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#help-26
topaz sinewBOT
Available help channel!
wild brook
So like
topaz sinewBOT
@wild brook Has your question been resolved?
topaz sinewBOT
@wild brook Has your question been resolved?
wet herald
Are you familiar with the Chinese Remainder Theorem?
wild brook
Are you familiar with the Chinese Remainder Theorem?
Yes
I just don't know how to apply it to
Well
Sum ._.
wet herald
The last two digits are equivalent to taking the remainder mod 100. What two modulos does the CRT let you reduce it to?
wild brook
The last two digits are equivalent to taking the remainder mod 100. What two mod...
I'm familiar with it, doesn't mean I know how to use it lol
wet herald
Try reading this https://brilliant.org/wiki/chinese-remainder-theorem/
wild brook
Try reading this https://brilliant.org/wiki/chinese-remainder-theorem/
gave me more questions than answers
wet herald
Keep reading. They give a lot of examples. See if you can apply some to your problem.
wild brook
Keep reading. They give a lot of examples. See if you can apply some to your pro...
I've read most of it in the pretty short span you gave it to me
I'm left with more questions than answers
that's the three line equal sign
what's mod
and even more
wild brook
So like
like no. 2, How do I even find the ones for 2022^2022^n, n>1
(22^2022)mod100=84^1011mod100
wet herald
$a \equiv b mod n$ means that $n$ divides $a - b$. So you can view $b$ as the remainder with respect to $n$.
I'm pretty sure you haven't seen the examples, but the short answer reduce the base of the exponent with modulos and use Euler's Totient function to reduce the exponents.
thorny flameBOT
chencking
wild brook
=-16^1011mod100
wild brook
**chencking**
I don't know who euler is '<'
wet herald
You don't want to work with mod 100. Mod 100 is difficult. Try reducing it to smaller mods that are easier to work with using CRT. It's much more manageable.
wild brook
=-16^1011mod100
4^337mod100
wet herald
I don't know who euler is '<'
I'm sure you can find the function on google. I strongly recommend looking through those examples if you are still unsure how to use the CRT.
wild brook
I'm sure you can find the function on google. I strongly recommend looking throu...
I learned how to use it '<'
It's just confusing to yk
use for this specific question
wild brook
4^337mod100
I wonder if you can separate mods such that 4^1 * 4^336mod100 or smth
wet herald
I wonder if you can separate mods such that 4^1 * 4^336mod100 or smth
You can separate mod 100 using the CRT. I strongly recommend reading the examples if you do not see how.
wild brook
topaz sinewBOT
@wild brook Has your question been resolved?
timid kraken
Hello. P(x) and Q(x) polynomials are equal. I need to find a,b,c,d,e. I found d,c,e, but can't find a and b. Please help
topaz sinewBOT
Hello. P(x) and Q(x) polynomials are equal. I need to find a,b,c,d,e. I found d,...
timid kraken
Hello. P(x) and Q(x) polynomials are equal. I need to find a,b,c,d,e. I found d,...
,rotate
thorny flameBOT
still urchin
You should equate the coefficients of the same powers like the coefficient of x^3 in p(x) is the same as the coefficient of x^3 in q(x)
clear lodge
and you should also do the same for the coefficient in x^6 on both
timid kraken
But there is no x⁶ on the Q
still urchin
this means that its coefficient = 0
timid kraken
а=0?
still urchin
a+4=0
frosty nacelle
topaz sinewBOT
topaz sinewBOT
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).
frosty nacelle
bruh i am asking questin in this
elder ocean
Ok
topaz sinewBOT
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@frosty nacelle Has your question been resolved?
topaz sinewBOT
frosty nacelle
.reopen
topaz sinewBOT
✅
topaz sinewBOT
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frosty nacelle
<@&286206848099549185>
topaz sinewBOT
@frosty nacelle Has your question been resolved?
tender girder
topaz sinewBOT
tender girder
how do i simplify this
I'm gonna throw up if I gotta spend half an hour doing another problem
icy sky
Ok start with the negatives, what happens when you have two negative numbers multiplied together?
tender girder
positiv3e
buoyant loom
its 6
tender girder
lol thank you Kaz
how did you get 6
I'm guessing like ummmmmmm 3 and 12 or something
neon iron
guys there is this math problem in which the bases of a trapezoid have a difference of 16cm . One of the bases is 7/3 of the other base and the area is of 240 cm². How do I find the height
topaz sinewBOT
guys there is this math problem in which the bases of a trapezoid have a differe...
