yeah
#help-10
wild forge
what topic is this called in math btw?
wild forge
the finding points one is system of equations?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
timid silo
Why are the multiplying it by xy
Can't i find the answer without multiplying whole equation??
obtuse pebbleBOT
Why are the multiplying it by xy
Can't i find the answer without multiplying wh...
timid silo
It gets rid of the fractions
And makes ur life easier
U will have to do something similar to that one way or another
Oh thx
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peak hamlet
obtuse pebbleBOT
royal basin
why do you think there should not be a two
high lily
also missing () around (x-3)
peak hamlet
Sorry I just realised I have posted the wrong image
This is the correct image
I derive with first principles and get the same result excluding the 2 in the denominator
high lily
you didn't distribute that 2 in the numerator to the h
formal echo
How would I work out question 9a
obtuse pebbleBOT
How would I work out question 9a
fallow cove
How would I work out question 9a
the double angle formula
warm shaleBOT
formal echo
the double angle formula
What’s that?
warm shaleBOT
obtuse pebbleBOT
@formal echo Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
indigo hinge
obtuse pebbleBOT
indigo hinge
can one of you guys help me with those two
sorry if the photo is not clear
hello?
indigo hinge
oml tysm
twin crater
welcome
twin crater
have a good day/night too)
proven zephyr
Suppose A is the set of all 8-digit numbers whose digits consist of 1, 2, or 3 and contain at least one digit 2. There are N numbers in "A" such that every 2-digit in N is enclosed by a 1 and a 3
obtuse pebbleBOT
Suppose A is the set of all 8-digit numbers whose digits consist of 1, 2, or 3 a...
proven zephyr
What I have tried:
Seperating it into cases where there is 1, 2, 3 number of 2s
For 1 2s:
There are 6 ways to place the 2
There are 2^6 ways place the other digits
so 6 * 2^6 = 6 * 64 = 384
For 2 2s:
I don't know
that's where I'm stuck
nvm I can do it for 2 2s
For 2 2s:
6 * 2^4 = 6 * 16 = 96
For 2 3s:
now i dont know
aight ima just switch questions
.close
north anchor
Hello the slope line tangent and definition of the derivate are same?
obtuse pebbleBOT
Hello the slope line tangent and definition of the derivate are same?
timid silo
obtuse pebbleBOT
timid silo
why doesnt this diverge
fickle turret
What's lim n goes to infinity of sin(10/n)?
timid silo
tbh i saw a youtubevid with a similar q ish and just followed the methods
id assume (-1)^n where n -> infinity makes it immediatly diverge
royal shard
(-1)^n is alternating between -1 and 1
so if the rest is a 0 sequence, then it converges
so no good
rain forge
10/n tend to 0 so sin tend to 0 and 0×1^n is 0 no ?
timid silo
oh so is this like a sin graph moment
royal basin
sin(10/n) approaches 0 as can be seen by, say, squeeze theorem.
royal basin
multiplying it by the bounded sequence (-1)^n does not affect its convergence to zero.
royal shard
oops
timid silo
sorry whats the first method to this apporach
sonic anchor
sin is also continuous so you can evaluate the limit of the argument no?
sonic anchor
+0=-0
high lily
(-1)^n is alternating between -1 and 1
timid silo
sin(10/n) approaches 0 as can be seen by, say, squeeze theorem.
so id need squeze for this
sonic anchor
yes what 2 functions could you choose?
obtuse pebbleBOT
@timid silo Has your question been resolved?
zinc yew
helloo
zinc yew
what does it mean when a number sohuld be "divisible"
in our econ assignment it is said that output is assumed as q>=0 and is divisible
sage geode
Does it say just "is divisible"?
zinc yew
yup
zinc yew
Let q = amount of the single output produced (output level). We also assume q is divisible.
that's what it says
sage geode
zinc yew
im thinking it should be divisible by a whole number but idk xD
since i got answer which is 100/3 and it's divisible by 1/3
welp ill just ask instructor tomorrow i guess, thanks!
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vernal schooner
obtuse pebbleBOT
vernal schooner
Need some help with this question please
rigid lintel
cos(n) is bounded
sage geode
Have you considered using the squeeze theorem?
vernal schooner
I have the squeeze theorem notes open right now
but having trouble understanding and how to apply it to this
okay so i get that cos(n) is bound to -1 and 1
sage geode
-1<= cos(n) <= 1
(-2 - 8n)/(n + 1) <= (3cos(n) + 1 - 8n)/(n + 1) <= (4 - 8n)/(n + 1)
vernal schooner
right I understand the working now thanks
but how do I find the limit from this?
unsure how to remove n from the left or right equation
sage geode
but how do I find the limit from this?
