Finding X intercept from the fifth question where f(x) must be zero
f(x) = (2x+4)/4x
0 = 2x + 4
-2x = +4
x = -2
#help-27
dreamy knoll
prime egret
x=-2 last line
dreamy knoll
So (12x^5)/(24x^6) is (1)/(2x)?
prime egret
Yes
dreamy knoll
Ah yes, thank you very much.
This solves my answer!
Thank you for confirmation
😁
winter patrol
So If there's no any value at numerator, I must always put one?
wdym by no value
dreamy knoll
> So If there's no any value at numerator, I must always put one?
wdym by no val...
as in there's nothing left at the top
winter patrol
that shouldn't happen
winter patrol
there aren't any legit actions that wipe whatever is on the numerator from existence
don't conflate cancellation with complete erasure
this shouldn't happen
$$\frac{\boxed{\text{blank void}}}{k}$$
woven radishBOT
ℝamonov
dreamy knoll
So basically k^2/k^3 is just k^2 being cancelled and not erased?
winter patrol
cancelling the common factor leaves you with 1 directly
the numerator doesn't get thanos snapped only to come back later
the common factor is "cancelled"
$\frac{k^2}{k^3} = \frac{1 \cdot \cancel{k^2}}{k \cdot \cancel{k^2}} = \frac{1}{k}$
woven radishBOT
ℝamonov
winter patrol
$\frac{\cancelto{1}{k^2}}{\cancelto{k}{k^3}}$
woven radishBOT
ℝamonov
winter patrol
and NOT
$$\frac{k^2}{k^3} \wthonk \red{\frac{}{k}} \wthonk \frac{1}{k}$$
woven radishBOT
ℝamonov
dreamy knoll
Oh, I forgot the invisible one.
Thank you for this precious information. @winter patrol
arctic field
\wthonk 
winter patrol
its crucial to remember that you're cancelling factors and not outright erasing values
dreamy knoll
Alright. Thanks. Keeping this knowledge until the end of 2 semesters.
winter patrol
which makes it clear why you can't cancel the ps in
(p+2)/(p-1)
dreamy knoll
Just literally went serious in math this year.
so I always get confused on other terms in math
.solved
.solve
prime egret
.close
devout snowBOT
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Available help channel!
red harness
How can I understand absolute value inequalities better? It's so frustratingly difficult to make sense of
devout snowBOT
How can I understand absolute value inequalities better? It's so frustratingly d...
violet wind
like |x-4|<7?
radiant drift
think its just |x|, if x>0, x=x. IF its x<0, x=-x😅
did u go on image search moni
lol
violet wind
no
red harness
like |x-4|<7?
yes
violet wind
ah so
red harness
It's the conditions that melts my brain
umbral creek
How can I understand absolute value inequalities better? It's so frustratingly d...
oh maybe u can try watching videos on youtube
red harness
that means -n < u <n
yeah not this, more like |x - y| <= |x| + |y|
red harness
oh maybe u can try watching videos on youtube
I tried but still don't make sense to me
violet wind
ah well those are definitely tricky in general
if you want to prove something like that you might just need to do casework
or substitute u=-y
to get the triangle inequality
red harness
case by case seems like ugly brute forcing no?
I could do case by case, but I don't understand what the inequalities are saying like
|x - 1| + |x - 2| > 1
How do you formulate this in words
red harness
what
arctic field
,w plot |x-1| + |x-2|
woven radishBOT
arctic field
perhaps looking at their graphs might provide some intuition
north depot
Amina is in charge of a small cafe at the festival and has an area of land which
is 6.0 m x 5.0 m. She wants to build a roof from a tarpaulin so that her whole
ground area is protected by this roof. The angle at the top in the middle of the roof must be 90°.
How long and wide must the tarpaulin be at least to cover the entire roof?
.
got the solution / answer
a^2 + b^2 = 6^2 . 36/2 = 18 , squareroot of 18 = 4.24
4,25^2 + 4,25^2 = 36
8.5 * 5 = the answer
why do I divide it by 2
devout snowBOT
Amina is in charge of a small cafe at the festival and has an area of land whi...
@north depot Has your question been resolved?
devout snowBOT
@north depot Has your question been resolved?
north depot
got it now
full charm
how do I do 4.4
devout snowBOT
@full charm Has your question been resolved?
shut whale
how do I do 4.4
if you add the degree of every vertex, you get twice the total number of edges of the graph
real fog
tulip swan
Do you know what the span of two vectors is?
real fog
No
tulip swan
Do you know what a linear combination of vectors is?
real fog
No
tulip swan
,tex Then you should probably learn all that material before doing work in it.
