silent gulch
Helpers
#help-23
vapid folio
zinc moat
can someone explain to me how to do this im really bad at graphs
lean otter
can someone explain to me how to do this im really bad at graphs
What does a limit mean to you?
zinc moat
a point where its not on the graph or a hole on the graph
i just cant get c i tried DNE -9, and 7
chilly lance
c is dne lol
zinc moat
let me try it again
steep plover
A state Senate has 230 Senators. On Wednesday several senators were absent due to the business trips. On thursday at the number of Senators asked to illness was five more than the number of absent ones on Wednesday. On Friday three Senators who are ill and absent on Thursday returned. 188 senators were present on Friday. How many senators were absent on Wednesday?
safe radishBOT
A state Senate has 230 Senators. On Wednesday several senators were absent due t...
@steep plover Has your question been resolved?
safe radishBOT
@steep plover Has your question been resolved?
safe radishBOT
@steep plover Has your question been resolved?
dull cliff
Discrete Math 7b and 7d
safe radishBOT
Discrete Math 7b and 7d
dull cliff
quick question: can i just say that for b, "for all comedians they are funny" and for d "there exists a comedian and they are funny
or would i have to write "for all people, they are comedians and they are funny"?
safe radishBOT
@dull cliff Has your question been resolved?
dull cliff
.close
stone tendon
The goal is to rotate (1,4) by 50 degrees, and I started but I'm not sure if this is the right path/what to do next
safe radishBOT
The goal is to rotate (1,4) by 50 degrees, and I started but I'm not sure if thi...
lean otter
The goal is to rotate (1,4) by 50 degrees, and I started but I'm not sure if thi...
Can't see the image
stone tendon
how do i share it without it being a donwload
lean otter
use a regular image format
lean otter
Do you have to use linear algebra?
stone tendon
yes
i think i figured it out tho
dont i just multjply it by 1,4 in a matrix representation
and then just add the values to get a 2x1 matrix
and thats my x and y
lost patrol
Why are you using a 2x2 matrix to write the coordinates 
stone tendon
the correct line is the bottom one
the left one is the rotation matrix, and the right one would be (1,4)
stone tendon
wdym
stone tendon
thats why im confused
lost patrol
$\begin{bmatrix}x'\ y'\end{bmatrix}=\begin{bmatrix}\cos \theta & -\sin \theta \ \sin \theta & \cos \theta\end{bmatrix}\begin{bmatrix}x\ y\end{bmatrix}$
flat frigateBOT
stone tendon
yes
lost patrol
This is the format you gonna be using for rotations.
So well
X' and y' are the rotated coordinates
lost patrol
You just put in values on the rhs
lost patrol
Also check your matrix multiplication it seems faulty
agile stream
me no undertsand on how to approach or do this wizardry
safe radishBOT
me no undertsand on how to approach or do this wizardry
quiet plume
Well you have a polynomial and the table gives you three roots of the polynomial
So you can write it as a*x(x+2)(x-1)
Where a is some value
Then you can plug in a non zero value from the table to find a
worthy hemlock
You can do that way, but the slightly easier way, is that it's multiple choice, just plug in one or the of the x values, like -3 and 2, into each choice, and see which equation gives the proper y value
agile stream
You can do that way, but the slightly easier way, is that it's multiple choice, ...
i dont know whats the y value
worthy hemlock
The table
If you plug in -3 and get -24, from one of those equations, you found the choice
safe radishBOT
worthy hemlock
Btw if you find multiple choices that results in -24 when you plug in -3, plug in a different x value
safe radishBOT
Available help channel!
zinc moat
im not sure which one is wrong
zinc moat
.close
dusty bramble
safe radishBOT
dusty bramble
need help on where to start and finish
dull sequoia
do you know what b is?
dusty bramble
i don’t
dull sequoia
do you know what this P (X < x) notation means?
dusty bramble
is it 0.9634
dull sequoia
im asking about the notation
dull sequoia
probability of what
dusty bramble
that a variable falls between 0.9634?
dull sequoia
forget the 0.9634
dusty bramble
😭
dull sequoia
do you know what this P (X < x) notation means?
