Try to factorise this
#help-38
twin mortar
2x+1
midnight kite
Yes, $(2x+1)(2x+1)$ right?
solid kilnBOT
hanzo
midnight kite
^2
Yeah same thing
So now if we subsitute that in our question we get
$\frac{(2x+1)}{(2x+1)^2}$
solid kilnBOT
hanzo
midnight kite
Yes
twin mortar
and then
midnight kite
In the denominator
twin mortar
1/2x+1
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flat spruce
Short questions for Modulo calculations
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Short questions for Modulo calculations
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SilberSeele
flat spruce
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idle nacelle
Can anyone help me with these questions please. I have zero clue what I doing..
idle nacelle
<@&286206848099549185>
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verbal gulch
not even number 5?
idle nacelle
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digital valve
hello, please could you help me with this exercise. Thanks . A girl weighing 35kg stands on a surface. Determine the sum of the surface modulus exerted on the surface for both cases shown in the figure. The area of the sole of each shoe is 3.5 x 10^2m^2 .(g=10m/s^2).
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hello, please could you help me with this exercise. Thanks . A girl weighing 35...
@digital valve Has your question been resolved?
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thorn shale
how do i start on this?
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how do i start on this?
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wraith hinge
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wraith hinge
I need help with number 18 please.
inland orbit
Do you know what cos(pi) and sin(pi) are equal to?
wraith hinge
Do you know what cos(pi) and sin(pi) are equal to?
-1 and 0
inland orbit
You're just being asked to multiply them
wraith hinge
You're just being asked to multiply them
How did you know it equals to cos(pi) and sin(pi)
solid kilnBOT
tatpoj
wraith hinge
It says x
inland orbit
That's what I thought at first, but it can't be, that doesn't make any sense
wraith hinge
Yeah, I agree, it must be pi. The answer is literally 0.
inland orbit
yeah lol
wraith hinge
Thanks
wraith hinge
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brittle blade
can someone pls explain how to solve this
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can someone pls explain how to solve this
long basin
Partial derivatives
pseudo rose
,ask what is a partial derivative
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pseudo rose
@brittle blade ☝️
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broken depot
are AEF ~ CDE ~ BDF
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are AEF ~ CDE ~ BDF
broken depot
H is the orthocenter of ABC
broken depot
are AEF ~ CDE ~ BDF
its probably the case but im not sure i have enough information
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broken depot
🙏please
sleek canopy
where did you get this problem?
broken depot
sleek canopy
uuu very good book..i ll read it in the future
broken depot
yea i like it
sleek canopy
check evan's webpage... hi posted a lot of typo in the text
sleek canopy
are AEF ~ CDE ~ BDF
the congruence of the agles are not given right?
broken depot
not sure what that is
currently trying to make the angles to equationw
but i only get 0=0
but im not that productive rn since im wathcing a movie
sleek canopy
what's movie
broken depot
saw 3
sleek canopy
broken depot
have you watched it?
sleek canopy
no i hate horror film
sleek canopy
because he wants scary you
broken depot
now i have 0 = 540 💀
sleek canopy
very strange
broken depot
yea because my equations are wrong
sleek canopy
more than saw 3
broken depot
wait 1sec
omfg
no im just bad at arithmetic
-
- is +
💀 i just cancelled some - because i wasnt paying attention
no
my equations are wrong
sleek canopy
so?
broken depot
i completely forgot about the big triangle because i was so focused on the smaller ones
now i have D + E + F = 180
i probably couldve skipped this part if i knew more abt similar triangles
but i dont
thus
prove that those three small triangles are similar to ABC
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worthy crystal
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wheat locust
Simplify
(a(z-x)+b)-(a(y-x)+b) = 0
I know that the b’s would cancel out but I’m not sure where to go from
a(z-x)-a(y-x)
It’s something to do with the a’s I think but I’m not sure
warm veldt
I have a question... can someone explain this step?
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I have a question... can someone explain this step?
warm veldt
Will the - sign always go behind the whole fraction if the denom or numerator is negative?
night zodiac
$\frac{-a}{b} = \frac{a}{-b} = - \frac{a}{b}$
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dldh06
night zodiac
They all mean the same
warm veldt
They all mean the same
hmmm so if either num or denom is negative I should just think of it as a negative fraction?
warm veldt
Alright thanks a lot!
warm veldt
You can think of it like that
another thing...
We used the negative to do -13 +22, I get that, but why did the numerators not add-up?
night zodiac
why did the numerators not add-up
What exactly do you mean?
warm veldt
> why did the numerators not add-up
What exactly do you mean?
