@twin nebula Has your question been resolved?
#help-33
marsh citrusBOT
twin nebula
<@&286206848099549185>
still temple
,rotate
elfin berryBOT
still temple
oh i am not qualified to do this whatever that ] means
twin nebula
its integrals
my question isnt to do with that though
my question is mainly if 0^(n+1) is 0
still temple
0^anything = 0 even for complex numbers i think
marsh citrusBOT
@twin nebula Has your question been resolved?
tender sparrow
0^anything = 0 even for complex numbers i think
except zero
marsh citrusBOT
@twin nebula Has your question been resolved?
main idol
<@&268886789983436800>
languid mural
Bro
marsh citrusBOT
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cold bloom
is there any way to find the answer faster without having the need to solve it, ( substitute equation 1 into equation 2 , then find a, b, c and put it into the quadratic formula? like a quick process of elimination.
marsh citrusBOT
is there any way to find the answer faster without having the need to solve it, ...
late geode
you could consider the discriminant first before resorting to the whole QF
cold bloom
okay so the fastest and easiest way possible would be to subsitute eq 1 into 2, find a b & c then discriminant instead of the qf
late geode
depending on what you have, factorisation could be a faster route, (but that's not applicable here)
discriminant first, whole qf if needed
cold bloom
yeah but im talking abt the options i have that are applicable
late geode
other alternatives since this is multiple choice would be to check their values
cold bloom
other alternatives since this is multiple choice would be to check their values
how can i do that
late geode
plug in the points/ordered pairs into an equation, both (if needed)
cold bloom
do u mind showing me how?
late geode
try subbing (-2,2) into the first equation
late geode
and is that equation true or false
cold bloom
false
late geode
which tells you that isn't a solution to one of the equations and thus can't be a solution to the system
similar idea for the other problems
cold bloom
okay thanks
late geode
for the purposes of demonstration
try plugging in the second point (3,0) into the first eqation
cold bloom
0= 3-3
late geode
is this true?
late geode
this satisfies one equation,
but you also need to ensure that it satisfies the other to be a solution to the system
late geode
yeh
marsh citrusBOT
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humble crescent
,,\lim_{x \to 1} \frac{2x^2 - 3x + 1}{x^2 - 1} = \quad ? \
\lim_{x \to -1^+} \frac{2x^2 - 3x + 1}{x^2 - 1} = \quad ? \
\lim_{x \to -1^-} \frac{2x^2 - 3x + 1}{x^2 - 1} = \quad ? \
marsh citrusBOT
,,\lim_{x \to 1} \frac{2x^2 - 3x + 1}{x^2 - 1} = \quad ? \\
\lim_{x \to -1^+} \f...
elfin berryBOT
レナト (renato , ping if reply)
humble crescent
,w lim x to 1 for (2x^2 -3x +1)/(x^2 - 1)
elfin berryBOT
unique cargo
factor the numerator
humble crescent
,,\lim_{x \to 1} \frac{2x^2 - 3x + 1}{x^2 - 1} = \lim_{x \to 1} \frac{x(2x - 3 + \frac{1}{x})}{x(x - \frac{1}{x})}
elfin berryBOT
レナト (renato , ping if reply)
humble crescent
factor the numerator
why not denominator aswell?
unique cargo
yeah denominator as well
you should factor the numerator with it's roots
open new thread
find the roots of the numerator and factor it
same thing for denominator
humble crescent
,,\lim_{x \to 1} \frac{2x^2 - 3x + 1}{x^2 - 1} = \lim_{x \to 1} \frac{2(x -\frac{1}{2})(x - 1)}{(x+1)(x-1)}
elfin berryBOT
レナト (renato , ping if reply)
humble crescent
,w solve 2x^2 -3x + 1
elfin berryBOT
humble crescent
,w solve x^2 -1
elfin berryBOT
humble crescent
,,\lim_{x \to 1} \frac{2x^2 - 3x + 1}{x^2 - 1} = \lim_{x \to 1} \frac{2(x -\frac{1}{2})(x - 1)}{(x+1)(x-1)} = \lim_{x \to 1} \frac{2(x -\frac{1}{2})}{(x+1)}
elfin berryBOT
レナト (renato , ping if reply)
unique cargo
yeah
humble crescent
why did we had to make all this jazz?
unique cargo
Now you can plug 1 in without any problem
humble crescent
cant we plug 1 to the original eq1uation?
marsh citrusBOT
As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.
humble crescent
we can't hand out solutions like that
?
humble crescent
since the denominator would be 0
true
unique cargo
yeah that s why we have to simplify the equation first
humble crescent
without having it explained first
wdym, that I used wa instead of quadratic formula?
