yes
#help-13
modern compass
modern compass
you just said left was going to 3
modern compass
^^ left limit is 3
marsh pond
oh lol
hmmm i may have mispoke
not sure why i said 3
it looks like 4 to me
because its going up and left diagonal
modern compass
but left side of -1 is going up towards 4
you want the left side as x goes towards -1. The function goes to y=4 as x goes towards -2
marsh pond
oh so the idea is where is the line heading towards the number, on the left or right side, not away from it
these seem pretty simple if that's the case
modern compass
yep
marsh pond
does it matter if it's solid dot or hollow dot?
modern compass
limits are always asking 'what is happening around this x value'
So you want to always be near that number, not headed away from it.
modern compass
does it matter if it's solid dot or hollow dot?
not for limits
marsh pond
f(-1)
hmmm
no limit
not sure what they want here
for 4.
and f(3)
Do these look correct?
modern compass
F(-1) is asking what the y-value is at x=-1
modern compass
4 and 9 are not correct
modern compass
oh, and 6 and 7, I read those wrong
modern compass
correct
marsh pond
6 and 7 are 4?
modern compass
yes
modern compass
oh, my bad.
marsh pond
no worries đ
modern compass
when the left and right limits don't agree the limit DNE
wispy flare
cedar kilnBOT
wispy flare
Trying to find out where I went wrong in the conversion
The third one should be 10^12pL
cedar kilnBOT
@wispy flare Has your question been resolved?
lyric wave
cedar kilnBOT
hybrid iris
cedar kilnBOT
hybrid iris
,rotate
wraith daggerBOT
hybrid iris
âThis isnât my problemâ so I donât know if the answers are correct but how do you calculate the Expected value of e^x
looking for help with b
I checked the values for the prob distribution and they are correct.
cedar kilnBOT
@hybrid iris Has your question been resolved?
icy sage
Is there a way to answer question 1a without the alternate segment theorem?
icy sage
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
crimson sedge
hey just to be sure, $A = {k\in\mathbb{Z} | k^2 \geq 0}$ is just the set of integers, correct?
wraith daggerBOT
dj swizzlefish đ§
solid juniper
yea
faint holly
<@&268886789983436800> spambot Qualman#2834 (ID: 300767534800699394)
warm skiff
Differential Equations: What methods should I use to solve the following three questions? One photo is a continuation of the other. Im a novice to diffEq, so any links or resources are appreciated. The course im taking has no textbook, so i currently dont know what to search or where to look for these problems.
cedar kilnBOT
Differential Equations: What methods should I use to solve the following three q...
@warm skiff Has your question been resolved?
warm skiff
<@&286206848099549185> Sorry to bother yall, I know this is a niche Q. Do you guys have recommendations for how to find help for something upper level and niche without having to pay 100/hour for a high level tutor on Wyzant?
cedar kilnBOT
@warm skiff Has your question been resolved?
cedar kilnBOT
@warm skiff Has your question been resolved?
meager tinsel
how do you rearrange x = Xo + Vo(t) + 1/2at^2 to make it solve for Vo
turbid bluff
Subtract Xo + 1/2at^2 from both sides?
meager tinsel
OHHHHHHH
wait what
ok well pretend Xo isnt there cause itâs 0
u would subtract 1/2at^2????
i thought you multiply it đ§đťââď¸
solemn torrent
i thought you multiply it đ§đťââď¸
why multiply
is 1/2at^2 added to Vo(t)?
it is ye
so
opposite of add
is subtract
so
solemn torrent
subtract both sides
meager tinsel
THANK YOU
solemn torrent
oh ur solving for Vo
cedar kilnBOT
solemn torrent
npnp
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Available help channel!
stable elm
what is (a+b)^3=?
hollow minnow
You can look it up on Google
livid hound
.close
cedar kilnBOT
stable elm
@hollow minnow ok
cedar kilnBOT
Available help channel!
pearl oracle
Can someone help me with this question- P(A)=0.25 and P(AuB)=0.4 .Find P(B) when A and B are Independant.
toxic moat
well
pearl oracle
The formula for independant is P(AnB)= P(A) x P(B) but how do i find it if i dont know either
toxic moat
.. i cant find a forula online to ss
toxic moat
The formula for independant is P(AnB)= P(A) x P(B) but how do i find it if i don...