OH sorry the denominators i mean
night zodiac
Because you don't add those when you are finding a common denominator
warm veldt
Because you don't add those when you are finding a common denominator
hmmm thank you, im still a bit confused but I will try to manage
night zodiac
Do you know how to add fractions with unlike denominators?
warm veldt
Do you know how to add fractions with unlike denominators?
yes?
warm veldt
It's adding fractions, with unlike denominators
yea makes sense
Thanks a lot dude!
sorry if im really bad at this. I just started so ummm yea, im stupid
languid pier
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languid pier
not sure how this is wrong, the integral is inputted correctly, that's an integral calculator and its never been wrong
slim moat
What do I do here?
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What do I do here?
inland orbit
you are not shadowbanned lol
I'm a bit confused, what did you do here exactly?
Where did 2x^2-5x-x come from?
and -2+7
@slim moat
slim moat
Actually I'm looking at my course, and I found out that what I'm doing is a bit above schedule
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slim moat
sorry for bugging you
inland orbit
you didn't, no worries
slim moat
thanks anyways, gn!
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languid pier
how did they get the 3 there? this is hydrostatic forces calculus II
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wraith hinge
integration seems weird
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integration seems weird
wraith hinge
what I know: two different expressions can have the same derivative
which implies that a given expression can have multiple integrals
which is represented by c
but what if theres an extra term
that wont make sense at all 😭
for example I was just integrating 1/(1-Cosx)
and I happen to have two different values for two different methods
when I multiply both numerator and denominator by 1+CosX
my answer is -Cotx-Cosecx+c
but when I use multiple angles my answer is -Cot(x/2)
I tried proving -Cot(x/2)=-Cotx-Cosecx
using multiple angles but it simply doesnt add up
oh my bad calculation error
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https://gyazo.com/d8b90c022cc96f838c73ed010cf07344
reef plaza
ERm
SO yea
i use e^lambda t as ansatz
got the quadratic, lambda was 1+-epsilon
and by A and B now some how are 0
So what did i do
wrong
whole coral
How did you get the very final line? Up until there seems fine to me
whole coral
Are they the same A’s though?
whole coral
Hmm, well in mines I had my solution being something like
[
y(x) = \alpha e^{ (1 + \epsilon) x} + \beta e^{ ( 1 - \epsilon) x}
]
For general constants $\alpha, \beta$ and so that gave me from the initial conditions that
[
y(0) = A \implies \alpha + \beta = A
]
and
[
y’(0) = B \implies \alpha ( 1 + \epsilon) + \beta (1 - \epsilon) = B
]
But that gives me some different values of $\alpha$ and $\beta$ in terms of $A$ and $B$
solid kilnBOT
@whole coral
reef plaza
Hm
So your saying that the A in initial conditions
is different from the A in the equation
whole coral
They basically would be (unless stated otherwise) I would want to assume
reef plaza
Hm
My lecturer taught us using variables like A and B and not alpha and beta when doing this
So i assumed they were the same
but tbf if your assumption was true
whole coral
Solving that I think gives you like $\alpha = \frac{ B - A(1 - \epsilon)}{2\epsilon}$ and $\beta = \frac{ A(1 + \epsilon) - B}{2\epsilon}$ if I haven’t messed it
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@whole coral
whole coral
Hmm, I have a feeling that if you rearrange it a bit you’ll get it looking like a derivative (but that’s from experience of where you take two solutions and make them get closer together)
Should try it out actually but then I’m running out of paper 
I’m using small post it notes 
reef plaza
I’m using small post it notes <:lolDog:543004265904472065>
Hahaa
reef plaza
Hmm, I have a feeling that if you rearrange it a bit you’ll get it looking like ...
what do u mean by making them closer togeather
whole coral
So you know like the thing where if you have a repeated root you multiply it by x
reef plaza
Yea
whole coral
The explanation for that I’ve seen is like take two solutions, say $a$ and $b$, then linearity would give you that
[
\frac{1}{a - b} e^{ax} - \frac{1}{a - b} e^{bx} = \frac{e^{ax} - e^{bx} }{a - b}
]
Is also a solution, but then as $b\to a$ that basically turns into $\dv{a} e^{ax} = x e^{ax}$
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@whole coral
whole coral
So I’m thinking it would look something like that here, as you basically have two solutions getting closer to each other
reef plaza
I see where you are coming from
But we have not learnt anything like this
Might be the case tho
Ill just email my prof
thank you tho
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wraith hinge
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wraith hinge
Im not sure how to do c
what do they mean by the total of the probabilities
when I search it up I get some theorem
lilac wind
think they just mean adding up the 4 possible choices
desert venture
How do I slove thos
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How do I slove thos
desert venture
zinc ginkgo
,rotate
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round mango
Start with finding FD using Pythagoras theorem.