elfin sparrow
The bases differ by 16, and one base is 7/3 times the other base
That's enough to find the length of both bases
After that you can find the height since you're given the area
neon iron
After that you can find the height since you're given the area
I knowww the problem is that I forgot how to find the 2 bases with those infos
elfin sparrow
The bases differ by 16, and one base is 7/3 times the other base
can you express these two relationships as equations?
then you can solve the system
neon iron
oh yeah I get it thanks
neon iron
topaz sinewBOT
neon iron
can anyone explain these 2 lines
meager apex
Idk i been stuck on so many different versions of this problem for a min
tall wolf
no 11 is mine
tall wolf
there we go
tall wolf
-1/3 is wrong just by plugging it in
do you know how to properly solve absolute value?
you have two cases
one where everything inside the absolute value is multiplied by negative and one where everything inside stays the same sign
tall wolf
3 was originally correct
meager apex
oh?
meager apex
I used -3x+2 tho
tall wolf
you did it wrong
meager apex
k
meager apex
-3/5 mmm
tall wolf
nope
meager apex
you added it to the 4 ok
topaz sinewBOT
topaz sinewBOT
Available help channel!
rotund coyote
ive figured out the rest but im kinda struggling on this one
topaz sinewBOT
ive figured out the rest but im kinda struggling on this one
wispy hedge
ive figured out the rest but im kinda struggling on this one
what do you know about ranges
jaunty wedge
Are they talking about line plot or domain and range?
Because if they are talking about line plot, then it is the biggest number minus the smallest
topaz sinewBOT
does anyone know the answer to this problem
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).
jaunty wedge
Because if they are talking about line plot, then it is the biggest number minus...
but if they are talking about domain and ranges than the ranges would be the numbers under y which are in this question, 9, 0, -7, and -1
jaunty wedge
jaunty wedge
Are you still stuck on that question?
rotund coyote
yes 😭
sorry man
i done retaken this bout 3,4 times this my final chance to redeem myself
rotund coyote
aight
jaunty wedge
I believe it is the second option
The first option is the list of the domains and the third and fourth options are the lists of both the domains and the ranges. Only the second option is the list of ranges.
keen scaffold
lemme look this up
which app did u look it up want to know
rotund coyote
okay tysmm
jaunty wedge
okay tysmm
u're welcome
jaunty wedge
which app did u look it up want to know
I also went on youtube and found a youtube explaining it
'Khan Academy' and 'The Organic Chemistry' specifically
they are pretty good at explaining things and it makes it easier to understand
keen scaffold
'Khan Academy' and 'The Organic Chemistry' specifically
ohh thanks
rotund coyote
this is an extra credit one idk if you wanna try and do it but if u do tysm 😭 @jaunty wedge
jaunty wedge
it's the third option
I think
because when the tub is full, it's at 40
but once it's empty it's at 0
and since the table is going to go on until the water is all drained
the range would be all the real numbers from 0 to 40
tall canopy
can someone explain this math problem for me
topaz sinewBOT
can someone explain this math problem for me
tall canopy
sour walrus
You find area of rectangles by multiplying length and width. So, if you're given a length and a width, how do you find the area?
topaz sinewBOT
@tall canopy Has your question been resolved?
tall canopy
You find area of rectangles by multiplying length and width. So, if you're give...
so 39.9 is what i got
sour walrus
39.9 square meters. Is it making you put units?
Or significant digits so you have to round or something?
Because 39.9 m^2 sounds right.
topaz sinewBOT
@tall canopy Has your question been resolved?
silver yacht
someone please help me with this - i’ve been stuck for quite a while now
silver yacht
i know that it goes to three but i don’t know how to show it
part b*
<@&286206848099549185>
topaz sinewBOT
@silver yacht Has your question been resolved?
topaz sinewBOT
@silver yacht Has your question been resolved?
keen venture
@silver yacht
Such a limit would be a solution to
x = ³√[7x + 6]
silver yacht
<@387528332603949056>
Such a limit would be a solution to
x = ³√[7x + 6]
But how do I solve that 🥲
keen venture
You don't necessarily need to. Just need to show x = 3 works.
So sub that in
But if you did want to, this is a cubic and you can solve it with factorization
But you shouldn't want to lol
@silver yacht
silver yacht
You don't necessarily need to. Just need to show x = 3 works.
ohhh okay thank you so much 🙂
topaz sinewBOT
topaz sinewBOT
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oblique hill
Why is this the sinuse if sinuse is the opposite/hypothenuse
topaz sinewBOT
Why is this the sinuse if sinuse is the opposite/hypothenuse
drifting swift
the hypotenuse is 1
oblique hill
.close
oak ginkgo
topaz sinewBOT
oak ginkgo
topaz sinewBOT
@oak ginkgo Has your question been resolved?
topaz sinewBOT
@oak ginkgo Has your question been resolved?
