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#help-0
tawdry flicker
I got 1/12 for the slope
lone heartBOT
I got 1/12 for the slope
worn fox
!show
lone heartBOT
Show your work, and if possible, explain where you are stuck.
alpine sable
You forgot to multiply by the internal derivative probably
alpine sable
Yup
alpine sable
This oh moment
tawdry flicker
.close
tawdry flicker
This one i got 4
lone heartBOT
This one i got 4
tawdry flicker
Idk what its asking for
shell coral
i need help
neat mango
i need help
Sorry, this channel is currently occupied. If you'd like help on a question, please use an available channel
lone heartBOT
lone heartBOT
Available help channel!
teal herald
okay I feel like im doubting myself now for h'(t) i got -16t + 79
teal herald
i split it to a power function and linear function
jagged cobalt
-16t^2 doesnt go to -16t
teal herald
using power function rule no?
jagged cobalt
x^n -> nx^(n-1)
jagged cobalt
you dont multiply by the new power
teal herald
mb
teal herald
coming back to this
lone heartBOT
coming back to this
teal herald
my question is
what does solving f acutally do
h`(t) = -32t + 79
when u solve for 0
you get 2.47
what does this represent
this is a more curious question than acutal help
median oar
What f
teal herald
i guess
median oar
Ah h
teal herald
part f
median oar
Well consider some function f(x)
What is the significance of f’(x) = 0
(You should’ve covered this at the beginning of calculus)
teal herald
well if prime doesnt mean anything than that just means x outputs 0
teal herald
i think i am overcomplicatiing it but its just an output no?
i know that acutally subbing x for a value gives the irc at a point
instantanious rate of change
median oar
Anything about critical values?
teal herald
mmm no
teal herald
ohh okay so that gives the min value that I can plug in and get output?
that makes sense
median oar
In terms of your question it solves for the min/max height
You don’t know if it’s min or max
median oar
You need the 2nd derivative to check concavity to know if it’s a local min or max or neither
Consider f(x) = x³
teal herald
i just realized that it acutally matches perfectly with the max that i found in step e
median oar
f’(x) = 0 is solved by x=0
But that’s neither a local min or max
Because f’’(0) is neither positive nor negative
median oar
i just realized that it acutally matches perfectly with the max that i found in ...
Well you’d hope it did
teal herald
interesting, yeah this is the first im hearing of this concept
maybe which he thought we would see the values and make a correlation ourselves
which i didnt
lmfao
super cool thankyou for explaining
.closer
.close
smoky moss
lone heartBOT
@smoky moss Has your question been resolved?
severe stone
How would I go about solving this problem. Its from a test I had earlier today and I know I got it wrong
lone heartBOT
How would I go about solving this problem. Its from a test I had earlier today a...
@severe stone Has your question been resolved?
lone heartBOT
@severe stone Has your question been resolved?
tacit arch
Multiply top and bottom bot cosx +1
honest sundial
can anybody tell me how it work
lone heartBOT
can anybody tell me how it work
lone heartBOT
@honest sundial Has your question been resolved?
honest sundial
its solve as 6sin(a)*cos(a)+4(cos^2(a)-sin^2(a) = 5(cos^2(a)+sin^2(a)
9tg^2(a)-6tg(a)=-1 by a=x/2
honest sundial
but miss understand what the f is this
lone heartBOT
@honest sundial Has your question been resolved?
lone heartBOT
@honest sundial Has your question been resolved?
limber oasis
i dont understand this
ancient saddle
how that numbers translate into sin/cos
Hello. You want it to look like a sine of a sum:
sin(x+y) = sinxcosy + sinycosx
So you can write those terms as a single sine and solve the equation
honest sundial
fcgvbh m ,v
hellow
its is not wat i request
sin(x+p) - is solve but how to sin and cos p
ancient saddle
Hello. You want it to look like a sine of a sum:
sin(x+y) = sinxcosy + sinycosx
You want to have it in this form. For that, you have to make sure that the sum of the numbers squared = 1. If it's 1, then they can be written as sine and cos of some angle
Also you can see it's not possible yet because 3 and 4 are greater than 1, which is out of the range of sin and cos
A strategy is diving both sides of the equation by some number k
So
Asinx/k + Bcosx/k = .../k
Now,.you want
(A/k)²+(B/k)² = 1
Solve for k and you get
k=√(A²+B²)
ancient saddle
So
Asinx/k + Bcosx/k = .../k
Now,.you want
(A/k)²+(B/k)² = 1
Solve for k and you...