sinful thistle
nothing
humble crescent
yeah that s why we have to simplify the equation first
do I have to do the same for $-1^+$ and $-1^-$?
elfin berryBOT
レナト (renato , ping if reply)
humble crescent
like factoring with its roots?
unique cargo
Here you can plug 1 in without any problem, so no need
humble crescent
oh because its not dividing by zero
unique cargo
yes
if your function was behaving differently if you come from the left or right side
we would have to do the two cases
here we dont need to do that
humble crescent
,,\lim_{x \to -1^+} \frac{2x^2 - 3x + 1}{x^2 - 1} = \quad ? \
\lim_{x \to -1^-} \frac{2x^2 - 3x + 1}{x^2 - 1} = \quad ? \
elfin berryBOT
レナト (renato , ping if reply)
humble crescent
so should be $\frac{1}{2}$ aswell for right and left side of -1?
elfin berryBOT
レナト (renato , ping if reply)
humble crescent
,w lim x to -1 for \frac{2x^2-3x+1}{x^2-1}
elfin berryBOT
humble crescent
mmmmm
unique cargo
$\frac{2x-1}{x+1}$
elfin berryBOT
ThibaultF02
unique cargo
This is the form we got by factorizing
For 1 it works great, you can just plug it in
But for -1, you get a division by 0
humble crescent
what should i do thibault 
unique cargo
Let's start from the left
so instead of -1
try plugging in -1.01
what do you get on the top and bottom
humble crescent
,,\frac{2x^2 - 3x + 1}{x^2 - 1} = \frac{2(-1.01)^2 - 3(-1.01) + 1}{(-1.01)^2 - 1}
elfin berryBOT
レナト (renato , ping if reply)
humble crescent
,w \frac{2(-1.01)^2 - 3(-1.01) + 1}{(-1.01)^2 - 1}
elfin berryBOT
unique cargo
So it's something positive
unique cargo
**ThibaultF02**
You can use this form directly
If you plug -1 directly you will get -3 on top, and 0 on the bottom
and with the sign in mind
you can now find the limit
humble crescent
,,\frac{2x-1}{x+1} = \frac{2(-1)-1}{(-1)+1} = -\infty
elfin berryBOT
レナト (renato , ping if reply)
humble crescent
you can now find the limit
but this is for right or left side?
unique cargo
for both side
top will always be -3
bottom, the sign will vary depending on if you come from the left or right
-1.01+1 is negative
-0.99+1 is positive
so depending on if you come from left side or right side you will get $\frac{-}{-}$ or $\frac{-}{+}$
elfin berryBOT
ThibaultF02
humble crescent
I see
very complicated to reason in my opinion
but makes sense
,w (-1.01)^2 + 1
,,\lim_{x \to -1} \frac{2x^2 - 3x + 1}{x^2 - 1} = \lim_{x \to -1} \frac{2(x -\frac{1}{2})(x - 1)}{(x+1)(x-1)} = \lim_{x \to -1} \frac{2(x -\frac{1}{2})}{(x+1)}
elfin berryBOT
レナト (renato , ping if reply)
humble crescent
,,\lim_{x \to -1^{\pm}} \frac{2x^2 - 3x + 1}{x^2 - 1} = \lim_ {x \to -1^{\pm}} \frac{2(x -\frac{1}{2})(x - 1)}{(x+1)(x-1)} = \lim_ {x \to -1^{\pm}} \frac{2x -1}{x+1}
elfin berryBOT
レナト (renato , ping if reply)
humble crescent
,, \lim_ {x \to -1^{\pm}} \frac{2x -1}{x+1}
elfin berryBOT
レナト (renato , ping if reply)
humble crescent
,w ,, lim x to -1 for \frac{2x -1}{x+1}
elfin berryBOT
humble crescent
,, \lim_ {x \to -1^{-}} \frac{2x -1}{x+1} = \frac{2(-1.01) -1}{(-1.01)+1}
elfin berryBOT
レナト (renato , ping if reply)
humble crescent
,w \frac{2(-1.01) -1}{(-1.01)+1}
elfin berryBOT
humble crescent
,w \frac{2(-0.99) -1}{(-0.99)+1}
elfin berryBOT
humble crescent
so depending on if you come from left side or right side you will get $\frac{-}{...
tysm for the help
I think i am starting to understand
.close
marsh citrusBOT
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warm prairie
Need help w ii)
Tried it myself but got 31.06°, answ key says 38.9°
marsh citrusBOT
Need help w ii)
Tried it myself but got 31.06°, answ key says 38.9°
@warm prairie Has your question been resolved?
warm prairie
<@&286206848099549185>
marsh citrusBOT
@warm prairie Has your question been resolved?