rocky harness
x^5 + 11 = t --> 5x^4 = dt --> x^4 = dt/5
Try now
atomic kestrel
Does notQ implying notP give that Q implies P?
topaz sinewBOT
Does notQ implying notP give that Q implies P?
gritty trout
no, ~Q => ~P is logically equivalent to P => Q
otherwise, suppose that you know if its not cloudy, then its not rainy. you can't conclude that if its cloudy, it is rainy
because you'd start from something true and end up at something false 
but you can conclude that if its rainy, then its cloudy
atomic kestrel
no, ~Q => ~P is logically equivalent to P => Q
Right so the implication gives that if P then Q because if not Q then it would be not P
gritty trout
Right so the implication gives that if P then Q because if not Q then it would b...
yeah!
tough viper
how come the average that in group A is higher than group B?
Group A has 3 people and now 6 school days passed
And how many days each person attended:
6, 5, 4
Group B has 6 people and 2 school days passed for them only
And how many days each person attended from group B:
2, 0, 2, 2, 2, 1
sweet shard
how come the average that in group A is higher than group B?
Group A has 3 peop...
,tex .original
thorny flameBOT
riemann
tough viper
,tex \.original
chill i was editing
tough viper
how come the average that in group A is higher than group B?
Group A has 3 peop...
literally group A failed 3 days and group B also failed 3 days...
and avg for group B is 75% OF OVERALL ATTENDANCE RATE but for group A it is 83%
knotty ledge
What does "average" in your question mean if not average attendance rate
knotty ledge
and avg for group B is 75% **OF OVERALL ATTENDANCE RATE** but for group A it is ...
A has a higher average attendance rate as per this
Missing 3 out of 18 is better than missing 3 out of 12
knotty ledge
There were 18 possible points of attendance in group A, they missed 3.
There were 12 possible points of attendance in group B, they missed 3.
Group B have a worse average as they missed 3 in 12, versus missing 3 in 18 for group A
topaz sinewBOT
@tough viper Has your question been resolved?
tough viper
There were 18 possible points of attendance in group A, they missed 3.
There wer...
ok i understand now
topaz sinewBOT
ok i understand now
rustic cedar
@tough viper .close
topaz sinewBOT
@tough viper Has your question been resolved?
topaz sinewBOT
topaz sinewBOT
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raven wagon
i need help with trigonometry
topaz sinewBOT
i need help with trigonometry
drifting swift
winged moat
There are a lot of things trigonometry
raven wagon
http://dontasktoask.com/
bro whats this
drifting swift
- don't call me bro
- that was an invitation to post your actual question rather than just "i need help"
raven wagon
- No need to be offended by that
- You need to actually read what I needed help with tf you acting like Greta Thunberg
main nova
drifting swift
1. No need to be offended by that
2. You need to actually read what I needed he...
i am not offended i am just asking you not to call me that
the correct course of action on your part is to apologize and correct yourself, that's it
winged moat
Let's all keep calm 🙂
reef harness
topaz sinewBOT
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safe sphinx
topaz sinewBOT
charred hearth
This doesn't feel like a full question?
Is the first matrix multiplied by anything?
@safe sphinx
topaz sinewBOT
@safe sphinx Has your question been resolved?
topaz sinewBOT
@safe sphinx Has your question been resolved?
kindred finch
what you want to do is match up the entries. So y = 2x -7 is one equation
can you do the rest?
@charred hearth
topaz sinewBOT
@safe sphinx Has your question been resolved?
cyan sand
topaz sinewBOT
cyan sand
This is a proof I wrote, however I'n not sure if the logic is correct and/or I am writing with the proper notation?
I feel like im supposd to state my assumptions a certain way, and my conclusion a certain way .
<@&286206848099549185>
topaz sinewBOT
@cyan sand Has your question been resolved?
topaz sinewBOT
@cyan sand Has your question been resolved?
topaz sinewBOT
@cyan sand Has your question been resolved?
urban grove
Where do you prove that A \subset B implies that A \cap (X \ B) = emptyset?
urban grove
This proof doesn't work because you only proved it for specific sets A and B
but you need to prove it for all finite sets A and B
surreal gazelle
is this lookign right?
topaz sinewBOT
@surreal gazelle Has your question been resolved?
surreal gazelle
well
i am just lost in general on how to do it
i pluged in 5 to the eqution and got 19
neon iron
is this lookign right?
question is asking for a tangent line at (1,-5) and you'll need to find the slope at that point right
do you know how to differentiate a function to get the 'gradient function'
surreal gazelle
do you know how to differentiate a function to get the 'gradient function'
um no
neon iron
um no
okay lets do this another way
do you know how to sketch tangent lines
or what a tangent line is
surreal gazelle
yes
neon iron
is this lookign right?