Compare this with sine sum formula
cosø = A/√(A²+B²)
ø = arccos(A/√(A²+B²))
lone heartBOT
lone heartBOT
Available help channel!
alpine sable
<@&286206848099549185>
lone heartBOT
<@&286206848099549185>
wheat isle
<@&286206848099549185>
!15m
lone heartBOT
<@&286206848099549185>
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.
alpine sable
ionic jewel
what are you trying to do
alpine sable
what are you trying to do
make trapezoid
im tryna make 4 shapes
quadrilaterals
so basically
i need to put each quadrilateral
in this graph
iron hull
<@&286206848099549185>
!15m
lone heartBOT
<@&286206848099549185>
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.
lone heartBOT
@alpine sable Has your question been resolved?
twin thunder
i dont understand the teachers procedure
lone heartBOT
i dont understand the teachers procedure
twin thunder
help
vale wigeon
your teacher first chooses 3 people to drive the cars
there are 5 drivers available and 3 cars to put them in, and it matters who goes where, thus 5P3 ways
do you understand? Y/N
vale wigeon
9 is the number of ways to pick who goes in the small car as a passenger
vale wigeon
so it appears, yes.
it matters who goes in what car but not the arrangement of passengers within each car
lone heartBOT
@twin thunder Has your question been resolved?
merry meteor
lone heartBOT
merry meteor
just a question
i thought if one isnt a multiple of another
then its L.I
why isnt this L.I?
merry meteor
That's only true for a list 2 vectors
ok so if there is 3
and we see a multiple
then we no its not L.I
but if we dont
we still have to test?
worn fox
That is true yes
merry meteor
alr makes sense
worn fox
Well no technically it is not
worn fox
Go to the definition of dependence
Can you add them up with non-zero coefficients to get 0
The presence of the zero vector is important
merry meteor
Can you add them up with non-zero coefficients to get 0
yea
by soving thru system of equation
worn fox
Okay fine then solve the system
merry meteor
i just get
c1 = 0
c2 = 0
c1 + c3 = 0
2c1+4c3=0
c1+3c3=0
c1 = -c3
c1 = -2c3
this isnt evne possible
wtf am i doing wrong here
worn fox
Is what even possible
merry meteor
c1 = -c3 from first eqn
worn fox
C1 and c3 are 0
merry meteor
ah i get it
worn fox
Take any multiple of the 0 vector and 0 multiples of the other 2
undone plover
lone heartBOT
undone plover
i dont know how to solve this?
coral thorn
do you know what a power function is?
undone plover
no
coral thorn
can you write the given function in the form $y = kx^{p}$?
ocean sealBOT
saad
coral thorn
no
A power function is a function with a single term that is the product of a real number, a coefficient, and a variable raised to a fixed real number.
coral thorn
**saad**
k is the coefficient, x is the variable and p is the power
how would you expand $(4x^{5})^{2}$ ?
ocean sealBOT
saad
coral thorn
like 4x^10?
are you sure thats the correct answer?
coral thorn
is that what you mean?
a power function is just a function with a single term that is the product of k, x, and p. $f(x) = kx^{p}$
ocean sealBOT
saad
coral thorn
i feel like im doing the opposite
whats 4 raised to the power of 2?
undone plover
16
coral thorn
whats $(x^{5})^{2}$
ocean sealBOT
saad
undone plover
okay okay ima sound dumb cause its either x^10 or x^25
coral thorn
the former
coral thorn
its x^10
undone plover
4x^10
coral thorn
4?
coral thorn
whats outside?
undone plover
the ^2
coral thorn
can you identify k, x, and p?
coral thorn
so is it a power function?
coral thorn
and uhh is x.... x?
yes
undone plover
yea
coral thorn
thats it
coral thorn
.close
undone plover
.close
cosmic spruce
lone heartBOT
vague coral
did you differentiate a ?
gloomy grove
I alr diffed it then subbed x=3 then I got this
then maybe you should put x as something else, look at the summation side
cosmic spruce
did you differentiate a ?
Yeah
vague coral
$2n (1+x)^{2n-1} = \sum_{k=1}^{2n} k \binom{2n}{k} x^{k-1}$
ocean sealBOT
Herels
vague coral
take x =1
gloomy grove
yes
vague coral
1^anything = 1 bro
alpine sable
lone heartBOT
lone heartBOT
@alpine sable Has your question been resolved?
alpine sable
<@&286206848099549185>
zealous lichen
use the fact that they are not parallel
alpine sable
use the fact that they are not parallel
I still don’t know what to do
zealous lichen
ok
we can do this another way
assume lambda and mu are not 0
try to show that the vectors are parallel
alpine sable
alpine sable
How does this prove that they’re not parallel?
zealous lichen
if lambda and mu are not both 0 then u and v are parallel
it's the same as saying if u and v are non-parallel then lambda and mu are both 0
alpine sable
Ohhhh
alpine sable
oh I forgot the case where only one of them is 0
So why must this be done?
zealous lichen
we need to consider all cases where lambda and mu are not both 0
alpine sable
we need to consider all cases where lambda and mu are not both 0
Oh ok
How did you know to do this though?
