Actually, if the two numbers are coprime, then a necessary/sufficient condition is that the larger number is greater than 7.
#help-10
dusk turret
drifting wraith
uh huh
dusk turret
Right, 1 is coprime to 8 and 9 I guess.
drifting wraith
so 9,1 9,2 9,4 9,5 9,7, 9,8 and 1 must be the start
8,1 8,3 8,5 8,7 and start can be a bit larger
dusk turret
Right. 8 also stops working after....
Yeah, 8 stops working after 8, too.
So that's it for purely increasing.
Purely decreasing is a simlar story, I bet.
So there are 38x2 purely increasing/decreasing combinations.
dusk turret
I think so; it's just 64-, no real difference.
dusk turret
Right, rows and columns can be exchanged.
No damn clue about where to go from here, though.
drifting wraith
if they go in different directions, you can think of it as increasing only, and you get no repeats for free
a + 7x + 7y
a + 7(x+y)
that's the last number
so that's a lot of possibilities
you can start with 30, and then 2,2, 1,2 2,1 ,1,1 wil fit
that's what i would call it gets worse :)
obtuse pebbleBOT
Available help channel!
hallow nest
Hello! I must find the LCM(Least Common Multiple) of these two expressions.
hallow nest
fierce lagoon
Well list what the variables they share
hallow nest
I got to the point of 3•2•u^8•y^2•x^4 and 5•3u^8•y^3, I don’t actually remember what to do next haha
livid creek
from what i can recall, you keep what is common and what is not common, here 3,2,5, u^5, y^2 and x^4
fierce lagoon
Well it's easier to just do this:
- Find LCM of the coefficients
- Identify common variables
- Compare exponents of common variables
hallow nest
I was lead to believe I should find the common variables, then find the product between the two, not sure how right that is
livid creek
i don't think you find the product of the two
fierce lagoon
It's to find a common multiple
fierce lagoon
I was lead to believe I should find the common variables, then find the product ...
So I'm gonna ask again; what are the common variables
hallow nest
3, Y, and U
livid creek
It's to find a common multiple
ah so that's what capao was trying to get at
warm shaleBOT
Umbraleviathan
fierce lagoon
Well it's easier to just do this:
1. Find LCM of the coefficients
2. Identify ...
Look at step 3. Which exponent is smaller
hallow nest
y^2
fierce lagoon
Yeah
So y^2 can be factored out
Look at the other common variable
$u^5$ and $u^8$
Which one is smaller
warm shaleBOT
Umbraleviathan
hallow nest
u^5
So 3yu^3 is relevant I’m assuming
Or 5•3•2yu^3?
I think I may have settled on the answer being 3u^8y^6x^4
Someone will have to check me on that if someone gets the chance though (:, thank you!
obtuse pebbleBOT
@hallow nest Has your question been resolved?
hallow nest
I went ahead and submitted what I had gotten, hopefully it went alright lolol
flat plume
flat plume
Solve each triangle (Law of Cosines). Round lengths to the nearest tenths and angle measures to the nearest degree.
obtuse pebbleBOT
@flat plume Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
pine scaffold
Hello, how do i calculate a discount in one go rather than subtracting it from the total
obtuse pebbleBOT
Hello, how do i calculate a discount in one go rather than subtracting it from t...
nocturne minnow
Hello, how do i calculate a discount in one go rather than subtracting it from t...
You mean if something was $10 and 20% off, instead of doing $10 * 20% = $2, so then $10 - $2 = $8 which is the final price?
grand bronze
nocturne minnow
pine scaffold
You mean if something was $10 and 20% off, instead of doing $10 * 20% = $2, so t...
Yes
nocturne minnow
Hello, how do i calculate a discount in one go rather than subtracting it from t...
Because if that's what you mean, just do $10 * (100% - discount) to get the final price
pine scaffold
Oh no i mean is there straight forward way to do it instead of having to subtract after?
nocturne minnow
So $10 * (100% - 20%) = $10 * 80% = $8
thick horizon
obtuse pebbleBOT
thick horizon
hi
i thought cuz of the fact that both top and bottom x's both have equal powers (10 and 2) that the answer would be infinity
how is it -5
or is the answer wron
g
brave bramble
i thought cuz of the fact that both top and bottom x's both have equal powers (1...
This is never true.