Divide top and bottom by n
For both of the limits
unreal musk
so for the left function I have ((-2/n) -8) / (1+(1/n))
but it should be easy to find the limit of this here though, no?
bleak maple
Need help with number 3
obtuse pebbleBOT
Need help with number 3
bleak maple
I did 1 and 2 but 3 i cant
obtuse pebbleBOT
@bleak maple Has your question been resolved?
obtuse pebbleBOT
@bleak maple Has your question been resolved?
buoyant horizon
obtuse pebbleBOT
https://cdn.discordapp.com/attachments/1072993257195311326/1085624957586919434/i...
buoyant horizon
How do I evaluate summtaions?
I know I have to use the formulas n(n+1)/2
etc
but I don't know how to split it up
obtuse pebbleBOT
@buoyant horizon Has your question been resolved?
buoyant horizon
<@&286206848099549185>
obtuse pebbleBOT
@buoyant horizon Has your question been resolved?
civic zealot
I know I have to use the formulas n(n+1)/2
etc
but I don't know how to split it ...
$\sum_{i=1}^n \frac{-12}{n} +\frac{108i}{n^2} = \sum_{i=1}^n \frac{-12}{n} +\sum_{i=1}^n\frac{108i}{n^2} $\
Since $\frac{-12}{n}$ is constant, the sum is just that multiplied by n\
Since $\frac{108}{n^2}$ is constant, you can pull it out of the sum and be left with $\frac{108}{n^2}\left(\sum_{i=1}^n i\right)$
warm shaleBOT
Zybikron
obtuse pebbleBOT
@buoyant horizon Has your question been resolved?
median tangle
obtuse pebbleBOT
median tangle
i have done the questions till q3 idk how to do 4. Also can you check if my answers are correct?
<@&286206848099549185>
pls gep
help
<@&286206848099549185>
pls help me pls
tardy epoch
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obtuse pebbleBOT
median tangle
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obtuse pebbleBOT
✅
median tangle
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obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
mellow compass
obtuse pebbleBOT
mellow compass
not sure on how the first part lead to the second part which i boxed in red
obtuse pebbleBOT
@mellow compass Has your question been resolved?
brave bramble
Let's say we have an animal. It is a 🦒.
Would you agree that it is a 🦒 or a 🐶?
If x is in A, then x is definitely in one of A or B.
mellow compass
so would x element b be dog in this case?
obtuse pebbleBOT
@mellow compass Has your question been resolved?
mellow compass
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olive kraken
Why does the 1.5 root equal 4? I'm not sure how the 1.5 root or whatever its called tells us that its equal to 4.
obtuse pebbleBOT
Why does the 1.5 root equal 4? I'm not sure how the 1.5 root or whatever its cal...
@olive kraken Has your question been resolved?
brave bramble
1.5 is 3/2, I'll use that from now on.
"3/2nd root" is really just taking your number to the 2/3 exponent.
And that means cuberoot(8²)
= 2² = 4
timid silo
obtuse pebbleBOT
timid silo
Hello, I'm stuck on part c)
obtuse pebbleBOT
@timid silo Has your question been resolved?
mystic spindle
Am I missing something here? Shouldn't the last term be + log_3(x-2), since the argument, (x-2), is being multiplied by (x-1)?
obtuse pebbleBOT
Am I missing something here? Shouldn't the last term be + log_3(x-2), since the ...
warm canopy
log(a/(bc)) = log(a) - log(bc) = log(a) - [log(b) + log(c)] = log(a) - log(b) - log(c)
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
timid silo
obtuse pebbleBOT
timid silo
How can I solve this?
for a fraction to equal 0, what would the numerator equal to
0?
timid silo
Now just find the roots of the numerator
What?
inner vault
are you familiar with finding the zeros of polynomials
timid silo
No
inner vault
do you know how to factor
timid silo
Yes
timid silo
To simplify?
inner vault
not in this case
so say i have the equation:
x^2 + x - 12 = 0
how do I figure out what x is?
first we need to factor
this factors to (x+4)(x-3) = 0
if you have 2 or more things that multiply together
you can say for a fact that if any of them are equal to 0
the whole thing is equal to 0
so for (x+4)(x-3)
we know that if x+4 = 0
the whole thing is
and the same for x-3
so what does x have to be for x+4 to equal 0?
-4
and x=3 to make (x-3)=0
timid silo
so what does x have to be for x+4 to equal 0?