Then use trigonometry on angle DFC to find useful relations between the side lengths of triangles DFC and AFC
You can find out the length of both AF and AC using trigonometry on angle DFC
And note how knowing AF will help you know AD since you know the full length of the diagonal
And lastly, By symmetry AD=BF
After this it should be a piece of cake
Try this and let me know how far you reach
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wooden moth
Determine the Taylor polynomial of order 1 to F(x) around x=0. $F(x) = \int_{0}^{x} e^{-t^2}$
solid kilnBOT
afeAlway
wooden moth
How in the hell am I supposed to integrate this? I'm pretty sure I saw somewhere that this is impossible to integrate.
But I used taylor and got right answer but the problem is that this is not what they asked, and it is probably a coincidence
wooden moth
fundamental theorem of calculus
F(a) - F(b)?
whole coral
More the $\dv{x} \int_{a}^{x} f(t) dt = f(x)$ one
solid kilnBOT
@whole coral
marble wharf
"derivative and integral are inverses of each other"
wooden moth
<@788085606483361802>
how does this help me?
marble wharf
well you dont have to evaluate the integral
wooden moth
"derivative and integral are inverses of each other"
yeah but the problem I am having is integrating this?
whole coral
yeah but the problem I am having is integrating this?
You don’t integrate it
wooden moth
but you dont have to integrate this
y
marble wharf
except the trivial case x=0
whole coral
How would you find the Taylor polynomial?
wooden moth
now I'm confused
marble wharf
but really you should be able to figure that one out without an antiderivative
wooden moth
now wait
marble wharf
abstractly, what is the taylor polynomial of a function g(x) at x=0
wooden moth
actually I don't get it, I thougt I did but no
whole coral
abstractly, what is the taylor polynomial of a function g(x) at x=0
You know how to find the Taylor polynomial right?
wooden moth
You know how to find the Taylor polynomial right?
yeah
whole coral
…which would be?
whole coral
As in let’s take some function g(x) and we want to Taylor expand it about zero, any general function we can expand out - how would you do that?
As in what would be the rule/steps to do it?
wooden moth
p(x) = f(x) + f'(x)(x-a) + ... + (f^(n)(x-a)^(n+1))/(n+1)!
wooden moth
As in what would be the rule/steps to do it?
But in this case I don't have f(x) tho only f'(x) and I can get eveything above the first derivative (which is unnecessary for the question)
no I get it the integral for f(0) - f(0)=0
p(x) = 0 + 1 (x) = x
whole coral
p(x) = f(x) + f'(x)(x-a) + ... + (f^(n)(x-a)^(n+1))/(n+1)!
shouldn’t f and f’ be evaluated at a?
But yea there you go haha
wooden moth
shouldn’t f and f’ be evaluated at a?
a = 0 tho?
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whole coral
a = 0 tho?
The general expansion you wrote
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ionic gull
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ionic gull
this is the picture
finite jewel
i figured a single integral would find area, not a double integral
do you have notes how to use a double integral instead?
ionic gull
do you have notes how to use a double integral instead?
not really
finite jewel
do you know how to find it for a single integral?
ionic gull
yes i can find the area with a single integral, thats fine
its just the questions asking for a double integral, and i cant figure out how you do that
finite jewel
its just the questions asking for a double integral, and i cant figure out how y...
its kind of dumb
ionic gull
mm i have read that
finite jewel
your limits for the x integral would be the two functions
ionic gull
i can kind of see what youre supposed to do
finite jewel
and then you just get back the single integral you know
ionic gull
but each time i try i get something wrong
finite jewel
but each time i try i get something wrong
what do you get
finite jewel
one time i got -37/3
you said you can set up the single integral, can you? what answer did you get?
ionic gull
you said you can set up the single integral, can you? what answer did you get?