ok here u know p a
P(A) + P(B) =P(A or B)+P(A and B)
P(A and B)= P(A)P(B)
toxic moat
P(A) + P(B) =P(A or B)+P(A and B)
all stuff here u can just plug in except P(A and B)
toxic moat
P(A and B)= P(A)P(B)
that u just sub in this n u shld b good
pearl oracle
P(A and B)= P(A)P(B)
But how am i able to find P(A and B) if i cant x P(A) by anythin
pearl oracle
Im sorry i dont get what you mean
toxic moat
P(A) + P(B) =P(A or B)+P(A and B)
this
and throw in the values u know
u shld get the ans
uk im feeling kind
ill do it
P(A) + P(B) =P(A or B)+P(A and B)
P(A and B)= P(A)P(B)
P(A) + P(B) =P(A or B)+P(A)P(B)
.25+ P(B) =.4+.25P(B)
.25+ P(B)-.25-.25P(B) =.4+.25P(B)-.25-.25P(B)
.75P(B) =.15
.75P(B)/.75 =.15/.75
P(B)=.2
@pearl oracle
pearl oracle
P(A) + P(B) =P(A or B)+P(A and B)
Thankyou, i just dont understand this formula i dont think ive learnt it
toxic moat
well
u kinda need this or some variant of it
u can get it by visually drawing it
this is P(A)+P(B)
pearl oracle
this is P(A)+P(B)
Is it the same as P(AuB)
toxic moat
Is it the same as P(AuB)
eh
im using
or to represent union
and to represent intersection
toxic moat
u can see both cover the center bit twice
manic roost
Is it the same as P(AuB)
No, P(A) + P(B) = P(AUB) + P(AnB)
pearl oracle
Aight i jus havent learnt that before
toxic moat
its just what these 2 r showing
that first image is the left
the other is the right
pearl oracle
.close
cedar kilnBOT
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Available help channel!
blazing temple
X^2 +6x +9
Gives
(X+3)^2
I am rly bad at doing this but i can do it backwards
Like i know
(X+3)^2
Gives
X^2 +6x+9
But i'd never be able to tell that
X^2 +6x +9 would give (x+3)^2
I want somewhere (website or anything) where i can train on how to do so
cerulean inlet
X^2 +6x +9
Gives
(X+3)^2
I am rly bad at doing this but i can do it backwards
...
I don't get it. What's your doubt?
What are the roots of x^2 +6x +9?
cerulean inlet
Ohh, alright
It's fairly simple
Use common factor
For the B value, search for 2 numbers that, when added give you that number
For C, search for 2 numbers that if multiplied give you that number
In this case, for B, it's 3. 3+3 = 6
For C, 3 * 3 = 9
And then for A
It's just x two times
So...
x^2 + 6x + 9
(x + 3)(x + 3)
(x + 3)^2
blazing temple
Ahh i see
I get it now
Thanks
U have any website that has some exercise about this specific thing?
cerulean inlet
Not really, no. You could search for ''complete quadratic equations'' and most of them can be solved this way
Khan Academy probably offers these type of equations though
hollow minnow
Donât you have a textbook with practice questions?
hollow minnow
Nice caption youâve got there (I meant the about me thing)
errant meadow
lets say i have 3 0's and 5 1's in how many unique ways i can arrange them? for example if i had 2 1's and 2 0's its (0011,0101,0110,1001,1100,1010) and then if i had n 0's and k 1's there are how many ways?
light ridge
thereâs a very easy way to answer questions like this
iâll talk you through how i do it
uneven light
Hi Doug
light ridge
the question is basically asking how many unique permutations are there of the set {0,0,0,1,1,1,1,1}
uneven light
I posted my ideas in the thread under help forum, lemme know if it works after you put up your method
light ridge
first consider the 0âs, there are 3x 0âs and 8 spaces they could go in. how many unique combinations are there of this? well, there will be 8choose3 unique ways to place 3x 0âs over 8 empty slots
now consider the 1âs, well, thereâs five 1âs and thereâs 5 slots left, so there are 5choose5 (= 1) unique ways to place 5x 1âs in 5 empty slots (obviously)
so the total number of unique permutations is 8choose3 * 5choose5 = 56*1 = 56
light ridge
well letâs see
errant meadow
put the 1's first
errant meadow
hmmmmm
light ridge
youâll get the same answer
itâs because of how the choose function works
n choose n = 1 (for all n in natural numbers)
errant meadow
so if i had n 1s and k 0s i just have to calculate either n+k choose n or n+k choose k?