warm prairie
<@&286206848099549185>
marsh citrusBOT
@warm prairie Has your question been resolved?
coral flame
marsh citrusBOT
@warm prairie Has your question been resolved?
marsh citrusBOT
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dusty flare
how would i solve a system of equations like this using linear algebra
1x + -2y = -3
5x + -6y = 1
-6x + 11y = 16
marsh citrusBOT
how would i solve a system of equations like this using linear algebra
1x + -2y ...
dusty flare
would i put it into a matrix like:
{{1, -2, -3}, {5, -6, 1}, {-6, 11, 16}}
and then put that into reduced row echelon form?
void elm
yeah
proud ice
not quite actually
well actually.. yeah I guess it works
but you have two equations with three unknowns
You can just do first two and verify in third, but I guess RREF does that for you anyway
dusty flare
i got {{1, 0, 0}, {0, 1, 0}, {0, 0, 1}} after putting it into rref
i'm not really sure what to make of that
restive sun
undo what you did to pack it into the matrix
the last row says that 0x + 0y = 1
so the system is inconsistent
dusty flare
so the system is inconsistent
ohh that is true
so that tells us there is no solution
thank you
rigid veldt
marsh citrusBOT
rigid veldt
i got pc for jonathans speed and since d=s * t i thought the answer was pc * p-q but it's wrong
rough fox
i got pc for jonathans speed and since d=s * t i thought the answer was pc * p-q...
Jonathan's speed is p
Anna's speed is q
If p >> q
Then time taken for Jonathan to reach Anna is basically
(The distance between them)/Their relative speed
So c/(p-q)
Now since we have the time
And we have Jonathan's speed
We can calculate the distance Jonathan will travel in that time
D = S x T
= p x (c/(p-q))
= pc/p-q
open ruin
another way to think of jonathan's speed is to consider what would happen if you brought anna's speed down to 0, you would have to bring down jonathan's speed down by the same amount that anna's speed went down. that makes jonathan's speed (p-q) km/hr
rigid veldt
another way to think of jonathan's speed is to consider what would happen if you...
OMG THAT MAKES SO MUCH SENSE THANK U
rigid veldt
Jonathan's speed is p
Anna's speed is q
If p >> q
Then time taken for Jonathan ...
OHH I SEE
thx guys👍
.close
marsh citrusBOT
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lyric kelp
marsh citrusBOT
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lyric kelp
marsh citrusBOT
brave marsh
You can't just subtract 10.
This -10 term is something you can integrate and compute yourself with the given bounds.
lyric kelp
This -10 term is something you can integrate and compute yourself with the given...
hwo could i do that if i dont have a function
brave marsh
What do you mean? The integral of a sum is the sum of the integrals.
You can compute the integral of a constant from 0.5 to 3
brave marsh
Yes it'll end up being 2.5*(-10)
frosty crow
So likeeee does one just send the question here...
brave marsh
brave marsh
There's no n
marsh citrusBOT
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slate wolf
ive got 5a downpat
marsh citrusBOT
ive got 5a downpat
slate wolf
but struggling to relate it to b and c
past frigate
!show
marsh citrusBOT
Show your work, and if possible, explain where you are stuck.
slate wolf
$let m = dk_1 and let n = dk_2
m - n = dk_1 - dk_2
= d(k_1 - k_2)$
elfin berryBOT
eugene krabs
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
slate wolf
ouch
slate wolf
OH
i follow
let $m = dk_1$ and let $n = dk_2$
$m - n = dk_1 - dk_2$
$= d(k_1 - k_2)$
elfin berryBOT
eugene krabs
slate wolf
that works
marsh citrusBOT
@slate wolf Has your question been resolved?
marsh citrusBOT
Available help channel!
fickle walrus
hello
fickle walrus
um
this is just simple deriviation
sohuld be really easy
i really dont know why im wrong
if anyone can point it out itd be nice
teal arch
np
marsh citrusBOT
@fickle walrus Has your question been resolved?
fickle walrus
round 2
i tried using product rule
because i dont know the derivative for sec x
splitting it into 5x^2 and sincosx
and i got it wrong
this is what i reached
btw
marsh citrusBOT
fickle isle
for every x there is an element of all real numbers?
devout mauve
"for all x in R, |x| equals x". or "for every real number x, |x| equals x"
quaint elm
"element of"
quaint elm
for every x which is an element of the real numbers, |x| = x
fickle compass
Urgent help pls
marsh citrusBOT
Urgent help pls
fickle compass
Ping if yk how to do it
quaint elm
Ping if yk how to do it
expand the square
fresh fern
Note that since $x^2+x+1=0$, we have $x^3-1=(x-1)(x^2+x+1)=0$. That is, $x^3=1$.
