hi all. could i get a hint/pointer as what im doing wrong here?
#help-38
dark snow
dark snow
im 99% sure i did each part right but im not sure if theres a different methodology for a lin equation?
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modest onyx
what does this Ce mean? does that say there is a constant value in the function of y inside exponent of e?
full hull
maybe C is constant and e is exponential
modest onyx
maybe C is constant and e is exponential
do you mean like they re multiplied?
full hull
do you mean like they re multiplied?
ye
modest onyx
ye
Is x*C and x+C same when you want to represent constants?
wait no it simply shouldn't
ionic pendant
not generally, but
e^(2x² + 56x + C)
with some arbitrary constant C is equal to
e^(2x² + 56x) * e^C
and e^C is also an arbitrary constant, so we can just call it C
modest onyx
ah okay got it now
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nocturne kernel
can someone explaine how the function should look like? so far what i understand is that there is a function H in complex plane which is defined by y=(x+4)/(x+2). i dont understand where is the "i" in y= (x+4)/(x+2)
nocturne kernel
or is it the same?
nocturne kernel
or is it the same?
no, apperently not, i inputed it in calculator, they are not the same
blissful bison
$Imz=\frac{Rez+4}{Rez+2}\text{, where: }z\in \mathbb{C}$
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Joanna Angel
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**Joanna Angel**
but will it be correct if i subtract from both side im(z)
blissful bison
listen the H is not a function, it is a set located on complex plane, you can only draw it as a set,
nocturne kernel
hm
blissful bison
in other word, it is the set of complex numbers that follow the condtion i wrote above for you
and that is all what you can take it from
nocturne kernel
and that is all what you can take it from
so it not possible to rewrite it in f(z) form yeah? i mean something like f(z) = z -2 +i
blissful bison
some notificaiot, artificial one is possible, bu t that doe snot change the meaning
i write such eventual form for oyu
$H=\left{ z\in \mathbb{C:}f\left( z \right)=0\wedge f\left( z \right)=Imz-\frac{Rez+4}{Rez+2} \right}$
but that is rather diffeerntr way of writng the same and definign the set H
maybe explain where did you find this set H ? mayeb it can help to understand why the set H appeard, but from waht you wrote, it is onyl a set, not a function
nocturne kernel
it was given
blissful bison
do you rememebr precise text ?
potent bone
(...what's x here?)
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Joanna Angel
nocturne kernel
do you rememebr precise text ?
so they gave me a function that is in complex plane f(z) = z+2 -i, and this set H, and they ask me to find f(H). So before you explained it to me that H is a set, i thought it is a function and to find was a function composition of foH
blissful bison
ah yes now all is clear)) but as you can see, the H is a set
and your task is =
to find the image of the set H via function f
nocturne kernel
what do you mean by image of the set H?
nocturne kernel
image is also a set
so its like the set, which i get after i plug the set H in f(z)? yes?
blissful bison
you can look at it in a such way: take, assume, few complex numbers belonging to the set H
if yo can do it
then take them
and put them into yoru funciton f
yes
yoru function f is a complex linear function
so
it works like
paralell shift
since it adss 2 - i
to every eleemnt from H set
nocturne kernel
do you know what this topic is called? i want to read it online, my class is in german and my teacher doesnt upload the script
blissful bison
do you understand it ?
nocturne kernel
and i couldnt find it in german
blissful bison
it can be shown in initial parts of algebra or
initial parts of analytical functions
also called comples analysis
tell me
what do you study ?
maybe it helps, to udnertsand why you need it
mein deutsch ist nicht zu viel aber ihc kann etwas helfen
nocturne kernel
what do you study ?
oh, i dont study yet, its like school for foreigners, whose school leaving certificate is not acknoledged in germany
blissful bison
Bilder von Mengen mit komplexen Funktionen
nocturne kernel
oooo
blissful bison
klar ?