light ridge
and n choose (r) = n choose (n-r)
yeah
it works if you have more than 2 different numbers
errant meadow
amazing .... any combinatorics book recommendations? cause i major CS
light ridge
so for example if you were looking for how many unique permutations the set {0,0,0,2,2,2,2,2,6,6,9,9,9} has, this still applies
youâd do 13choose3 * 10choose5 * 5choose2 * 3choose3
or you could do it in any order
light ridge
amazing .... any combinatorics book recommendations? cause i major CS
i actually donât know anyđ i learned from my combinatorics lecturer and he was amazing
errant meadow
the original problem was this : u have a NxM grid and u need to get from A to B the shortest way possible. the problem is to find how many ways there are to do that.. i said let 0 be going right and 1 be going down. So the answer would be the problem i just described
did i do it correctly?
light ridge
yes if 0= âgo rightâ and 1=âgo downâ then yes the problem you described is correct
however
wouldnât it be 5x 0âs and 7x 1âs ?
errant meadow
we have to generalize it that was just an example man
i wanted NxK
you solved it no worries
thanks
.close
lucid grove
the question says square root of xx but the answer from the book only matches with the square of xx
drifting marlin
That's weird because what the question says is the norm
Generally $se = \frac{\sigma}{\sqrt n}$
wraith daggerBOT
Steakanator
drifting marlin
sigma being the population standard deviation
But that's not relevant, the question can be solved regardless
lucid grove
the answer makes sense logically
the more people the less error
but it says square room or x so i should be using x^1/2
drifting marlin
Do you know what it means when I say "x is inversely proportional with the square root of y?"
drifting marlin
That works
I'd probably put the sqrt and k on the same side but either works
Now it's just a matter of using the given information to determine k
lucid grove
Do you know what it means when I say "x is inversely proportional with the squar...
i see, wasnt paying attention with the wording
drifting marlin
Np
drifting marlin
,calc 36/sqrt(8)
wraith daggerBOT
Result:
12.727922061358
Yeah looks like they're wrong
lucid grove
little mistake in the rounding
lucid grove
Do you know what it means when I say "x is inversely proportional with the squar...
so for this
well i want to find y and not square root of y
so i multiply the left by the left and the right by the right
but then do i multiply 1/x by 1/x or k/x by k/x
lucid grove
ill write it ddown on paper
sending it through
the top of works
but the bottom one makes sense
so which is it
drifting marlin
Either
The constant k can be anything, so you can square both sides
You'll get y = k^2/x^2
But k is just a constant so we can replace it with anything, like m
So y = m/x^2
lucid grove
sort of get it but not quite
drifting marlin
Not white?
lucid grove
quite
lucid grove
i see, so comnstant is something that doesnt change
drifting marlin
Basically, the square of a (yet unknown) constant is just another constant
lucid grove
i see, so comnstant is something that doesnt change
but why does it not
part of the formula for it to work?
drifting marlin
It does change, but it changes from an unknown constant to another unknown constant
So the notation doesn't really matter, if that makes sense
drifting marlin
You'll get y = k^2/x^2
You can square both sides to remove the sqrt from y, you'll get this
lucid grove
yup
drifting marlin
But k, which is our unknown constant, is still unknown
lucid grove
oh i see now
drifting marlin
So because it goes from "unknown constant" to "unknown constant," nothing fundamentally changes about it
lucid grove
oh i see now
because its squared its basically the same
drifting marlin
It represents the same thing
lucid grove
(i tried with an example)
drifting marlin
It's the so-called "constant of proportionality" I think
It might have a different name idk
But yeah it's pretty chill, you can do lots of manipulations and it'll still be a constant
drifting marlin
Np
somber mason
Find a relation independent of m between x1 and x2(The roots of the equation)
cedar kilnBOT
Find a relation independent of m between x1 and x2(The roots of the equation)
@somber mason Has your question been resolved?