6 * sqrt2 -3
(unless im wrong there)
finite jewel
$\int_{-4}^{2} \int_{\frac{y^2}{2}}^{\frac{-y+4}{2}} dx dy$
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walczyk
finite jewel
$= \int_{-4}^{2} \frac{-y+4}{2} - \frac{y^2}{2} dy$
solid kilnBOT
walczyk
ionic gull
i got 3 as the answer
finite jewel
i got 9
finite jewel
i got 3 as the answer
you didn't find the typo yet clearly
finite jewel
i got 3 as the answer
why don't you try following the steps yourself
finite jewel
cool good
ionic gull
**walczyk**
the issue i have is i cant see how youre supposed to arrange the integrals in the first place
ionic gull
well why is x=y^2/4 at the bottom of the integral and x=-y/2 + 2 on the top?
finite jewel
if you look at your graph that you linked about and turn your head, then the y^2/4 is the lower or smaller curve. its bounded the area below
so it goes on the bottom
still patrol
In a ranch there is a grassland. It is known that the grass in the grassland grows at a constant rate and the growing rate of every hectare of grassland is equal. It is known that 48 sheep can consume all grass of a 10-hectare grassland in 18 days; 21 cows can consume all grass of a 30-hectare grassland in 36 days. It is also known that a cow consume 4times as much grass as a sheep and the consumming speed of both animals remained constant throughout the process how many sheep are needed to consume all the grass of a 60-hectare grassland in 10days?
still patrol
Could someone please tell me how to approach this question? (As I have never seen this type of question before)
finite jewel
In a ranch there is a grassland. It is known that the grass in the grassland gro...
what's a can "21 cans"
finite jewel
it is 21 cows sir
the final question is asking solely about sheep, nothing about cows; is that okay? will they ask more about cows later?
still patrol
Maybe the cow was given to calculate the growth rate of grass
still patrol
10/(48*18)?
finite jewel
that is the rate r of hectares grass eaten per sheep per day
60 hectares = r * 10 * #sheep
6/r = number of sheep ---> 48*6 sheep is what i get
288 sheep
still patrol
10/(48*10) i think
what is 10 in 48*10?
finite jewel
what is 10 in 48*10?
10 hectares grass per 48 sheep per 10 days
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silk helm
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silk helm
<@&286206848099549185>
delicate meteor
<@&286206848099549185>
What GCSE paper is this
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silk helm
Ahh I don't know
delicate meteor
Ahh I don't know
im also doing a GCSE past paper
silk helm
I'm doing igcse Edexcel o level
silk helm
Oh good luck
delicate meteor
thanks you good luck too if you are doing it also
silk helm
Thanks it's next week monday
delicate meteor
cool gotta get back to revising
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cloud silo
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dull thorn
I'm on a tournament with 8 persons, I beat them all except 1 person, each peer drawn at random for the first round, the winners of the first round are drawn for the second round, the winners of the second round go to the final, what is the probability that I will go to the final?
woeful jetty
- Find the number of ways people can be paired in each round. So it is ||$\frac{8!}{2!}^{no._of_matches}$ for the first round, multiply this (using the distribution formula for the second one and so on...)||
- Now, among these find the number of ways where you and your rival are in the same match in any round. ||Do this by making a set of you and your rival and then going on to find permutations of other ones.
||3. Add these up and divide by total.
dull thorn
I think we can do it like easier, I don't need calculator on this
but don't know how to do it
woeful jetty
Sure.
Umm...
Find permutation of 8 people and divide by 2^(no of pairs) to simplify 1.
But thats the same thing as the one I mentioned.
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jade flint
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zinc ginkgo
does y = 2x + c?
A is probably not 0
jade flint
ah
jade flint
A is probably not 0
what would you recommend as the first step to solving the equation? so far all I've done is integrated 2
jade flint
Ax + 2?
zinc ginkgo
so find y' first
y' = ?
jade flint
y' = ?
uhh, is it not something x + a constant
because when you sub in 0 you get 2
oh
Ay + 2?
zinc ginkgo
you're given y. differentiate y with respect to x
jade flint
dy/dx = -Ae^(-x) + 3
zinc ginkgo
right
rough linden
The orphanage should get a new sandbox. It will be rectangular in shape and its length will be twice its width. The surface of the sandbox should be 12 m².
The carpenter builds the sides rounding their length to the nearest centimeter.
What will be the length of the sandbox and its width?
rough linden
Did I do this correct?
width=x
length=2x
P=2x×x
P=2x²
12=2x²
6=x²
x=v6
x=2.4m
x~3m
width=3m
length=6m
long basin
You rounded the meters not centimeters
Convert 2.4m to centimeters
Or rather
Convert sqrt(6) meters into centimeters
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rough linden
Convert sqrt(6) meters into centimeters
What is sqrt6?
240 cm?
@long basin
Why to centimeters
?