elfin berryBOT
Girl
fickle compass
Note that since $x^2+x+1=0$, we have $x^3-1=(x-1)(x^2+x+1)=0$. That is, $x^3=1$.
wait wait wait
how did u know u gotta use x^3 - 1^3
quaint elm
probably recognized the form x^2 + x + 1
marsh citrusBOT
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spring stirrup
marsh citrusBOT
next ravine
divide the x out of the 4x
spring stirrup
instead of the x^2 ?
still temple
,, \abs x = \s{x^2} = \begin{dcases*}
x &if $x \ge 0$ \ -x&if $x <0$
\end{dcases*}
elfin berryBOT
hardy slate
spring stirrup
ohh
spring stirrup
would the absolute value be negative or positive since the limit g oes to negative infinity ?
still temple
well a number going to negative infinity is definitely lesser than 0
spring stirrup
oh cuz i thought since it was square rooting by two it would get rid of the negative sign
idk im just confused
i get it now
spring stirrup
if it was |x^2| then it would be positive ?
still temple
x = -3 means -(-3) = 3 with waht we are working with
spring stirrup
oh
still temple
if it was |x^2| then it would be positive ?
idk what u mean by "would be positive"
,, \abs{x^2} = x^2
elfin berryBOT
still temple
i cant see the full thing but like
that seems correct yeah
in addition with what kaisheng said
spring stirrup
sqrt(x^4) becomes x^2 ?
still temple
yes
spring stirrup
this is what i confused myself on
if the x was alone then it would be negative right?
but since its squared its positive
still temple
well like, $\3{x^4} = \abs{x^2} = x^2$
elfin berryBOT
still temple
the idea is that with |x^2|, you always have something positive coming out
like, x^2 is never negative
spring stirrup
ohh yes
still temple
but x is sometimes negative
spring stirrup
so if i get a |x| nad it goes to negative infinity then its negative
still temple
no
spring stirrup
sorry sorry i meant negative
still temple
yeah
marsh citrusBOT
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still temple
should you change the subscript of a constant in a DE when you apply operations to it, or does it not really matter
marsh citrusBOT
should you change the subscript of a constant in a DE when you apply operations ...
@still temple Has your question been resolved?
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zenith bloom
Three vectors have that v+u=w. What must be so that the absolute value of v + absolute value of u, is equal to the absolute value of w?
marsh citrusBOT
Three vectors have that v+u=w. What must be so that the absolute value of v + ab...
zenith bloom
Sorry if the question is weirdly worded, I had to translate it
boreal rose
Three vectors have that v+u=w. What must be so that the absolute value of v + ab...
the magnitude or the absolute value?
vernal forge
it helps to draw out a picture
vernal forge
the magnitude or the absolute value?
magnitude most likely
boreal rose
magnitude most likely
yeah that's what I was thinking haha
zenith bloom
well im not sure how to draw it tbh
vernal forge
just draw two random vectors v and u
doesn't matter
add them together to get w
compare those values
boreal rose
^^
also think about how we calculate magnitudes
in the geometric sense
consider the R^2 case
where you can draw a right triangle
vernal forge
triangle inequality can come into play if you know it
tbh this is more of an abstract visualisation question than pure math rigour
zenith bloom
So something like this?
vernal forge
So something like this?
now try rotating u around its origin to make the distances the same
boreal rose
try this @zenith bloom https://www.geogebra.org/m/FCknj7c3
vernal forge
try this <@486224372726497285> https://www.geogebra.org/m/FCknj7c3
this is really good
zenith bloom
my brain is melting rn
boreal rose
my brain is melting rn
take a break and come back then
zenith bloom
oo I mightve figured it out?
boreal rose
oo I mightve figured it out?
oooh what's ur report
zenith bloom
boreal rose
okay wow
zenith bloom
Red = V
Blue = U
boreal rose
but if they are opposite they remove each other
interesting
zenith bloom
which means that if they have the same magnitude and they are opposite to each other the resulting vector will not exist
right..?
boreal rose
wait so |v| = 3, |u| = -3. That means that 3-3 = 0
no no no
magnitude can not be negative
boreal rose
but then my theory is false
yeah what about the theory
that if it's in the same direction
you can add up the magnitudes
boreal rose
but wont the vectors always have a larger magnitude than the resultant
try it
marsh citrusBOT
Available help channel!
paper herald
how i can solve this limit
marsh citrusBOT
how i can solve this limit
wary kite
simple substitution
plug in 1
it’ll be a vertical asymptote
just determine the sign of the fraction
wary kite
you can plug in 1 for x
what do you get
you should always substitute first
when evaluating limits
@paper herald
paper herald
-2/0
wary kite
mhm and what happens when you get a number divided by zero
what does the function approach
paper herald
infinity?
wary kite
yes
but be careful
the sign of the numerator is negative
what’s the sign of the denominator
because it’s not exactly zero
is it zero positive or zero negative
paper herald
aaa
wary kite
1^-
is essentially 0.99999
1 minus means 1 from the left
so subtracting 1 will always be negative
correct
so negative/negative is
paper herald
thx
wary kite
ur welcome
mighty swift
marsh citrusBOT
blazing shoal
yea
blazing shoal
idk waht that is..