crimson delta
or maybe no one can help
no one that is online atm anyway
what exactly do you mean with relation
somber mason
any type of relation between x1 and x2
like x1 + 3x2 = x2 * x1
something like this
crimson delta
do you have any restriction on m?
somber mason
nope
the only condition is that the relation between x1 and x2 should be m independent
I tried using the sum and product properties (-b/a and c/a)
I'm pretty sure I'm on the right track
but I just got stuck
crimson delta
show your work
somber mason
that's about it tbh
I did try and cross multiply both equations
but i don't know how to continue
crimson delta
what you can do is notice that $\frac{4m-3}{2m-1} = \frac{4m-2}{2m-1} - \frac{1}{2m-1} = 2 - \frac{1}{2m-1}$
wraith daggerBOT
Denascite
somber mason
what you can do is notice that $\frac{4m-3}{2m-1} = \frac{4m-2}{2m-1} - \frac{1}...
I'm not sure how this would help, can you elaborate please
crimson delta
this now expresses x1x2 in terms of 1/(2m-1)
can you express 1/(2m-1) in a different way?
somber mason
this now expresses x1x2 in terms of 1/(2m-1)
yeah but m shouldn't be present in the expression
crimson delta
well we arent done yet
somber mason
bro I'm completely lost here
crimson delta
can you just answer my question even if you dont see the big picture yet
somber mason
can you express 1/(2m-1) in a different way?
I'm not sure what do you mean by this profile
wraith daggerBOT
Denascite
wraith daggerBOT
Denascite
crimson delta
ok. I rewrote the LHS of the second equation and got $$2-\frac{1}{2m-1} = x_1x_2$$
wraith daggerBOT
Denascite
crimson delta
yes?
somber mason
yep
crimson delta
so now this expresses x1*x2 in terms of 1/(2m-1)
the idea is to now express 1/(2m-1) in terms of x1+x2
using the other equation we have
then we can plug that in and in that way eliminate the m
somber mason
so now this expresses x1*x2 in terms of 1/(2m-1)
This expresses x1 * x2 in terms of 2 - 1/(2m-1)
not 1/(2m-1)
right
crimson delta
"in terms of" doesn't mean "equal to"
somber mason
aha ok gotchu
crimson delta
it just roughly means "as a formula of"
somber mason
so we have to somehow someway express 1/2m-1 in terms of x1 + x2
crimson delta
yes
somber mason
did you manage to get it?
crimson delta
well yes I know the solution. I'm trying to lead you to it
somber mason
ok now that i know that it's possible, i'm gonna try my best
am I on the right track?
somber mason
you just need to make a tiny rearrangement
In what sense
crimson delta
what happens if you divide both sides by 2
somber mason
crimson delta
so you have $\frac{1}{2m-1} = \frac{x_1+x_2}{2}$
wraith daggerBOT
Denascite
crimson delta
and now you can just plug that into the other equation to get $x_1x_2 = 2-\frac{1}{2m-1} = 2-\frac{x_1+x_2}{2}$
wraith daggerBOT
Denascite
wraith daggerBOT
Denascite
cedar kilnBOT
@somber mason Has your question been resolved?
somber mason
**Denascite**
alright, thank you very much
cedar kilnBOT
cedar kilnBOT
Available help channel!
crimson sedge
cedar kilnBOT
hollow minnow
Yes
crimson sedge
would it not be (22*(1^p)/p) - (22/p) ?
wait
dude what im goofy isnt it just 22*(1^p)/p
but thats wrong
hollow minnow
Integral of x^-p is x^(1-p)/1-p
hollow minnow
crimson sedge
<:catthumbsup:614540188747563008>
shouldnt it be this?
hollow minnow
Well yeah but thatâs just 22/1-p
hollow minnow
Should be right 
wraith daggerBOT
hollow minnow
Yeah
crimson sedge
.close
hearty lily
I'm trying to figure out the rate.
cedar kilnBOT
I'm trying to figure out the rate.
hearty lily
Halving 225 to get 112.5 and then rounding it to 0.1125 didn't work
<@&286206848099549185>
velvet mortar
Show work
mortal vessel
baskala
velvet mortar
r is the growth constant
Not sure why you are taking about rate
It doesn't work like 225/2
Do as I told you
velvet mortar
Soo like 225= 100 e ^ (2r) right?