Instead, it's the ratio of the leading coefficients
10/-2 = -5
brave bramble
(When equal degrees)
thick horizon
and if the lower part has a higher power the answer is 0 right?
wait also
if the top does have a higher power is it infinity
or is that wrong
brave bramble
Infinity, or negative infinity
thick horizon
ok thank you
brave bramble
Depending on signs
trail tiger
you can solve this another way
trail tiger
factor x^3 on the top, and x^3 in the bottom
brave bramble
x is positive, so |x| = x
Limit of Ax² / (x² + 3) = 2
Huh, we have a quick way to get that limit of the left
pine scaffold
I have a question : 2(5+3)-4^2. I got (16)-4^2 after clearing the brackets does my "16" have a power of one? and when i multiply?
warm canopy
Yeah, any number on its own secretly has a power of 1
pine scaffold
so the answer should be -64^3?
warm canopy
Why do you think that
pine scaffold
because 16 * -4 is -64 and the exponents add up because theres a bracket
warm canopy
It's not multiplying
devout solar
but you arent multiplying
warm canopy
It's subtraction
pine scaffold
but dont exponents add up when they multiply?
ohh nevermind i see where i meassed up
2(5+3)-4^2 i just checked the worksheet again and the only options where : -4
-2
4
0.0
devout solar
whats -4^2
pine scaffold
-16
devout solar
ok
obtuse pebbleBOT
Available help channel!
stark ether
how do I solve this inequality
$\sin x+\cos2x > 0$
obtuse pebbleBOT
how do I solve this inequality
$\sin x+\cos2x > 0$
warm shaleBOT
ホタル
lusty cedar
expand cos2x
stark ether
into sin?
stark ether
1-2sin^2x
lusty cedar
yea
stark ether
$-2sin^2x + sinx + 1 > 0$
warm shaleBOT
ホタル
stark ether
now quadratic?
lusty cedar
and then solve it like a quadratic inequality but only in the domain [0,1]
cuz that is the value that sine can take
trail tiger
how do you prove than cos(2x) = 1-2sin^2(x) ?
trail tiger
no, asking out of genuine curiosity
stark ether
google it
lusty cedar
yes would be better if you google it
trail tiger
true
stark ether
and then solve it like a quadratic inequality but only in the domain [0,1]
2u^2-u-1=0
2u^2 - 2u + u - 1=0
2u(u-1)+1(u-1)=0
(2u+1)(u-1)=0
u = -1/2, u=1
why just [0,1]
isn't it [-1, 1]
lusty cedar
isn't it [-1, 1]
ohh exactly, my bad
stark ether
2u^2-u-1=0
2u^2 - 2u + u - 1=0
2u(u-1)+1(u-1)=0
(2u+1)(u-1)=0
u = -1/2, u=1
for the inequality it becomes
u > 1 or u < -1/2
lusty cedar
2u^2-u-1=0
2u^2 - 2u + u - 1=0
2u(u-1)+1(u-1)=0
(2u+1)(u-1)=0
u = -1/2, u=1
no
see
to solve it you multiplied the quadratic equation by -1
so the inequality is now reversed
lusty cedar
yes
stark ether
but sinx is always in that
lusty cedar
basically between the roots
stark ether
oh its not for some cases
stark ether
-1/2 < sinx < 1
-pi/6 < x < pi/2
stark ether
principal domain*
lusty cedar
yea exactly dude
stark ether
how do I get the other answers
stark ether
what
lusty cedar
ik
stark ether
-1/2 < sinx
lusty cedar
or if you want just use the graph for that
lusty cedar
why not?
stark ether
need to do it algebraically
stark ether
i know this
lusty cedar
so use this
stark ether
so we have sinx = sin(-pi/6)
lusty cedar
yes
stark ether
x = npi - (-1)^npi/6
lusty cedar
yes
stark ether
$x = n\pi - (-1)^n\pi/6$
warm shaleBOT
ホタル
stark ether
how do I do the inequality
stark ether
Its possible
lusty cedar
but instead leave it in the form of n
stark ether
I'm supposed to write a solution set
lusty cedar
yes if you leave it in the form of n
stark ether
yeah ik that
lusty cedar
but they are infinite you cant
stark ether
ik
lusty cedar
you cant list all of them
lusty cedar
bruh
stark ether
not roster
lusty cedar
yea so do it now
stark ether
but how?