Its in meters
<@&286206848099549185> help me.
cursive musk
Why to centimeters
Reread the question
long basin
The orphanage should get a new sandbox. It will be rectangular in shape and its ...
Read the question
It literally says "rounding their length to the nearest centimeter"
Verbatim
solid kilnBOT
long basin
I'd start by turning 2.449 m to cm
long basin
You don't need to ping me every second
I'm literally right here
They want the nearest centimeter
2.449 m is not 240 cm
rough linden
245cm?
long basin
Yeah
solid kilnBOT
Result:
490
490cm = length
245cm = width? @long basin
whole coral
You don't need to ping me every second
cursive musk
^
knotty locust
^
rough linden
Ok sorrey
rough linden
490cm = length
245cm = width? <@349354952961032192>
Is this the final answer?
People..
Dont leave me
long basin
I gave you a thumbs up reaction
rough linden
Ok ok
mossy quarry
thought the domain was (0,5/2)
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thought the domain was (0,5/2)
mossy quarry
x can not be less than 0
zinc ginkgo
,calc log(5-2 * (-1))
solid kilnBOT
Result:
1.9459101490553
the argument of log cannot be less than 0
you're confusing 5-2x with x
charred storm
ln(u), u>0 and u=5-2x
mossy quarry
the bottom says -infinty
mossy quarry
you're confusing 5-2x with x
its under parenthesis inside ln
ok i understand now
but just not the - infinity part
at the bottom of that
mossy quarry
thought the domain was (0,5/2)
here
zinc ginkgo
ln(u), u>0 and u=5-2x
just understand this
mossy quarry
5/2 is one of the roots
but
domain should not be
negative infinity
ever
wait
oh
i see
it doesnt matter
-infinity times -2
=0
+5
is 5?
oak topaz
How do I Solve a System of Equations Graphically?
charred storm
huh
you have x<5/2
which numbers are smaller than 5/2?
its kind of self explanatory
mossy quarry
thought the domain was (0,5/2)
if u plug in negative infinity into 5-2x
you get x=5?
charred storm
no you get x= -infinity
becuase you plugged in -infinity for x
or are you asking what u is
wraith hinge
How do I Solve a System of Equations Graphically?
!onechannel
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How do I Solve a System of Equations Graphically?
Please stick to your channel.
mossy quarry
u is a function
oak topaz
!onechannel
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Please stick to your channel.
charred storm
yes and you are taking ln(u)
not ln(x)
'plugging in -infinity' is kind of a weird thing to do but lets just do it anyways
u=5-2*(-infinity)=5+infinity=infinity
ln(u)=ln(infinity)
and domain of ln(u) is u>0 so thats perfectly fine
or you could scratch all that and just consider that you found x<5/2 so the domain of f(x) is x<5/2
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cerulean hearth
$F = { (x,y,z,t) \in \mathbb{R}^4, x+y=z+t = 0 } \newline$
so $F = Ker f$ with $f((x,y,z,t)) = (x+y, z+t) \newline$
i don't understand why $f: \mathbb{R}^4 -> \mathbb{R}^2$
i mean why when we have 2 constraint (here x+y = z+t) the consequences is that f loose 2 degree, here f(x)€R^2 not R^4 which is really perturbing for me
solid kilnBOT
Max.cc
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
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<@&286206848099549185>
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final coyote
I am not sure, if I understand your question right, but I try to answer it - in the way I understand it.
You have a function f(x,y,z,t) which takes a point in R^4 and maps this point to (x+y, z-t). So the function is from R⁴ into R²
Then you are interested in the kernel of the function. The kernel of f is the set of points which are mapped to 0, so you get the criteria x+y=0 and z+t = 0.
@cerulean hearth
cerulean hearth
i have a set F
final coyote
thats what i said. F = kernel of f.
cerulean hearth
You have a function f(x,y,z,t) which takes a point in R^4 and maps this point to (x+y, z-t). So the function is from R⁴ into R²
that's the part i don't get
final coyote
its your definition: f(x,y,z,t)=(x+y,z+t).
cerulean hearth
i mean i don't get this definition
i don't get the correction in other world
why the function go in R^2
verbal gulch
the output of the function is an ordered pair of real numbers
therefore it's in R^2
final coyote
i mean i don't get this definition
I dont know why you or the person you gave this example (maybe you give some context) is interested in the function f(x,y,z,t)=(x+y,z-t).
cerulean hearth
well we have (x,y,z,t) and the condition that x+y = z+t = 0
honnestly i don't see the link with f((x,y,z,t)) = (x+y, z+t)
final coyote
i just can explain that this function goes from R^4 to R^2, and that F is the kernel of f.
final coyote
well we have (x,y,z,t) and the condition that x+y = z+t = 0
honnestly i don't se...
its the other way round.
first you have the function f.
second you are interested in the kernel of f, which means the subset which is mapped to 0.
final coyote
you wrote F = ker f.
cerulean hearth
ye
final coyote
so F is the kernel of f.
cerulean hearth
the exercise was to interpret F as a kernel and the answer is what i wrote ker f
and basically i don't get the answer
cerulean hearth
so F is the kernel of f.