im asking this
if you want to answer the question you need to understand what it's asking
dusty bramble
it just means that a variable falls between b and -b
dusty bramble
right so in this case would it be the 0.9634
dull sequoia
or more formally we can define it as $P(X<x)=\int_{-\infty}^xf_X(t), dt$
flat frigateBOT
Frosst
dusty bramble
right
dull sequoia
so for the question
they are scuffed because they used small x to represent an RV
which is not convention
we normally like to use capital letters for random variables
it'd be nicer if they wrote P(-b < X < b) = bla bla bla
dusty bramble
right cuz i’m confused
dull sequoia
**Frosst**
you see how here we have small x
they used b for small x
and small x for big x
so they've done
$P(x<b)=\int_{-\infty}^bf_x(t), dt$
dusty bramble
i see i see
flat frigateBOT
Frosst
dull sequoia
which is scuffed because by convention we like capital letters
but whatever that is their choice
so for the question $P(-b<x<b)$
flat frigateBOT
Frosst
dull sequoia
we have $P(-b<x<b)=\int_{-b}^bf_x(t), dt$
flat frigateBOT
Frosst
dull sequoia
we know what f_x(t) is
$x \sim N(0, 1)$ meaning that $f_x(t)=\frac{1}{\sqrt{2\pi}}e^{-\frac{1}{2}t^2}$
flat frigateBOT
Frosst
dusty bramble
wtfff😭
dull sequoia
have you not seen this before
dusty bramble
not what i expected
a little bit
it’s my first couple days working on these types of problems
dull sequoia
tell me what you dont understand
dusty bramble
on my own
dull sequoia
that's ok
dusty bramble
i understand but i don’t get where the (0,1) is from
flat frigateBOT
Frosst
dusty bramble
yes
dusty bramble
i think i can
dull sequoia
ok go ahead
dusty bramble
doesn’t it mean distribution
dusty bramble
mean and variance
dull sequoia
of X
right
ok
great
let's look at the question
it is a NORMAL distribution
with MEAN 0 and STANDARD DEVIATION of 1
and we know that std dev = √var
so std dev of 1 means var = 1
so then X ~ N(0, 1)
i've just plugged in the values given in the question
dull sequoia
it all makes sense you just have to go step by step and understand what oyu're looking at
going back to this then
dusty bramble
that’s true
dull sequoia
do you understand the second part?
dusty bramble
yes
dull sequoia
that's just the pdf but i've plugged in the parameters of mean = 0 and var = 1
ok so then our problem is now this
$P(-b<x<b)=\int_{-b}^bf_x(t), dt = \int_{-b}^b\frac{1}{\sqrt{2\pi}}e^{-\frac{1}{2}t^2}, dt$
flat frigateBOT
Frosst
dull sequoia
agree?
dusty bramble
yes
dull sequoia
ok good news and bad news
bad news is
we cant solve this analytically
it has no closed form
😦
good news, we have z tables!
dusty bramble
i see i see
dull sequoia
ok but first we want to recognise something as well
do you notice anything interesting about f_x(t)
something that's useful for evaluating integrals going from -b to b
dusty bramble
i don’t think so
dull sequoia
Hmm do you know about odd and even functions?
dusty bramble
i might think so
flat frigateBOT
Frosst
dull sequoia
how would you do this?
dusty bramble
that’s where i’m stuck
dull sequoia
,w graph sinx from -pi/2 to pi/2
flat frigateBOT
dusty bramble
probably cuz the negative and positive
dusty bramble
yes
dull sequoia
and odd functions have a very good property for integration
dusty bramble
yes
dull sequoia
if $f(-x) = -f(x)$ then $\int_{-a}^af(x), dx = \int_{-a}^0f(x), dx + \int_0^af(x), dx=-\int_{0}^{a}f(x), dx + \int_0^af(x), dx= 0$
flat frigateBOT
Frosst
dull sequoia
hmm that's a bit wack
dull sequoia
anyhow the point is that f(t) that you have is an even function
dusty bramble
right okay i had this written down from earlier when i tried
but anyways i think i understand what you saying
we’re
dull sequoia
**Frosst**
the manipulations we want to make at this point is that
dusty bramble
were
dull sequoia
$\int_{-\infty}^a f_x(t), dt$
flat frigateBOT
Frosst
dull sequoia
this is what's on the z tables
so we need to transform $\int_{-b}^b\frac{1}{\sqrt{2\pi}}e^{-\frac{1}{2}t^2}, dt$ into that
flat frigateBOT
Frosst
dull sequoia
first thing is that this is an even function
dusty bramble
yes?