I think it should be smth like this
$x \in [n, pi+n something] where n \in \mathbb{Z}$
warm shaleBOT
ホタル
stark ether
some intervals
distant moth
bruh
If i found out the answer from 0 to 2pi and then added 2npi to all of them would it work?
lusty cedar
If i found out the answer from 0 to 2pi and then added 2npi to all of them would...
idts bro
stark ether
If i found out the answer from 0 to 2pi and then added 2npi to all of them would...
its an inequality
lusty cedar
dude
distant moth
its an inequality
I can see that
lusty cedar
we have to find the upper boundary in terms of n
distant moth
Sinx between -1/2 and 1 right?
stark ether
$x = n\pi + (-1)^n\pi/2$
warm shaleBOT
ホタル
lusty cedar
yes i think so this is it
lusty cedar
Sinx between -1/2 and 1 right?
yes
stark ether
$n\pi - (-1)^n\pi/6 <x < n\pi + (-1)^n\pi/2, n \in \mathbb{Z}$
warm shaleBOT
ホタル
lusty cedar
absolutely
stark ether
,w sinx>-0.5
warm shaleBOT
lusty cedar
,w -0.5<x<1
warm shaleBOT
warm shaleBOT
lusty cedar
what is that?
distant moth
The answer for x
For -1/2<sinx<1
distant moth
if all satisfies then i'd say you havent listed all answers
What
lusty cedar
@stark ether is our answer correct?
stark ether
im not sure, let me check
lusty cedar
alr
distant moth
For n=0, it come [0,pi/2)U(pi/2,7pi/6)U(11pi/6,2pi]
stark ether
if n = 0,
$$- \pi/6 <x < \pi/2$$
if n = 1,
$$\pi + \pi/6 <x < \pi - \pi/2$$
warm shaleBOT
ホタル
stark ether
the second one isn't a correct inequality
I mean positive n dont have solutions/ are straight up wrong
lusty cedar
the second one isn't a correct inequality
did you check ours?
distant moth
the second one isn't a correct inequality
Are you talking about mine
lusty cedar
wai t what
stark ether
**ホタル**
for some reason, if the < are changed to > its correct
$$7\pi/6 > x >\pi/2$$
warm shaleBOT
ホタル
warm shaleBOT
ホタル
lusty cedar
ohh i think i got it
we would have to reverse the bounds alternatively then
as n changes
stark ether
how is this done
lusty cedar
,w sinx>-0.5
lusty cedar
graphically
stark ether
what they've written is
$\frac{1}{6} (12 \pi n - \pi) < x < \frac{1}{6} (12 \pi n+ 7\pi), n \in \mathbb{Z}$
warm shaleBOT
ホタル
lusty cedar
lemme bring my weapons
stark ether
how did they get this? its correct, n = 0 gives us
-pi/6 < x < 7pi/6
lusty cedar
pen and paper
lusty cedar
hmm
stark ether
Hmm yes
distant moth
Which is what my answer gives👺
obtuse pebbleBOT
@stark ether Has your question been resolved?
lusty cedar
You dont have equalities
ik i'm just finding where sin would be that cuz it is the boundary
@stark ether did you get it?
boreal bay
Pls help with the circled question numbers......
obtuse pebbleBOT
Pls help with the circled question numbers......
@boreal bay Has your question been resolved?
obtuse pebbleBOT
@boreal bay Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
weary quarry
does every doubly stochastic matrix have an eigenvector of [1,1,1,1...1]?
obtuse pebbleBOT
does every doubly stochastic matrix have an eigenvector of [1,1,1,1...1]?
@weary quarry Has your question been resolved?
proper raptor
obtuse pebbleBOT
hexed agate
what have you tried
hexed agate
what did you get for RQ and SR?
proper raptor
√(ab)^2-(a^2)^2 for rq, √(b^2)^2-(ab)^2 for sr
hexed agate
also since PS and PR are opposite to the right angle, couldnt we say they are corresponding sides?
lets do the ratio of the corresponding sides
PS/PR = b^2/ab = b/a
proper raptor
ohhh then PR/PQ = ab/a^2 = b/a which is the same
proper raptor
a^2/b^2
hexed agate
can you show the process
proper raptor
well isnt it just (√(ab)^2-(a^2)^2)/(√(b^2)^2-(ab)^2)
expand and then factorise out a^2 and b^2
cancel out b^2-a^2
and then you add back the root on the top and bottom and get b/a again
so the triangle is similar
is that fine?
proper raptor
RS over RQ
yea mb
proper raptor
and that proves it right
hexed agate
yes
rain coral
obtuse pebbleBOT
https://cdn.discordapp.com/attachments/734065147970322483/984570806937976852/unk...
tranquil arch
you can use $e^x>x+1, \quad(x \neq 0)$, then you can compare a vs b, b vs c. but a vs c is more difficult
warm shaleBOT
秋水
cobalt orchid
For question 24 where did the +2 come from?
obtuse pebbleBOT
For question 24 where did the +2 come from?