I didn’t think of this
zealous lichen
oh it's a pretty common proof technique
if you want to prove that P implies Q, it's the same as proving not Q implies not P
you might want to learn some basic mathematical logic
lone heartBOT
@alpine sable Has your question been resolved?
lone heartBOT
lone heartBOT
Available help channel!
obtuse spindle
[3 2 1]
and B = [2 3]
[1 4]
[2 1]
then find rank of matrix AB```
AB i found is [ 11 25 ]
[ 10 18 ]
i am trying to find the rank of matrix using method of highest order square submatrix with non-zero determinants and the order of this matrix is 2x2 and the determinant is -52 so why isn't the rank 2?,w rank((11,25);(10,18))
ocean sealBOT
median oar
Looks 2 to me
obtuse spindle
wait so chatgpt was wrong
round geyser
wait so chatgpt was wrong
bro 💀 ...
median oar
Chatgpt is not great at maths
obtuse spindle
fr
median oar
It’s very confidently wrong
limpid spade
It can't even do 1+1
obtuse spindle
It’s very confidently wrong
lmao thats so true
muted hornet
wait so chatgpt was wrong
chat gpt will present very intricate reasoning that is slightly incorrect in some hard to find steps, but sounds correct, for many things
be careful 
median oar
So if you don’t know the content well you won’t be able to distinguish if it’s confidently correct or confidently wrong
median oar
Which actually makes chatgpt is very very bad tool for learning maths
glacial patrol
most often very incorrect and not hard to find 
median oar
Because you can’t even tell if it’s right or wrong
obtuse spindle
```if A = [1 5 2]
[3 2 1]
and B = [2 3]
[1 4]
[2 1]
the...
the answer in my book is 1
median oar
Show it
obtuse spindle
alr 1 min
median oar
,w rank(((1,5,2);(3,2,1))*((2,3);(1,4);(2,1)))
ocean sealBOT
obtuse spindle
oo wait a min so the answer in the book is wrong too
cinder sundial
given a random experiment has 2 random variables X and Y, and adding these two variables up can obtain new random variable called X+Y.
Then by the "definition," E(X+Y)=E(X)+E(Y)
cinder sundial
Above is a line written on my math book.
lone heartBOT
To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.
cinder sundial
could you delete your message and open an new channel
cinder sundial
Above is a line written on my math book.
thank you
cinder sundial
Above is a line written on my math book.
However, i cannot understand why E(X+Y)=E(X)+E(Y)
median oar
Are we looking at continuous or discrete RVs?
tardy stag
if you roll two dice would you not expect to get twice as much on average as if you rolled one?
cinder sundial
Are we looking at continuous or discrete RVs?
discrete RVs, I suppose
median oar
Do you know the definition of expectation of discrete RVs
cinder sundial
if you roll two dice would you not expect to get twice as much on average as if ...
no, I expect to get twice the average of one roll with two rolls
cinder sundial
Do you know the definition of expectation of discrete RVs
it is Sigma Pi Xi, in which P is the probabilty of sth and X is the random variable of sth
ocean sealBOT
Frosst
median oar
Yes?
cinder sundial
yes
ocean sealBOT
Frosst
median oar
Yes?
cinder sundial
what does (x+y) stands for?
median oar
Well X and Y are functions
So the addition of functions is not the same as adding their values at particular points (we need to define this)
cinder sundial
lets say someone flip a coin two times and X,Y is the expected head and tail respectively
median oar
No no let’s not do that
cinder sundial
then what does (X+Y) stands for?
median oar
Well
There’s your problem
What is X?
X is a function from the sample space to the reals
$X:\Omega \to \mathbb R$
ocean sealBOT
Frosst
cinder sundial
X = 2 head in 2 flips
median oar
No
cinder sundial
Y = 2 tails in 2 flips
median oar
You have {heads, tails}
This is your domain set
And you have ℝ
This is your target set
cinder sundial
ok
median oar
Tell me a mapping from your domain to your target
X(heads) = ?
And
X(tails) = ?
They need to equal numbers
Real numbers
cinder sundial
X(heads) = 2 , X(tails) = -2
median oar
Ok
Now we need to also assign to each event a probability
$P:\Omega \to [0,1]$ such that the total probability is 1
ocean sealBOT
Frosst
cinder sundial
X(heads) = 2 , X(tails) = -2
that is X (a head)= 1/2 = X(a tail)
X(2 heads)=1/4=X(2 tails)
median oar
X(heads) = 2 , X(tails) = -2
X is a function defined here
I need you to now tell me about P
cinder sundial
I suppose we flip the coin two times?
median oar
What is P(heads) =? And what is P(Tails) = ?
cinder sundial
What is P(heads) =? And what is P(Tails) = ?