dull sequoia
$\int_{-b}^b\frac{1}{\sqrt{2\pi}}e^{-\frac{1}{2}t^2}, dt=2\int_0^b\frac{1}{\sqrt{2\pi}}e^{-\frac{1}{2}t^2}, dt$
flat frigateBOT
Frosst
dull sequoia
and then we observe that the integral from -inf to inf is 1
and it's symmetric about x = 0
which means the integral from -inf to 0 is 0.5
dusty bramble
i see i see
dull sequoia
then we can simply write it as $\int_{-\infty}^{-b}f_x(t), dt + \int_{-b}^0f_x(t), dt = 0.5$
flat frigateBOT
Frosst
dull sequoia
then by simply rearranging the integrals we have
$\int_0^bf_x(t), dt = \int_{-b}^0f_x(t), dt = 0.5- \int_{-\infty}^{-b}f_x(t), dt$
flat frigateBOT
Frosst
dusty bramble
that makes sense
dull sequoia
if we just multiply this by 2 we can get the left hand side we want
dull sequoia
**Frosst**
remember we want 2 of the integrals from 0 to b
dull sequoia
**Frosst**
this gives us 1 of them from 0 to b
so the answer is simply $2\left(0.5- \int_{-\infty}^{-b}f_x(t), dt\right)$
flat frigateBOT
Frosst
dull sequoia
as in this is equal to 0.9634
then just rearrange to get the integral by itself
then look at the z-table
dusty bramble
hmmmm
dull sequoia
let me draw you something
dusty bramble
would it be 1.94
dull sequoia
would it be 1.94
that sounds much more plausible
dusty bramble
this makes sense
dull sequoia
that's good
dusty bramble
i don’t think i got the right answer
dull sequoia
,w P(X<k)=0.0183
flat frigateBOT
Requested by frosst
dull sequoia
,w P(Z<k)=0.0183
flat frigateBOT
flat frigateBOT
dull sequoia
would it be 1.94
how did you get 1.94
dusty bramble
😭i don’t know at this point i’ll probably get back to this tomorrow but i appreciate ur help and i’m screenshotting what you sent for help
.close
coarse heron
hey is any one on?
safe radishBOT
hey is any one on?
coarse heron
I needed help with a question in discrete math
pine pine
how discrete
plucky elk
I needed help with a question in discrete math
coarse heron
I have this question, is it possible to prove this statement true or false formaly?
Like with some actual supposition etc to prove that this is true
stoic dune
People normally define "prime" as "not composite", no?
coarse heron
prime and composite are the opposite in a sense
sure
prime is number x whose multiple are either itself or 1
that means a number x that can only be divided by x or 1
composite number y is a number which has more more than one multiples z, p such that z * p = y
informaly 14 would be composite
15 would be compsite as well
since u can do 3 * 5
but 3 is prime
5 is also prime
because there is not any two integers that can be multiplied to produce 5
other than 1 and 5 itself
untold inlet
I mean really 1 is the only integer that would be considered not a prime nor composite, so the statement is incorrect (also depends on your institutions definitions)
@coarse heron
coarse heron
Oh I see okay i was thinking about the same thing
but like is it possible to prove it tho?
the question in my homework is just true/false question but i wanna know if it'd be possible to prove it
untold inlet
I mean you can prove it via contradiction
assume there exists some integer n which is both a prime and a composite => state the definitions of prime and composite numbers => a number must either be a composite number or prime number => contradiction
coarse heron
assume there exists some integer n which is both a prime and a composite => stat...
here u said either
would it be 'and' ?
like assume there is a integer n such that n > 1 which is neither composite nor prime
then state definitonns
even with definition how would we prove it
untold inlet
why would it be and?
untold inlet
in order for a number to be prime it must have only exactly 2 divisors (itself and 1), in order for a number to composite then it must have more than 2 divisors, so you can't have a number that has exactly 2 divisiors but also more than 2 divisors it doesnt make sense
untold inlet
well, yea 15 has 4 total factors
coarse heron
in order for a number to be prime it must have only exactly 2 divisors (itself a...