cobalt orchid
please help :’>
timid silo
please help :’>
after we get the half of the initial, $a_1$, we add 2 onto it
warm shaleBOT
kav
timid silo
since the values were 16, 10, 7 after looking for the pattern, you would see they're basically the half of each other
half of 16 is ... well 8. we add 2, half of 10 is ... well 5. Add 2
timid silo
They looked at the formula and devised, "ok the previous value becomes half and they add 2"
cobalt orchid
can I ask another question?
timid silo
are you allowed to use calculator in class for this?
cobalt orchid
I got this instead :’>
cobalt orchid
are you allowed to use calculator in class for this?
yes
timid silo
I'm not so sure on this one, I'm sorry! I'm sure someone else can help you
frosty river
For question 24 where did the +2 come from?
This proves this kind of exercises are stupid.
frosty river
Someone please help
Use the Newton Binomial
$(x+2z)^7=\sum_{k=0}^7{7\choose k}x^{7-k}2^kz^k$
warm shaleBOT
jnkena
frosty river
For which k you have x⁵, well k=5 so
$${7\choose 5}2^{7-5}x^5z^{7-5}=\frac{7!}{5!2!}2^2x^5z^2$$
warm shaleBOT
jnkena
frosty river
$$=4\frac{7\cdot 6}{2}x^5z^2=84x^5z^2$$
warm shaleBOT
jnkena
frosty river
@cobalt orchid
warm shaleBOT
jnkena
frosty river
I don't ask you to prove the formula, but at least memorize it
obtuse pebbleBOT
@cobalt orchid Has your question been resolved?
wanton dagger
I need to prove LHS is equal to RHS
obtuse pebbleBOT
I need to prove LHS is equal to RHS
wanton dagger
The sin^2 @ is a problem here
tranquil arch
use $$1 = \cos^2x +\sin^2 x$$
warm shaleBOT
秋水
tranquil arch
$$\frac{\cos^2x +\sin^2 x}{\cos^2 x}-\sin^2 x$$
warm shaleBOT
秋水
wanton dagger
Oh yh mb
Wait but how?
If we evaluate back 1-sin^2 0 this is equal to cos^2@
So we would have sin^2@+cos^2@(cos^2@)/cos^2@
tranquil arch
what do you mean?
$$\frac{1-\sin^2 x \cos^2 x}{\cos^2 x} = \frac{1}{\cos^2 x}-\frac{\sin^2 x \cos^2 x}{\cos^2 x}$$
warm shaleBOT
秋水
trail tiger
simplify the fraction, and find a way to make cos appear
wanton dagger
do you get this now?
Yh
wanton dagger
simplify the fraction, and find a way to make cos appear
Ok
tranquil arch
$$\frac{\cos^2x +\sin^2 x}{\cos^2 x}-\sin^2 x = 1+\tan^2 x-\sin^2 x = \tan^2 x+\cos^2 x$$
warm shaleBOT
秋水
balmy tapir
Hello. I have a problem which i dont know whats happening:
If f(2x - 3)=2x-1800, whats the value of f(2019)?
obtuse pebbleBOT
Hello. I have a problem which i dont know whats happening:
If f(2x - 3)=2x-1800,...
tranquil arch
you can solve 2x-3=2019 first
timid silo
obtuse pebbleBOT
timid silo
how do i find the inverse of this function within a limited domain
graph looks something like this
obtuse pebbleBOT
@timid silo Has your question been resolved?
timid silo
<@&286206848099549185>
obtuse pebbleBOT
@golden canyon Has your question been resolved?
mossy echo
erm
mossy echo
could someone please tell me what is wrong?
this are the solutions, u might say it's A
now A) is only diagonalizing the matrix but not in making it an orthogonal diagonalisation
alr nvm i'm saying it's B
.close
unreal notch
Question: A is directly proportional to the cube root of B. B is increased by 60%. Work out the percentage increase in A.
obtuse pebbleBOT
Question: A is directly proportional to the cube root of B. B is increased by 60...
unreal notch
I don't really know how to do this
So far I just wrote is down, A = k x cube root 1.6B
Not sure where to go from there
warm canopy
Cube root of 1.6 instead
fierce lagoon
My bad yeah because it's increased by 60%
warm canopy
I don't really know how to do this
So far I just wrote is down, A = k x cube roo...