blissful bison
Komplexe Funktionen | geometrische Interpretation
nocturne kernel
Bilder von Mengen mit komplexen Funktionen
thank you stranger danger 🙏
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nimble stone
i wouldnt say its necessary
wraith hinge
there an easier way to go about it?
nimble stone
do actually know about limits
wraith hinge
I see how he got -7 and 1 now
i dont think so
maybe in dif words idk
but when he factors it what happens to the x^2
why is that just gone
nimble stone
youre asking me about something i cant even see
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quasi void
Which of the vectors does not belong to the subspace spanned by -2i + 3j + k and i + j + 2k:
a) -4i + 6j + 2k
b) 3i + 8j + 11k
c) 11i -4j + 6k
d) 10i -5j + 5k
fossil kraken
What does "belong to" mean here?
What does spanned by mean here?
.... And what things do you know how to do with vectors?
Asking Sam
sharp heart
Oh, OK.
fossil kraken
You try. I'm getting no response
sharp heart
Which of the vectors does not belong to the subspace spanned by -2i + 3j + k and...
!status
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Which of the vectors does not belong to the subspace spanned by -2i + 3j + k and...
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
@quasi void Has your question been resolved?
quasi void
So I think I need to put them in an augmented matrix like:
[-2 1 x
3 1 y
1 2 z ]
sharp heart
Right.
quasi void
and then use gaussian reduction to solve it
and then if I get values for x1,x2,x3 it is within the span of the two vectors
my understanding was if one of the answer vectors is a linear combination of the other vectors then it is within the span
sharp heart
Well, what you want is to get two values and a zero.
You're solving for two variables, what you multiplied the first span vector by and what you multiplied the second span vector by.
So, you should have:```
[1 0 a]
[0 1 b]
[0 0 0]
Then you can check that a(-2i + 3j + k) + b(i + j + 2k) equals your vector.
quasi void
So, you should have:```
[1 0 a]
[0 1 b]
[0 0 0]
```
and if I get it in that form that means the vector is within the span of the other two?
sharp heart
Yes, that's right.
You have the scalar multiples for each vector in the span, so you have a linear combination of those vectors.
And all linear combinations of the vectors are in the span.
sharp heart
OK.
quasi void
For vector a) I get x1=2 and x2=0 and b) I get x1=1 and x2=5
sharp heart
OK, so check that those work.
2(-2i + 3j + k) + 0(i + j + 2k) = (-4i + 6j + 2k)
And so forth.
quasi void
ah ok
quasi void
2(-2i + 3j + k) + 0(i + j + 2k) = (-4i + 6j + 2k)
Yes it works for both
sharp heart
OK, so far so good.
quasi void
d) I get x1=-3 and x2=4 and then for c) i'm not getting values so I think c is not spanned within those two vectors
sharp heart
What do you get for the matrix after Gaussian reduction?
quasi void
I get:
[ 1 0 0]
[0 1 0]
[0 0 1]
sharp heart
,w RREF[{{-2, 1, 10}, {3, 1, -5}, {1, 2, 5}}]
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quasi void
I get:
[ 1 0 0]
[0 1 0]
[0 0 1]
this is for C
sharp heart
Oh!
quasi void
I got the same answer for D
sharp heart
,w RREF[{{-2, 1, 11}, {3, 1, -4}, {1, 2, 6}}]
solid kilnBOT
quasi void
,w RREF[{{-2, 1, 10}, {3, 1, -5}, {1, 2, 5}}]
that's so cool woah
sharp heart
That last row means that you have two vectors multiplied by 0 added together to get 0, but you're not getting 0.
So, that's impossible, so that must not be in the span.
sharp heart
Yes, that's right.
quasi void
ah ok thank you so much! This has been very helpful and informative
sharp heart
If you get less nonzero rows than the number of vectors that are spanned, the spanned vectors are linearly dependent.
You're welcome.
You should never get a [0, 0, 0, k] where k isn't 0, though. That's the "it's not in the span" sign.