I see, so this is how we would be able to define it
untold inlet
pre much, you can formalise it a bit more but thats essentially the definition
coarse heron
I see, lol idk why but I can understand it informally/intuitively but not like formally etc
idk how
thnx for explaining tho
untold inlet
Writing formal proofs comes with experience, its completely normal. All I can say is practice and you'll get the hang of it
coarse heron
I see, but understanding wise is that how usually students feel or something wrong w me lol
untold inlet
Nothing is wrong with you, its very common to have difficulty translating your thoughts into coherent proofs
coarse heron
I see, but like what is is it that initially makes it hard to translate it into coherent proofs, from ur xp
xp/understanding
untold inlet
lack of experience, school's not teaching correct notation.
also high school's based on doing not understanding so theres that
coarse heron
I see, is it that most us atleast initially don't have clear deep understanding through definitions
like we know how 1 + 1 = 2
cuz 1 apple + 1 apple = 2 apples
but we're not quite taught the 'why' of it
untold inlet
yea precisely, but like i said the more you do the better you become, math is just practice practice practice
final rain
is this right
safe radishBOT
is this right
final rain
.close
quartz ridge
safe radishBOT
dapper venture
!status
safe radishBOT
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
idk where to begin
dapper venture
let's write everything in equations first
quartz ridge
let's write everything in equations first
how
dapper venture
the question told you the length of fences
and the pen is rectangular
also we want area
Try to put these into equations
quartz ridge
the question told you the length of fences
we dont know if the house is the length or width tho right
dapper venture
yea
you can set the length of fence on opposite side of house wall be x
the other two sides be y
quartz ridge
the other two sides be y
?
quartz ridge
form a equation of the sides of the fenc
2y + x = 60
quartz ridge
have you learnt differentiation
isnt length * width area
dapper venture
yes
dapper venture
yes
quartz ridge
ok so now what
dapper venture
have you learnt differentiation
^
dapper venture
a part of calculus
dapper venture
ok
quartz ridge
do i needa know that to solve this
dapper venture
we have a simpler way
quartz ridge
what does maximize mean
dapper venture
find the highest possible value of y(60-2y)
maybe you are more familiar with the vertex
dapper venture
find the y value of the vertex
quartz ridge
find the y value of the vertex
how
dapper venture
you have a quadratic equation area = y(60-2y)
if we change the notation a bit it's equivalent to y=x(60-2x)
quartz ridge
if we change the notation a bit it's equivalent to y=x(60-2x)
how did u get that
tho
quartz ridge
Area = y(60-2y)
do we just set area to 0 and solve
dapper venture
no
we're not looking for roots
but vertex
how familiar are you with quadratics
quartz ridge
ya
quartz ridge
how familiar are you with quadratics
decently
dapper venture
then it shouldn't be hard to find the vertex
quartz ridge
then it shouldn't be hard to find the vertex
how do u find it
dapper venture
you can either turn the quadratic into vertex form
or use the roots to find the vertex
or just memorize the vertex formula
dapper venture
complete the square
quartz ridge
is that the fastest way to do it
dapper venture
no
quartz ridge
or is the roots faster
dapper venture
let's use the roots
dapper venture
yes first find the roots
since parabola are symmetric, the x value of vertex would be the mid point of the roots
quartz ridge
(0,0) right
dapper venture
what's the other root
quartz ridge
what's the other root
so aos would be 15
dapper venture
that's the x value of vertex
quartz ridge
ya
dapper venture
we want the y value
quartz ridge
and u just plug back in
quartz ridge
15 would be the length of shorter side of fence
how do u know that
dapper venture
remember how we got our quadratic?
we wrote area in terms of length of shorter side of fence
dapper venture
correct
dapper venture
no problem
quartz ridge
oh wait the answer is 450 cus its asking for area
mellow mountain
need help on 10
safe radishBOT
need help on 10
mellow mountain
10th grade math
thin bridge
did you do Q9?
mellow mountain
i know that the y=mx+b equation comes to y = 5x -6, so the perpendicular slope is -1/5. plugging -4 = -1/5(-10) + b, b comes to -6
mellow mountain
did you do Q9?
yes, got it correct
yes i nkow i do it the same way
its the numbers that trip me up
thin bridge
there's a more efficient formula that gives you the distance directly
mellow mountain
there's a more efficient formula that gives you the distance directly
would a 10th grader be expected to know it?
mellow mountain
i know that the y=mx+b equation comes to y = 5x -6, so the perpendicular slope i...