It’s just a graph plotter
blazing shoal
i js wanna know if its correct
Then plug in a value for example 2 for your x and see if both expressions output the same value
stark trail
mighty swift
https://www.desmos.com/calculator
im not studying this atm
blazing shoal
It’s a tool, it’s not something you study
mighty swift
yes i dont know how to know it
mighty swift
use it
blazing shoal
have you never graphed anything?
mighty swift
no
stark trail
that's hard to believe
type in the equations of the two things you want to see is equal
it will plot both their graphs
if their graphs are the same
blazing shoal
Surely graphing functions is a prerequisite to partial fractions
stark trail
then good
if not
then bad
for example
instead of plotting x^2 and 5x, plot the things you care about
mighty swift
guys in the quadratic formula we need to find whats a,b and c right but what if we dont have c?
do we just continue\
like this for example
if we didnt have c
marsh citrusBOT
@mighty swift Has your question been resolved?
mighty swift
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marsh citrusBOT
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knotty sail
i got to expressing the series ak^1/k as sigma n=1 to 2k 1/k+n but dont know how to continue, questions says use root test
marsh citrusBOT
i got to expressing the series ak^1/k as sigma n=1 to 2k 1/k+n but dont know how...
main idol
i got to expressing the series ak^1/k as sigma n=1 to 2k 1/k+n but dont know how...
Can you show the original instructions
main idol
Bound the sum from below by the lowest term times the number of terms
knotty sail
can u explain
main idol
can u explain
1+2+3 > 1+1+1 = 3 * 1
1 is the lowest term in 1+2+3
And there are 3 of them
marsh citrusBOT
@knotty sail Has your question been resolved?
knotty sail
can you write it out
main idol
can you write it out
Why can't you do it
main idol
i got to expressing the series ak^1/k as sigma n=1 to 2k 1/k+n but dont know how...
Here are the terms
1/(1+k) + 1/(k+2) +1/(k+3) > ?
main idol
1+2+3 > 1+1+1 = 3 * 1
Using this
knotty sail
wait nvm thanks
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valid cape
Evaluate $\int f(x)e^{2x}dx$
marsh citrusBOT
Evaluate $\int f(x)e^{2x}dx$
elfin berryBOT
FungusDesu
valid cape
$f(x) + f'(x) = e^{-x}$, $\forall x \in \mathbb{R}$ and $f(0) = 2$
elfin berryBOT
FungusDesu
novel juniper
cool, try solving this differential equation to obtain f(x)
elfin berryBOT
FungusDesu
sand fable
seems incorrect
valid cape
**FungusDesu**
solving this differential equation gets me $f(x) = \frac{x}{e^x} + 2$
elfin berryBOT
FungusDesu
sand fable
it's (x + 2) / e^x
valid cape
how so
sand fable
how did you solve the differential equation?
elfin berryBOT
FungusDesu
novel juniper
$e^{-x} not e^x$
elfin berryBOT
WhyAmIHere?
sand fable
**FungusDesu**
and how did you solve this?
valid cape
$\Leftrightarrow (e^xf(x))' = 1$
elfin berryBOT
FungusDesu
valid cape
$\Leftrightarrow e^xf(x) = x$
elfin berryBOT
FungusDesu
sand fable
but otherwise pretty good way of solving 👍
marsh citrusBOT
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fresh osprey
Does this look right so far? (It’s a SSA)
marsh citrusBOT
Does this look right so far? (It’s a SSA)
fresh osprey
I feel like 10.6 is too short for a 102.4 degree lol
especially if 9 is the side length of a 56 degree
looks wonky
late geode
your triangle is drawn heavily off scale
fresh osprey
why
late geode
well your B that looks pretty much like a right angle is supposed to be 21.6 degrees
and your side that's supposed to be 4, the shortest is longer than the others
fresh osprey
21.6 is the smallest degree out of the other ones
late geode
yes...
you don't seem to be reading what I'm saying though
it looks wonky because your drawing is horrid
try to make the lengths and angles more reasonably sized based on what you calculated
marsh citrusBOT
@fresh osprey Has your question been resolved?