do you have an idea of where that line would lie
surreal gazelle
somewhere around (2,-3.5) ?
neon iron
the line would hit (1,-5) 
there could be a way to approach this problem without finding the gradient function idk
surreal gazelle
bro
neon iron
neon iron
hummmmmmmmmmmmmmmmmmmmmmmm
you havent done any calculus
topaz sinewBOT
@surreal gazelle Has your question been resolved?
surreal gazelle
eh, i give
eager hill
kinda lost on how to get started on this question
topaz sinewBOT
kinda lost on how to get started on this question
@eager hill Has your question been resolved?
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teal lark
given a manifold in n dimensions that lies in n+1 space (like a napkin on the table), how do we define a deformation along some axis so that some of its point get closer in dimension n+1 without changing their position on the manifold? (like folding a napkin in 2)
topaz sinewBOT
given a manifold in n dimensions that lies in n+1 space (like a napkin on the ta...
@teal lark Has your question been resolved?
sour dirge
given a manifold in n dimensions that lies in n+1 space (like a napkin on the ta...
If $$\Phi: \mathcal{U} \subset \mathbb{R}^n \rightarrow \mathbb{R}^{n+1},
$$ (under valid conditions) we can say deformation function smth $$F_t : \mathcal{M} \rightarrow \mathbb{R}^{n+1},$$ $$F_t(x) = x + t\mathbf{v}(x),$$ where $\mathbf{v}(x) = c(x) \mathbf{N}(x),$ and $c(x)$ is a smooth scalar function.
thorny flameBOT
adzetto
sour dirge
topaz sinewBOT
@teal lark Has your question been resolved?
teal lark
thanks. im not sure i get it tho can u give a little bit more details
sullen plover
if the integration of ( ln x) dx = x ln x - x, thn similarly the integration of (log x) dx = x log x - x, if the base for the log is cost let say a= 10?
topaz sinewBOT
if the integration of ( ln x) dx = x ln x - x, thn similarly the integration of ...
mellow arrow
$\log_{10}x=\frac{\log_{e}x}{\log_{e}10}$
thorny flameBOT
B-eard
mellow arrow
log_e(10) is a constant
thorny flameBOT
B-eard
sullen plover
like x log{10} x - x
mellow arrow
no
sullen plover
ohh
mellow arrow
$\int_{ }^{ }kx=k\int_{ }^{ }x$
thorny flameBOT
B-eard
sullen plover
yhe
teal lark
but how did you get to that equation
sullen plover
if the integration of ( ln x) dx = x ln x - x, thn similarly the integration of ...
this ?
thick inlet
You have to do integration by parts I believe
mellow arrow
no
thick inlet
at least that's how I learned it
rewrite integrand as ln(x)/ln(a)
pull out 1/ln(a) as a constant
mellow arrow
$\int_{ }^{ }\frac{\log_{e}x}{\log_{e}10}=\frac{1}{\log_{e}10}\int_{ }^{ }\log_{e}x$
thorny flameBOT
B-eard
sullen plover
yh
topaz sinewBOT
Available help channel!
main sparrow
topaz sinewBOT
thorn raven
hey I have a question. is cos^2(2x) equal to (cos^2 (x) - sin^2(x)) ^2?
silk delta
hey I have a question. is cos^2(2x) equal to (cos^2 (x) - sin^2(x)) ^2?
!help
topaz sinewBOT
hey I have a question. is cos^2(2x) equal to (cos^2 (x) - sin^2(x)) ^2?
To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.
main sparrow
restive inlet
how would you solve something like
3x=7
devout creek
What's the issue here?
main sparrow
how would you solve something like
3x=7
3x_=7?
restive inlet
you didn't seem to do anything except make a typo while copying what I asked
main sparrow
i need help not additude
restive inlet
I'm trying to help, but the intentions/meaning of your reply was very unclear
main sparrow
im confused on how to answer the question so i wouldnt know how to do that
restive inlet
I was attempting to give you similar less intimidating examples
for which the same idea can then be applied to this question
main sparrow
ok
restive inlet
try first reading the following, might take a while for the bot to compile
split igloo
If x=2, what's 3x?
restive inlet
,tex .algebra lesson
main sparrow
x=3?
split igloo
x=2
topaz sinewBOT
split igloo
💀💀
split igloo
u said wuts 3x
As in 3x = ?
topaz sinewBOT
Available help channel!
maiden basalt
Hi
maiden basalt
So i tried searching geometric sequence because im confused now.im more confused
Im confused on how he got -16 and -128 it doesnt make sense
It just messed up sequencing
knotty ledge
Maybe don't ask chatgpt next time
maiden basalt
Maybe don't ask chatgpt next time
So he is wrong?
knotty ledge
Clearly
maiden basalt
256, _, _, -32, 16
I need help at this
Im confused on hownit become positive to negative to positive
kindred finch
So he is wrong?
it* is wrong 🙂
topaz sinewBOT
@maiden basalt Has your question been resolved?
maiden basalt
<@747744987801976834> Has your question been resolved?