But anyway a linear combination of two vectors $v_1$ and $v_2$ is something of the form $\alpha v_1+\beta v_2$ for numbers $\alpha, \beta$
woven radishBOT
tulip swan
And the span of two vectors is the set of all linear combinations of them
With me so far?
real fog
Yes
tulip swan
Also how come you said you don’t know what a linear combination is if you answered a question regarding it in your other channel #help-37
tulip swan
The weights in this case would be $\alpha$ and $\beta$
woven radishBOT
tulip swan
So just take four different $\alpha$ and $\beta$s and compute $\alpha v_1+\beta v_2$ for question 8a
woven radishBOT
pastel cloak
Does anybody know how to solve this? It’s Pythagoras and they want you to solve the thing
devout snowBOT
Does anybody know how to solve this? It’s Pythagoras and they want you to solve ...
rotund heron
have you tried anything?
devout snowBOT
@pastel cloak Has your question been resolved?
devout snowBOT
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Available help channel!
restive river
can someone help me?
devout snowBOT
can someone help me?
restive river
please tag me when responding
devout snowBOT
@restive river Has your question been resolved?
restive river
<@&286206848099549185>
devout snowBOT
@restive river Has your question been resolved?
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@restive river Has your question been resolved?
elfin hill
can someone help me?
First it would be in 0
Then $5e^{-x} \underset{x \to 0}{\sim} 5(1-x)$
woven radishBOT
black_couscous
dusk agate
royal tiger
Hello!
dusk agate
hi
royal tiger
so what do we know here
dusk agate
royal tiger
we dont need 2 channels
royal tiger
all good
royal tiger
so lets think about this, what do we know about the perimeter of a rectangle
dusk agate
2(l+w)
dusk agate
royal tiger
ok
so algebraically what is that
w= ?
"next consecutive integer" means one more then the legnth
west forum
hi
royal tiger
what you wrote was 4 times the width +1
west forum
guys
royal tiger
hi
#❓how-to-get-help if u need help!
west forum
ok
royal tiger
I am assisting korumisa rn!
dusk agate
so we know 4 times the next consecutive integer
yes
royal tiger
so first we need to find the consecutive integer
before we multiply by 4
how would we write first adding 1 to L then multiplying the answer by 4
dusk agate
4(x+1)
dusk agate
how do u do that
royal tiger
instead of writing W write 4(L+1)
dusk agate
(4L+4)
dusk agate
ohhh
royal tiger
But the actual equation would be 2(L+4(L+1))=168
now that we know that just solve for L
dusk agate
L=16
dusk agate
thanks
royal tiger
I am aswell!
velvet bluff
faxs!!!!
royal tiger
run .close if you have no more questions
royal tiger
no problem 
dusk agate
.close
desert anchor
anyone know what I goofed up here?
devout snowBOT
anyone know what I goofed up here?
desert anchor
i have checked that my evaluation of the integral is correct
btw any time the bounds are a and b, they are the same i was just too lazy to rewrite it every time
<@&286206848099549185>
devout snowBOT
@desert anchor Has your question been resolved?
devout snowBOT
@desert anchor Has your question been resolved?
uncut frigate
i have checked that my evaluation of the integral is correct
why are you squaring things
desert anchor
why are you squaring things
using this formula
uncut frigate
using this formula
why?
uncut frigate
it looks like you have the positions flipped, the 4 - cos should be above the 3 + cos
does it tell you to find area using polar coordinates?
desert anchor
all it says is what it says on the pinned image
i think i misinterpreted the question
i thought the first equation had to be f(theta) and the second g(theta)
desert anchor
it looks like you have the positions flipped, the 4 - cos should be above the 3 ...
nvm i just put that in the calculator and it isn't correct
devout snowBOT
@desert anchor Has your question been resolved?
fair spruce
Does this seem right?
pulsar dock
No. Take for example -1. It is an element of codomain, but its preimage is empty.
All you have right now is that it is not an injective function.
devout snowBOT
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Available help channel!
clever minnow
Problem 1.c
devout snowBOT
Problem 1.c
clever minnow
I need help doing the whole problem
mellow lintel
1?
that's asking u to calculate derivative of all functions basically
for 1st subpart
mellow lintel
f(x) =3/x²
clever minnow
Yup
mellow lintel
u need to find derivative
u can write eq as 3.x^-2
so after differentiation it becomes -6.x^-3
so -6/x³
that should be the answer
clever minnow
Ahhh ok thank you
mellow lintel
np
clever minnow
.close
devout snowBOT
wanton canyon
devout snowBOT
wanton canyon
i’m not sure where my mistake was
can someone pls help
please ping me if you respond to this
tall knoll
Rip
wanton canyon
?
tall knoll
Someone tried to do WA magic
prime egret
I think you use n=14 for the GP
wanton canyon
still doesn’t work
prime egret
Do you know the answer
wanton canyon
no
prime egret
So how do you know it doesn’t work
tall knoll
I imagine doing that doesn't get any of the 4 answers given
wanton canyon
it isn’t one of the mc options
tall knoll
Is what jrt means
wanton canyon
^
wanton canyon
.
tall knoll
I reckon you should also compound the principal for 15 years instead of 14
wanton canyon
tried that aswell
tall knoll
End of 2028 tends to be functionally the same as start of 2029
wanton canyon
using n=15 doesn’t get one of the answers either
tall knoll
Ah, there are only 14 deposits of 200, but the last one is at the beginning of 2028
So it should be accumulated for an additional year as well
wanton canyon
wdym
tall knoll
Wait 1s
prime egret
I think this is right?
tall knoll
Bad eyesight need to confirm
wanton canyon
I think this is right?
how did you get this
wanton canyon
why do u minus 200
prime egret
Because John didn’t deposit 200 at the beginning of 2029
wanton canyon
oh
tall knoll
Yeah that also works
prime egret
prime egret
I think this is right?