midnight granite
I think they were trying to say that 102,4 degrees should look like the one between red and blue
That one looks more like a 20 degree than a 102,4 one
marsh citrusBOT
@fresh osprey Has your question been resolved?
trail flint
marsh citrusBOT
trail flint
This feels right to me
Where could I possibly be going wrong, Isn't it just uv - integral of vdu
so if v is 1/8 * sin(8x) then you would have just that under the integral * du
main idol
looks right to me
main idol
,w diff sin(8x) / 8
elfin berryBOT
main idol
idk maybe just formatting
trail flint
weird
the formatting is correct though that's why I'm tripped up
lol
the answer was v
😂
It didn't want the actual representation of v
man I hate online homework portals
.close
marsh citrusBOT
main idol
It didn't want the actual representation of v
lmao that sucks
trail flint
yeah, I got it wrong cause of it, I pressed skip without thinking and now I can't go back
even though the answer I gave is still correct
main idol
don't open help channels if you don't have a math question for yourself
hearty hamlet
Sorry
marsh citrusBOT
marsh citrusBOT
Available help channel!
dense socket
marsh citrusBOT
dense socket
So for this problem
I am needing help for b and c by the way
I do know that row reduction is the fastest method to solve this problem
Atleast from what I know of
However I am not sure how to interpret the results after row reducing to produce a proper solution
dense socket
This is not an exam by the way, its a practice exam from her previous semester classes. The exam is Thursday
marsh citrusBOT
@dense socket Has your question been resolved?
dense socket
<@&286206848099549185>
dense socket
<@&286206848099549185>
marsh citrusBOT
@dense socket Has your question been resolved?
marsh citrusBOT
@dense socket Has your question been resolved?
dense socket
<@&286206848099549185>
vital oracle
you dont need to use all four vectors to reach (6, -7)
,,\qty[\begin{array}{cc|c}-1&0&6\2&1&-7\end{array}]\
\text{row reduce}\
\qty[\begin{array}{cc|c}1&0&-6\0&1&5\end{array}]
this is all you needed to do
elfin berryBOT
mtt07734
vital oracle
(c) wants you to see if you can get to (6, -7) by travelling in only one direction instead of using two or move like above
elfin berryBOT
Rebag9
rugged rapids
$=(-w+3y,2w+x-6y-2z)$
elfin berryBOT
Rebag9
rugged rapids
This is what you wrote in matrix form
marsh citrusBOT
@dense socket Has your question been resolved?
marsh citrusBOT
marsh citrusBOT
✅
dense socket
you dont need to use _all four vectors_ to reach (6, -7)
Now what if
I wanna see if I can get there using all 4 modes of transportation
I would then have to use all 4 in that scenario?
marsh citrusBOT
@dense socket Has your question been resolved?
wicked canyon
I need help solving this
marsh citrusBOT
I need help solving this
wicked canyon
Not sure how to solve it correctly I got it wrong
slim jay
hey nighthaven
the second part that the teacher has circled - can you write your answer here? I can't quite understand your pencil handwriting
wicked canyon
Does not mean above it means below. Basically I was saying like the number couldn’t be over it had to be below 2
But that entire thing was wrong it looks like
slim jay
if you like, i can call and go through the ideas here in a mini-lesson, and stream you a whiteboard or something
you have some ideas right you just dont understand the theory
wicked canyon
I didn’t solve it correctly at all
severe island
Not sure how to solve it correctly I got it wrong
you have to evaluate both the two sides limit before making a conclusion
slim jay
your arguments just don't make sense, because you are not confident in the limits
slim jay
also, your working has some errors
wicked canyon
How do I join a lesson thing like you said
slim jay
dm me
marsh citrusBOT
@wicked canyon Has your question been resolved?
wispy ledge
marsh citrusBOT
wispy ledge
i need help with this
wispy ledge
yea pythagorean idnetity
polar fable
solve for sin^2(x) in that
yes
marsh citrusBOT
marsh citrusBOT
Available help channel!
livid maple
If the variance of a random variable is finite, then mathematical expectation is as well. How can i rprove that?
marsh citrusBOT
If the variance of a random variable is finite, then mathematical expectation i...
pliant siren
If the variance of a random variable is finite, then mathematical expectation i...
im not so sure but if the variance of the variable is n, then the chance that it is a specific value is 1/n. if n is infinity, the chance is 1/infinity which is basically zero
not sure if you can argue like that though
spark otter
Recall the koenig-huygens formula for variance
or just use the definition of variance
spark otter
no
raw saddle
That's wrong
spark otter
That's wrong
<@&268886789983436800>
raw saddle
To define the variance, you needed to use E(xi)
It has a fatal error against the maths func
idle ridge
Please don't tell helpees or helpers to DM you
spark otter
Please don't tell helpees or helpers to DM you
not just that I can sense trolling
raw saddle
Please don't tell helpees or helpers to DM you
Okay, I got it
livid maple
To define the variance, you needed to use E(xi)
Using this i still can't 
idle ridge
This?