Find r from here
hearty lily
i dont know how to find r from there
velvet mortar
You aren't allowed calculator?
hearty lily
You aren't allowed calculator?
no
velvet mortar
,w log (3/2)
wraith daggerBOT
velvet mortar
This should be r according to Wolfram
hearty lily
Is there something useful on "need help? Read it"?
it just opens textbook pages and makes it more confusing
iu dont really know what that means
velvet mortar
I can't find a way to do this without calculator
velvet mortar
Ok so we begin from 225 = 100 e^(2r)
I plugged in n=225 and t=2 in n(t)=100 e^(rt)
hearty lily
ok
velvet mortar
Divide both sides by 100
hearty lily
so 2.25=e^(2r)
velvet mortar
Apply ln on both sides
velvet mortar
Ye
hearty lily
ok and then
velvet mortar
Can you simplify RHS
velvet mortar
Right hand side
hearty lily
uhh idk
velvet mortar
Apply log rules
hearty lily
idk that either
velvet mortar
do you know what is ln?
hearty lily
natural log
velvet mortar
Yeah
hearty lily
ok but idk what to do
velvet mortar
What is ln e?
hearty lily
it cancels out right?
velvet mortar
Yes
hearty lily
so its just ln(2.25)=2r
wraith daggerBOT
velvet mortar
There should be natural log in your calculator
hearty lily
so the r would 0.405?
velvet mortar
Yeah
velvet mortar
Why round?
hearty lily
cause it says I have to round by 4 places
(b) Find a function that models the bullfrog population t years since the bullfrogs were put into the pond. (Round your r value to four decimal places.)
hearty lily
oh ok
cedar kilnBOT
@hearty lily Has your question been resolved?
hearty lily
I may have further questions
cedar kilnBOT
@hearty lily Has your question been resolved?
hearty lily
,w 225 = 100e^(2r)
I have to do something like this similar again. Would the equation be
31,000 = 20,000(e)^(4r)
grim yacht
Have you tried setting t equal to some really large number and seen what it might approach?
cedar kilnBOT
@hearty lily Has your question been resolved?
hearty lily
Have you tried setting t equal to some really large number and seen what it migh...
yeah, I got it
Doing (b), I ended up with ln(1.55) = 4r
but that doesn't seem right for the answer
velvet mortar
Show all your working
floral light
Hi, I need help understanding how to solve a quadratic equation where the equals sign is on the left side
floral light
X² = - 14x - 24
solemn torrent
aye aye
wassup
so
for a quad equation
u want
a 0 on one side
ye?
so
just shift everything
to one side
floral light
the equals sign have to be on the right side right?
static yarrow
x2-(-14x-24)=0
floral light
I move the - 14x - 24 to the left of the = sign?
floral light
the signs change?
static yarrow
then distribute
floral light
I don't remember which though
obsidian coral
x2+14x24=0
Horribly typed and don't do the work for people
static yarrow
oh sorry
floral light
is not - 14x - 24 (- or +) X^2 = 0?
floral light
I move the - 14x - 24 pair to the left of x^2
lone oar
so wut do u want to learn
solemn torrent
x^2 = -14x -24
lone oar
ok
solemn torrent
to move -14 x to the left
lone oar
make it 0
solemn torrent
the sign change
lone oar
no
lone oar
make it x^2+14x+24=0
solemn torrent
adding 14x on both sides
lone oar
yes
lone oar
factorize it
floral light
why is the x^2 on the far left?
solemn torrent
we want =0
lone oar
yes
obsidian coral
why is the x^2 on the far left?
Terms are normally organized, highest power to lowest
floral light
got it
floral light
so the signs of the terms being shifted changed
lone oar
factorize it
floral light
all of the ones being moved?
solemn torrent
mhm
floral light
kk
floral light
so then we have X^2 + 14x + 24 = 0
lone oar
(x+2)(x+12)
lone oar
x = -2 or x=-12
floral light
okay, I know the leading co eff factoring after that
lone oar
now u know the concept
floral light
I also know the zero product rule
floral light
I just didn't know how to deal with that = sign on the left
solemn torrent
đŞ
floral light
lol thanks guys
floral light
.close
cedar kilnBOT
lone oar
lol
cedar kilnBOT
Available help channel!