it is impossible to tell without knowing how many flips of coin there are
median oar
There is 1 flip of a coin
cinder sundial
ok
cinder sundial
There is 1 flip of a coin
then i suppose it is P(head) instead of the plural heads?
cinder sundial
P(head)=1/2 and P(tali)=1/2
median oar
You have {heads, tails}
But to be fair I defined them with s’
Ok
Now we have $\mathbb E[X] = \sum_{i=1}^2 x_ip_i$
cinder sundial
ocean sealBOT
Frosst
cinder sundial
yes
median oar
$\mathbb E[X] = 2\times\frac{1}{2} + (-2)\times \frac{1}{2}=0$
ocean sealBOT
Frosst
cinder sundial
like EV is the expected value
cinder sundial
**Frosst**
the E[X] seems not clear defined
median oar
Why not
cinder sundial
as we dont know what it represents
median oar
I can be more explicit
$\mathbb E[X] = \sum_{x\in\Omega} X(x)\cdot P(X^{-1}({x}))$
Is that clearer or no
cinder sundial
my mind cannot comprehend the right hand side, it seems like an ancient text before jesus was born
ocean sealBOT
Frosst
median oar
So right, there’s 2 things in omega
$\mathbb E[X] = X(\text{heads})\cdot P(X^{-1}({\text{heads}})) +X(\text{tails})\cdot P(X^{-1}({\text{tails}}))$
ocean sealBOT
Frosst
median oar
Ok let’s dissect this
cinder sundial
i cannot figure out what the X^-1 represents
median oar
It’s the inverse of X
cinder sundial
I suppose it is 1/X?
median oar
Um it’s a little weird looking because it’s not necessarily a function
It’s also why there’s a {} around the argument
Hmm this is still a little wrong
The notation is kinda annoying
The idea is we look at all the events
And we sum their (value * prob)
Value is defined by X
Prob is defined by P
cinder sundial
the sample space = { the head, the tail} = {2, -2}
P(2)= 1/2 = P(-2)
cinder sundial
BUT P(2) = P(head with one flip), as we using 2 to represent the event of getting a head
median oar
$\mathbb E[X] = \sum_{x\in\Omega} X(x)\cdot P(X=X(x))$
This is probably easier notation
cinder sundial
yes
ocean sealBOT
Frosst
cinder sundial
**Frosst**
then I suppose let X=R+S
median oar
Let’s just say $\mathbb E[X] = \sum_{x\in\Omega} X(x)\cdot P(x)$
ocean sealBOT
Frosst
median oar
This probably makes the most sense
cinder sundial
yes, it is the definition
median oar
Ok now
median oar
BUT P(2) = P(head with one flip), as we using 2 to represent the event of gettin...
You can’t stick 2 into P
cinder sundial
You can’t stick 2 into P
really? doesnt that 2 stands for the event of getting a head
median oar
No that’s X(heads) = 2
Now let’s say you want to add another RV say Y
Y has all the same properties as X
cinder sundial
Y has all the same properties as X
for sure
median oar
$\mathbb E[X + Y]=$undefined
ocean sealBOT
Frosst
cinder sundial
$\mathbb E[X + Y]=$undefined
can we assume E[X] as getting two head within 2 flips and E[Y] as two tails
cinder sundial
ohhh
i got you
lets E[X] be expected heads within 2 flips and E[Y]= expected tails
median oar
Let $\bold{X}$ be the set of all mappings from $\Omega\to\mathbb R\+_{\text{RV}}:\bold{X}\times\bold{X}\to\bold{X}$
ocean sealBOT
Frosst
median oar
And then, let $X, Y\in \bold{X}$, define $X+{\text{RV}} Y (a) = X(a) +{\mathbb R} Y(a)$
ocean sealBOT
Frosst
cinder sundial
X,Y belongs to Bold X
median oar
Now we can add random variables together and the result is the separate parts’s values
cinder sundial
X,Y belongs to Bold X
what is the bold X?
median oar
Yeah bold X is all the different RV mappings
median oar
**Frosst**
.
median oar
X(heads) = 2 , X(tails) = -2
Here you chose a particular X in X
cinder sundial
ok, then i think bold X is just a set of diffrent events
median oar
Now we have $\mathbb E[X +{\text{RV}} Y] = \sum{x\in\Omega}(X(x)+_{\mathbb R}Y(x))P(x)$
ocean sealBOT
Frosst
median oar
From now on I will omit the subscript on the plus symbols it should be obvious which is which
cinder sundial
From now on I will omit the subscript on the plus symbols it should be obvious w...