-4
timid silo
and x=3 to make (x-3)=0
3
inner vault
now we know that if x=3 or x=-4, then (x+4)(x-3)
this is the solution to x^2 + x - 12 = 0
if we plug 3 or -4 into that original equation
we can see that it is true
now going back to the original problem
inner vault
0?
if the numerator is 0, the whole thing is 0
because 0 / anything = 0
another way we could see this is by multiplying both sides by x
so we get the equation:
x^2 * (x-2) = 0
how do we find what x is equal to?
timid silo
get rid of the -2?
inner vault
not quite
we have 2 things multiplied by each other: x^2 and (x-2)
how can we make the whole thing equal to zero
inner vault
if 2 things multiply together, and you make one of them 0, the whole thing will be equal to 0
so what happens if you plug in 0 for x
then x^2 comes out to be 0
and it doesn't matter whatever else happens because anything * 0 = 0
so now do the same thing for (x-2)
what do we plug in for x to make that 0
timid silo
0?
timid silo
I am so lost
inner vault
so say i have the equation:
does it make sense what i did here or can i explain it more
inner vault
ok
timid silo
I understand that
inner vault
ok
use that method to find the roots of (x^2)(x-2)=0
im sorry i have to go now
there's one more thing to remember once you do that
inner vault
use that method to find the roots of (x^2)(x-2)=0
after this you'll get x=0 and x=2
but x=0 is called an extaneous solution
that's because if you plug 0 into the original equation then you will get 0/0
and dividing things by zero is not allowed
so the only solution is x=2
goodbye sorry i couldn't help more
obtuse pebbleBOT
@timid silo Has your question been resolved?
obtuse pebbleBOT
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Available help channel!
slow robin
Plssssssssss help makes no sense on 1
obtuse pebbleBOT
Plssssssssss help makes no sense on 1
slow robin
2 and 3
fiery birch
What doubt are you having? @slow robin
slow robin
I dont see any paterns
fiery birch
See the exponents
fiery birch
I believe you are referring to column 1
Not all exponents are adding up to 7. Besides, you have to compare column 3 and column 1.
Let's take a very simple example
If I asked you what's (2^1) * (2^1) where the number after the '^' symbol represents the exponent , what would be your answer?
slow robin
Uhhhhh
fiery birch
,tex $(2^1) * (2^1)$
slow robin
The numbers after ^ would be gone
warm shaleBOT
RaphaelZZZ
fiery birch
This is what I mean ☝️
slow robin
Was i right
fiery birch
Was i right
For column 2 yes but for column 3, I am not able to see what you wrote
fiery birch
Yep it's correct, so what's the pattern?
slow robin
2x2
fiery birch
So what would be the value if I asked you to write it in a similar way as column 3 shows
slow robin
So what would be the value if I asked you to write it in a similar way as column...
15384
16384*
slow robin
4
warm shaleBOT
RaphaelZZZ
slow robin
So the pattern is thAt the columns are equal
fiery birch
**RaphaelZZZ**
We went from here
fiery birch
**RaphaelZZZ**
to here
Look at the exponents
Hint: it's a simple addition thing going on
slow robin
Adding the exponents gives me same amount on other column
fiery birch
Adding the exponents gives me same amount on other column
Keep in mind that the base number has to be the same to add the exponents
slow robin
Ya
fiery birch
That's all, we are done , do you have any further doubts?
willow tulip
I need help
obtuse pebbleBOT
I need help
willow tulip
daring rock
Have you tried anything so far?
torn zenith
Consider the ratio of the bases of the triangles in the diagram.
You will find the answer from it
obtuse pebbleBOT
@willow tulip Has your question been resolved?
fallow atlas
obtuse pebbleBOT
tiny basin
expand (x+2)^2 and plug them in
royal basin
no need to expand anything.
tiny basin
no need to expand anything.
agreed but less room for errors
royal basin
nah
supple pumice
only where f''(x) is positive
tiny basin
plug n chug
royal basin
MORE room for errors that way
tiny basin
either way just plug in x
royal basin
you really do not need to expand fuck all
you want to know when f''(x) > 0
it is already factored for you
tiny basin
yeah im not sure what his issue is
i thought it had something to do with the formatting
royal basin
@fallow atlas are you still here?
thick gyro
expand (x+2)^2 and plug them in
why though, you already know (x+2)^2 will always be positive
tiny basin
why though, you already know (x+2)^2 will always be positive
no need to but idk why he was confused
whether it was definition of concave/convex or he didn't understand the plug n chug
obtuse pebbleBOT
@fallow atlas Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
tender musk
if there is 4 choices but you can only pick 3 how many choices are there. No duplicates can use a choice more than once
obtuse pebbleBOT
if there is 4 choices but you can only pick 3 how many choices are there. No dup...
tender musk
no
ruby path
gleaming ridge
Then since duplicates is not allowed, for your next pick you have 3 choices and so on..