Yeh and no
topaz sinewBOT
topaz sinewBOT
Available help channel!
copper bay
topaz sinewBOT
copper bay
Hi, what does "negatively-sloped line passing through the equilibrium point which separates the graph of $f(x)$ from the horizontal axis." mean? The context is the phase plane of the 1D dynamical system $x'(t) = f(x(t))$
thorny flameBOT
Paschalis Chinos
copper bay
I guess that's what it means, where f(x) is in green?
if f(x) is differential at the equilibrium point and its a stable equilibrium, shouldn't such a line always exist?
Actually if the derivative of f(x) at 0 is is 0 then I guess it's not exponentially stable
topaz sinewBOT
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topaz sinewBOT
topaz sinewBOT
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candid sandal
Hi, F(x)= ∛x
- Calculate in f’(1)
- Determine the linear approximation of the function f at a=1
- What values does this linear approximation of ∛0.99, ∛1.01, ∛1.05 and ∛4 provide? Are these approximations by excess or by default? Justify graphically.
- Compare these 4 values to the values provided by the calculator. What do we observe?
topaz sinewBOT
Hi, F(x)= ∛x
1) Calculate in f’(1)
2) Determine the linear approximation of the ...
candid sandal
Can someone help me please?
keen raptor
First, find f'(x)
candid sandal
i have already done a, b and c but i don't know how to find if it's by excess or by default
keen raptor
Maybe it's asking if they're over approximations or under approximations?
Did you translate it from another language?
candid sandal
yeah from french
candid sandal
yeah
keen raptor
ok so it's asking whether the approximations are too high or too low
And it suggests looking at the tangent line on the graph to do that
candid sandal
so if L(4) = 2 and f(4) = 1,5 so its by excess?
keen raptor
Yeah
keen raptor
Yeah
candid sandal
okey thank you so much
keen raptor
no prob
topaz sinewBOT
keen raptor
u2
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Available help channel!
plush prawn
Hi guys, why
topaz sinewBOT
Hi guys, why
plush prawn
$\frac{1}{n} < \epsilon \Longleftrightarrow n > \frac{1}{\epsilon}$
drifting swift
inappropriate use of = -- should be \iff instead
also it should be known that n and epsilon are both positive
plush prawn
yup
thorny flameBOT
Raid
plush prawn
My question is how can I isolate n?
prisma mesa
can we assume that n is natural number?
prisma mesa
so since n is positive, you can multiply both sides by n
plush prawn
if I multiply n on the left and right side I get 1 < epsilon * n
prisma mesa
yeah, this works iff n is positive btw
if n was negative it would be 1 > epsilon * n
plush prawn
why do I have to change the direction of my disequality?
sorry for the bad english if that's the case
prisma mesa
generally, multiplying/dividing by negative number changes the "direction"
if 1 < 2 then -1 > -2
plush prawn
yeah but if I have 1<epsilon * n
I would have to divide epsilon
so it changes the direction?
plush prawn
I would have to divide epsilon
to get n
prisma mesa
so it changes the direction?
it depends
do you have information about epsilon?
Like epsilon > 0
plush prawn
yea assuming that its > 0
prisma mesa
so epsilon is positive
so you can divide both sides by epsilon without changing the direction
so 1/epsilon < n
thorny flameBOT
Raid
plush prawn
so n > that
prisma mesa
yep
prisma mesa
yw
plush prawn
.close
topaz sinewBOT
@drowsy frost Has your question been resolved?
gritty trout
yeah 
when you have <stuff> = 1/B, you can also just say that <stuff>^{-1} = B
or 1/<stuff> = B
crisp niche
topaz sinewBOT
crisp niche
im still struggling to turn the 1st equation to the 2nd
im left with this, can we just think e^C as C since its a constant?
stuck forum
if that's ln, yes
crisp niche
it was from here
crisp niche
if that's ln, yes
still yes?
stuck forum
i'm looking at pg 90 and i'm guessing they took exponential of both sides
then took out e^K and turned it into another constant
bit of a poor notation, but they just called it K again
cedar kindle
Why is there a ( -2x )?
topaz sinewBOT
Why is there a ( -2x )?