ok
median oar
To continue, $\mathbb E[X +{\text{RV}} Y] = \sum{x\in\Omega}(X(x)+{\mathbb R}Y(x))P(x)=\sum{x\in\Omega}\left[X(x)P(x) + Y(x)P(x)\right]= \sum_{x\in\Omega}\left[X(x)P(x)\right] + \sum_{y\in\Omega}\left[ Y(y)P(y)\right]$
ocean sealBOT
Frosst
cinder sundial
**Frosst**
yes, that is how sigma works
median oar
Naturally we then have E[X] + E[Y]
cinder sundial
Naturally we then have E[X] + E[Y]
what do you mean naturally, is there any exception
median oar
Nope
Well I mean
It needn’t exist
Expectation of an RV isn’t guaranteed to exist
Some kinds of RV have no expectation
cinder sundial
Some kinds of RV have no expectation
it is hard to imagine, is there any intuitive example
median oar
Uh, Cauchy distribution
It’s a continuous RV
We define expectation with integrals from -inf to inf
But the Cauchy distributed RV when you try to evaluate the integral you get inf-inf = undefined
cinder sundial
I see
median oar
So then it has no expectation
cinder sundial
I see
median oar
An RV need not even have a pdf in fact
It needs only the CDF to exist
I did skip an intermediate step somewhere early on
cinder sundial
given a random experiment has 2 random variables X and Y, and adding these two v...
got it. then I think the proof is just using the properties of sigma and the definition of EV
median oar
But explaining that will take forever
median oar
got it. then I think the proof is just using the properties of sigma and the def...
Yes but also implicitly we did
median oar
**Frosst**
This
cinder sundial
Y has all the same properties as X
that is quite important tho
median oar
The + in X+Y is not the same + as 3 + 5
median oar
that is quite important tho
It didn’t need to
lone heartBOT
@cinder sundial Has your question been resolved?
karmic osprey
does anyone know a link or youtube video for solving this?
$$
A=\left[\begin{array}{cc}
\cos \theta & 1-2 \sin \theta \
1+2 \sin \theta & 4 \cos \theta
\end{array}\right]
$$
Find $\operatorname{det}(A)$, prove that for any value of $\theta, A$ is invertible, and then find $A^{-1}$.
(b) Find all the values of $\lambda$ such that $C=\left[\begin{array}{cc}\lambda-2 & -3 \ -5 & \lambda\end{array}\right]$ is singular.
ocean sealBOT
baguette
worn fox
Which part specifically? All you really need to know is how to compute a determinant and how to invert a 2x2 matrix
pallid scarab
What's the formula for the determinant of a 2×2 matrix?
latent drum
Coefficient of x¹¹ in (2x²+x-3)^6
worn fox
There is a formula for the determinant of a 2x2 matrix, look it up
cobalt blaze
lone heartBOT
cobalt blaze
how do i rearrange this make "e0" the subject
i tried a bunch but they all feel wrong
feral raptor
Bro if this is what I'll have to learn in the future, I give up on my future math grades
cobalt blaze
same im like 4 days into class i just don't know how anymore
feral raptor
same im like 4 days into class i just don't know how anymore
My mid-term math grade is 9,6/100 💀
cobalt blaze
Gotta make the academic come back tho 😭
feral raptor
Gotta make the academic come back tho 😭
Let's pray for our academics
lone heartBOT
@cobalt blaze Has your question been resolved?
alpine sable
Guys can someone help me with vectors please?
peak hare
can you multiply both sides by 4πER and then divide both sides by 4πRV
alpine sable
is -ln(x-1) + ln(x+1) = ln(x+1/x-1)
lone heartBOT
is -ln(x-1) + ln(x+1) = ln(x+1/x-1)
alpine sable
because you could rewrite it as ln(x+1) - ln(x-1) right? then its just a log rule
because -4 + 2 = 2 - 4
gray isle
missing a few ()
need to be careful when attempting to combine logs like that
$$\ln(x+1) -\ln(x-1) \tbp \ln\br{\frac{x+1}{x-1}}$$
note that the domains are different. \
e.g the right side is defined when $x=-3$, whereas the left side isn't
ocean sealBOT
ℝam()n()v
lone heartBOT
@alpine sable Has your question been resolved?
alpine sable
hmmm
alpine sable
missing a few ()
need to be careful when attempting to combine logs like that
so how would you go about simplying -ln(x-1) + ln(x+1) then?
gray isle
do nothing
alpine sable
i dont know what i did wrong here but i see the point youre making
gray isle
unless you're told specific restrictions on x
lone heartBOT
lone heartBOT
Available help channel!
winter tide
lone heartBOT
winter tide
I need Help at Question a
lone heartBOT
@winter tide Has your question been resolved?
kind hare
ig now im allowed to ping <@&286206848099549185>
No 2x bridge sorry unity theory
lone heartBOT
@winter tide Has your question been resolved?
winter tide
Noo 
winter tide
No 2x bridge sorry unity theory
what?
lone heartBOT
@winter tide Has your question been resolved?
winter tide
nope :/
cobalt kindle
this server helps with 7 grade?
lone heartBOT
this server helps with 7 grade?