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sharp heart
No problem.
blazing narwhal
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old plank
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unique pine
what's the issue
old plank
unique pine
what's the doubt
old plank
this is what I did and i am getting the answer as B
unique pine
what's the doubt
^
unique pine
you got the answer as B, which, to me, seems to be correct, and you solved it by yourself, so what did you not understand
its right
the answer is B
well technically all options are wrong
but yeah your best match is B
old plank
But the correct answer according to the solutions is C
wraith hinge
No the right answer is C
old plank
How tho
wraith hinge
For example h=6 satisfies option B but isnt allowed in the problem
unique pine
all the options are technically wrong
wraith hinge
You can see |h-a| as the distance between h and a
inland orbit
6 1/2 is the "ideal" length for each hot dog, halfway between the min and max lengths allowed. The hot dogs are allowed to vary by up to 1/4
from that ideal length
unique pine
yeah, my bad, I'm a bit dumb
inland orbit
The problem with this is that the absolute value being less than 1/2 doesn't mean the actual value is between 0 and 1/2, it would mean between -1/2 and 1/2
If you subtract 6 1/2 instead, you get x-6 1/2 between -1/4 and 1/4
which is exactly what it means to say its absolute value is less than 1/4
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old plank
The problem with this is that the absolute value being less than 1/2 doesn't mea...
Ahhh ok Thanks so much guys!
river shard
please help me to prove this one
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please help me to prove this one
sleek canopy
it was used the triangle inequality |a+b|<|a|+|b|
marble wharf
in general only <=
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muted harbor
Could someone please check if i got these questions correct ?
muted harbor
Also i have a problem for the IVT question
where when i used -2 and 2 i got two negatives
but when i used -3 and 3 i got one negative and positive
not sure what i am supposed to do there
and for 5 (iii) i got a minimum but also 0 = 0 so does that mean it doesnt have a max or a min when x = 0 ?
muted harbor
Which question do you have a problem
5(a) and (b)(iii)
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muted harbor
@hazy light
torn mantle
Hey
Not sure i can hep you with all the questions but I'll do what i can
The first limit was done correctly
The second one, idk why you just said directly that it equals to
1
torn mantle
5(a) and (b)(iii)
Ah OK you want help in these ones
So for 5 a), we know that the equation has at least one real root between x=-3 and x=3
The only thing I would think of, though I'm not sure it's the smartest approach, would be to get two other intervals that are outside of the interval [-3,3] in which IVT also lets us say there must exist some number c such that f(c)=0
@muted harbor
Can you please @ mention me if you text back
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echo jasper
so i did this problem
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so i did this problem
echo jasper
well not really problem lol
BUt how come
On desmos if i plug in that function the graph looks different from what is provided for me
Like -_
trail obsidian
What is the problem
echo jasper
echo jasper
Yeah
trail obsidian
Just know the characteristics of sine graph
ripe topaz
zoom in the desmos graph (it will look the same)
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red loom
Ok, there's gonna be something elementary I'm just missing how do I evaluate: $\lim_{h\to0}\frac{a^{h}-1}{h}$ to be $\ln(a)$, I can't use l'Hôpital's nor can I use the exponent rule of derivatives
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red loom
for some reason all websites/resources I look at take this to be a given/trivial
I am really struggling to find anything that shows why this is the result without using the above two metioned
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wraith hinge
how did they get the h
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how did they get the h
wraith hinge
h=0.1686
onyx plover
how did they get the h
Isn't h = c
silent canyon
c = a * e
onyx plover
And c = sqrt(a²-b²)
wraith hinge
ohhh okay
thanks for the help guys!
ima close this now for the next person 🫡
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lofty arch
Using cylindrical coordinates (R, ϕ, z), where R2 = x
2 + y
2
, find the volume of a hyperboloid R2 = z
2 + a
2 between z = 0 and z = b.