cedar kindle
In step 2
crisp niche
its a derivative from -x^2
cedar kindle
Why do I need that. I thought I only needed the derivative of (1-x^2)^1/2?
cedar kindle
.close
topaz sinewBOT
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fair drift
please can somone helo me wth this 3^(x+1) - 3^x = 162
topaz sinewBOT
please can somone helo me wth this 3^(x+1) - 3^x = 162
fair drift
problem
tulip sequoia
You can do by trial and error. Try substituting values
fair drift
hello?
fair drift
You can do by trial and error. Try substituting values
I got the value is 4
but I want to work it out
tulip sequoia
Okay
fair drift
If you could help?
tulip sequoia
Write 3^(x+1) as 3×3^x
fair drift
yh
fair drift
yh
tulip sequoia
3^x × (3-1) =162
tulip sequoia
x is in exponent power
tulip sequoia
No
3^x × (3-1) =162
3^x × 2 = 162
Dividing by 2 on both sides
3^x = 81
fair drift
No
3^x × (3-1) =162
3^x × 2 = 162
Dividing by 2 on both sides
3^x = 81
but the 3-1 is in exponect power tho
uve been helpfull thanks alot
im going to close it now
.close
topaz sinewBOT
fair drift
im done
topaz sinewBOT
Available help channel!
queen jasper
I am revising and need answers to these questions. I have answers to them.
Questions 7,8,10 and 1 ii
topaz sinewBOT
I am revising and need answers to these questions. I have answers to them.
Ques...
@queen jasper Has your question been resolved?
queen jasper
<@&286206848099549185>
digital spire
Do you… need help on them?
I think it is generally inadvisable to just give the answers
queen jasper
Oh mb
queen jasper
I think it is generally inadvisable to just give the answers
I have the answers I figured out question one but for the others I can never get the answer right
I’m close but not the answer
digital spire
Where are you up to for number 9?
queen jasper
I did number 9
queen jasper
I meant I finished question 1 ii
digital spire
I’m a little bit confused. Which ones specifically would you like help on?
digital spire
I see
queen jasper
If it’s purely imaginary then the real part has to be 0 ?
Therefore x + 3 should equal 0
So x = - 3
Oh right there can’t be imaginary on the bottom
digital spire
We have (x + 3) + (2 + y)i as the numerator
queen jasper
Idk
digital spire
Try multiplying the top and bottom by the conjugate of the denominator
queen jasper
But surely that would times the x + 3 too so that would not help
digital spire
What do you mean?
queen jasper
Doing that would time (x + 3 ) aswell no ?
digital spire
Yes, but why is that an issue?
queen jasper
Because u would still have imaginary on bottom no ?
digital spire
The (x + 3) is the real part
queen jasper
Yes
digital spire
multiplying by the conjugate always gives you a real number
That was actually one of the questions you had to do!
Question 9
queen jasper
Yes but would u not have to multiply (x + 3 ) by the conjugate
digital spire
Ah, I see your confusion
The entire complex number is (x + 3) - (2 + y)i
They are not 2 separate complex numbers
digital spire
so multiplying by the conjugate, which is
(x + 3) + (2 + y)i
eliminates the imaginary bits
queen jasper
Yeah that makes sense !
digital spire
Now, then you simplify the top and then eventually get to where you need to be
queen jasper
Yeah that’s not that bad I just couldn’t figure out what to do
Ty
Acc if u have time I have one more question
digital spire
Sure
queen jasper
Lemme find the question rq
For part ii
If w is a root you should divide the whole thing by W right ?
round gorge
is it AoPS volume 1?
digital spire
The approach for that is noting that if all coefficients are real then also 1 - 2i will solve the equation
queen jasper
is it AoPS volume 1?
What does that stand for ?
round gorge
art of problem sovling
queen jasper
art of problem sovling
No it’s not
round gorge
ok
queen jasper
The approach for that is noting that if all coefficients are real then also 1 - ...
Sure but still there are two unknowns
digital spire
so then you can divide (personally dislike) or write
(z - (1 + 2i))(z - (1 - 2i))(z^2 + Bz + C)
and expand, compare coefficients
digital spire
Sure but still there are two unknowns
Or
queen jasper
so then you can divide (personally dislike) or write
(z - (1 + 2i))(z - (1 - 2i...
Sure that makes sense
digital spire
Substitute in 1 + 2i and use the factor theorem to note that the polynomial will equal zero
then 1 - 2i, same thing
digital spire
then 1 - 2i, same thing
Then simultaneous equations
digital spire
so then you can divide (personally dislike) or write
(z - (1 + 2i))(z - (1 - 2i...