Anyone uses Photomath ?
I want to know how to change from , to .
wanton canyon
what’s photomath d
prime egret
Nvm don’t worry about it
weary arch
Could anyone help me prove this for G(x,t) = B(xt)
devout snowBOT
Could anyone help me prove this for G(x,t) = B(xt)
pseudo basin
what's B?
weary arch
Any vector field
pseudo basin
if i understand correctly, this is equivalent to proving $\paren{x \pdv{x} + y \pdv{y} + z \pdv{z} - t \pdv{t}} \bd{G} = 0$
woven radishBOT
Ann
weary arch
$\vbG(\vb x, t) = \vbB(\vb x t)$
woven radishBOT
π=√g
pseudo basin
is xt to be understood here as just x times t
weary arch
Yeah
pseudo basin
right
ok let's see
ok so what are the derivatives of tx wrt x, y, z and t
ti, tj, tk and x i guess
weary arch
Yep
devout snowBOT
@weary arch Has your question been resolved?
steady pulsar
Hello everyone, Can I ask how do I solve this ? I do not understand what does it mean by "Find the limit"
devout snowBOT
Hello everyone, Can I ask how do I solve this ? I do not understand what does it...
rich summit
what happens if n becomes really large, goes to infinity, what value does S_n go to?
steady pulsar
It'll be still infinity ?
rich summit
will it?
do you know the sum of a geometric series formula?
of the form r^0 + r^1 + r^2 + r^3 + r^4 + ...
steady pulsar
Is it this ?
steady pulsar
a = 1 and r = 4?
rich summit
r = 1/4
because the series is (1/4)^0 + (1/4)^1 + (1/4)^2 +...
so S_n = (1 - (1/4)^n)/(1 - 1/4)
woven radishBOT
Jelle
steady pulsar
Ohh so when it comes to a infinity number sequence, I'll have to use Geometric Sequence formula, find R, and swap it in ?
What about the a ? It doesn't matter ?
rich summit
it's just 1 here, doesn't matter
but if you look at the formula above, when n gets really large, (1/4)^n becomes really small
rich summit
but if you look at the formula above, when n gets really large, (1/4)^n becomes ...
in the limit as n goes to infinity it is equal to (1 - 0)/(1 - 1/4)
steady pulsar
.close
orchid pike
So I’m trying to solve for t
devout snowBOT
So I’m trying to solve for t
orchid pike
this is physics but I’ll turn the variables into just letters
d = 1/2(v0 + v) t
so what I tried to do is subtract the whole 1/2 -> end of parenthesis
which became t = d -1/2(v0 + v)
first, what’s wrong with that approach? why can’t you subtract - is it because what’s happening there is multiplication and not addition, so you have to add?
could you at least subtract the 1/2 first then go on to the rest? or can you not subtract at all?
vestal dirge
well yeah like you said
you multiply and not add there
What would be your approach if you cant subtract?
left robin
$d=\frac{1}{2}(v_{0}+v)t \ \frac{d}{\frac{1}{2}(v_{0}+v)}=t$
orchid pike
subtract t probably as thats easiest?
left robin
division
division is the inverse of multiplication
notice that t is multiplied as it is a factor
woven radishBOT
~Martin
orchid pike
notice that t is multiplied as it is a factor
is that why you can’t subtract t
left robin
let's say we have a=b*c and want to solve for c
vestal dirge
ye
left robin
if we subtract b we get
a-b=bc-b=b(c-1)
orchid pike
but why can you choose to not divide by t
left robin
which does not get us anywhere
orchid pike
if its also being multiplied
left robin
a=bc
to get c isolated, we want to remove b so we need the inverse
$b^{-1}a=b^{-1}bc=c$
woven radishBOT
~Martin
left robin
the inverse of multiplication is division
therefore the multiplicative inverse of b is dividing by b
$b^{-1}=\frac{1}{b}$
woven radishBOT
~Martin
orchid pike
but why can you choose to not divide by t
what about this
since t is also being multiplied, the opposite of it is division n not subtraction, so u cant subtract. But why can you choose to not divide by it and leave it there?
here it was possible to subtract
the whole value
which has a lot of multiplication..
@left robin do u know physics by any chance
left robin
yes i do actually
orchid pike
Ok here I put speeding up for a because the line looks like its going up
but my teacher drew those lines on the graph to demonstrate the slope
do u understand it
orchid pike
which has a lot of multiplication..