F is the set wich is equal to ker f but don't know how they found f
and to be more precise why it goes into R^2
final coyote
i am sorry, i do not understand what your question is. why it goes to R² had you explaind in your question, as the constraints means a loss of 2 degrees.
cerulean hearth
perhaps when we try to interpret a space where x + y = z + t it is a plan which can explain why go into R^2
but i lack of that interpretation
cerulean hearth
i am sorry, i do not understand what your question is. why it goes to R² had you...
then why when we have constraints we loose degrees x)
final coyote
do you understand what a kernel is?
cerulean hearth
it's all the x that f(x) = 0
(well f can be anything)
final coyote
this is a formal explaination, thats right. but do you understand what this means?
final coyote
maybe the explanation from wiki helps you to understand (read "homomorphism" as "function"):
The kernel of a homomorphism is reduced to 0 (or 1) if and only if the homomorphism is injective, that is if the inverse image of every element consists of a single element. This means that the kernel can be viewed as a measure of the degree to which the homomorphism fails to be injective.
cerulean hearth
the kernel can be viewed as a measure of the degree to which the homomorphism fails to be injective.
i don't see the link honestly, if the kernel is not reduce to 0 then f is not injective, why are they talking about degree
glacial slate
Also, maybe that answers one of your questions: the choice of f here is completely arbitrary. f(x,y,z,t)=(x+y,z+t,0,0) has the exact same kernel, but the output values are all in R^4
cerulean hearth
ye it s R^2 * {0}^2
it is not he same than R^2
do they really have the right to say that it is R^2
glacial slate
Doesnt matter
It only needs to be linear (or a homomorphism whatever you like to call it)
final coyote
do they really have the right to say that it is R^2
as f is defined in the way you wrote its obviously R^2. I asked you for context earlier., but you didnt answer.
cerulean hearth
i gave you the context
cerulean hearth
the exercise was to interpret F as a kernel and the answer is what i wrote ker f
^
final coyote
and you gave the answer f in this way?
cerulean hearth
sry but i don't get what's unclear for you
if x + y = 0 and z + t = 0
then we have x = -y and z = -t
so i would say f(x,y,t,z) = (x, -x, z, -z)?
final coyote
if x + y = 0 and z + t = 0
then we have x = -y and z = -t
so i would say f(x,y,...
for which (x,y,z,t) is f(x,y,z,t) = (0,0,0,0)?
cerulean hearth
x = y= t=z =t = 0
final coyote
yes, so your kernel is (0,0,0,0) and it is not the given set F.
cerulean hearth
i see
glacial slate
Is it tho? What about (0,1,1,0)?
final coyote
Is it tho? What about (0,1,1,0)?
the point is: it is not the given F:
glacial slate
Yea thats true
final coyote
you have to decide: is F given and you are searching for a f so that F = ker f? Or is f given and you search for Ker f?
cerulean hearth
ye sry it's f not F
well it doens't matter does a set without any contraint have one only solution for the kernel which is 0
glacial slate
Thats a weird way of saying that the zero vector is the only zero vector
cerulean hearth
anyway, so i have x + y = 0 and z + t = 0 and i want that x=y=z=t=0
therefore if y =0 and t = 0 it works
the same if x = 0 and z = 0
so f((x,y,z,t)) = (x,0,z,0)
or f((x,y,z,t)) = (0,y,0,t)
where am i wrong this time
final coyote
in your first example (0,0,27,42) is in the kernel of f. but not in F.
in your second exampl (87, -131, 0,0) is in the kernel of f but not in F.
cerulean hearth
i edited
but ye i se it's not working
fuck idk how to got the result by my own
final coyote
i am not sure what you want to do. you have F with x+y=0 and z+t=0, you need a function where (x,y,z,t) maps to 0 if (x,y,z,t) in F and to something else when it is not in F:
the simpliest function with this is f(x,y,z,t) = (x+y, z+t).