warm shaleBOT
NEONPerseus
hardy gale
.
woeful wedge
hi everyone
obtuse pebbleBOT
hi everyone
woeful wedge
this is a weird version of the law of cosines
the version i im used to is this
yet all the physics teachers are telling us to use a version that has a plus instead of a minus in the middle
what difference does the plus make
obtuse pebbleBOT
@woeful wedge Has your question been resolved?
obtuse pebbleBOT
@woeful wedge Has your question been resolved?
woeful wedge
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obtuse pebbleBOT
obtuse pebbleBOT
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neat smelt
Hi
neat smelt
This is my question
MPNS is a quadilateral, a line is drawn through N to cut SP at Q < MNQ = 132°, <SMN is twice angle MSQ and < NPQ is twice <QNP. If NP bisects the acute angle at N find
i) < SQN
ii) < MSQ
Relevant image is below
This is what I've been able to deduce
We are given that MPNS is a quadrilateral, and a line is drawn through N to cut SP at Q, with MNQ = 132°. We are also told that NP bisects the acute angle at N.
Since NP bisects the acute angle at N, we have <PNQ = <QNS, and therefore, <QNP = <SQN.
Let x be the measure of angle MSQ, then <SMN = 2x (as given in the problem statement).
Since NP bisects the acute angle at N, we have <MNP = <NPS. Therefore, we have:
<NPS = 180° - <MPS - <MPN
= 180° - <SMN - <MPN
= 180° - 2x - <MPN
Since <NPQ is twice <QNP, we have:
<NPQ = 2<QNP = 2<SQN = 2x
Therefore, we have:
<NPS + <NPQ + <QNS = 180°
Substituting the values we have found above, we get:
(180° - 2x - <MPN) + 2x + <PNQ = 180°
Simplifying this equation, we get:
<PNQ - <MPN = 0
Since NP bisects the acute angle at N, we have <MPN = 90° - <PNM. Therefore, we have:
<PNQ - (90° - <PNM) = 0
Solving for <PNM, we get:
<PNM = <PNQ - 90°
Since <NPQ is twice <QNP, we have <NPQ = 2<SQN = 2x. Therefore, we have:
<PNM = 2x - 90°
Now, we can solve for the angles we need to find:
i) <SQN = <QNP = 2x/2 = x
ii) <MSQ = 180° - <NPS - <SQN = 180° - (180° - 2x - <MPN) - x = x + <MPN/2
Since <MPN = 90° - <PNM, we have:
<MPN/2 = (90° - <PNM)/2 = (90° - (2x - 90°))/2 = 90°/2 - x = 45° - x
Therefore, we have:
<MSQ = x + <MPN/2 = x + (45° - x) = 45°
Would like to some knowing if I'm right.
obtuse pebbleBOT
@neat smelt Has your question been resolved?
obtuse pebbleBOT
@neat smelt Has your question been resolved?
obtuse pebbleBOT
@neat smelt Has your question been resolved?
scarlet talon
need help with this question
obtuse pebbleBOT
need help with this question
timid silo
you can use implicit differentiation
obtuse pebbleBOT
@scarlet talon Has your question been resolved?
obtuse pebbleBOT
@scarlet talon Has your question been resolved?
rocky shale
need help with this question
differentiate this
youll get slope
then write the slope intercept form equation youll get your coordinates
scarlet talon
thank you
rocky shale
👍
shadow lava
obtuse pebbleBOT
timber fox
third line at the end when you factor an x out of the (12-x^2) you write it as x(12-x) which is not true, this would give 12x-x^2
not 12-x^2
shadow lava
third line at the end when you factor an x out of the (12-x^2) you write it as x...
oddly enough, that would not change my answer
as x = 1
I worked out the math and still got this
obtuse pebbleBOT
@shadow lava Has your question been resolved?
sonic anchor
you put 3/4 inside argument when typing it on calculator
and yea not oddly enough it doesnt change your answer when x=1
cause 12-x^2=12x-x^2 when x=1
sonic anchor
I worked out the math and still got this
subtract what you can in the denominator and type it in. should be correct
shadow lava
you put 3/4 inside argument when typing it on calculator
this would be the correct way to write it?
sonic anchor
you can still subtract bottom
shadow lava
you put 3/4 inside argument when typing it on calculator
not sure what you meant here
shadow lava
hmmmm you are right
that's weird
apparently the extra brackets are needed for symbolab
sonic anchor
lol
shadow lava
so this is symbolab's fault, my work is correct lol
sonic anchor
oh yea the 2 cancels aswell
if you are actually paying attention to the problem your simplifying work should stop here
shadow lava
shadow lava
these are both the same, right?
wicked current
is the correct answer option "B" ??