lofty arch
all the tvariables are squared not multiplied by 2
i got 2pib^3divided by three
but i swear it should depend on a
for R limits i got a to sqrt(b^2+a^2)
for z 0 to b
and phi from 0 to 2pi
but the answer sheet i have says 0 to sqrt(b^2+a^2) for R but i dont understand
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craggy sinew
Is this statement true or false? for any M that belongs to the set of real numbers, 1/2 > M. I think its false.
hazy olive
Hi, I've been on and off with this probelm for about a month now and am really stuck on it. I've tried using the fact that the area of the quadrilateral is between 0 and 1 (as shown), and stuff to do with the sum of 2 sides of a triangle being longer than the third side in all cases, but I got stuck with that too. Any suggestions on things I could try or inequalities related to geometry? Thanks!
hazy olive
It wasn't my first thought, but I got stuck and wanted to try different things
And say that the perimeter of the quadrilateral is between 0 and 4?
oh wait
i think i get you
gimme a sec
Is this what you were talking about?
Not sure how to form an inequality for that tho
I guess some can be factored as like (a - 1)^2 but ultimately interpreting the square terms to form an inequality in this geometric context is kinda unclear to me
I can find a logic for why that should be smaller than or equal to 4, but not a rigorous logic for why they should be greater than or equal to 2
ohh wait
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hazy olive
I think that suffices as a proof, but I just wanna be sure
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wanton meteor
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wanton meteor
I know what an indirect proof is, but I don't know where to go from there
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wheat cypress
Q: graph the INVERSE of y-4=3^(x-2)
so would the inverse be: log_3(x-2) + 4?
wheat cypress
idk how to convert exponential fxn's to log fxn's? can someone help me out please
wooden mural
Let me see if I can give it a try.
So inverse functions are reverse engineering
where input becomes output and output becomes input.
got it.
Do you know the base change rule?
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wraith hinge
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fervent loom
how does one factor this? and in general, if ac and b dont factor nicely, what should i do? thanks
nimble stone
itll be messy
fervent loom
orchid wagon
how does one factor this? and in general, if ac and b dont factor nicely, what s...
find the roots of the equation when it = 0, then rewrite it in (x-x1)(x-x2) form
fervent loom
the b squared b^2 -4ac etc thing?
nimble stone
this has irrational roots so theres no nice factorisation
solid kilnBOT
AℤØ
fervent loom
find the roots of the equation when it = 0, then rewrite it in (x-x1)(x-x2) form
so i can set it equal to 0 and solve from there?
x^2 +10x +12 = 0 ?
balmy matrix
if the problem doesnt specify u dont have to set it to 0
u would js leave it as (x-a)(x-b)
fervent loom
here ill send the whole problem
not sure how they want me to fill in this table when i would have to use the quadratic formula
fathom ivy
oh, then this works like any other complete the square
only you get to put in radicals instead of nice whole numbers
fervent loom
wdym by radicals
nimble stone
the bottom right shouldnt be 12
the columns and rows should be x and 5
bottom right as 25
fervent loom
interesting
nimble stone
you add a value to correct it to 12 later
nimble stone
no
nimble stone
-13 somewhere
fervent loom
what number goes in front?
also its telling me that we didnt add -13 to not change the expression..
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@fervent loom Has your question been resolved?
fervent loom
yes
brittle otter
Aight
Looking at the way they formatted the answer
We'll be completing the square
There is no specific a value
So we won't be needing that first value
Keep it at 1
The value after the (x+5)^2
Should be the value that makes it so that x^2+10x+25 (your squared x+5) is equivalent to x^2+10x+12
In this case it'd be...