@left robin do u know why? by the logic above, the number starting with 1/2 simply had a + value in the front. Doesn’t my other equation also have a positive even tho its not visible?
left robin
,rotate
woven radishBOT
left robin
what we have here is position in terms of time
the velocity is indeed the slope here
velocity is the change in position
if we look at how the position changes, we notice that while the position does increase (meaning we move forward), the rate at which we move forward slows down meaning we get slower and slower but still move forward
for B, this is a bit different
our velocity does decrease further but that does not mean we get slower
this is because in B we start to move backwards
basically, if the slope gets steep, the velocity increases
notice that at the point between A and B, the slope is 0 so we stand still for a moment
orchid pike
So here you don’t have numbers so you can’t do any calculation
all you have is the picture
and just the calculation of slope based on how steep it is?
What does the slope need to be for it to be getting faster?
is it clear that its slowing down when it starts curving?
devout snowBOT
@orchid pike Has your question been resolved?
devout snowBOT
@orchid pike Has your question been resolved?
fair spruce
Does this seem okay? Also... how to prove it's a "general function" what the hell is a general function in a nut shell?
devout snowBOT
Does this seem okay? Also... how to prove it's a "general function" what the hel...
fair spruce
sorry not f(a) but f(x)
devout snowBOT
@fair spruce Has your question been resolved?
quiet ember
I think "general function" in this case should only mean that it's neither surjective not injective (but the notation is very weird, "general function" normally just means any function)
Also, I think your proof is right but it's written up in a very unclear way, so if you submit it like this, you'll probably lose points
fair spruce
It's actually written like so Determine whether each of the following is an injection, surjection, bijection or general function (none of mentioned above). Provide a proof for your answer
But still the same imo
quiet ember
So general function should mean "none of mentioned above", so neither injection, surjection nor bijection
At least I would read it like that
(Google doesn't give me any proper definition of general function, only some SQL commands)
fair spruce
hah
quiet ember
And also, you cannot write up your proof like this
fair spruce
For general function I found this:
"A General Function points from each member of "A" to a member of "B".
It never has one "A" pointing to more than one "B", so one-to-many is not OK in a function (so something like "f(x) = 7 or 9" is not allowed)
But more than one "A" can point to the same "B" (many-to-one is OK)"
This is just a definition of the mathematical term "function"
woven radishBOT
Mathemaddict
quiet ember
I think my interpretation is the only thing that makes sense
fair spruce
.close
rich crow
Does anyone know why the result is so low ? !13 is equal to a massive number and the result of 13-6! is !7 and the result of !7 is 5040 so why is the result number (1716) so low?
wooden wraith
6! * 7! is also a pretty big number
rich crow
oh how did i ignore that 6 😂 im sorry thank you so much
wooden wraith
Lol no problem
rich crow
.close
devout snowBOT
long kettle
What don't you understand specifically
devout snowBOT
midnight dirge
hm
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Available help channel!
fathom verge
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fathom verge
Ive looked at videos but they all seem to be finding slightly different things
magic thicket
There's infinitely many solutions
So them not agreeing on the best answer is understandable
fathom verge
i mean videos on the same topic
not this specific problem
i dont know how to get started on this one because no videos have functions that are fractions
magic thicket
The idea of each proof should be that g has a degree strictly higher than the numerator's
For quotients of polynomials
fathom verge
does the polynomial have to be able to be canceled out
magic thicket
Irrelevant
You're looking at +inf anyways
All non constant polynomials go to infinity (+ or -) as x -> +inf
fathom verge
x^2+x-1
would this be correct?
f(x) approaches zero g(x) increases
g(x)=x^2+x-1
devout snowBOT
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magic thicket
For b) yes, it does approach 3
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daring notch
How do you get a the charge of a suspended Q? (Charged Pendulum)
devout snowBOT
How do you get a the charge of a suspended Q? (Charged Pendulum)
@daring notch Has your question been resolved?
daring notch
.close
untold magnet
devout snowBOT
untold magnet
Im stuck on this, can someone take me through it step by step
devout snowBOT
@untold magnet Has your question been resolved?
untold magnet
<@&286206848099549185>
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@untold magnet Has your question been resolved?
jaunty gazelle
devout snowBOT
jaunty gazelle
How did they get 2(4) after applying the power law?
Did they just plug in 2 for lim of x as x approaches 2?
oak harness
I think they had already applied the power law in that line. SO what they did here is "Apply the basic limit laws"
and yes, they plugged x=2 in
the limit of x as x approaches 2 is 2
2^2 = 4
jaunty gazelle
and yes, they plugged x=2 in
Couldn’t we solve this by substituting as opposed to using the limit laws?
oak harness
well, I am pretty sure substitution counts as a basic limit law
Whatever you may call it, that is what they did.
jaunty gazelle
Whatever you may call it, that is what they did.
So they chose to use different limit laws instead of substitution because substitution wouldn’t work?
jaunty gazelle
It's the same.