obtuse pebbleBOT
is the correct answer option "B" ??
obtuse pebbleBOT
@wicked current Has your question been resolved?
inland matrix
$$\frac{-1^{\infty}}{\infty}$$
obtuse pebbleBOT
$$\frac{-1^{\infty}}{\infty}$$
warm shaleBOT
allarkvarkk
inland matrix
what is dis
slim leaf
Indeterminate form
kind hawk
symbols
obtuse pebbleBOT
@inland matrix Has your question been resolved?
inland matrix
Indeterminate form
so for a sequence it just dies?
what do i say
the sequence converges?
diverges*
slim leaf
More work needs to be done
vital frost
hi
tame narwhal
how do i difffeentiate
Differentiate w/ respect to what? What have you tried?
tame narwhal
think -alphaBe^-alphat
that should be right
vital frost
ok
obtuse pebbleBOT
@vital frost Has your question been resolved?
torpid rover
i am indeed lost
obtuse pebbleBOT
i am indeed lost
tame narwhal
It's asking you to "solve for" n
torpid rover
i know n= a-z but idk what to do with the w part
does it become divid
divide sorry
tame narwhal
Solve for it the same way you would solve for any variable in an algebra equation
torpid rover
wat may that be
tame narwhal
Guess if you have to. Start with w = an + z. You want to "isolate" n, so what's the first thing you would do?
tame narwhal
Yes
eternal jewel
For some reason I'm struggling a lot with being able to find eigenvectors for matrices. I have no problem finding the eigenvalues, but getting the eigenvectors from the eigenvalues is what I'm stuck at. Currently just at 2x2 matrices, so here's an example.
A =
0 2
1 -1
The two eigenvalues I've found for it is 1, and -2
So when putting λ = 1 into A - λI we get
0-1 2
1 -1-1
-1 2
1 -2
Now I don't know what to do from here. I know you can set it up like this sort of:
-1 2 | 0
1 -2 | 0
obtuse pebbleBOT
For some reason I'm struggling a lot with being able to find eigenvectors for ma...
unreal musk
You could but of course notice how the rows depend on each other
Use that to find the dependencies between the entries of your eigenvector
eternal jewel
Not sure what you mean
I can see that they're dependent on each other, but not sure what I'm supposed to do with that
rustic glacier
Can you help me calculate the first derivative of this one? I have trouble with simplifying
obtuse pebbleBOT
Can you help me calculate the first derivative of this one? I have trouble with ...
ebon torrent
you can start by seeing the fifth root of x as x^(1/5)
then since it is at the denominator you can but it to the numerator and it becomes x^(-1/5)
you understand so far?
rustic glacier
wait so we dont do quotient rule?
we can just move it up and do sums and differences?
ebon torrent
you don't need to I'll show you a trick that's pretty good
rustic glacier
ohh alr thank you
rustic glacier
yeah
rustic glacier
ohh alr
ebon torrent
idk if you already know the derivative of sqrt(x)
but you can see it works in this particular case aswell
rustic glacier
where did the square root come from?
ebon torrent
which one?
rustic glacier
the last pic
ebon torrent
the last picture?
oh I was juste showing you other examples
so you understand
better
rustic glacier
Ohh, thank so much man
ebon torrent
it's another example with sqrt(x)
ebon torrent
but yea that's the answer
rustic glacier
wouldnt you have to bring an x out?
rustic glacier
I need to know this for my next test, could you show me how to simplyfy ((x)^-4/5) / ((x^1/5)^2)?
rustic glacier
I think, the top is fs right but im not sure abt the bottom its X to the power of 1/5 then its all squared
rustic glacier
Yeahh
torn wave
this is some serious drawing dedication
ebon torrent
this is some serious drawing dedication
yeaa bro you gotta help people out you know
warm shaleBOT
Modus
rustic glacier
Ohh I see now thanks so much man I appreicate it
ebon torrent
No problem
acoustic osprey
I have the vector field $$F(x,y,z)=(-y,x,-1) $$ and surface S which is the part of a cone $$x^2+y^2-z^2=0 $$ where $$ 3 \geq z \geq 0 $$
I'm supposed to calculate the flow of F through S oriented upwards (not sure what that means)
obtuse pebbleBOT
I have the vector field $$F(x,y,z)=(-y,x,-1) $$ and surface S which is the part ...
warm shaleBOT
natti
acoustic osprey
How to calculate the flow?
obtuse pebbleBOT
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obtuse pebbleBOT
@acoustic osprey Has your question been resolved?
obtuse pebbleBOT
@acoustic osprey Has your question been resolved?
obtuse pebbleBOT
@acoustic osprey Has your question been resolved?
obtuse pebbleBOT
@acoustic osprey Has your question been resolved?
royal delta
I have forgotten how to convert a natural number into a log. I have the number 2, and need to write it in log form with preferable a base of 3.]
obtuse pebbleBOT
I have forgotten how to convert a natural number into a log. I have the number 2...
steady horizon
I have forgotten how to convert a natural number into a log. I have the number 2...