From here you separate the cuberoot
unreal notch
So A^3 = k x 1.6B
teal prawn
A = k B^(1/3)
(1.6)^(1/3) A = k (1.6)^(1/3) × B^(1/3) = k (1.6 B)^(1/3)
unreal notch
Dont really understand what you did there king
teal prawn
A proportional to B^(1/3)
A = k B^(1/3) for some k
rest is algebraic manipulation
new value of A - old value of A = (1.6)^(1/3) A - A
divide by A and multiply by 100 to get percentage increase
unreal notch
Alright
I think I understand now
I got another question similiar to this aswel
A is directly proportional to the square root of B. B is inversely proportional to the cube of c. If B is increased by 40%, then what is the ratio of A to C?
Do you have to find an equation for C in terms of B then do what I done in the question you just helped me with to find a percentage increase with C. Then after that I could put the equation of B = k/cube root of c into A and find a ratio?
obtuse pebbleBOT
@unreal notch Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
half marsh
Hi, I was wondering, are the purple angles equal here ?
obtuse pebbleBOT
Hi, I was wondering, are the purple angles equal here ?
strange musk
yes
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
potent onyx
one question, in this exercise, what should I do ...
obtuse pebbleBOT
one question, in this exercise, what should I do ...
potent onyx
Find the function $f$ such that $\nabla f=e^{x}cos(y)i-e^{x}sin(y)j+zk$.
warm shaleBOT
Aylou-210
Find the function $f$ such that $\nabla f=e^{x}cos(y)i-e^{x}sin(y)j+zk$.
potent onyx
I don't know exactly what to do
I think I have to integrate, I know it's a vector function and I have to find f but I don't know if I'm right?
nocturne sun
assuming $f$ as in $f(x, y, z)$, you can integrate $e^x\cos(y)$ wrt x and so on
warm shaleBOT
Doggo
nocturne sun
$\nabla f(x, y, z) = \begin{pmatrix}f_x \ f_y \ f_z\end{pmatrix}$ keep the definition in mind
warm shaleBOT
Doggo
potent onyx
mmmmm
nocturne sun
I don't remember exactly but IIRC when you integrate a partial derivative you got a function instead of a regular constant then you compared the results?
like $\int f_x(x, y) \mathrm dx = f(x, y) + h(y)$ I think like such?
warm shaleBOT
Doggo
nocturne sun
then you gotta apply that to 3 variables which I'm not sure how
cedar lichen
For 3 variables, you get + h(y, z), because that goes to zero when you take the partial derivative w.r.t. x
potent onyx
potent onyx
cedar lichen
The first component of the gradient is the partial derivative of f with respect to x, yes?
That's how the gradient is defined
cedar lichen
Based on the first component, you have that f(x, y, z) = e^x cosy + c(y, z), right?
potent onyx
Based on the first component, you have that f(x, y, z) = e^x cosy + c(y, z), rig...
yes!
cedar lichen
And you know, based on the second component, that ∂f/∂y = -e^x siny, right?
potent onyx
aha
potent onyx
And you know, based on the second component, that ∂f/∂y = -e^x siny, right?
the gradient is composed of the partial derivatives with respect to x,y and z
then....
I have already verified that its partials are equal, so that means that it is a conservative field.
cedar lichen
Here's a bit of a hint: try taking the partial derivative of e^x cosy + c(y, z) with respect to y and compare it to -e^x siny
potent onyx
uh
cedar lichen
If somethings confusing you, I cannot help if you only say "uh"
potent onyx
moment
cedar lichen
Looks right to me
potent onyx
Looks right to me
oki
thanks
It was to integrate the first component
and then find the derivative of the second one and then equal it to the end... oh well that's what I saw in a video
the book didn't tell me anything about it
.close
small kestrel
hey there, i have a problem here:
My job is to construct all circles tangent to the circles a and b, which simultaneously go through the point C. Does anybody have an idea on how to solve it?
obtuse pebbleBOT
hey there, i have a problem here:
My job is to construct all circles tangent to ...
@small kestrel Has your question been resolved?
frosty river
Are a, b same radii?
obtuse pebbleBOT
wicked tundra
idk how to find an angle
slate cosmos
do you know the formula?
wicked tundra
no
wicked tundra
is there more than one dot product @brave bramble
brave bramble
a•b is a unique number
There's two different ways to get a•b, though
a•b = (-5)(1) + (2)(3) + (5)(-4)
But also a•b = |a||b|cosθ
tardy epoch
is there more than one dot product <@356908116429897729>
Yes but you don't need to know them
wicked tundra
demos scientifc calculator is so useful sometimes it feels like I am cheating
@tardy epoch
tardy epoch
<@261933205387477002>
What?