I’m confused. What is the same?
oak harness
I think you are taking the comments far too literally
Here is a random list of "basic limit laws"
As you can see, they e.g. list direct substitution as a basic limit law
so you're making a difference where there is none.
they used substitution
nothing more
jaunty gazelle
they used substitution
I didn’t know that was a law…
jaunty gazelle
nothing more
So do we only use the other laws when substitution doesn’t work? And does not work only when it leads us to an undefined value?
oak harness
So do we only use the other laws when substitution doesn’t work? And does not w...
yes. I mean, no one is stopping you from using those.
Those are still correct.
But why would you do that if you can just use substitution.
devout snowBOT
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austere sail
devout snowBOT
austere sail
can someone help me with this question?
I don't know where to start
it tells me it's all prime but then tells me prove that it's not always prime
trim vine
I’m not a number theorist, but what about for n=0?
oak harness
and then you multiply from k=1 to 0
oak harness
Well, the task gives you "the first few values"
It excludes 1
It starts with 3 = 1 + 2
austere sail
yep
I don't know how my classmates find these really large number and then they somehow know it's not a prime number
hollow pollen
maybe some modular arithmetic?
austere sail
divisible by 59
how did you figure it out?
My prof won't let me use calculator on exams
bleak sun
30031 is the first composite euclid number its just something I knew
not sure how u would figure that out in a test w/o a calculator
austere sail
okay thanks
bleak sun
maybe look into properties of euclid numbers
silk crest
how does this prove that A is a subset of b
devout snowBOT
how does this prove that A is a subset of b
silk crest
In mathematics, set A is a subset of a set B if all elements of A are also elements of B
but isnt it as in the quuestion A is sin(n)>0 , therefore A can be sin(n)= 2,3,4,5,6,7,8 etc
but B is only sin(n)<=1, so it cant be = to 2,3,4,5,6,7,8
doesnt this prove A is not a subset of B?
silk crest
sin(n) <= 1 in any case
this is set B right?
topaz axle
this is absolutely any set
like there's implied sin(n) <= 1 in the set A too
and this is not a trick
maybe i don't understadn what you mean
topaz axle
right
silk crest
that means B is include the numbers 1 2 3 4 5
topaz axle
sure
silk crest
refer back to the question, it is proving that A is a subset of B
meaning that everything in A should also apply in B
is that corrrect
topaz axle
yeah
silk crest
umm so when A is sin(n)>0, are we talking about the numbers inside the bubbles is those n values can achieve that the function will end up greater than 0?
topaz axle
yes
topaz axle
that's just not a thing
silk crest
o yeah.
topaz axle
like if you find an n that does that, sure, A can accept it
silk crest
cause y values can only be within -1 and 1 right
topaz axle
but you won;t find an n that does that
silk crest
yeah but if assuming that n can do that, as in Sin(n) can be = 2
so that will mean that A is not a subset of B right
devout snowBOT
@silk crest Has your question been resolved?
urban dome
if sally accidentally divide 24 by 10 instead of 20 she get a mean of 2.4 how can she tell immediately that she made a mistake answer
devout snowBOT
if sally accidentally divide 24 by 10 instead of 20 she get a mean of 2.4 how ca...
wooden wraith
Mostly I'm just curious what the smallest number is
urban dome
idk
wooden wraith
It's too big
The mean should be somewhere near the middle
If 2 is the biggest number in the set, the mean can't be 2.4
steel sapphire
Goodnight. I have a question about complex numbers.
In some exercises I have to locate the affixes (points) of various complex numbers. (In the picture I put 4)
And they ask me to calculate the area of the formed figure and the perimeter. I clarify that the figure that is formed in these cases is not centered at the origin (it is not related to the nth root)
For either case, you would need to find the distance between each complex number. For this the only thing I can do is use the "module" between two complexes. (the formula is noted below in the image)
Then, having these distances, calculate the area or the perimeter will depend on the figure.
My question is: Is that always the only way to do it? Or can homothety, rotation, translation and rotohomothety be applied?
Thank you very much
devout snowBOT
Goodnight. I have a question about complex numbers.
In some exercises I have to...
@steel sapphire Has your question been resolved?
umbral obsidian
Hello!!
umbral obsidian
So like the cos becomes cosxsin / sin?
restive river
yes u can say so if u do fraction addition like that
$\frac{cos}{sin}-cos=cos(\frac{1}{sin}-1)$
woven radishBOT
pure maths>>>physics
restive river
simplify the numerator like that
umbral obsidian
Ohhhh
And then that all over 1 -sin?
Does the 1 - sin in the denominator equal to cos?
Oh hello?
Um
<@&286206848099549185>
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knotty sphinx
why is it = -324 and not 324
devout snowBOT
why is it = -324 and not 324
knotty sphinx
i did the steps
( (3+3i)^2 )^2
= (9 18i^2 + 9i^2)^2
= ( 9 - 18 - 9 )^2
= (-18)^2 = 324
but still don't understand why when i double check it is -324
tropic dune
i did the steps
( (3+3i)^2 )^2
= (9 18i^2 + 9i^2)^2
= ( 9 - 18 - 9 )^2
= (-18)...