now 5x - 6 = -1/5x - 6, simplifies to x=0
thin bridge
it may have been taught to you if given this type of question
mellow mountain
it may have been taught to you if given this type of question
what is it
i might not be remembering it atm
thin bridge
look up perpendicular distance from point to a line
mellow mountain
look up perpendicular distance from point to a line
looked at it, 100% sure i havent been taught it in class, teacher wont accept that work if i used it
thin bridge
ok.
mellow mountain
unfortunately i have to do the long way round
thin bridge
take a pic of your work
its a bit hard to read it like this
mellow mountain
take a pic of your work
its a bit hard to read it like this
my work is even harder to read
neever mind
i ended up solving
.close
safe radishBOT
safe radishBOT
Available help channel!
sonic night
help
sonic night
Can anyone help me find the global minmimum of
i found the global maximum
but cant seem to show the global minimum
dapper venture
what's the minimum value you can get from a square root
safe radishBOT
@sonic night Has your question been resolved?
sonic night
what's the minimum value you can get from a square root
sorry didnt get a notification thank you
humble maple
I need help with how to find the 2 blanks
safe radishBOT
I need help with how to find the 2 blanks
little mesa
can you show your working
humble maple
figured it out, thanks though
safe radishBOT
Available help channel!
viscid tartan
safe radishBOT
safe radishBOT
Show your work, and if possible, explain where you are stuck.
viscid tartan
Ok
One sec
I did the case where b < 0 , to get the result but don't think I can do that since both a and b are just integers
peak estuary
y=1 and x=1 is not the only solution to a+b=ax+by
for example a=2, b=3 then you also have 5=4*2-3
instead, try pluggin (1) into (2)
viscid tartan
Hmm I see alright thanks will try
I get a= a(xy) , showing that a is a factor of itself
Ig comparing it to (2) it shows a =b xy= y , but not sure where to go
peak estuary
a=axy implies xy=1
i.e. x and y are integers which multiply to 1
which options are there for what x and y can be
viscid tartan
Ayyy I see , didn't catch that , then we have 1,1 and -1,-1 for y
Then subbing in we get the answer , thanks for making me go through the steps
Thanks
peak estuary
you're welcome
safe radishBOT
@viscid tartan Has your question been resolved?
winter kernel
Not able to solve factorization question
safe radishBOT
Not able to solve factorization question
winter kernel
Just give me some hints, and I'm sorry for making you solve this
also post answer in spoilers I'll check after an hour
quasi bison
$5t^2 + 6t - 8$
factorize this
flat frigateBOT
Ann
quasi bison
also post answer in spoilers I'll check after an hour
we don't do that here
winter kernel
we don't do that here
oh, ok 👍
winter kernel
$5t^2 + 6t - 8$
factorize this
ok should I try this then?
safe radishBOT
hoi
To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.
flat frigateBOT
sim
winter kernel
I tried factorizing via bot lol
little mesa
do it yourself kek
quasi bison
$5t^2 + 6t - 8$
factorize this
this was my hint to you
winter kernel
$5t^2 + 6t - 8$
factorize this
(5t-4)(t+2)
that was just simple split the term tho?
the question I asked was wayy harder
real iris
You can sub in t as 3x+y
winter kernel
hmm
quasi bison
the question I asked was wayy harder
my whole point was that it is not
safe radishBOT
safe radishBOT
Available help channel!
lean otter
safe radishBOT
lean otter
I do not understand this intuitively
I sort of get why number of 5s = numbers of 10s
So if I understand correctly
if we take 100
we can divide by 5
divide by 25
hence 2 0s
and for 1000 for example, it is divisbe by 5,25,125 but not 625, hence only 3 0s
grim plover
lean otter
thanks
@grim plover yes I understand the process
but I don't understnad why
why is it that for $1000 \cdot 999 \cdot 998 ...$ we can just look at 1000
and ignore the rest
flat frigateBOT
Mushaar
thin bridge
dividing 1000 by 5 tells you the multiples of 5 between 1 and 1000 inclusive
dividing 1000 by 25 tells you the multiples of 25 between 1 and 1000 inclusive (since 25=5^2, these will contribute another 0 to the product)
etc
lean otter
dividing 1000 by 5 tells you the multiples of 5 between 1 and 1000 inclusive
div...