obtuse pebbleBOT
@wicked tundra Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
broken shard
I’m using complex analysis for this integral and I’ve already used the residue theorem to find the contour. How do I get rid of the integral from -r to -epsilon. Also since I’m doing this on the upper half of the unit circle do I need to do the residue of -i or just ignore it
obtuse pebbleBOT
I’m using complex analysis for this integral and I’ve already used the residue t...
earnest parrot
Is the statement of the problem the integral in the top left?
broken shard
Yeah
earnest parrot
Ok
obtuse pebbleBOT
@broken shard Has your question been resolved?
obtuse pebbleBOT
broken shard
.reopen
obtuse pebbleBOT
✅
obtuse pebbleBOT
@broken shard Has your question been resolved?
earnest parrot
,w poles of (sin^2(z))/(z^2(z^2+1))
obtuse pebbleBOT
,w poles of (sin^2(z))/(z^2(z^2+1))
warm shaleBOT
earnest parrot
Do you know what the answer should be? I got $-\pi \sin^{2}{i}$
warm shaleBOT
seth.delacroix
earnest parrot
I'm not the best at CA however so someone might want to check that
I used Cauchy Integral Formula
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
timid silo
how do you find the range of a trig function with a given equation?
obtuse pebbleBOT
how do you find the range of a trig function with a given equation?
leaden ibex
the range of sine and cosine is [-1;1], the range of tan and cot is (-inf;inf)
waxen radish
how do you find the range of a trig function with a given equation?
by their definitions, if you refer to mathematically, idk
timid silo
the range of sine and cosine is [-1;1], the range of tan and cot is (-inf;inf)
what about when it has transformations>?
leaden ibex
I mean, then the range is changed accordingly.
🤷
sin^2(x) has a range of [0;1]
69*sin(x) has a range of [-69;69].
timid silo
$Asin(\omega x + \phi) + k$
warm shaleBOT
sqrt(-1) is approx -30
timid silo
ye
obtuse pebbleBOT
@timid silo Has your question been resolved?
timid silo
help pla
timid silo
timid silo
wait
first one is 30/42=25/? = ?/28 = 15/21= ?/14 = 5/?
the question marks are unknown
zealous tangle
Right
Give me a sec
@timid silo, take all the question marks as x. So, 30/42=25/x = x/28 = 15/21= x 14 = 5/x
timid silo
ok
zealous tangle
Let's first tackle: 30/42=25/x. How do you go about solving this equation?
zealous tangle
30/42=25/x
=> 30x = 42 X 25
timid silo
man just nvm it i dont understand how ur doing it
timid silo
anyone else can help me?
obtuse pebbleBOT
anyone else can help me?
pale mortar
I csnt see the numbers
night moth
For the fractions to be equal the ratio of the numerator to the denominator has to be the same
I mean fraction is just the ratio between 2 numbers
night moth
Yes?
timid silo
can u help
night moth
For the fractions to be equal the ratio of the numerator to the denominator has ...
This
timid silo
i dont get it
night moth
We are diving the numberator by 6 (30/6 = 5)
Then we also have the divide the denominator by 6. The denominator will be 42/6 = 7 and the fraction becomes 5/7. You can find the rest in a similar way
timid silo
ok
night moth
No
Subtracting the same number from numerator and denominator does not keep the fraction same
You can only multiply and divide by the same number
night moth
Yes
night moth
However, instead of having to deal with decimals you can pick convenient fractions and get to work with nice whole numbers
timid silo
yeah but this is exam revision
night moth
For example 5/7 and 25/?
timid silo
and my teacher said all the questions will be similiar but they will change the number
night moth
and my teacher said all the questions will be similiar but they will change the ...
Sorry i wrote the message wrong, read it again
obtuse pebbleBOT
night moth
Youre welcome
obtuse pebbleBOT
Available help channel!
gritty nest
$\int_{1/N}^{N} \frac{\ln(x)}{x^2+2022x+1} = 0. \text{given $u = 1/x$}$
obtuse pebbleBOT
$\int_{1/N}^{N} \frac{\ln(x)}{x^2+2022x+1} = 0. \text{given $u = 1/x$}$
warm shaleBOT
onsheldon
gritty nest
sorry had to prove it = 0
gritty nest
**onsheldon**
this haha
gritty nest
see idk how to find a substitution of $-x^{-2} dx = du$
warm shaleBOT
onsheldon
gritty nest
yk what i mean righht
tardy epoch
Have you done u sub before?
gritty nest
yea haha
tardy epoch
I suggest doing simpler u sub problems first
gritty nest
no bruh i know how to do u sub
tardy epoch
x = 1/u, what's dx?