In your second line, shouldn’t it just be 18i
Not 18i^2
viral rapids
yo
knotty sphinx
okay but now i end with 18i ?
serene burrow
The sum of the interior angles of a regular polygon is 21,240°. what is the measure of its exterior angle?
devout snowBOT
The sum of the interior angles of a regular polygon is 21,240°. what is the meas...
wooden wraith
The sum of the interior angles of a polygon with n sides is
(n-2)*180 degrees
wooden wraith
The sum of the exterior angles of any polygon is always 360 degrees
serene burrow
The sum of the exterior angles of any polygon is always 360 degrees
right
and int+ext=180?
wooden wraith
Oh, that's also true
Yeah, if you find a single interior angle, then just subtract it from 180
serene burrow
Yeah, if you find a single interior angle, then just subtract it from 180
right but how do we find the ext with this
im quite stuck
wooden wraith
and int+ext=180?
Like this, just like you said
wooden wraith
The sum of all the interior angles is 21240
What's the measure of a single interior angle?
woven radishBOT
Result:
177
that?
wooden wraith
Yep
serene burrow
,calc 180-177
woven radishBOT
Result:
3
that's it?
wooden wraith
That's it
wooden wraith
No problem 👍
restive river
devout snowBOT
restive river
is q19b all types?
2 x 80% = 1.6
6 x 80% = 4.8
8 x 80% = 6.4
24 x 80% = 19.2
62 x 80% = 49.6
98 x 80% = 78.4
(1.6 + 4.8 + 6.4 + 19.2 + 49.6 + 78.4)/200 = 80%
that’s my working out
devout snowBOT
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restive river
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restive river
<@&286206848099549185>
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restive river
<@&286206848099549185>
restive river
<@&286206848099549185>
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midnight dirge
so when finding residue of $f(z) = \Gamma(z)$ at $z=n, n \in \mathbb{Z}_{\le 0}$ we left shift the function and compute residues right, like $\Gamma(z) = \frac{\Gamma(z-n+1)}{z(z+1)(z+2)...(z+n)}$
devout snowBOT
so when finding residue of $f(z) = \Gamma(z)$ at $z=n, n \in \mathbb{Z}_{\le 0}$...
woven radishBOT
midnight dirge
can we do something similar for $g(z) = \Gamma(1/z)$?
woven radishBOT
midnight dirge
so g has poles at $z=b=-1/b', b' \in \mathbb{Z}_{\ge 1}$
woven radishBOT
woven radishBOT
woven radishBOT
midnight dirge
idk trying that now but feels weird
midnight dirge
hm
how wld i find residues
also
idt i can split it into prod not like i did prev with gamma(z) right
woven radishBOT
arctic field
and then at z = -1/n you get
woven radishBOT
woven radishBOT
arctic field
i think we need one more
midnight dirge
i think we need one more
hour of slp
woven radishBOT
midnight dirge
yes that looks normal
woven radishBOT
woven radishBOT
midnight dirge
yes
arctic field
so i guess what we can do is
midnight dirge
which cancels TnT
restive river
this looks advanced 😳
woven radishBOT
arctic field
@midnight dirge did you die lol
devout snowBOT
@midnight dirge Has your question been resolved?
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restive river
is q19b all types?
2 x 80% = 1.6
6 x 80% = 4.8
8 x 80% = 6.4
24 x 80% = 19.2
62 x 80% = 49.6
98 x 80% = 78.4
(1.6 + 4.8 + 6.4 + 19.2 + 49.6 + 78.4)/200 = 80%
^ that’s my working out
or is it stock shortage and delivery fee because added up they equal 160
160/200 = 80%
lofty condor
2 x 80% = 1.6
6 x 80% = 4.8
8 x 80% = 6.4
24 x 80% = 19.2
62 x 80% = 49.6
98 x...
seems about right
but someone check it
devout snowBOT
Available help channel!
wary ruin
Graph the following functions:
$$𝑓: \mathbb{R}\rightarrow \mathbb{R},𝑓(𝑥)=\left\lfloor x\right\rfloor+1$$
wary ruin
Help
woven radishBOT
dgh
restive river
Is it the floor function you don't understand?
⌊x⌋ is the greatest integer less than or equal to x
⌊2.4⌋=2
⌊-2.4⌋=-3
wary ruin
@restive river how doo i graph it
restive river
by hand? you need to notice that from x to x+1 not included, floor(x) is x
wary ruin
wdym
restive river
⌊2⌋=2, ⌊2.99999999999999999⌋=2, ⌊3⌋=3
so it's a constant (1) between 1 and 2 not included, then the constant (2) changes between 2 and 3 not included
etc
then you add 1 to the constant and you can graph f(x)
wary ruin
@restive river thanks, one question, do you know if i should have a full circle at the ends of the lines
or non-full circles
restive river
non-full
you can add full circles at the beginning of each segment too if you want
fickle bloom
Given that p is true
devout snowBOT
Given that p is true
fickle bloom
This statement is also true?
Since its only false in the case where p is false?