i don't really understand
thin bridge
which part
thin bridge
wdym in 999
lean otter
dividing 1000 by 5 tells you the multiples of 5 between 1 and 1000 inclusive
div...
like overe here you said 1000 by 5 tells you multiples of 5 for a number between 1 and 1000 inclusive, 999 is in between
so there 1000/5 tells you multiples of 5 for 999 if my reading comprehension isn't failing
thin bridge
why are you considering the difference here
lets use a smaller example like multiples of 5 between 1 and 15 inclusive
lean otter
ah I see
thin bridge
starting from 1, and 15 being a multiple of 5,
15/5 gets you the number of multiples of 5
5,10,15
lean otter
so you were saying that dividing 1000 by 5 tells you all the multiples of 5 from 1 to 1000
thin bridge
yes
thin bridge
we're not
each factor of 5 in the prime factorisation will contribute to a trailing 0 in the product
lean otter
so if we have 1000 * 999 * 998 * 997 * 996 * 995, etc, 200 of those numbers are divisble by 5
thin bridge
yes
lean otter
ok and then for 975, it is also divisibley by 25
thin bridge
don't forget the 1000
lean otter
so we need add 1
thin bridge
1000 is also divisible by 25
lean otter
don't forget the 1000
oh right, that's my bad
thin bridge
yes, each multiple of 25 will contribute (at least) one more 0
similar with 5^3
etc
manic path
I have a question, when you differentiate tan(x) you get sec^2(x)
manic path
but when you differentiate sec^2(x), why do you get 2sec^2(x)tan(x)?
is it because of that power of 2?
peak estuary
what do you mean with why. you just do
what does it have to do with sec^2 being the derivative of tan
manic path
because my logic says when you differeniate sec^2(x) =tan(x)
peak estuary
why should that hold
manic path
because like differentiation of sin(x) is cos(x)
peak estuary
yes but tan and sec are not sin and cos
manic path
so its just like that
you have to use... chain rule for sec^2(x)
and same applies for when you intergrate right
peak estuary
yes
well you could also use product rule or quotient rule to diff sec^2. but same result anyway
lost patrol
Integration is the inverse process of differentiation, kinda
peak estuary
are you confused about the +c?
manic path
no
lost patrol
kinda: family of curves
manic path
ok how I imagine intergration and differentiation is like levels on a building
so you go up its intergration go down is differentiation
I can't comprehend how intergration sec^2(x) is tanx + c
peak estuary
well from tanx going down is sec^2
thin bridge
because differentiating tan(x) gives sec^2(x)
peak estuary
so going up gives tanx. but going up also always gives the +c
manic path
just to be clear
frigid locust
but when you differentiate sec^2(x), why do you get 2sec^2(x)tan(x)?
isnt that wrong though?
manic path
isnt that wrong though?
no its right
frigid locust
differentiating sec^2(x) gives 2sec^2x secxtanx
cuz derivative of secx is not tan x, its secxtanx
nvm im wrong , i forgot how power rule works
manic path
just to be clear
if we derive all the way down, there is nothing saying it should repeat on itself right
peak estuary
yes
manic path
oh
peak estuary
only for very few functions it repeats
for most functions it tends to get very complicated
manic path
huh, I kind of assumed since cos and sin do that they ALL do that
guess not
welp thanks for the clarification
.close
supple rover
can anybody help me with this question?
safe radishBOT
can anybody help me with this question?
safe radishBOT
@supple rover Has your question been resolved?
supple rover
channel occupied
safe radishBOT
@supple rover Has your question been resolved?
safe radishBOT
@supple rover Has your question been resolved?
quaint vault
I don’t know what this problem is asking me
safe radishBOT
I don’t know what this problem is asking me
urban eagle
Differentiate it with respect to x and then plug in that value
safe radishBOT
safe radishBOT
Available help channel!
burnt nest
An algorithm that needs no inputs is : ambiguous?
safe radishBOT
An algorithm that needs no inputs is : ambiguous?
peak estuary
can you give context
safe radishBOT
@burnt nest Has your question been resolved?
burnt nest
Hmm , they give us question and some options. Without algorithm 🥹
Ambiguous
General
No general
No ambiguous
All previous answers
This is the options
@peak estuary
An algorithm that needs no inputs is :
This is the question
burnt nest
.close
cerulean tusk
So in this I have differentiated with chain rule to get the answer at the end, however, the mark scheme shows something completely different and I dont understand how they got there
safe radishBOT
So in this I have differentiated with chain rule to get the answer at the end, h...