gritty nest
just i cant find the alegrabic manipulation for this one
BRUH 💀
-u^-2
du
NAHHH
i forgot you can change it in terms of x 😔
u still there?
tardy epoch
?
tardy epoch
Do the problem and find out
gritty nest
ok
obtuse pebbleBOT
@gritty nest Has your question been resolved?
clear field
obtuse pebbleBOT
clear field
we just started "completing the square" in quadratics and idk how to do these ones
i know that you're supposed to half the co efficient of x
but idk what to do with the fraction
i've tried just halving 5 into 2.5 but that didn't work
high lily
what's the coefficient of x
clear field
and 1.25 didn't work either
clear field
what's the coefficient of x
5
high lily
no
clear field
5/2?
high lily
yes
clear field
ohh
high lily
and what's half of that
clear field
5/4?
high lily
yes
clear field
ohh ok now i see
ok i was just being dumb ty
so for the next one
it'd be half of 2/3
which is just 1/3
alr i see now ty
.close
dawn osprey
I missed a week at school due to complications and now I'm stumped. Please help me.
obtuse pebbleBOT
I missed a week at school due to complications and now I'm stumped. Please help ...
dawn osprey
I need help with c specifically
main cedar
Have you learnt what the discriminant means
dawn osprey
I googled it but yes i know what it equals
main cedar
For part b i, what did u get for k
main cedar
nah, it should be fine for now
then do you know the quadratic equation that is being represented by the graph in part b i?
main cedar
what do you get if you replace y
dawn osprey
0 = 6x - x^2 - 6
main cedar
yes, now what would the discriminant become for that equation
dawn osprey
i got 12
dawn osprey
there are 2 solutions
main cedar
yup that's it
dawn osprey
ok i get it now tysm
main cedar
algs
dawn osprey
.close
devout hatch
just going over revision for limits, what are the various limit rules you can use?
there's squeeze theorem and l'hopitals room as far as i remember, are there others?
and l'hopitals rules, does it apply when its 0/infinity or infinity/0 ? what do you do when the limit is found to be those limits?
thx:)
obtuse pebbleBOT
just going over revision for limits, what are the various limit rules you can us...
trail tiger
0/0 and inf/inf
also not a theorem as far as i'm aware, but compare how fast functions grow
devout hatch
ah thats right, so if the limit is for x, you substitute x = 0.001 or 1000000 (depending if its 0 or infinity) to find the real limit
are there other rules or do i have them all?
trail tiger
no
if it's 0/0 or inf/inf it's l'hospital
if it's trig, you generally use the squeeze
if it's neither, simplify as much as needed, and then use common sense
obtuse pebbleBOT
Why is the channnel not having my name
west sierra
A 5.2 molal aquous solution of methyl alcohol CH3OH is supplied. What is the mole fraction of methyl alcohol in the solution?
If anyone knows chemistry then please do help
restive ridge
ask in the chemistry discord not here
restive ridge
then have patience
west sierra
Yes i am trying to
I asked this same question in 3 chemistry discord servers
Including this one
It's already been 5 minutes
Once I get answered in any one of them, maybe here as well it's considered a great help
warm shaleBOT
scarlet locust
.
scarlet locust
1 kg solvent not soln
scarlet locust
scarlet locust
Happens
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
devout hatch
what goes into determining if if an equilibrium is stable? i dont quite understand the graph with t. thanks!
ive taken this space im not sure why its not getting occupied
<@&286206848099549185>
.close
candid halo
.try again @devout hatch
devout hatch
what goes into determining if if an equilibrium is stable? i dont quite understand the graph with t. thanks!
.try
.try again
i got this other one nvm
obtuse pebbleBOT
static patio
what is a sufficient condition for differentiating power series ?
static patio
u know that this s a power series?
yes
candid halo
@static patio btw please ask your question in a new channel. bot had a restart that messed up some things
static patio
<@692635975678951464> btw please ask your question in a new channel. bot had a r...
ok
obtuse pebbleBOT
Available help channel!
timid silo
obtuse pebbleBOT
timid silo
how we get to the last step
is it some variation of the geometric series?
why is 1/(1+3(z-zk)/zk +o(2)) = 1-3(z-zk)/zk + o(2)?
okay sorry
got it now
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
timid silo
Hello
timid silo
I have a question about my exercise of irrational limit
fierce lagoon
Just show the problem
timid silo
This was the exercise (from my test)
Sorry for my writing
I tried to remake it but can’t get the answer (which is 1/3)
fierce lagoon
Hm
Well there's a couple of things
I'm gonna start with the most-asked question
Are you familiar with L'Hopital's Rule?