Yeah sure
royal basin
so you want to write 2 = log_3(?)
steady horizon
so you want to write 2 = log_3(?)
Isn't it 2= Logx_3
royal delta
Oh, thank you! I got it! I feel really stupid for asking this question. But it has been ages since I worked with logs hahaha
Thanks guys!
steady horizon
Oh, thank you! I got it! I feel really stupid for asking this question. But it h...
Ahhh
Take care dude
Peace
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obtuse pebbleBOT
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hot dawn
is there a faster way to do this question?
obtuse pebbleBOT
is there a faster way to do this question?
hot dawn
for A., do I really need to write out $ax^2+bx+c$, and then rearranging with the set condition to get an SLE?
warm shaleBOT
normalAtmosphericPa=101,325
timid silo
Do you know how to show something is a subspace of a vector space
hot dawn
yeah
v.s. criterion righjt?
show that the set is closed under vector add and scalar mult
timid silo
don’t forget the additive identity
kind hawk
(well, nonempty but most of the time that's done by 0, yes)
timid silo
Yep
kind hawk
well some of these are of the form L(p)=something for a linear map L
you could use general knowledge about linear maps for those
but then again you'd of course have to show that those things are linear
so whether it really saves time, who knows
hot dawn
wait so for A.
how would I approach it
using the p(X) notation in the set restriction?
and showing closure under the 2 V.S. axioms
kind hawk
yes. every subspace needs to contain 0
hot dawn
oh wait
kind hawk
does p(x)=0 satisfy p'(x)+7p(x)+9=0 ?
hot dawn
no
hot dawn
ah that's cheeky
wait so for B.
can I just apply the conditions directly to the set restriction's notatoin
i.e. check that a * P(6) = 0
and P(6) + P(6) = 0 is true
which is always true
so it's a subspace
kind hawk
well you have to check that if p and q are polynomials in that space, then (p+q)(6)=0
timid silo
^
hot dawn
I am not used to that notation lol
hot dawn
and again, check that the space is not empty
meaning to check for the additive identity, right?
hot dawn
well you have to check that if p and q are polynomials in that space, then (p+q)...
Can I then go like, (p+q)(6) = p(6) + q(6) = 0 by linearity
hot dawn
ah true
kind hawk
the polynomial p+q is defined by (p+q)(x)=p(x)+q(x)
or well, technically polynomial addition is defined by adding all the coefficients, bla bla
but if we view polynomials as functions then this is how the addition would be defined
hot dawn
but if we view polynomials as functions then this is how the addition would be d...
is this like, abstract algebra specific notation
or was this supposed to be from high school and I'm just liek
stupid
kind hawk
I mean even in school you added functions by (f+g)(x)=f(x)+g(x)
I mean more that for polynomials technically you would add them as symbols first
and then evaluate
so like p=x^2+3 and q=x^3-2x^2+x+7, then p+q=x^3-x^2+x+10
and then you evaluate
but ehh, technical stuff
not the important part here
hot dawn
I mean even in school you added functions by (f+g)(x)=f(x)+g(x)
I thought that was only for linear functions
hence, my mind went to "by linearity"
kind hawk
no that's just function addition in general
hot dawn
even for like (sin + arccot)(x) ?
kind hawk
yes
sin(x)+arccot(x)
that should be nothing new
it's how you always added functions
you just never really paid attention to it
hot dawn
what is the scope
kind hawk
wdym scope
kind hawk
well of course here we are using the plus in R by writing f(x)+g(x)
that's the addition in R
if we dont map into some set where we can add then we cannot define function addition
hot dawn
I see
hot dawn
for C., does "is constant" refer to it literally being a constant?
hence p(X) should be all degree 1 polys/lines
kind hawk
yes
hot dawn
idk lol
I feel geometric interpretaion is still easiest here
since it's only degree 2
so lines and parabolas
kind hawk
well does it really change if I consider the same subspace but inside R[x]_17 ?
hot dawn
it does right?
because I can not longer easily visualise R[x]_17 polynomials
unless I am looking for counterexampels
the higher degree polys could be potential sources of counterexamples
hot dawn
oh for C.
maybe not
ah
I guess it doesn't really matter in this question
Wait a secondd
For the zero vector question, I feel like it doesn't really make sense
@kind hawk I'm adding a zero vector with a zero scalar
right? ...