safe radishBOT
@cerulean tusk Has your question been resolved?
safe radishBOT
@cerulean tusk Has your question been resolved?
safe radishBOT
@cerulean tusk Has your question been resolved?
idle grove
what is going on here, there is not even a single question in the picture
hallow elk
lean otter
I am very confused by this practice SAT question
safe radishBOT
I am very confused by this practice SAT question
lean otter
I simply am choosing the first one because if a is 29 then it doesn't fullfil a>30?
but if someone could show a process or walk me through the process of arriving tot he correct answer that would be great
granite idol
I think it's asking you to solve for x
so III would be x=29. is that the correct interpretation?
so your answer is not right
safe radishBOT
@lean otter Has your question been resolved?
lean otter
so III would be x=29. is that the correct interpretation?
I don't know
that is what I am asking
graceful imp
I am very confused by this practice SAT question
Put it into the desmos calculator
And set a range of a
So its like 31≤a≤10000 or something
Then just play around
U will see that a+1 is a solution and 29
I think idk i did it like 15 min ago
safe radishBOT
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karmic garden
why do they IGNORE the 2+ and 2- when finding out what k (the constant) is in this problem
safe radishBOT
why do they IGNORE the 2+ and 2- when finding out what k (the constant) is in th...
karmic garden
ik how to do the math but i just don't understand why they're ignoring it and j setting whatever is in the sqrt = to 0
little mesa
if the square root =0, then 2+() and 2-() are the same solution
that's what you want for there to be only one solution
These two values are equal and represent exactly one solution when sqrt(8-k/5)=0
karmic garden
okay
but i don't get why they took the 2's out
in the first place
when x = 0 we have one solution
that's what ik ab these problems
thin bridge
when the root and/or stuff under the root is 0, you'll have one solution
safe radishBOT
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amber geyser
i got 55
amber geyser
am i correct ?
solar needle
do you prove this with induction
safe radishBOT
do you prove this with induction
solar needle
whats the proof method?
solar needle
that's show that it'll be true for integers
thats a good point
i wouldnt have thought of that
solar needle
it says no calculus
thin bridge
ok, simplify and solve the quadratic inequality
eager dock
hi
solar needle
ok, simplify and solve the quadratic inequality
i get 1 +3x +3x^2 + x^3 >= 1 + 3x
then x^2(3 + x) >= 0
is this then proof by cases sorta deal
solar needle
ok, simplify and solve the quadratic inequality
is this one inductive?
like i imagine thats a way more difficult inequality to work with
oh u need the. binomial theorem
i forgot about this
safe radishBOT
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Available help channel!
wise schooner
safe radishBOT
wise schooner
wouldn't I need to divide matrices here? how do I do this
safe radishBOT
@wise schooner Has your question been resolved?
sage shore
We don't really have "division" of matrices, like real numbers
What we have is, multiplication by inverse
it's kinda the division in the matrices world
So, when you have matrices A, B, and C such that: BA=C
What you want to do is, multiply both sides by the inverse of B
On the left
$$B , A = C$$
$$B^{-1} , B , A = B^{-1} , C$$
flat frigateBOT
Luna
wise schooner
right, so B and B inverse cancel out right
sage shore
Yes, they become the identity matrix
Disappears
And you're left with
$$A = B^{-1} , C$$
flat frigateBOT
Luna
wise schooner
ok another question, how do I know if I do B^-1 * C or C * B^-1
flat frigateBOT
Luna
sage shore
imagine if you multiplied by the inverse of B ON THE RIGHT
$$B , A , B^{-1} = C , B^{-1}$$
flat frigateBOT
Luna
sage shore
What would happen now?
Nothing!
No cancellation
And therefore, you can't get the A
wise schooner
makes sense, thanks.
sage shore
Multiplication in this case must be on the left
sage shore
makes sense, thanks.