timid silo
Yes
fierce lagoon
I would always try to use L'Hopital's just for the sake of avoiding multiplying by conjugates
timid silo
Yes I know, but that's on the derivatives test. Here the teacher wants us to also be able to do this through limits.
fierce lagoon
L'Hopital's applies on limits
timid silo
Yes, but we also learned that for the limit of an irrational function, we have to use the added expression (as applied here)
The derivative was later on the test with l'hôpital
fierce lagoon
Well you can start with this:
You have $\frac{f(x)}{g(x)}$, where $f(x) = \sqrt{x^2-7}-3$ and $g(x) = 4x-x^2
Show that $\lim_{x\to 4} f(x) = 0$ and show that $\lim_{x\to 4} g(x) = 0$, state that because of such conditions that L'Hopital's Rule applies. Then use L'Hopitals
It's being an egg
Hold on
warm shaleBOT
Umbraleviathan
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
kind hawk
I tried to remake it but can’t get the answer (which is 1/3)
you can't cancel the x^2 in the denominator with the x^2 under the sqrt
after canceling x-4 you can just plug in 4
and then it simplifies to 1/3
no need to do whatever you tried to do here
timid silo
Uh can you maybe write that, because I don’t understand this English (sorry I’m Belgian)
Can you send a picture
timid silo
Uh can you maybe write that, because I don’t understand this English (sorry I’m ...
I’m not familiar with English math terms
kind hawk
\begin{align*}
\lim_{x\to 4} \frac{\sqrt{x^2-7}-3}{4x-x^2}
&=\lim_{x\to 4} \frac{\sqrt{x^2-7}-3}{4x-x^2} \cdot \frac{\sqrt{x^2-7}+3}{\sqrt{x^2-7}+3} \
&=\lim_{x\to 4} \frac{x^2-16}{x(x-4)(\sqrt{x^2-7}+3} \
&=\lim_{x\to 4} \frac{x+4}{x(\sqrt{x^2-7}+3} \
&=\frac{8}{4\cdot (\sqrt{16-7}+3)} \
&=\frac{8}{4\cdot 6} \
&=\frac{1}{3}
\end{align*}
warm shaleBOT
Denascite
obtuse pebbleBOT
@timid silo Has your question been resolved?
true fractal
how can 0^0 be 1 but 0/0 be undefined
obtuse pebbleBOT
how can 0^0 be 1 but 0/0 be undefined
alpine raven
not its not
alpine raven
people defined 0^0 = 1 because of something with taylor expansion if i remeber correctly
true fractal
so is there a real proof that 0^0 is 1 or are we just saying it is?
scarlet locust
The closest "proof" is the limit
alpine raven
^
scarlet locust
lim x^x = 1
x -> 0
leaden ibex
,w limit of x^x as x goes to 0
warm shaleBOT
scarlet locust
,w plot x^x
warm shaleBOT
true fractal
alright but its not certain then
leaden ibex
,w plot 0^x
warm shaleBOT
leaden ibex
Again, it's a convention.
nimble wing
hi
sullen slate
ask your question please
slate cosmos
Give them a sec
nimble wing
been given a task to "invert" the base of 100² and calculate the value
i interpret this to mean 1 / 10 000 = 0.0001² = 0.0002 correct?
drifting wraith
makes sense yeah
sullen slate
so ig it should be (1/100)^2
nimble wing
makes sense too 🙂
sullen slate
,eval (1/100)^2
warm shaleBOT
nimble wing
the final task was invert the exponent of the same expression 100²
so 100^ 1/2 ?
slate cosmos
,eval (1/100)^2
,w (1/100)^2
warm shaleBOT
orchid root
obtuse pebbleBOT
orchid root
can someone help how to get through ?
restive ridge
multiply out the parenthesis then use u sub
orchid root
its root(x-3) correction
orchid root
multiply out the parenthesis then use u sub
umm i could not get you
restive ridge
what part
I guess you don't even need to multiply out the parenthesis
you can just u sub sqrt(x-3)
orchid root
umm you mean integral (x-2)t dx ?
orchid root
then 😐
restive ridge
do you have class notes?
orchid root
yes some
kind hawk
$(x+2)\sqrt{x-3} = ((x-3)+5)\sqrt{x-3}$. can you work with that?
warm shaleBOT
Denascite
orchid root
is this the answer in any case ?
kind hawk
,w int (x+2)sqrt(x-3) dx
warm shaleBOT
kind hawk
yup
kind hawk
yes
warm shaleBOT
YashMajor