To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.
lone heartBOT
@winter tide Has your question been resolved?
winter tide
this server helps with 7 grade?
ig with all grades except mine XD
lone heartBOT
@winter tide Has your question been resolved?
nimble sequoia
hello chat
lone heartBOT
hello chat
nimble sequoia
so i just need help finding the derivative of 120xsqrtx cuz google aint helping
jagged cobalt
$120x\sqrt{x}$?
ocean sealBOT
AℤØ
jagged cobalt
or $120\sqrt{x}$
ocean sealBOT
AℤØ
jagged cobalt
in either case the fact $\sqrt{x}=x^{\frac{1}{2}}$ will help
ocean sealBOT
AℤØ
jagged cobalt
but...?
nimble sequoia
ok so my answer was sqrtx+180sqrtx but apperently thats wrong and i dont know how
jagged cobalt
im not sure how you did that
nimble sequoia
yeah me neither i think im messing up my product rule
jagged cobalt
ik it goes to 120x^(3/2) because of the exponents
its not product rule if you know this
jagged cobalt
its just plain old power rule
errant yoke
lone heartBOT
errant yoke
sorry fogot to specify
upbeat onyx
You flipped the root 3 and 1 but otherwise it looks good.
errant yoke
i am supposed to label teh side lengths
errant yoke
You flipped the root 3 and 1 but otherwise it looks good.
wdym isnt xroot3 for 60deg angle?
upbeat onyx
Yes.
jagged cobalt
You flipped the root 3 and 1 but otherwise it looks good.
im not sure they did
upbeat onyx
You put it opposite of the 30 deg angle.
upbeat onyx
im not sure they did
I am assuring you they did.
errant yoke
You put it opposite of the 30 deg angle.
pi/3 is a 60 degree angl
errant yoke
im not sure they did
would what i did be correct?
jagged cobalt
errant yoke
it seems to easy to be true
upbeat onyx
I didn't even see the pi/3, I was just going off the 30 they wrote in the angle.
jagged cobalt
ah
errant yoke
I didn't even see the pi/3, I was just going off the 30 they wrote in the angle.
sorry i had corrected it to 60
upbeat onyx
I have extremely bad vision at midnight
errant yoke
I have extremely bad vision at midnight
me too
errant yoke
woudl taht be it?
So for the top two
It would be this?
Give me a sec
The values cired
Circled
@jagged cobalt
upbeat onyx
Can we see the actual instructions at the top?
errant yoke
Can we see the actual instructions at the top?
word for word it is: Label the side lengths of the following right triangles.
upbeat onyx
That's a Ask your Professor type question.
Only your professor can tell you what they exactly wanted.
upbeat onyx
Maybe your teacher hates your handwriting?
Messed up, but I've seen multiple teachers straight up say "If you have bad handwriting, you need to see a counselor or something because you shouldn't be writing like a 6 year old in high school."
They didn't last long, to be fair.
errant yoke
Messed up, but I've seen multiple teachers straight up say "If you have bad hand...
thats a bit much
only seen one case that bad before
but no i just straight up blanked on the question
i neglected that i could convert radians to degrees
.close
lone heartBOT
errant yoke
.done
lone heartBOT
Available help channel!
honest merlin
Can anyone help me with this?
lone heartBOT
Can anyone help me with this?
solemn juniper
!status
lone heartBOT
What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
I have solved it with a>0 but when a<0 I’m literally stuck
solemn juniper
a and b have to have the same sign so it shouldn't be an issue
honest merlin
oh and btw I could only be able to approximate its value but cannot calculate it exactly
honest merlin
i could only approximate it to be bigger than 1.5 so I think the answer is D
honest merlin
I substituted b for [log2(7/3) + 3a] /2
solemn juniper
I'll need you to show your work
You're right to use logs but that seems unnecessary
honest merlin
solemn juniper
,rccw
ocean sealBOT
solemn juniper
It's not $7 \cdot 8^a = 3 \cdot 4^b$
ocean sealBOT
Steakanator
solemn juniper
It's (7.8)^a = (3.4)^b
lone heartBOT
@honest merlin Has your question been resolved?
solemn juniper
no it isn't
honest merlin
anw thanks for your help @solemn juniper
I really appreciate it
I guess I might have to figure out another ways myself
.close
merry meteor
so
merry meteor
can sm1 help
im following the steps to prove subspace
and i dont get why this isnt a subspace
the solution says its not
vapid shuttle
what if c*(x) and c<0
merry meteor
what if c*(x) and c<0
yea i saw
wb this
How do we know that x1+x2 is in the set
and also we are proving closed scalar + closed addition vector at one time here correct?
original question
@vapid shuttle why u leave me on read
😦
i have midterm
tom
.close
molten pivot
How many elements are in the union of all quadratic extensions of GF(5)?