@fervent loom
brittle otter
(12-25)
fervent loom
-13
brittle otter
Yayyy
fervent loom
brittle otter
There is no specific a value
This
brittle otter
So we won't be needing that first value
This
brittle otter
Keep it at 1
This
brittle otter
:)
brittle otter
Yep
brittle otter
weird that it needs me to specify that but ok <:big_think:815135573152628757>
Yeah ik right
fervent loom
if there was something like a 3x^2 would a 3 go in place of it or something?
brittle otter
Kind of
You would put a 3 in front
But
You would also multiply the expanded values by 3 as well
So don't forget that
fervent loom
ah right
brittle otter
As an example, 3x^2+36x+19
Is the same thing as 3(x+3)^2-8
Oh wait shit mb
Change the values rq
fervent loom
hmm
so what waould be the process for figuring that out
taking 36 cubed or something
?
fervent loom
ohh
fervent loom
what if it doesnt factor nicely like 3x^2 + 35 
just put he square root in front i assume?
actually/
maybe you could do like..
brittle otter
If it doesn't factor nicely?
Well then
That's when we either factor normally
Or use the quadratic formula
fervent loom
oh right
brittle otter
Steps to factor quadratics
- Try using basic factoring into two basic factors
- Try completing the square
- Use the quadratic formula
Quadratic formula should be last method
fervent loom
completing the square as in what i did above?
brittle otter
Mhm
brittle otter
Glad I helped :)
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jolly sail
hi
jolly sail
need help with this
i know deriv is just slope
but its hard to tell slope in that graph
I got these so far
but I can't tell the rest
thorn trout
you can use decimals
kind of a bad question imo, it is a bit hard to estimate the gradient
just draw a linear line at the point and estimate the gradient of it
f’(2) looks like -1
jolly sail
you can use decimals
so like what decimals would I use
jolly sail
so it said a and d were wrong
what should I put for those 2
nvm got it
put in 3/4 and -1.75
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timber bronze
this is a graph of the second derivative of a function where i am asked to find where it is concave up and concave down, i can see the intervals of concavity from the graph but how would i determine them mathetmatically?
timber bronze
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lofty arch
A car park attendant loses the name tags for a set of seven car keys, so hands out
the keys randomly when the seven owners return.
lofty arch
) How many ways are there of returning the keys so that nobody receives their
own keys? #
i got 7!-6! but i think im wrong
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jan Nejon
frozen plover
why does my sigma look stunted
lofty arch
weird this is in past paper but we never covered dearrangements in class
thank you
How many ways are there of returning the keys so that at least two people
receive their own keys?
i got 5! for this or is it also derangments
@frozen plover
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runic ferry
As n grows, which would result in smaller values, log_2(n) or 2*log_3(n)? Why would that be the case?
dull temple
use log rules to make those comparable
runic ferry
I’m not sure what u mean, i guess i could have log_2(n) compared to log_3(n^2)?
split chasm
consider change of base law
runic ferry
Ah ok, so i would compare log_2(n) to 2*log_2(n) / log_2(3)? And here 2/log_2(3) gives about 1.26
So log_2(n) gives a smaller value
When compared to 2*log_3(n)
proven violet
hi
proven violet
i'm doing this question
integral test might work because it's monotonically decreasing, but the integral i need to calculate has no answer in terms of standard elementary functions (and we haven't done integrals in analysis yet so i'm not expected to bound it in terms of another integral)
ratio test is looking terrifying
cauchy convergence criterion is looking terrifying
comparison test idk what to compare it with
i am very stuck on how to approach this
okay so i've made some very handwavey progress
$\forall x\geq 2: \frac{x^{-a}}{1+a^{-x}}\leq \frac{1}{1+a^{-x}} \therefore \int_0^\infty \frac{x^{-a}}{1+a^{-x}}\mathrm{d}x \leq \int_0^\infty \frac{1}{1+a^{-x}}\mathrm{d}x=\lim_{n\rightarrow\infty}\log(a)\log\Big(\frac{a^n+1}{a^2+1}\Big)$
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george clooney real account
proven violet
and clearly the limit at the end doesn't shoot off to infinity only in the case that $0<a\leq1$
solid kilnBOT
george clooney real account
proven violet
but proving those inequalities in my big step was done entirely by looking at the graphs on desmos
not at all rigorously, which is what this course expects
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graceful river
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graceful river
<@&286206848099549185>
unique pine
It's basic substitution
wraith hinge
plug in n = 1
graceful river
Ty
wraith hinge
then n = 2
wraith hinge
same method
graceful river
Can u help me on 3d
wraith hinge
kk
graceful river
Ty
wraith hinge
graceful river
Is it 9
graceful river
Can u do 3e or 3f then
wraith hinge
might as well say do all xD
graceful river
Oh alr
graceful river
I still dotn understand srry
wraith hinge
kk
graceful river
My teacher never taught us this and expects us to learn on our own
graceful river
Dayum
wraith hinge
did you put it to 3 d.p?