yet the answer of -2 is apparently still correct
kind hawk
you need that 0_v+u = u for all u
it turns out from the vector space axioms you also get that 0_R * v=0_v for all v
hot dawn
yeah
kind hawk
where 0_R is the 0 in the field
so that's what you are doing here
technically you are letting the vector space axioms do a bit of work cause you haven't explicitly shown that -2 satisfies 0_v+u=u
hot dawn
wai t
I'm still kind of lost sorry
above, with their definition of scalar multiplication, I will end up with 0_R * v + 2(0) - 2
and by the vector space axioms, 0_R * v = 0_v
so why am I able to do 0_v - 2 = -2?
am I not adding a vector to a scalar?
of which is undefined
kind hawk
well the vector space elements are real numbers themselves
so you are using them as both
hot dawn
well the vector space elements are real numbers themselves
I see!
kind hawk
but yes straight from the definition of a*u=au+2a-2 you see that you are adding au which is a vector and 2a-2 which is a scalar
hot dawn
because elements of a vector space needn't be "actual" vectors right?
kind hawk
not in the sense you are thinking of , yes
technically speaking, by definition "vector" means element of a vector space
hot dawn
wait
so for this question, would the answer be A?
B. and C. clearly appare nonsensical
and in D., I am adding a scalar and a vector ... in the traditional sense right?
because there is no mention of a vector space or field in the question
hot dawn
and in D., I am adding a scalar and a vector ... in the traditional sense right?
as in I can do so
because (u)c_2 is simply scalar multiplication of u by c_2
oh
oops
it's undefined haha
because I am adding a scalar and a vector
soooo, A. is the best statement?
why not 
it's a true statement isn't it?
unreal musk
Because as per what you said for d, neither side is defined (in a)
hot dawn
unreal musk
You’re adding a scalar to a vector for both, which you can’t do
hot dawn
ok so in mathematics
is illogical expression = same illogical expression rewritten in a different way not valid?
is this something to do with logic?
unreal musk
I mean in general it isn’t, at least from my experience
hot dawn
ok
do you know the proper terminology of why it is so? (so I can maybe go read up on it :> )
the cats are cute btw
whoever set them up has good taste
unreal musk
Hmmm I’m actually not too sure, maybe someone else can elaborate on that for me 
but at least from what I know, you can’t do that
thorny olive
In how many ways 2 patients of asthama , 3 patients of jaundice and 4 patients of typhoid of a hospital can be placed in 9 rooms in a row so that patients of each disease are in the room besides to each other and one patient in each room?
obtuse pebbleBOT
In how many ways 2 patients of asthama , 3 patients of jaundice and 4 patients o...
@thorny olive Has your question been resolved?
viral blade
probably a helpful first step is find as many examples that work as possible
for example: AAJJJTTTT
viral blade
doesn't seem right
viral blade
the question is poorly worded tho so maybe it means something else i can't think of
viral blade
,w 362880/288
warm shaleBOT
thorny olive
thanks tho
tame narwhal
Yeah
viral blade
for example: AAJJJTTTT
So you take the number of patterns like this and multiply by the number of ways to assign people per pattern
thorny olive
huh
viral blade
answer doesn't seem right tho
by one interpretation there are 6 patterns
AAJJJTTTT
AATTTTJJJ
JJJAATTTT
JJJTTTTAA
TTTTAAJJJ
TTTTJJJAA
then, per pattern, 24 ways to assign the T, 6 ways for the J and 2 for the A
,w 6246*2
warm shaleBOT
thorny olive
tysm😭😭
viral blade
no prob
thorny olive
.close
umbral spear
Was wondering if i did this right. Its linear algebra and i have 3 points. a , b and c. And i am suppose to find the plane that they all are on.
obtuse pebbleBOT
Was wondering if i did this right. Its linear algebra and i have 3 points. a , b...
@umbral spear Has your question been resolved?
obtuse pebbleBOT
@umbral spear Has your question been resolved?
obtuse pebbleBOT
@umbral spear Has your question been resolved?
obtuse pebbleBOT
@umbral spear Has your question been resolved?
lean ember
well it is correct
u can confirm your self by substituting first to numbers and check if z value matches the question's or not
shadow lava
Just curious, why is “u” always used for the argument with derivatives?
obtuse pebbleBOT
Just curious, why is “u” always used for the argument with derivatives?
warm canopy
Well your formulas should be for $\arcsin(u(x))$
warm shaleBOT
ΣAC
median dome
but what you wrote here doesn't make much sense
shadow lava
you can use anything
But if I used x, dx/dx would = 1
shadow lava
Well your formulas should be for $\arcsin(u(x))$
Noted ty
median dome
yes
shadow lava
Well your formulas should be for $\arcsin(u(x))$
Fixed now
warm canopy
Personally i would do u(x) to highlight the fact that u is a function of x
obtuse pebbleBOT
@shadow lava Has your question been resolved?