For this one?
queen jasper
Yes I thought so ?
digital spire
What we are doing there is expanding all that out and comparing with the known terms of the quartic in the question
neon iron
(send help i need an study buddy and i know such an small number of people that i have resorted to come back to my 2020 discord account because i have no other social media account)
digital spire
?
queen jasper
What we are doing there is expanding all that out and comparing with the known t...
Right but if we substitute z as w
Surely we can not figure out yet
digital spire
We can because we’ll have expressions involving B and C
queen jasper
Sorry but I don’t understand how
How will u able to compare the coefficients of p and q
queen jasper
Yes
digital spire
We will make use of those
to find out B and C
then, we will substitute into the expressions of B and C representing p and q
to find them
Pretty long though
queen jasper
Okay we haven’t rlly been taught about quartile yet
If I just use an equation solver on calc could I just find B and C quickly
We are allowed to do so
digital spire
Okay we haven’t rlly been taught about quartile yet
Quartile?
queen jasper
Quartic it was autocorrect srry
digital spire
If I just use an equation solver on calc could I just find B and C quickly
You still would have to expand the whole thing
like the easier thing is to sub in w and w*
set equal to 0
queen jasper
Okay sub it in
digital spire
Umm…
just a little bit concerning because it should stipulate p and q are real
but I’m sure that’s an oversight
queen jasper
Yeah it wouldn’t be that hard I hope 😅
digital spire
🕺
queen jasper
Okay ty so much for the help
I still don’t understand how to get B and C once u sub in W but I will watch a video about quartics in the morning
Ty
digital spire
I still don’t understand how to get B and C once u sub in W but I will watch a v...
Not specific to quartics
queen jasper
Alr so how would it work on a quadratic for example
So if u sub in eg 25 + p5 + 65 = 0
Obviously u can figure out p
But if there’s two terms ?
queen jasper
Ok ty so much
digital spire
See here
Now, there are no unknowns in the original equation, true
But if there were, they would be findable as long as we still had the last terms
See that they have only compared the z^4, z^3 and constant terms
That means the z^2 and z terms could have had unknowns
and it still would have worked
queen jasper
Yes that makes sense now 👍
We haven’t rlly gone through in class properly but we have done some stuff like this
Except I remember that our teacher put a k infront of the the brackets e.g k(x - r/s)(x-x/y)
Anyway I need to go now
But Tysm!
If u have anything more advice or help feel free to dm me because it rlly helped !
.closed
.close
quartz sigil
Goal is to reduce the number, and the correct answer is -8. I have been struggling and have no idea why the answer is 8x^14 instead of just x^14 on a)
topaz sinewBOT
Goal is to reduce the number, and the correct answer is -8. I have been struggli...
solemn jay
Goal is to reduce the number, and the correct answer is -8. I have been struggli...
the power goes to all the terms including 2
solemn jay
the power distributes to every term
ur just faster 
quartz sigil
But wouldn't that make it 16x^14?
vital relic
theres a 2 on the bottom
solemn jay
,w (2x^5)^4
thorny flameBOT
solemn jay
so its gona be
quartz sigil
i think thats enough help, ill close this thanks ill ask again if i fail to understand .close
solemn jay
$\frac{16x^{20}}{2x^6}$
quartz sigil
.close
topaz sinewBOT
solemn jay
alr ig
thorny flameBOT
ahaan
tawdry yoke
I need help with the last one what should the angle be
topaz sinewBOT
I need help with the last one what should the angle be
neon iron
I need help with the last one what should the angle be
what have you tried
neon iron
what was tan(\alpha) = ?
tawdry yoke
For the last three we have to find it
It doesn’t tell you
That’s what I need help with
neon iron
okay what is the definition of tan
neon iron
I need help with the last one what should the angle be
from your SOH CAH TOA
tawdry yoke
For the last one I got 41.2
Second to last I got -41.2
And third to last I got -41.2
But the answer key is different answers
tawdry yoke
So is my answer wrong?
thorny flameBOT
sen
$$\tan{\alpha}=?/?$$
thorny flameBOT
sen
neon iron
Tan-1=7/-8
you do arc tan when you want to get the angle
$$\alpha=\tan^{-1}{(7/8)}$$
@tawdry yoke do you understand what i just did
thorny flameBOT
sen
neon iron
But it’s -8
what was tan \alpha?
neon iron
Opposite/adjacent
you told me tan is opp / adj right
tawdry yoke
Yes
tawdry yoke
Which one
neon iron
What’s alpha
do you want to use A? as the angle instead of alpha
tawdry yoke
For angle I did tan for all of em
tawdry yoke
Yes for the last one
tawdry yoke
neon iron
ah i see
- tan^-1 = -7/-8 is wrong
tan^-1 is a function
like tan
eg tan(45)
tan^-1(3/2)
you do tan^-1 to get the angle
for example lets say we had sin(x) = 5/4 how would we get the angle x?