graceful river
YESSS
wraith hinge
it worked?
graceful river
5.906?
graceful river
Didjt wlro
Work
Rip
Ite not event hats it's so hard to put in calculator
Cna ut ry it for me
wraith hinge
kk
graceful river
Is substitution this minus sighn
wraith hinge
I just plug in n from until a number
it's like saying
x + y = 1
y = 3
then you substitute it in
x + 3 = 1
x = -2
graceful river
Can u dot his kn calcultor
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graceful river
Ye
mortal coyote
Find the function for a secondary function, that crosses y-axis in 2 and only has one zero point 2
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mortal coyote
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warped jasper
<@&268886789983436800> are you guys all nerds?
merry gyro
yes. Don't ping mods for memes
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wicked quartz
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clever ferry
Anyone able to help me?
wicked quartz
Oops
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runic cloak
whats the question even
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tall aurora
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clever wind
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clever wind
i couldnt find a way to do it without using the cosine theorem
i will be glad if i get help before 12 because i have an exam about this type of questions at 12 😬 stressing myself realy
wide ruin
@clever wind i’m in the same boat as u lmao, are u in pre calc
clever wind
the class code is calculus 101 so you can say that i guess
wide ruin
ohhh
i have a quick question not sure if you’d know the answer
do u know what a period in a graph is?
clever wind
if i see the graph maybe i can help
wide ruin
u mind if i dm u?
clever wind
u can dm let me check if my dm's are open or not
wide ruin
idk if it’s against the rules to post stuff in ur help channel lmao
clever wind
i domt know too
haughty tundra
you can post i think
wide ruin
ohh ight
clever wind
okay you can dm me
wide ruin
its not working i’ll just post it in here
so this is my graph, the period is 8 and idk what that means tbh. i don’t know how the period correlates to the graph
clever wind
ughhh i need an answer i will take any ideas helpers
clever wind
so this is my graph, the period is 8 and idk what that means tbh. i don’t know h...
so,
perios is
period* is when something
finishes the action where they begin,
odd onyx
@clever wind DM me for a second
wide ruin
finishes the action where they begin,
yeah but how does the graph finish at 8? or is it just an approximation
haughty tundra
its not working i’ll just post it in here
period is how long it takes for one full wave to complete
wide ruin
it restarts at 26 pi/3
haughty tundra
yes it also starts at 2pi/3
clever wind
a time value or a number like time per lap while running etc. If you need to understand the logic,
haughty tundra
Let h be the distance between the point x and the heli
wide ruin
stressing for this pre calc exam, i always study last minute like an idiot
haughty tundra
It is known dh/dt=20
let v be h's velocity
vx=20costheta
vy=20sintheta
Thus
hx = 20tcostheta
hy=20tsintheta
actually
nvm
The total distance from the observer to heli position on the x axis
is given by
100+(heli speed in x)*t right?
and the distance from the obs. to heli on the y axis is given by 0 + (helispeed in y)*t
right
?