foggy mason
a tad bit confused how to solve this
foggy mason
this is homework but people are allowed to help but just dont like dump the answer explain steps or a similar problem (diff numbers)
flint plinth
seems to be the same question posted by a different user in #help-11 ? are the two users one and the same?
flint plinth
you can formulate this as an Ax=b question
and then solve via the usual methods (row reduction etc)
red pumice
A being a matrix
flint plinth
as in (matrix) times (unknown vector) = (known vector)
flint plinth
how do you usually convert a system of linear equations into matrix form?
do the same here
foggy mason
ahhhh gotcha
sorry turned my brain off
then I row reduce that
and thats my asnwer?
toxic moat
um
no
so what did u get after rref
ill just not work it out but asume the ans is some
x+az+bw=0
y+cz+dw=0
then shld be what u get aft rref
then parametrise the free variables
in this case the free vars are z and w
so we can let z = t, w=s
then
x = at+bs
y=ct+ds
thats ur set of solns
if u wanna write it in matrix form its
(x,y,z,w) = (0,0,0,0) + t(a,b,1,0) + s(c,d,0,1)
(x,y,z,w) = t(a,b,1,0) + s(c,d,0,1)
@foggy mason
mellow solstice
cedar kilnBOT
royal wasp
im just wondering why u didnt click the read it
anyway do u know what a tangent line is
royal wasp
ok
mellow solstice
then i tried with symbolab and mathway
royal wasp
do u know what a tangent line is
royal wasp
ok, so how do u find a tangent line?
mellow solstice
to like the 5th degree for me
mellow solstice
ofc
mellow solstice
1s 1s
royal wasp
IROC
mellow solstice
i was on a dif assignment helping a friend
royal wasp
instantaneous rate of change
mellow solstice
slow internet
royal wasp
so the first step would be to find the derivative of the function
royal wasp
btw im wondering if it gave u a coordinate when u clicked read it
royal wasp
they're given in the problem
mellow solstice
yee
royal wasp
its asking for the equation
mellow solstice
idk that tho
royal wasp
no
royal wasp
its the coordinate
royal wasp
ok.
mellow solstice
im messing with you sorry haha
royal wasp
OK
wait brb
k back
so u found derivative
now plug in X
and solve
to the derivative
cause u want M
the slope
of the tangent line
so what we did was, we found the derivative of the function, we plug in X back into the derivative to find the slope at the given point of the derivative
so do that
royal wasp
im not solving it so u better be doing correct algebra đ
just guiding u on the steps
ok
so now
u have X, Y and M
mellow solstice
mf
royal wasp
how is an equation usually written
mellow solstice
x(x+12)/x+6^2
mellow solstice
NO
royal wasp
:)))
royal wasp
OK
SO LOOK
U HAVE X, Y, AND M
x and Y are given
u just solved for M
the slope at the given point of the derivative
which is the slope of the tangent line
make sense?
mellow solstice
x(x+12) / (x+6)^2
royal wasp
ok
im not verifying ur work
just giving u steps
do u understand what we did so far
royal wasp
no i am i just dont have
pen and paper
do u know how to take derivatives
and do algebra
yes?
then ur good
royal wasp
whats next is u tell me u understand what we did so far
mellow solstice
i understand dad
royal wasp
u understand M is the slope of the tangent line
livid hound
how are you getting 1/3
mellow solstice
omg
mellow solstice
@livid hound
Derivative y= x^2/6+x
x(x+12) / (x+6)^2
which is 12/36
simplify 1/3
or am i sped
royal wasp
whats 1+6
royal wasp
ok
royal wasp
.
mellow solstice
WHAT
mellow solstice
I AM
royal wasp
SO QUESTION
mellow solstice
ONG
mellow solstice
UH
mellow solstice
21
mellow solstice
oh
royal wasp
what is it conceptually
royal wasp
right
mellow solstice
B)
mellow solstice
ik
mellow solstice
woo hoo
royal wasp
so now what do we have
royal wasp
we have Y, X, and M
mellow solstice
yes'
mellow solstice
y=13/49x+y
mellow solstice
ok
royal wasp
so we have Y, X, and M
mellow solstice
what now
royal wasp
so now
royal wasp
what do u think we should do
mellow solstice
uh
royal wasp
y=mx+b
we have Y, X, and M