neon iron
yes
tawdry yoke
How
neon iron
for example lets say we had sin(x) = 5/4 how would we get the angle x?
answer this
neon iron
for example lets say we had sin(x) = 5/4 how would we get the angle x?
what is x
dont calculate anything just tell me what x is in terms of sin^-1
neon iron
hmm i see
neon iron
no we dont do it this way this is why we use sin^-1 or cos^-1 or tan^-1
for my example
sin(x) = 5/4
x = sin^-1(5/4)
see what i did there?
tawdry yoke
Yes
neon iron
so what is y in cos(y) = 3/2
tawdry yoke
3.0
neon iron
sin(x) = 5/4
x = sin^-1(5/4)
no i dont want the calculation
tawdry yoke
-1
neon iron
sin(x) = 5/4
x = sin^-1(5/4)
see how we got x here in terms of sin^-1
cos(y) = 3/2
y = cos^-1(?
tawdry yoke
Cos^-1
tawdry yoke
cos(y) = 3/2
y = cos^-1(?
Yes
neon iron
sin(x) = 5/4
x = sin^-1(5/4)
did you understand what i did here
neon iron
yes
tawdry yoke
Ok but what did I do wrong
neon iron
ok now what about if i want to find the angle y in cos(y) = 3/2
tawdry yoke
Y=cos-1
neon iron
of what?
tawdry yoke
3/2
tawdry yoke
Y=Cos^-1=3/2
neon iron
no remember what i told you
glossy acorn
Y=Cos^-1=3/2
Use parentheses
neon iron
Use parentheses
wait a min pls
glossy acorn
ok
neon iron
Y=Cos^-1=3/2
cos^-1 is a function like cos and other
tawdry yoke
Adjacent and hypotenuse
neon iron
not a number
neon iron
sin(x) = 5/4
x = sin^-1(5/4)
lets go back here again...
i gave you sin(x) = 5/4
i want the angle x
we did the arc sin on the 5/4 to get x = sin^-1(5/4)
neon iron
were sin^-1 cos^-1 tan^-1 explained to you in school
neon iron
Yes they use to find angle that’s it
exactly to find the angle
tawdry yoke
Yes
neon iron
not cos^-1=3/2
that doesnt make sense
tawdry yoke
Yes
neon iron
okay one more last question
cos a = 10/3 find me the angle a
tawdry yoke
Calculator dose t work tho
neon iron
without the use of a calculator
tawdry yoke
Cos-1(10/3)
neon iron
ok now back to your question
neon iron
Still get same answer 41.2 for last one
pls leave your calculator for a second
we'll use it later
tawdry yoke
Ok
neon iron
in your last question you were given a=-7 b=-8 c=? A=? A(is the angle we want to find)
tawdry yoke
I get 654.96
tawdry yoke
in your last question you were given a=-7 b=-8 c=? A=? A(is the angle we want to...
Yes angle and c
neon iron
Yes angle and c
before you do tan^-1 you first represent your answer in terms of tan
so again .. what is tan A = ?/?
neon iron
I get 654.96
no calculators for now pls
tawdry yoke
Tan-1(-7/-8)
neon iron
Tan-1(-7/-8)
that is correct tho
tawdry yoke
Yea that’s fine
tawdry yoke
Oppos and aj
tawdry yoke
It’s already listed
neon iron
It’s already listed
then give me
tawdry yoke
-7//8
neon iron
neon iron
Tan-1(-7/-8)
that is not an equation
tawdry yoke
I honostly can’t really get through this I gotta study for the quiz I got tom
There’s more topics
neon iron
tan A = ?/?
A = tan^-1(?)
tawdry yoke
A=tan^-1(-7/-8)
neon iron
yes
neon iron
but you first start with
tan(A) = -7/8
then
A = tan^-1(-7/8)
neon iron
Can you help me with another page after this
sure i have an hour to spare
tawdry yoke
w
neon iron
but you first start with
tan(A) = -7/8
then
A = tan^-1(-7/8)
pls pls pls always start like this, else the marker wont know where the tan^-1 came from
tawdry yoke
Ok
neon iron
A=tan^-1(-7/-8)
now this is where you plugin to your calculator
neon iron
btw -7/-8 = 7/8 just write like this
tawdry yoke
Oh
neon iron
we can get c
neon iron
btw -7/-8 = 7/8 just write like this<:kekw:752021756650455061>
do you understand why right?
tawdry yoke
Cos
neon iron
full equation pls