@clever wind
clever wind
i just came back lst me look
haughty tundra
k
clever wind
right
i guess right but arent we gonna turn back to the theorem to find the values again how can i do it without that
o wait
clever wind
cosine theorem is basically phytogoran thorem Expressed in terms of cosine
haughty tundra
ok
clever wind
if you use geometry we always have to use it in my question but
i am trying not to bacuse eacher said there is a way
haughty tundra
ok
clever wind
but whoever i ask doesnt matter if they are an other teacher they sah i cant I can't deal with this stuff u shouldnt too like what 💀
haughty tundra
I am not going to use this: c=a2+b2﹣2abcosγ
to solve it
is this what your teacher is talking about?
smoky path
how can x be constant 🤔
haughty tundra
x cannot be 100?
smoky path
as @haughty tundra said v_x = 20cos(120) which means x shouldn't be constant?
smoky path
v_x is the speed in the x direction right?
haughty tundra
x is defined as the distance from obs. to that point
clever wind
how can x be constant 🤔
it means that observer is not moving
smoky path
it means that observer is not moving
yeah but the heli is?
haughty tundra
anyway
clever wind
how can x be constant 🤔
Of course, the horizontal distance changes, only the distance of the observer to the starting point does not change.
clever wind
v_x is the speed in the x direction right?
yea
haughty tundra
It is known dh/dt=20
let v be h's velocity
vx=20costheta
vy=20sintheta
Thus
hx = 20tcostheta
hy=20tsintheta
actually
nvm
The total distance from the observer to heli position on the x axis
is given by
100+(heli speed in x)*t right?
and the distance from the obs. to heli on the y axis is given by 0 + (helispeed in y)*t
right
?
so
the positin in x
lets call it
clever wind
yes, but yhthe hthing is i cant find numerical values without using geometry i guess
o kay im listening
clever wind
no but phytogoran and cosinus etc is not allowed
everything you can find similar woth cosine is forbidden
teacher said that you should think it like physics
analyze with maths
not geometry whatsoever
haughty tundra
so a^2+b^2=c^2 cannot be used?
clever wind
i guess it can i mean if we dont use that we cant use anything i suppose
haughty tundra
I'd like to see your teacher solve it without geometry
clever wind
me too lol
haughty tundra
Because the answer is expressed with pythagoren theorem
clever wind
i mean there is a geometry but we cannt use something with cosine similarly
haughty tundra
wdym
clever wind
yes but teacher wants us to find a deriative equation gives ius the change
of the distancd
we are going to use some geometry-like logic but explain it with deriatives
haughty tundra
ok
it wanys the velocity?
from the obs.?
thats easy
it already tells you
actually nvm
clever wind
not exactly, becauseteacher doesnt wants relative velocity more like just the equation eith deriatives which gives us the change of distance between the h and the observer relates with time
related*
We need to define something like dx/dy but without cosine theorem
maybe i can tag helpers idk it has been 30 minutes
haughty tundra
ok
clever wind
almost
clever wind
<@&286206848099549185>
haughty tundra
Theyre gonna tell you the same thing
haughty tundra
Let's try to find the angle between the hypoteneuse and the ground at any time t
the velocity will then be given by dh/dt*cos(that angle (t)
clever wind
Yep
clever wind
Thank u lol i am thinking the problem is the teacher too
trim joltBOT
@clever wind Has your question been resolved?
smoky path
@clever wind did you find the answer?
wraith garden
Hello, I am a noob at math looking to improve my basics/foundations on math. Anyone have a order on what to learn?
I'm done with basic algebra
I have lots of trouble with variables on weird places
Complex functions trouble me also, and rational inversion??
I also have trouble with weird symbols....
And geometry (lots of formulas)
And many more, idk i suck
wraith garden
An example of levels I can't reach yet but supposed to be:
trim joltBOT
@wraith garden Has your question been resolved?
trim joltBOT
@wraith garden Has your question been resolved?
dapper swift
An example of levels I can't reach yet but supposed to be:
$|x| \le c$ means $-c \le x \le c$
solid kilnBOT
south
dapper swift
Hello, I am a noob at math looking to improve my basics/foundations on math. Any...
just curious, what makes you want to improve your maths foundations?
it's useful to have a goal in mind to study all of this
I imagine you're at the precalc stage if I'm not wrong
wraith garden
just curious, what makes you want to improve your maths foundations?