Maybe it'd help to think about the contrapositive: if E xi is infinite, what is the variance of xi?
Using this formula
idle ridge
It has a fatal error against the maths func
If you're not going to help, please don't talk in this help channel
marsh citrusBOT
@livid maple Has your question been resolved?
still temple
marsh citrusBOT
still temple
my answer is x<2
but the righr answer it x>2
apparently the base is supposed to be 3/7
not 7/3
but i dont see any mistakes in my calculation
still temple
21/9
still temple
perhaps the one below?
not sure
higher exponent higher number
init
any ideas?
calm harbor
perhaps the one below?
yea
calm harbor
That’s how it works too
calm harbor
calm harbor
but my calculation is alright
yes, your calculation is Alr
still temple
buuuut my answer is wrong?
calm harbor
yeah, so it applies this rule too
still temple
neither
am i allowed to ping helpers again
maybe we can get someone more experienced
calm harbor
marsh citrusBOT
@still temple Has your question been resolved?
warm wyvern
@sage onyx it is a question i wanna know how to do it Make 18,19,22,8 and 14 into 23
marsh citrusBOT
<@265194746715045888> it is a question i wanna know how to do it Make 18,19,22,...
warm wyvern
you can say its not possible but it is
i think it is
you can use =
-
-
- and division
-
and brackets
mystic minnow
do you have to use all the numbers?
sacred idol
<@265194746715045888> it is a question i wanna know how to do it Make 18,19,22,...
oh
i can only think of a way with 18 19 and 22
marsh citrusBOT
@warm wyvern Has your question been resolved?
gray shale
maybe it's specific to the exercise and then never mind, but where this egality come from?
i don't know if it's basic or not
(A is a function IE is the identity)
marsh citrusBOT
maybe it's specific to the exercise and then never mind, but where this egality ...
static quarry
telescoping
brave marsh
You can expand out the LHS with relative ease and it telescopes nicely
marsh citrusBOT
marsh citrusBOT
Available help channel!
south goblet
I was doing this excercise and I don't see why this is 0
marsh citrusBOT
I was doing this excercise and I don't see why this is 0
south goblet
nimble timber
I was doing this excercise and I don't see why this is 0
By applying LH rule you will have n [(lnt) power (n-1) ] /(-1/t)
Doing it again and again expression would look something like n(n-1)(n-2).... lnt power n-x /( -1/t)
You differentiate it the point so that x = n so that lnt becomes 1
And you will have -1/t in the denominator as it is
Now since t tends to zero
Lim would turn up to be zero
south goblet
By applying LH rule you will have n [(lnt) power (n-1) ] /(-1/t)
wait u also have 1 / t
because
of
chain rule
nimble timber
Yes
nimble timber
Yes but that 1/t in thr numerator would cancel it so you will have -1/t in the denominator ultimately
south goblet
ooohh
south goblet
Yes but that 1/t in thr numerator would cancel it so you will have -1/t in the d...
that is smart but
the bottom one
say u differentaite 1 /t^2
u get -2
because
like * -2
too
nimble timber
What
south goblet
Doing it again and again expression would look something like n(n-1)(n-2).... ln...
like
so say u differentaite it a couple time
the bottom part
nimble timber
Yup
south goblet
Yup
okay I think I got this part now thank you alot
I will see if I can finish up this uqesiton
but it's not an easy one
nimble timber
Ya its good
nimble timber
I was doing this excercise and I don't see why this is 0
Rest is easy
Just like you did for integral (lnx) power n and got -n integral (lnx) power n-1 finally similarly on integrating (lnx) power n-1 you will have -(n-1) integral (lnx)power n-2
Similarly you will do it till it becomes (lnx) power n-n which means (lnx) power 0 =1
blazing pulsar
If you want to make the argument less messy, you should just use induction so that you are only applying lhopital's rule once in the inductive step instead of n times.
south goblet
Doing it again and again expression would look something like n(n-1)(n-2).... ln...
btw u don't know if it's - or positive right it sohuld be (-1)^n right?
nimble timber
If you want to make the argument less messy, you should just use induction so th...
Yes i was just telling the logic behind it ,which basically is induction, obviously we are not going to solve it n times
You dont need to worry about any constants there since lnt finally becomes one since it has power 0 and you will have -1/t in the denominator
Which will make the whole expression zero
south goblet
Just like you did for integral (lnx) power n and got -n integral (lnx) power n-1...
is this the same?
nimble timber
is this the same?