mortal trellis
how many quadratic extensions are there
molten pivot
2, but it's not that simple
like of course 2 and 3 are the non squares in GF(5). but some elements of GF(5)[sqrt(2)] and GF(5)[sqrt(3)] will square to the same number
mortal trellis
do you not know that all finite fields with the same number of elements are isomorphic?
molten pivot
maybe i'm phrasing my question wrong
i just want to count the number of unique square roots. like uh:
sqrt(2)^2= 2sqrt(3)^2 mod 5
they both square to 2
mortal trellis
x and -x square to the same thing
and x^2=c can only have 2 solutions
so thats them
lone heartBOT
@molten pivot Has your question been resolved?
languid sable
I am a self-taught calculus student. Whilst working on the Gamma Function, I am confused as to the different derivatives with respect to each other, such as du/dx, which differentiates u with respect to x, and I am confused on how that works. Additionally, I wish to know about how to integrate with substitution and how to change integral bounds accordingly whilst doing so.
worn fox
I think you need to be more specific with your first point
languid sable
Should I reword it?
worn fox
maybe give an example
Like du/dx is just the derivative of u wrt x its unclear what you want explaining
languid sable
For example, the product law in derivatives, if the pronumeral u was substituted in place of, for example, (3-x^2), the first part of the formula is in the format of v * du/dx. I am confused on how the du/dx stands for and how it works.
mortal trellis
du/dx is the same as u' if you have seen that notation before
worn fox
So u and v are just names you are giving to functions of x
u(x)*v(x) and you're applying the product rule to this product of functions
languid sable
du/dx is the same as u' if you have seen that notation before
I have seen that before. However, what is the x for, and could it not just be d/du if it were referring to the derivative of u?
languid sable
So how would I format a derivative of one variable with respect to another?
vocal heron
So how would I format a derivative of one variable with respect to another?
You mean like d/dx of u² for example?
mortal trellis
this isnt as important now in single variable calculus, but later if you for example have f(x,y)=x^2+3y^3 or something, then you need to somehow make it clear whether you are differentiating with respect to x or y. but that's a topic you will see later
languid sable
this isnt as important now in single variable calculus, but later if you for exa...
So in single variable calculus, the thing that matters is the variable which goes on the bottom and the function being differentiated on the top?
mortal trellis
yes
languid sable
Apologies if I am a little slow, I am 14 and I have a lot to learn. Calculus is simply a hobby of mine :)
But thank you for the explaination, I understand now.
worn fox
Paul's online maths notes are a good resource if you haven't seen them yet
languid sable
Oh? Could you provide a link?
languid sable
Thank you.
worn fox
You can probably jump in at the derivatives section and review the functions section when/if needed
Limits is something worth looking at if you want to know what a derivative really is and its formal definition
misty moat
need help
barren portal
@misty moat
vast burrow
Yes seems right
barren portal
For 1) you just have to evaluate P(20) as you did
misty moat
yes?
barren portal
For 2) compute P’(20)
misty moat
do you know the answer to this?
vast burrow
Do you know quotient rule?
misty moat
yeah
vast burrow
Yes use that
vast burrow
Oh so diffrentiate the bottom part what do you get?
And diffrentiate the top part aswell
You get 3x^2 and 30x(6x-7)^4
Now just use quotient rule
misty moat
i did
i dont know how to do it
i didnt get any of the answers
ive got this
this is not 1 of the answers
vast burrow
A
cinder sundial
lone heartBOT
cinder sundial
That means the difference of all a-b where the range of a as well as b goes from 1 to 6
cinder sundial
That means the difference of all a-b where the range of a as well as b goes from...
Is it what it means?
flint shoal
p much. fix one a/b, compute the difference for every other b/a (respectively) in the range of this other summation index
so for example, for each value of a, there are 6 things to calculate (one for each b)
lone heartBOT
@cinder sundial Has your question been resolved?
cinder sundial
p much. fix one a/b, compute the difference for every other b/a (respectively) i...
a/b, b/a??? What are they?
zealous lichen
I think the slash means or
cinder sundial
p much. fix one a/b, compute the difference for every other b/a (respectively) i...
That “pretty much” adds some uncertainty to your answer
cinder sundial
That means the difference of all a-b where the range of a as well as b goes from...
I suppose my understanding is either correct or incorrect?
cinder sundial
Or is there any other ways to look at it
lone heartBOT
@cinder sundial Has your question been resolved?
lone heartBOT
@cinder sundial Has your question been resolved?
vestal pilot
Ordinary Differential Equations
vestal pilot
I'm not sure why they do what they do between 10-12
They multiply the equation by the integrating factor mu(t), but they they want the left side to be the derivative of the product mu(t)y?