cerulean hearth
so it exists possibly others functions
glacial slate
I already gave you an example earlier so yes
cerulean hearth
with 0,0 at the end?
glacial slate
There are an infinite amount of functions that have the same kernel, and thats easy to see: (2x+2y,z+t), (x+y,πz+πt) and so on, and you can add arbitrarily many zeros to that
cerulean hearth
true
final coyote
so it exists possibly others functions
yes, there are many other functions. for example f(x,y,z,t) = 0, if (x,y,z,t) in F, and f(x,y,z,t) = 1 if (x,y,z,t) not in F.
earnest carbon
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random citrus
Think about how to move from one circle to the other visually
By transformations
Like translation and scaling
earnest carbon
I originally thought of using two points to get two equations of w=az+b
to solve the system equations
but then when I plug other points in it won't work
so I realized that there's a rotation going on
but I just don't know how to find the angle of rotation..
earnest carbon
Think about how to move from one circle to the other visually
...there is a bit of rotation that I don't know how to find
these are the only two equations I can find
random citrus
I'm not sure if it will be in the form az + b
earnest carbon
ohhh ummm
random citrus
Maybe it is
earnest carbon
at least that was from my teacher's note
random citrus
It's easier to dilate when the centre is the origin
So I'd say translate it to the origin, dilate by 3/2, then translate it to -i
Yea so it would az + b
earnest carbon
so this is an example of a triangle's transformation
random citrus
Didn't ask
random citrus
I originally thought of using two points to get two equations of w=az+b
Anyway you made the blue equation so now make the green one
Then solve for a and b
earnest carbon
and it has the actual point-to-point translation so we can use w=az+b
earnest carbon
Anyway you made the blue equation so now make the green one
wait let me show you what I meant
:0 I apologize I must did something wrong previously because before this when I checked other points I didn't get the same answer so I thought there must be a rotation of the circle going on but
both of these "other points" all gave the right answer so there are only translation and dilation going on
thank you
@random citrus
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light dragon
Hello I got stuck here and can’t seem to find a solution
night zodiac
Hello I got stuck here and can’t seem to find a solution
For question 4?
night zodiac
Looks like a possible mistake
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violet nest
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violet nest
how would i do something like this
leaden nacelle
why is there a x?
violet nest
oh
can you tell me how the t^-3/5 turned into that
like there is something we do when theres is a - power or is it a fraction thing or both?
long basin
-3/5 - 1 = -8/5
violet nest
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fierce surge
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fierce surge
ik i have gone wrong but i cant tell where
i since found a faster way to do it but i dont know whats wrong with my completing the square
verbal gulch
can you write the quadratic you get
wraith hinge
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knotty locust
if u=-lambda * x then what is u when x= infinity?
assuming the upper bound of the original integral was infinity
wraith hinge
if u=-lambda * x then what is u when x= infinity?
It should be infinity right?
knotty locust
u=negative lambda * x
wraith hinge
Negative infinity
knotty locust
i suppose it depends on the sign of lambda
but yes
other than potentially something weird going on with the bounds, it looks good to me
knotty locust
read #rules and #❓how-to-get-help if you are confused jk.CTM
wraith hinge
other than potentially something weird going on with the bounds, it looks good t...
Hmm
dense hatch
what book do u suggers
wraith hinge
knotty locust
this is not the place for that question
don't interrupt other peoples help-channels
knotty locust
I linked you the rules
earlier
read them
Twerkingbee, basically if lambda is positive then the bounds should be from 0 to negative infinity, and if lambda is negative then the bounds should be from 0 to infinity. These might end up giving the same result either way
and it might not matter to seperate by case
if so
solid kilnBOT
wraith hinge
and it might not matter to seperate by case
Any idea what is going on with wolfram
But one thing
What should be -infinitylambda(e^-infinitylambda)?
,w -infinitylambda(e^-infinitylambda)?