subtle warren
Hi I need help with this differentatial equation question. I don't understand why the mark scheme did it that way, instead of doing the easier product rule way.
obtuse pebbleBOT
Hi I need help with this differentatial equation question. I don't understand wh...
tardy epoch
Hi I need help with this differentatial equation question. I don't understand wh...
then do it the easier way
thorny wave
Hello
tardy epoch
as long as you get the same answer it doesn't matter
subtle warren
yh, but it doesnt give me the answer they want me to sho
thorny wave
Can anyone help me with logical math problem
tardy epoch
Can anyone help me with logical math problem
!help
obtuse pebbleBOT
Can anyone help me with logical math problem
Please read #❓how-to-get-help
thorny wave
!help
obtuse pebbleBOT
Please read #❓how-to-get-help
tardy epoch
yh, but it doesnt give me the answer they want me to sho
is the part in yellow not the answer?
tardy epoch
then do it the easier way
.
subtle warren
i dont understand what the reasoning is behind using their wierd method, like how would I know in an exam
warm canopy
I think you need to explicitly describe to us the method you're using
That you say isn't giving you the same answer?
thorny wave
ΣAC can u pls help?
tardy epoch
i dont understand what the reasoning is behind using their wierd method, like ho...
learn their method and practice
obtuse pebbleBOT
ΣAC can u pls help?
Please read #❓how-to-get-help
subtle warren
I used the product rule normally
tardy epoch
ΣAC can u pls help?
stop spamming and read
tardy epoch
I used the product rule normally
!show
obtuse pebbleBOT
I used the product rule normally
Show your work, and if possible, explain where you are stuck.
thorny wave
I ddiiiidd
subtle warren
I ddiiiidd
you need to get help in above help section
timid silo
Wdym easier product rule
subtle warren
in the answer, they multiplied everything by dN, but I'm not sure about I'm supposed to know to do that
timid silo
Ok so, we know that v=L-N
subtle warren
im not sure what you mean
subtle warren
.close
reef loom
hey, i was doing the demonstration of the trigonometry relations, and i got i little confused about similarity of triangles
obtuse pebbleBOT
hey, i was doing the demonstration of the trigonometry relations, and i got i li...
reef loom
so, i have a triangle retagle cos(x)^2+sen(x)^2=1^2
thorny wave
reef loom
<#903481102591750184>
what?
thorny wave
Nothing
reef loom
oh ok
warm canopy
Stop it razer
thorny wave
Wdym
warm canopy
Stop spamming your channels in other people's and interrupting
reef loom
so, i have a triangle retagle cos(x)^2+sen(x)^2=1^2
and another one with sen and tg, i think you get the drill. anyway, i was confused because i got cos(x)/1=sen(x)/tg(x). But in the internet is 1/cos(x)=sen(x)/tg(x)
are they both correct?
if not, how can i know which one should i put below and who should i put on the top?
when researching i came across images like
warm canopy
How else do I find it?
By using the menu bar??
reef loom
where it seems that the biggest side is the one to be in the bottom part of the fraction
and if this is the correct form then Cos(x)/1=sen(x)/tg(x) would be correct
wheres my mistake?
.close
fair bridge
fair bridge
@obtuse pebble how to remove
plain stag
.close
obtuse pebbleBOT
fair bridge
Thanks
obtuse pebbleBOT
Available help channel!
deep brook
how could i isolate x in the equation:
cos(x) = 15/17
obtuse pebbleBOT
how could i isolate x in the equation:
cos(x) = 15/17
deep brook
do I take the arccos of 15/17?
hexed agate
Yes
deep brook
oh ok
robust sleet
yes
deep brook
to double check
is this correct?
cos(theta) = adj /hyp = 15/17
arccos(15/17) = approx 28.07 degrees?
1/sin of that = about 17/8
the sin is 8/17 im guessing
obtuse pebbleBOT
@deep brook Has your question been resolved?
obtuse pebbleBOT
@deep brook Has your question been resolved?
deep brook
.close
shadow valve
I need help with discrete math
I'm working on decoding the code 5192 2604 and 4222 using the modulus 7081 and the exponent 1789.
I know that it would look like:
x^1789 tribar=- 5192 (mod 7081)
Though I don't know how to solve for the code. What am I supposed to do to solve this problem?
obtuse pebbleBOT
I need help with discrete math
I'm working on decoding the code 5192 2604 and 42...
@shadow valve Has your question been resolved?