question been resolved?
copper heath
I need a swedish person if possible here is the question (Picture)
But it translated to A frame has the shape of a rectangle, with length (3x+y) and width (y) cm.
Write an expression for the perimeter of the frame, then simplify the expression.
still temple
whats the formula for the perimeter of a rectangle
copper heath
idk what perimeter is I just translated it
still temple
then how'd you do the question
still temple
thats area
copper heath
I don't know
still temple
its 2(length + width)
copper heath
I kind of need a swedish person here lol
bright jay
If google translate is accurate,
Kan du formeln för omkretsen av en rektangel?
copper heath
ok
so
Längden
holdo n
The length
is
(3x+y)
and the with
is
(Y)
and they want me to get the circumference and make the equation easier
@still temple
copper heath
dude
Im mentally stupid
I just need to get the answer
The perimeter of a rectangle can be expressed as 2 * (length + width). So the perimeter of this frame can be expressed as:
2 * ( (3x + y) + y ) = 2 * (4x + 2y) = 8x + 4y.
Ok
still temple
(3x + y) + y
still temple
marsh citrusBOT
still temple
wouldnt the answer be R excluding the number that makes l1 = l2?
open shale
what is consistent
still temple
when theres a solution to the system
ty lex! After i row reduced i got
1 -3/8 | 3/4
0 -36/8 -k | -7/4
so now im doing -36/8 -k = 1
open shale
I don't follow
This system has no solution if the lines are paralell
so you just have to check that
still temple
i got 9 /2 by cross multiplying the coeeficients
marsh citrusBOT
@still temple Has your question been resolved?
elfin berryBOT
exotic terrace
marsh citrusBOT
waxen bridge
I think you need to make factors and then cross out everything.
marsh citrusBOT
@exotic terrace Has your question been resolved?
gleaming garden
@exotic terrace
22^2 * 55^2 = (22 * 55)^2 = 1210^2
10^2 = 2^2 * 5^2
Go from there
tawny vapor
marsh citrusBOT
tawny vapor
should i consider the x intercept of the red line -0.5?
cunning fiber
Check the scale of the graph
tawny vapor
accidentally wrote y 😅
cunning fiber
See for yourself - there’s already points with integer coordinates on the graph, so you can find the equation and thus the x-intercept algebraically.
still temple
I'm stuck on 1c. All I wrote was
"Suppose a and b are integers and a > 1, b >1"
However I'm not sure how to go from there. How would I prove gcd(2a,2b) = 2gcd (a,b)?
still temple
Okay I wrote some more
"Let c = gcd(a,b), therefore c divides a and c divides b" but idk if im heading in the right direction?
desert dirge
its a good start yes
still temple
- Suppose a and b are integers and a > 1, b > 1
- Let c = gcd(a,b), therefore c divides a and c divides c
- a = kc, and b = lc for some non-zero integer k and l.
- Substituting into gcd(2a,2b) --> gcd(2kc, 2lc)
now I'm stuck
<@&286206848099549185>
nevermind I got it
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marsh citrusBOT
marsh citrusBOT
Available help channel!
somber ridge
marsh citrusBOT
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marsh citrusBOT
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marsh citrusBOT
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marsh citrusBOT
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hollow wing
marsh citrusBOT
hollow wing
how do i do this?
novel fjord
fundamental theorem of calculus
nova totem
,tex \ftctwo
elfin berryBOT
Umbraleviathan
keen plover
keen plover
nova totem
Shit don't kill a homeless man now
marsh citrusBOT
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lament valve
help
marsh citrusBOT
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lament valve
<@&286206848099549185>
lament valve
😦
marsh citrusBOT
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marsh citrusBOT
@lament valve Has your question been resolved?
still temple
marsh citrusBOT
devout mauve
anything epsilons is usually positive
still temple
anything epsilons is usually positive
Can we prove that L=M
by saying |L-M| converges to 0
and is that what this proof is saying?
devout mauve
well we are assuming |L-M| is positive and then arrive at a contradiction
cause it has to be smaller than 1/5th of itself
still temple
well we are assuming |L-M| is positive and then arrive at a contradiction
can we do a direct proof that L-M -> 0?
devout mauve
I mean L-M is a fixed expression
nothing converges there
or well, it's constant and converges because of that but I doubt that's what you want
still temple
or well, it's constant and converges because of that but I doubt that's what you...
can we say that an - an converges to zero?
and therefore for an limits L, M
their difference has to be zero
devout mauve
well you are using there that you can pull limits apart
lim a-b = lim a - lim b
if you know that, ok. if not, then you need to do something like in the picture
and like they mention, usually you would prove uniqueness before proving those rules for limits
still temple
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marsh citrusBOT
marsh citrusBOT
Available help channel!
slow rover
G(x, y) = ((y^3)x − xy + 1, y − 2x + ye^x)
how can i calculate ∂H2/∂x being H2 the second component of H = G o G
marsh citrusBOT
G(x, y) = ((y^3)x − xy + 1, y − 2x + ye^x)
how can i calculate ∂H2/∂x being H2 t...
main idol
chain rule and coffee
still temple
coffee? 
slow rover
so is it like ∂H2/∂v times ∂v/∂x
elfin berryBOT
riemann
slow rover
i forgot to mention that in the exercise its said to use the composite function derivative theorem
what is that
marsh citrusBOT
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marsh citrusBOT
@slow rover Has your question been resolved?
still temple
Did I do this right?
marsh citrusBOT
Did I do this right?
cunning fiber
$\sqrt{x^2-1} \neq \sqrt{x^2} \cdot \sqrt{-\frac{1}{x^2}}$
elfin berryBOT
Civil Service Pigeon
cunning fiber
Idk if you meant to divide the numerator and denominator by $x$ or something else
elfin berryBOT
Civil Service Pigeon
still temple
Better?
marsh citrusBOT
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marsh citrusBOT
marsh citrusBOT
Available help channel!
stable path
marsh citrusBOT
stable path
i keep getting
3 sqrt 2 / 2
i dont get 2.1
im using a Ti-36x Pro
what am i doing wrong?
see the only way i get it is if i use my dumber calculator and i type
sin 45 equals
then times that by 3
my "better" calculator keeps giving me 3 sqrt 2/2
no matter what
even when i do
sin 45 equals on my "better" caluclator i get
sqrt 2 over 2
marsh citrusBOT
@stable path Has your question been resolved?
gray jolt
3 sqrt 2 / 2
that’s approximately 2.1
smoky geyser
marsh citrusBOT
sleek adder
im pretty sure you set up an augmented matrix and row reduce
smoky geyser
yes I did
I end up with
1 0 -2 -1
0 1 1 0
@sleek adder
I just dont know what to do after. Im assuming
there are infinite vectors
marsh citrusBOT
@smoky geyser Has your question been resolved?
minor forge
How do I know how to plot these points? I tried doing the question and the answer is completely different from the answer keys
marsh citrusBOT
How do I know how to plot these points? I tried doing the question and the answe...
minor forge
marsh citrusBOT
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marsh citrusBOT
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minor forge
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untold glacier
Hello, I am having some difficulty with this question. It was my first day of the new semester today i just need a refresh. Thanks!
marsh citrusBOT
Hello, I am having some difficulty with this question. It was my first day of th...
untold glacier
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