Thank you
.close
devout snowBOT
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flint flax
Im stuck on b how do you make an equivalence relation that splits a number into either class Z+ or it is 0
devout snowBOT
Im stuck on b how do you make an equivalence relation that splits a number into ...
@flint flax Has your question been resolved?
flint flax
<@&286206848099549185>
flint flax
okay i did this:
We define the equivalence relation $\sim$ on $N$ by
$n \sim m =_{def} n\neq 0$
This gives the equivalence classes:
$[0]_{\sim} = {0}$
${[1]_{\sim}} = {1,2,3,4,5,6,\dots, n}$
Hence the quotient set $N/\sim$ is ${Z^+, {0}}$
woven radishBOT
Bonjoeri
flint flax
would this be correct? since it will make a class of all numbers that are not equal to zero and 0 will be a class on its own
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flint flax
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stuck birch
hello am i on the correct path here?
devout snowBOT
hello am i on the correct path here?
stuck birch
$F(x_1,x_2,x_3)=(x_1,x_2,f(x_1,x_2,x_3))\
det(DF(0)) = det(\begin{pmatrix}
\partial F_1\over{x_1} & \partial F_1\over{x_2} & \partial F_1\over{x_3} \
\partial F_2\over{x_1} & \partial F_2\over{x_2} & \partial F_2\over{x_3} \
\partial F_3\over{x_1} & \partial F_3\over{x_2} & \partial F_3\over{x_3}
\end{pmatrix}) =a \ne 0$
woven radishBOT
b3s4d
stuck birch
so the the jacobian matrix is regular and i can use the implicit function theorem?
Edit: i forgot to write the partial for x1,x2,x3 there and a is just a real number thats not 0
devout snowBOT
@stuck birch Has your question been resolved?
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@stuck birch Has your question been resolved?
stuck birch
okay i forgot that $\partial F_1\over{\partial x_1}$ is also 0 because i take $DF(0,0,0)$, the result for the determinant then is 0, but should be $\ne 0$:
$\begin{pmatrix}
0 & 0 & 0 \
0 & 0 & 0 \
0 & 0 & a
\end{pmatrix}, a\ne0\in\mathbb{R}$
woven radishBOT
b3s4d
devout snowBOT
@stuck birch Has your question been resolved?
stuck birch
Ok i did some things very wrong...
now i landed here:
$F(x_1,x_2,x_3)=(x_1,x_2,f(x_1,x_2,x_3))\
DF(0) = J_F(0)=\begin{pmatrix}
\partial F(0)\over{\partial x_1} & \partial F(0)\over{\partial x_2} & \partial F(0)\over{\partial x_3}
\end{pmatrix}=\begin{pmatrix}
0 & 0 & a
\end{pmatrix},~a\ne0\in\mathbb{R}\
\det(DF(0)) =~?$
woven radishBOT
b3s4d
stuck birch
but i dont quite understand how i can get the determinant of a nonsquare matrix
devout snowBOT
@stuck birch Has your question been resolved?
analog trellis
hello am i on the correct path here?
View the delta neighbourhood as a cube around the origin.
It is no restriction to suppose f_3 > 0.
Since f_3 is nonzero there and f_3 is continuous you can show that f_3 is positive in a whole neighbourhood of the origin. Make this neighbourhood the original delta neighbourhood. Now fix x_1 and x_2 and then since f_3 is positive there exists a point below where f is negative and above where f is positive. Now due to the continuity of f there’s a common neighbourhood (a plane) of these two below and above points where f is completely positive and completely negative. Then for each x_1 and x_2 being fixed there can only be one value of x_3 where f = 0. Hence x_3 is uniquely determined by x_1 and x_2. That is x_3 = g(x_1, x_2).
I’m not super familiar with the notation of your problem. Maybe you have a system of equations and not a single one?
stuck birch
well my professor told me that i need to find that the determinant of the jacobian isnt 0 and that if one entry is not 0 i can prove that the determinant is not 0
where the one entry is $\partial F(0) \over{\partial x_3}$
woven radishBOT
b3s4d
analog trellis
Yea you can.
stuck birch
View the delta neighbourhood as a cube around the origin.
It is no restriction ...
i dont quite understand how you can get x_3 = g(x_1, x_2) out of this
analog trellis
It’s easy to see if you write out the 3x3 jacobian.
analog trellis
i dont quite understand how you can get x_3 = g(x_1, x_2) out of this
Remember the transpose of a determinant gives the same output.
I think it’s notation but it’s actually a 3x3 matrix.
stuck birch
but there is only one function F
so the jacobi matrix is actually the grad i guess?
what would the other 2 functions be?
analog trellis
You might be combining two different exercises too.