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sick crane
In a football league of 20 teams, each team plays two matches, one in its own field and the other in the field
on the contrary, against all others. The winner of a match gets 3 points and the loser none, if any
in the event of a tie, one point is awarded each. If the league is over, the points obtained by all are added up
teams, what is the difference between the largest and the smallest value that this sum can have?
sick crane
i dunno where to start please help me
eager comet
what do you think a team has to do to get the highest and smallest amount of points at the end of the league?
sick crane
win all n lose all
eager comet
yeah
sick crane
but were talking of all the teams
eager comet
what do you mean?
sick crane
"the points obtained by all are added up"
sick crane
yeah
eager comet
the outcomes are either
team a wins (+3)
team b loses (+0)
total: (+3)
team b wins (+3)
team a loses (+0)
total: (+3)
team a ties (+1)
team b ties (+1)
total: (+2)
eager comet
the less ties, the more total points
now take into account how many games there are total
sick crane
1 team does 38
eager comet
Yes
sick crane
38·6·10
eager comet
where are you getting 6 and 10 from?
sick crane
yes
eager comet
but you need to take into account that we cant count a match twice
sick crane
each team plays 38 games
eager comet
so you cant just do 38*20
sick crane
yeah
we got only the half
if we assume the logic that the most wins more points
that means that the max value is when 10 teams are winners
like 10 winners 10 losers
well its not exactly like that
because there are 38 games each team
eager comet
total matches will be (no. of times each team faces one opponent) * (total no. teams) * (total no. teams -1)/2
2 * 20*(19/2)
eager comet
to account for doubles
lets say we have teams1-20
when we count team 1 vs team 15s first match
when we come to counting team 15's first matches
we dont count team 15 vs team 1
because they already played
eager comet
this overall accounts to half the total matches not being counted
so we / the last number by 2
sick crane
each team faces each team * 2
eager comet
total matches will be (no. of times each team faces one opponent) * (total no. t...
you can just follow this formula for examples like this though
sick crane
thats the formula in word mode
eager comet
T x n(n-1)/2
T = times each opponent faces eachother
n = number of teams total
try this with your example and see how many you get
sick crane
380
eager comet
Yes
eager comet
the case of all ties is actually +2 per game
sick crane
oh yes sorry
eager comet
remember each team gets +1 each
eager comet
and the case of all wins is +3 per game
eager comet
or just 3(380) - 2(380)
sick crane
or 380 directly XD
eager comet
👍
eager comet
sure, i have a bit more time left
sick crane
A train has five carriages, each of them contains, as a minimum, one passenger. Two passengers are considered neighbors
whether they are in the same wagon or whether they are in adjacent wagons. Each passenger only has 5 or 10 neighbors,
exactly How many passengers are in the train?
@eager comet
eager comet
convert this question into algebra
and it'll be easier to make sense of
from left to right assign the amount of people in each carriage a b c d e
now with the limitation of 'each passenger has only 5 or 10 neighbors' you can start to make a system of equations
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stone mirage
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wraith hinge
i dont underdstand how to solve |-x+1| < 1
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i dont underdstand how to solve |-x+1| < 1
wraith hinge
so -1 < -x+1 < 1
trim lichen
keep going
scarlet escarp
what did you do to get from the step before to that last one?
wraith hinge
*-1
craggy sage
when u multiply by negative no. the sign of inequality reverses
wraith hinge
when u multiply by negative no. the sign of inequality reverses
why?
wraith hinge
ooo
craggy sage
yes thats why
blazing jacinth
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BunkerBaby
blazing jacinth
now i just dont know what to do for the domain and range of it
i would assume the domain is infinite since it can be any year from the first measurement so there is no restrictions on the domain
but im not sure if thats right
@verbal gulch get over here brother man i need ur brains guidance
verbal gulch
domain seems like it could be all real numbers, yeah
verbal gulch
well to be fair, the model clearly stops working at some time
but I don't think they care much about practicality
the range? just find the range for that domain
blazing jacinth
well to be fair, the model clearly stops working at some time
what u mean by this
verbal gulch
for example, if you let t = 1000, the numbers become astronomically large
clearly not possible on planet Earth
blazing jacinth
LOOL okay yeah sure but i think ur also right they dont care about it like that
symbolab states
that the range is just the 97.4
f(x) > 97.4
but i dont really know how they got that
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blazing jacinth
@verbal gulch for part c of the question is it as simple as changing t in the equation to month since first measurement instead of years?
blazing jacinth
well originally wouldn't i be inputting 2 since its 2 years from 2018-2020
but if its asking for months
i would be putting 24?
t in the equations is represented as time in years since the first measurement
its asking me to create an equation for the concentration as a function of the number of months since jan 2020
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blazing jacinth
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wraith hinge
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kindred pier
Consider what a parallelogram is.
What properties on the side lengths and angles come from the definition of parallelogram?
covert gazelle
can someone give me a tip
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wraith hinge
ty
wraith hinge
i only found the second twonumbers in triangle tho
its 56 and 56
but what do i do nxt?
covert gazelle
Slowly think about it
alpine lava