@ me if anyone answers 🙏
plucky sluice
@vestal pilot (11) is just the product rule. Then they look at the rhs of (11) and the lhs (10) with the idea to find some function $\mu(t)$ that will work in both cases
ocean sealBOT
Xenophon
plucky sluice
If you set the rhs (11) equal to the lhs(10) you get (12)
Now they try to solve that equation, which is a differental equation
vestal pilot
Yeah I'm just not sure why they decided to take the rhs of 11 and the lhs of 10. Like what made them say "we should put those together"?
plucky sluice
Well, it could be that no function matches both of those, which would be sad
But if you can find such a function, then you can solve the original differential equation
Notice that the lhs of (11) is of the form d/dt(something)
If d/dt(something) = some function of t, then you can integrate directly
It's not like it's necessarily easy to think of this idea just by looking at the ode
But once you have the idea, you check that it works (which it does)
vestal pilot
I'm missing something
Like I don't really get the entire point of why we're actually multiplying by the integral factor mu(t)
plucky sluice
Mhmm, the point is to turn an ode into an integral problem
vestal pilot
Because the ODE can't be integrated without it?
plucky sluice
Yes
Well, any method that does integrate it is a generalization of the integrating factor
Or a special case
plucky sluice
Yes, because we choose mu(t) to satisfy (11)
plucky sluice
I should say satisfy (11) AND (10)
(10) makes mu(t) specific to the ode in question and (11) ensures that we can then solve the ode
I think the key insight is to look at the lhs of a linear, first order ode, and notice that its structure is similar to the identity from the product rule
i.e. that's just the derivative of another function with the form y*mu(t)
vestal pilot
Yeah, I saw that
plucky sluice
Buuut, I will say that there are a lot of things in math that are not easy to come up with in a vacuum but have been proven to work
vestal pilot
mfw I got like 80+ on this course all while not actually knowing what the hell is going on lol
plucky sluice
Some really smart guys in 18th century tried everything for decades and found stuff like this
vestal pilot
but it was a year ago, and I've got PDE coming up, so I'm going over it again
why couldn't they invent it simpler
plucky sluice
lol
vestal pilot
well, thanks for the help
plucky sluice
np
vestal pilot
Do you maybe know what they did between 15 and 16?
@plucky sluice sorry for the ping btw 🙏
obtuse mango
Hello!
obtuse mango
I do not understand why z cannot be between 1 and -2i
A bit of help would be great, thanks!
nvm I did it myself. This chat's hopeless
.close
little spear
lone heartBOT
fickle sandal
fallen verge
Is this an ad?
dim oasis
Definitely not a math question
fallen verge
<@&268886789983436800> ad i think
real gazelle
wdym this seems like a totally legit question
fallen verge
ah of course, ahat a lapse i my judgment
it must be my mistake because i cannot spell so clearly i cannot discern a question from an ad
real gazelle
Smh you helpers just slacking on your job
dim oasis
,w will brainy give me all the answers?
real gazelle
Want excuses to not help people
ocean sealBOT
Requested by lexitorius
real gazelle
.close
regal surge
Hi! I'm stuck on this math question from homework and I don't understand how to do it. I thought maybe I was supposed to complete the square, but that does not give me the right answer.
According to the textbook, the answer is x = 0.15, 1.02, 2.12, or 2.99
Any help is appreciated :')
cinder sundial
Hi! I'm stuck on this math question from homework and I don't understand how to ...
The common way to solve it is by substitution
For example, by substitute the sinX by t
fickle sandal
Hi! I'm stuck on this math question from homework and I don't understand how to ...
how many solutions did you get out of completing the square
mellow grail
For example, by substitute the sinX by t
*correct english is substitute sin x = t
regal surge
how many solutions did you get out of completing the square
I'm redoing it right now because I think I did it wrong 😭 hold on
regal surge
For example, by substitute the sinX by t
I did do that which gave me 8a^2 - 8a + 1 = 0
but it doesn't factor nicely
cinder sundial
*correct english is substitute sin x = t
Thank you
coral flower
I did do that which gave me 8a^2 - 8a + 1 = 0
u cant factor , use quadratic formula or completing square
fickle sandal
a=sinx, not sinx=0
mellow grail
also u can simplify your vaue for x
fickle sandal
*a, not even x
coral flower
a*
coral flower
sinx = a
sinx = (2+- sqrt 2) / 4
coral flower
sinx = (2+sqrt2)/4 , sinx = (2-sqrt2)/4
regal surge
OH I GOT IT :D
coral flower
yeah sinv inverse both sides for value of x
regal surge
wait but
I only got 1.022 and 0.15
how did the textbook get 4 answers? 😭
they also got 2.12
and 2.29
oh is it pi subtract the first two values I got
coral flower
this is cuz x lies between 0 and 2pi , sinx is positive which means it is either in 1st quadrant or 2nd aka 4 values
coral flower
the command is very sensitive