The question looks like a single equation case but if you're including jacobians it must be a system of equations.
stuck birch
im trying to use implicit function theorem here
analog trellis
i dont quite understand how you can get x_3 = g(x_1, x_2) out of this
Since it has shown for each x_1 and x_2 there is only one value of x_3 which makes f = 0, then x_3 is determined by the values of x_1 and x_2. Since f_3 > 0 it's unique too.
analog trellis
im trying to use implicit function theorem here
The question looks like it's asking you to prove the implicit function theorem to me.
analog trellis
This definitely looks like a implicit function theorem.
stuck birch
"Apply to the mapping F(x1, x2, x3) = (x1, x2, f(x1, x2, x3)) the inverse function theorem"
analog trellis
I don't know anything about that.
stuck birch
me neither
analog trellis
I have no idea, it seems like something is being confused with the jacobian. The question makes no mention of a jacobian either.
stuck birch
thats what i read on wikipedia
analog trellis
thats what i read on wikipedia
Yeah but this is completely different to the problem.
I can help prove this one too but the problem is not asking for this.
stuck birch
im so confused
analog trellis
There's Theorem 14 I put above which is like the problem but then you're posting about another theorem.
stuck birch
well what i thought i had to do was prove that i can use the implicit function theorem here which already yields me everything the question asked
stuck birch
Okay but i dont have the functions G and H
analog trellis
You must do.
Then again I don't understand all this vector notation people use so maybe there's something I don't know.
woven radishBOT
b3s4d
analog trellis
I've not studied the inverse function theorem sadly.
analog trellis
This definitely looks like **a** implicit function theorem.
I think Theorem 14 I posted is a exact copy of this problem and it definitely doesn't use any jacobians.
Are you sure there's not more than one problem being mixed up?
stuck birch
very sure
theorem 14 does look similar but i dont understand what delta or eta is doing there
analog trellis
It just means a neighbourhood.
The eta one is a smaller one. Note that I used continuity at the lower and higher points in here for a common neighbourhood.
stuck birch
okay
analog trellis
Sadly, I do have to go work now. 😢
analog trellis
I'd recommend looking at page 121 Intergral and Differential Calculus by R. Courant Volume 2 and Advanced Calculus by David V. Widder at like page 55 or something.
stuck birch
okay thank you
stuck birch
does anyone else have a clue?
devout snowBOT
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umbral root
Should both the exes on the blue post it notes be > or =?
devout snowBOT
Should both the exes on the blue post it notes be > or =?
marsh dagger
do not understand any of that
is this something to do with quadratics
messy handwriting 💀
umbral root
is this something to do with quadratics
Yes
marsh dagger
I can't really comprehend the question
umbral root
messy handwriting 💀
I know, I usually write in cursive and I did so too in this paper thinking that it's just for practice, but now I need help
umbral root
I can't really comprehend the question
I need to find the range of values of x of that inequality
marsh dagger
can I have the original question
marsh dagger
sqrtx + 7 ?
restive river
Sadly, I do have to go work now. 😢
are you an engineer
marsh dagger
that's a equation not an inequality
analog trellis
are you an engineer
No, I look after annoying old people twice a week. 🧐
restive river
funny
analog trellis
(Sadly, also a true story. We can't continue talking in this occupied channel.)
restive river
yes
marsh dagger
It's root (x squared +7)
what is the boundaries
umbral root
what is the boundaries
Both are rooted, I used the boundaries to signify that
devout snowBOT
@umbral root Has your question been resolved?
glass narwhal
devout snowBOT
glass narwhal
Can someone explain this
Why is i multiplied
This would imply the transformation of i is scalar when it’s not?
pseudo basin
what do you mean?
glass narwhal
So this here is describing the linear transformation of i after 2 transformation
To get the i vector after these two transformation he uses matrix multiplication
but why?
pseudo basin
"the linear transformation of i" is... weird wording
i feel there's a bit of a language issue here
glass narwhal
hmm maybe
to find the total effect for the i vector
He multiplies the first m1 i vector by m2
And I get why this works
Very intuitive
But the other no
devout snowBOT
@glass narwhal Has your question been resolved?
dapper gazelle
But the other no
What is this other
crude pine
marsh dagger
simple
y intercept 11
so 11 = f(0)
and f(3) = 193
you can already find b with this information
crude pine
Can you provide a solution? Cause all I did was trial and error and im not sure if my answer is correct :((
marsh dagger
Can you provide a solution? Cause all I did was trial and error and im not sure ...
no
i do not personally provide solutions unless you show me ur workings
we help you do maths, we dont do maths for you
crude pine
7(3^x)+4
marsh dagger
alr
woven radishBOT
habukichan
marsh dagger
$ab^{3} + c = 193$
woven radishBOT
habukichan
marsh dagger
so ur answer is correct i think
crude pine
Can I ask how to get the asymptote?
marsh dagger
take the limit
unborn laurel
<@&286206848099549185> hi i'm having trouble with finding lcm. can somebody help me?
devout snowBOT
<@&286206848099549185> hi i'm having trouble with finding lcm. can somebody help...
midnight dirge
!15min
devout snowBOT
Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
midnight dirge
idk
its similar to hcf
just write out factors
then for each prime number
just pick the highest power
hcf just pick the lowest
unborn laurel
Thanks
devout snowBOT
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