I just turned the clockwise angle
#help-26
lean meteor
To anticlockwise angle
Yeah if u cant observe it
I dont know
How you solve that
quasi elbow
nice btw how did u get 28 tho
lean meteor
Because tan
acoustic tangle
Wait, let me try something
lean meteor
Is negative
In the second quadrant
Aswell
There
Tan 180-x =-tan x
So tan 115
5y-35 =115
5y=140
quasi elbow
interesting
lean meteor
Y=28
lean meteor
You know sign scheme of trig functions according to quadrants right
Well just do unit circle
quasi elbow
i unforunatly do not
lean meteor
Search up unit circle
acoustic tangle
Because arctan(-1/sqrt3) is obviously -30
lean meteor
And 150
acoustic tangle
Yeah
lean meteor
Theres a better way for 4th step
Applying componendo dividendo
Directly get step 6
quasi elbow
wait im a little confused when i put it in to the calculator tan(-75) comes around 5 degrees
also how do u even find tan of a negative number
lean meteor
Because calculator takes radians
quasi elbow
isnt tan = opposite/adjacent
quasi elbow
Because calculator takes radians
no i specifically removed radians
lean meteor
What -75 means is just that the angle is taken
In cloclwise direction
Its not coming 5?
Its 3.73
-3.73*
quasi elbow
correct why tho
lean meteor
wait im a little confused when i put it in to the calculator tan(-75) comes arou...
Tan cannot generate degress
Can you specify
Wdym why
You mean why does tan 75 have that value?
quasi elbow
You mean why does tan 75 have that value?
hm i think im getting a little muddles up in my concepts
ill brb, try to wrap my head around this a little better
fallow heart
Tan cannot generate degress
This is very important to know @quasi elbow
lean meteor
If youre having difficulty with this
Go look up
Unit circle
It will help you to understand about quadrants and negative angles
fallow heart
To prove that tan(75°) has that value, you can write it as tan(30° + 45°) and apply to this the tangent addition formula (if you have been taught this of course) @quasi elbow
lean meteor
I forget the geometrical proof of this formula
fallow heart
I don't think there is, it's just using tan(a+b) = sin(a + b)/cos(a + b) and then you use the formulas for sin and cos addition
lean meteor
Perhaps
quasi elbow
ok so i just searched up unit circle
and i understand what negative degrees are now
so
tan(5y - 35) = tan(-75) ==
tan(5y-35) = tan(285degrees) =
285 + 35 =
320/5 = 64
ahhhhhh
lean meteor
Yep
lean meteor
Refer unit circle
Tan 90+x is what
-cot x
Cot x is what
Tan (90-x)
So
Tan 90+x = -tan (90-x)
We had -tan 75
Which will be equal to
Tan 105
quasi elbow
Cot x is what
cot?
quasi elbow
not many lol im in year 9 so i kinda only know basic ones
lean meteor
Theres 6
Like you know sin cos and tan
Now think
If theres a ratio
For opposite/hypotenuese
Its only natural
Theres ratio for
Hypo/opposite
Thats cosec
Similarly
The reciprocal of tan
Is cot
topaz sinewBOT
@quasi elbow Has your question been resolved?
neon iron
how the negative denominator became positive after we solve it, like d^-1 or e^-4
topaz sinewBOT
how the negative denominator became positive after we solve it, like d^-1 or e^-...
fringe marten
how the negative denominator became positive after we solve it, like d^-1 or e^-...
Use the fact that $a^{-n} = \dfrac{1}{a^n}$
thorny flameBOT
Alex88
neon iron
Use the fact that $a^{-n} = \dfrac{1}{a^n}$
how can this turn 2d^-1 to positive numerator?
lean meteor
As 2/d
lean meteor
Yes
fringe marten
how can this turn 2d^-1 to positive numerator?
if we know that $a^{-n} = \dfrac{1}{a^n}$, then what would $\dfrac{1}{2d^{-1}}$ be?
lean meteor
Unless the power -1 is on 2d
thorny flameBOT
Alex88
fringe marten
well take it step by step $\dfrac{1}{2d^{-1}} = \dfrac{1}{2}\times\dfrac{1}{d^{-1}} = \dfrac{1}{2}\times\dfrac{1}{\frac{1}{d}}$
thorny flameBOT
Alex88
fringe marten
how would you simplify that?
fringe marten
have you ever done compound fractions?
thorny flameBOT
dldh06
neon iron
**dldh06**
1 * d/1 ?
neon iron
how can I search this lesson in youtube, so I can understand it with more videos
is it compound fractions?
fringe marten
yepp
neon iron
**dldh06**
this lesson
fringe marten
its basically dividing fractions by fractions
neon iron
how "a^-2*a^-3" became a^-1 instead of a^-5 ?
topaz sinewBOT
how "a^-2*a^-3" became a^-1 instead of a^-5 ?
drifting swift
where do you see any a^-3?
steel crow
neon iron
where do you see any a^-3?
in ab^-3
drifting swift
^
neon iron
how I can solve this as "x^..."?
topaz sinewBOT
how I can solve this as "x^..."?
tall wolf
you can go two ways
either turn the fraction inside the ^{1/4} into one and then raise it to the power of 1/4
or raise both sides of the fraction first and then divide
fallow heart
$${\left(\frac{x^\frac{1}{2}}{x^\frac{1}{5}}\right)}^\frac{1}{4} = {\left(x^{\frac{1}{2} - \frac{1}{5} }\right)}^\frac{1}{4} = {\left(x^{\frac{5 - 2}{2 \cdot 5}}\right)}^\frac{1}{4} = {\left(x^{\frac{3}{10}}\right)}^\frac{1}{4} = \ldots$$
thorny flameBOT
Alberto Z.