I want to improve because we are learning so much more complex stuff that requires to need basic stuff first, but i seem to have forgotten.\
wraith garden
I imagine you're at the precalc stage if I'm not wrong
Yes, but my foundations suck
dapper swift
I want to improve because we are learning so much more complex stuff that requir...
like are you still in high school or at uni?
wraith garden
like are you still in high school or at uni?
is senior high school counted
dapper swift
yeah
dapper swift
ok ok
wraith garden
my subjects are gen math and pre cal
dapper swift
ahhhh I see
wraith garden
but my teacher said
u need to have basics first
so it will be easier
so i came here
thats all for my story
dapper swift
Khan Academy has decent practice: it's useful for testing your understanding which is super important in maths
wraith garden
https://www.khanacademy.org/math/precalculus
i dont have miney
dapper swift
i dont have miney
what?
wraith garden
money
dapper swift
oh it's free
wraith garden
oh
wraith garden
Khan Academy has decent practice: it's useful for testing your understanding whi...
what courses should i take other than that
dapper swift
Paul's Maths Notes is better but has fewer practice problems
this is much more standard
dapper swift
what courses should i take other than that
basically listen to your teacher's feedback
like after each test review all your mistakes and then study from that
there are a few big misconceptions people who aren't used to algebra have
can't find a complete list but these are some of them
wraith garden
like after each test review all your mistakes and then study from that
my teacher kinda sucks
dapper swift
a big thing is with operations, like 1/(x + y) is not 1/x + 1/y
e^(x + y) is not e^x + e^y
dapper swift
my teacher kinda sucks
that really sucks
dapper swift
yeah
you should start with the basics like this
if you want to understand the laws of indices
these are with whole numbers
and then move on to like fractions and later irrational numbers like e
wraith garden
i understand that
wraith garden
how do i do with fractions
dapper swift
how do i do with fractions
so like $(a/b)^n = \frac{a^n}{b^n}$
solid kilnBOT
south
wraith garden
maybe
all i know is u cant do something with the other exponent unless the "a" or "b" is equal
dapper swift
all i know is u cant do something with the other exponent unless the "a" or "b" ...
could you give an example of this?
wraith garden
$9^x = 81$
solid kilnBOT
Inuji
wraith garden
$9^x = 9^x$
solid kilnBOT
Inuji
wraith garden
because 9 and the other 9 is equal
dapper swift
yeah, so 9^x = 81 means 9^x = 9^2
you can do that cause 9^x is one-to-one
that means it's always increasing
dapper swift
(one-to-one also can be always decreasing)
dapper swift
it gets harder
yeah, like with quadratics right
wraith garden
yes
dapper swift
ok
solid kilnBOT
Inuji
wraith garden
how do i find x
wraith garden
log9 8 = x
dapper swift
yep
wraith garden
but how do i do it manually
dapper swift
ah so take log9 on both sides
wraith garden
without calculator
dapper swift
without calculator
you can't find it without a calculator
dapper swift
yeah, you need to go back to your rules of indices
wraith garden
there are only a few rules right
dapper swift
yeah
there's also (a/b)^n = a^n / b^n which I mentioned earlier
so if we have like $4^x + 3 \cdot 2^x + 4 = 0$
solid kilnBOT
south
dapper swift
the first step would be to realise this is a quadratic
the next step is $4^x = (2^2)^x = 2^{2x} = (2^x)^2$
(here we did 2 * x = x * 2)
solid kilnBOT
south
solid kilnBOT
Inuji
solid kilnBOT
Inuji
dapper swift
$2^{2x}$
solid kilnBOT
south
dapper swift
i understand none
which part don't you understand?
wraith garden
how do u add $4x = 2^2x$ if the other exponent 2^x has to multiply with 3
solid kilnBOT
Inuji
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
dapper swift
how do u add $4x = 2^2x$ if the other exponent 2^x has to multiply with 3
so 4^x = (2^x)^2 right
wraith garden
yes
dapper swift
yeah