You're welcome
wise schooner
btw is there like a shortcut to finding the inverse of a matrix
or do I just have to augment it with the identity matrix until I get it to reduced row echelon form
flat frigateBOT
Luna
sage shore
$$A^{-1}=\frac{1}{det(A)} , \begin{pmatrix} d ,,,,,,, -b \ -c ,,,,,,, a \end{pmatrix}$$
flat frigateBOT
Luna
sage shore
Basically, you swap a and d
And negate b and c
And as always, divide by the determinant
sage shore
or do I just have to augment it with the identity matrix until I get it to reduc...
But for 3x3 matrices, you can either do that
Or you can use the adjoint matrix method
You find the cofactor matrix, then the adjoint matrix, and then the inverse
i prefer this myself!
wise schooner
is it faster?
sage shore
i mean, the first times, it will look slow and complicated
but with practice, yes, definitely faster for me!
it's so tedious for me to transform random matrices into indentity
wise schooner
yeah it takes me like half an hour 🤣
sage shore
😂
The matrix in the exercise does not look very random
i mean, only 2 and 1
Try rref
wise schooner
aight will try it now
sage shore
i gotta go @wise schooner
wise schooner
aight its all good im nearly done I think I've figured it out
sage shore
i won't be here to check whether what you will find will be correct or not
The inverse is
1.5 2 1
2 3 1
1 1 0
You should be finding this
Otherwise, you're wrong somewhere
And don't forget to multiply too 😛
wise schooner
ty
safe radishBOT
@wise schooner Has your question been resolved?
fleet pine
can someone explain this to me? how do you determine what numbers will be on the integral
safe radishBOT
can someone explain this to me? how do you determine what numbers will be on the...
plucky elk
can someone explain this to me? how do you determine what numbers will be on the...
a=0 and b=2
The question is a template for multiple problems. There are more you're not showing after a)
plucky elk
Yes these are the multiple problems I was talking about
plucky elk
Yes
They use symmetry
Oh
It's a typo
Or no
Not a typo
Total area is different from integral
Integral is signed area
fleet pine
yea
plucky elk
So they took -(negative integral) to get +
plucky elk
What about it
fleet pine
how and why did they get to 0 and 1
plucky elk
Integral is signed area
.
plucky elk
So they took -(negative integral) to get +
Figure out where the function is negative
fleet pine
is it possible to do that without graphing?
fleet pine
do you mean like x-1>0
plucky elk
What part of that is confusing
fleet pine
why are there 3 parts
and how did they get those numbers
when i plug in the integrals i dont get that
plucky elk
What do you get for the x=0 endpoint
plucky elk
when i plug in the integrals i dont get that
Do you mean endpoints
fleet pine
i get 0, right?
i think so
idk my english is not very great when it comes to math terms, i'm dutch
nvm i get it
ty though
.close
safe radishBOT
safe radishBOT
Available help channel!
young yacht
I would like help with these problems particularly part B
safe radishBOT
I would like help with these problems particularly part B
normal moss
!noclopen
safe radishBOT
Please don't repeatedly close and claim a new channel with the exact same question. This erases all previous progress made towards your problem and is confusing for helpers, making it more difficult to help you. Please be patient, even if your channel has not received much attention.
quasi bison
op said his friend showed him the solution
in the last channel
when i had to disappear
young yacht
it was wrong though
when i typed it out
into the online thing
im sorry if it came off as rude
quasi bison
can you show a screenshot of what you typed and what the feedback was
young yacht
sure
quasi bison
@young yacht so...?
quasi bison
ok so your friend assumed $\nrm{3u+4v} = \nrm{3u} + \nrm{4v}$
flat frigateBOT
Ann
quasi bison
this is incorrect, as u and v are not parallel
(not merely not known to be parallel, they definitely aren't parallel)
u and v are perpendicular
AND u · v is not 1, for that precise reason... the dot product of two perpendicular vectors is 0.
between you and your friend, have either of you done anything involving vectors before?
safe radishBOT
@young yacht Has your question been resolved?
young yacht
im still working on the problem
i got this final answer but im not sure if i know what im doing
young yacht
<@&286206848099549185>
little mesa
assuming you did dot product here, you need to denote that with
flat frigateBOT
chlamydia
young yacht
ok
young yacht
so is it wrong then ?
little mesa
no it's right, your notation is wrong
young yacht
what would the correct npotation be in that case
little mesa
**chlamydia**
this for dot product
you did that on the left hand side, but not on the right of each equation
young yacht
so it would 3 u' u'?
would that be the correct notatiion in which u' is representing a vector ?
little mesa