Yes
south goblet
Yes
wait what did he used here
oh wait
he is using induction?
so basically first he establish a formula which the integer is equal to
nimble timber
he is using induction?
Yes and you solved it previously
nimble timber
Yes you solved it for n and same thing with happen with n-1, n-2 and so on
south goblet
Yes you solved it for n and same thing with happen with n-1, n-2 and so on
I also had 1 question about induction which I didn't realy understood intuively so for the induction hypothesis there is the mathemetical and the other one
so I know how they both work
but for the mathematical u basically only asume if it's true for n it's also true for n + 1
and for the other one u can assume for n-1 n-2 etc then it's true for n+1
but intuively they seems quite the same to me
nimble timber
Yes but we dont assume there is a perfectly logical explanation
What is n here?
When you are solving
?
nimble timber
The n for which we solved the question previously
south goblet
a positive integer?
nimble timber
Its any integer,right?
south goblet
ye
nimble timber
N is representation of a integer it could be 2,3 anything
If it works for n
It will work for n+1
Just think like this n+1 is basically your new n
south goblet
N is representation of a integer it could be 2,3 anything
btw about the question I originally asked how should I view it as I solve it, so I am thinking I know I have to use induction, so should I just start with induction and then when I am at the red underlined part I know I have to do some extra work
because isn't the base step also possible
without that formula
I first thought when I see this question I just simplify the left side and then gotta see I gotta use induction
or do I gotta notice I gotta use induction and then simplify left side
marsh citrusBOT
@south goblet Has your question been resolved?
quasi coyote
marsh citrusBOT
quasi coyote
Not to sure how to find RSQ
I did
4x+5=8x-11 and got x=4
What is the next step ?
cunning fiber
quasi coyote
I don’t understand
quasi coyote
Like that is the answer
halcyon crown
You have x
full orchid
you have found an x value
quasi coyote
Yes
full orchid
expression*
quasi coyote
?
full orchid
correct
halcyon crown
Indeed
quasi coyote
RSQ=21
halcyon crown
Indeed
marsh citrusBOT
@quasi coyote Has your question been resolved?
quasi coyote
.close
ashen owl
Hello, I could benefit check if what feels like a pretty whacky answer to a proof. Here is problem..
marsh citrusBOT
Hello, I could benefit check if what feels like a pretty whacky answer to a proo...
marsh citrusBOT
@ashen owl Has your question been resolved?
marsh citrusBOT
marsh citrusBOT
Available help channel!
wise oxide
Help
dim schooner
isn't it just arctan(squareroot of 3) ?
dim schooner
$tan(x)+\sqrt{3}=0\
tan(x)=-\sqrt{3}\
x=arctan(-\sqrt{3})$
elfin berryBOT
nico
wise oxide
Shouldn’t it be positive
Also I’m finding the radians on unit circle where it equals to positive sqrt 3
elfin berryBOT
nico
wise oxide
$arctan(-\sqrt{3})=\frac{-\pi}{3}$
So that’s the answer?
dim schooner
it's one solution
pliant siren
$arctan(-\sqrt{3})=\frac{-\pi}{3}$
\arctan does exist btw
dim schooner
oh?
pliant siren
$\arctan\alpha$
elfin berryBOT
DerTheo
dim schooner
nice, thank you
pliant siren
lmao you’re welcome
same with sin, cos, etc
if it doesn’t work for any, you can use
$\rm{sin}\alpha$
elfin berryBOT
DerTheo
wise oxide
it's one solution
Along with 2pi/3?
dim schooner
yes it's another solution
dim schooner
hint: $x=\frac{5\pi}{3}$ is another same for $x=\frac{8\pi}{3}$
elfin berryBOT
nico
wise oxide
Well I would go on forever then
dim schooner
that's why you need to use the parameter "n" to get all possible solution
dim schooner
very close $n*\pi-\frac{\pi}{3}$
nvm i solve the wrong equation you were right it's $n*\pi+\frac{\pi}{3}$
elfin berryBOT
nico
dim schooner
@wise oxide
wise oxide
👍
dim schooner
i took tan(x)+sqrt3 rather then tan(x)-sqrt3
marsh citrusBOT
@wise oxide Has your question been resolved?
sonic pivot
marsh citrusBOT
sonic pivot
Can someone help me with the second question?
stray hound
Can someone help me with the second question?
how far have you gotten?
sonic pivot
I know the answer, but idk how, like I know the find the integral of [0,1] + [1,4]
But what if it was 1≤x≤4, what numbers would be in the brackets?
stray hound
why are you separating them?
oh are you trying to make it so the area is always positive?
sonic pivot
Yeah
stray hound
,w plot x^3-5x^2+4x