fallow heart
**Alberto Z.**
This is one way to approach it @neon iron
neon iron
you can go two ways
I get "x^8 / x^20 = x^28" but it's wrong answer
fallow heart
I get "x^8 / x^20 = x^28" but it's wrong answer
How did you get x^8 and x^20? You should get x^(**1/**8) and x^(**1/**20)
tall wolf
its x^{8-20}
fallow heart
If you have already done some steps, please send them
neon iron
If you have already done some steps, please send them
I understand your steps
$$x^{\frac{3}{10}}\right)}^\frac{1}{4}$$
thorny flameBOT
Chocolate
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
fallow heart
I understand your steps
Alright nice 👍
neon iron
Alright nice 👍
but we did not get the answer in the correct format as "x^..."
fallow heart
**Chocolate**
Compile Error! Click the <:errors:504266556054962196> reaction for...
This is correct btw
And $\frac{3}{10} \cdot \frac{1}{4} = ?$
thorny flameBOT
Alberto Z.
neon iron
This is correct btw
not yet, we need to simplify it more, should I just multiple 3/10 and 1/4 ?
fallow heart
**Alberto Z.**
@neon iron
neon iron
x^3/40 ?
fallow heart
Exactly that yes
neon iron
Exactly that yes
is x^1/2 is equal to x^-2?
if yes, why not x^-2 + x^-5 = "(x^-7)^1/4"
fallow heart
is x^1/2 is equal to x^-2?
No, it's not
$$x^{-2} = x^{\textit{0} - 2} = \frac{x^0}{x^2} = \frac{1}{x^2}$$
thorny flameBOT
Alberto Z.
fallow heart
Whereas $x^\frac{1}{2} = \sqrt{x}$
thorny flameBOT
Alberto Z.
fallow heart
And if you plot/know $y = \sqrt{x}$ and$ y = \frac{1}{x^2}$ you will recognize those are completely different graphs and have also different domains. Hence, they cannot be the same
thorny flameBOT
Alberto Z.
neon iron
thank you
neon iron
.close
tardy vapor
can someone check if i did this correctly
topaz sinewBOT
can someone check if i did this correctly
empty sail
can someone check if i did this correctly
Plug your answer back in to check
wispy abyss
lemme solve it rq and ill check
astral owl
can someone check if i did this correctly
should be correct
wispy abyss
yep can confirm
lean meteor
It does work
woven bramble
How do I solve this question?
topaz sinewBOT
How do I solve this question?
woven bramble
I have no idea how to solve this so please try to explain it as concise as possible for me thank you!
woven bramble
thank you...
oops sorry this is precalculus the expansion of my math skills only reach to 8th grade
.close
neon iron
cube root of xy is wrong ? or how it is xy?
topaz sinewBOT
cube root of xy is wrong ? or how it is xy?
neon iron
should not it be cube root of all of each of then, 27 * x * y ?
lean meteor
The cube root x y is indeed wrong
craggy haven
yeah that doesn't make sense, it should be $\sqrt[3]{27}\cdot\sqrt[3]{x}\cdot\sqrt[3]{y^3}$
thorny flameBOT
hayley!
neon iron
$\sqrt[3][27]$
thorny flameBOT
Chocolate
neon iron
I ended up getting [
(\mu^2 + 4\eta)u_{\mu \eta} + \mu u_\eta= 0 ]
For the canonical form with $\eta = xy$ and $\mu = x +y$
topaz sinewBOT
I ended up getting \[
(\mu^2 + 4\eta)u_{\mu \eta} + \mu u_\eta= 0 \]
For the can...
thorny flameBOT
neon iron
Maybe I'm dumbing out but I can't seem be able to get to the general solution
Ik I have to integrate twice but my solution just doesn't match the form they gave
Is my canonical form wrong or something 
Maybe I fucked up my derivatives
Oh wait duehdvwg
.close
low crest
for what values of a is the function f(x)=x/(x-a) its own inverse
craggy haven
vale jacinth
$\begin{pmatrix}1&0\1-a&a^{2}\end{pmatrix} =\begin{pmatrix}1&0\1&-a\end{pmatrix}^{2}= \begin{pmatrix}1&0\0&1\end{pmatrix}$
thorny flameBOT
Cogwheels of the mind
craggy haven
can you show your work? x^2 - x - a isn't an equation
craggy haven
xy - ax = y and then what?
low crest
y=(ax)/(x-1)
craggy haven
so $\frac{ax}{x-1} = \frac{x}{x-a}$
thorny flameBOT
hayley!
craggy haven
(for all x)
vale jacinth
Yeah, 1-1=0, 1^2=1
low crest
alr thanks
vale jacinth
I wrote matrix only because composition of fractional linear transformations is easier to calculated using matrices
low crest
I wrote matrix only because composition of fractional linear transformations is ...
lol
ye looks pretty foreign to me
i'm eager to learn though
vale jacinth
Wikipedia, under the term linear fractional transformations
I am wrong about the order, linear first
topaz sinewBOT
topaz sinewBOT
Available help channel!
toxic bane
hi
restive inlet
chain rule
simple orchid
Where is 2 coming from?
fossil flare
try using the substitution $u=2x-1$
thorny flameBOT
qianqian07
long beacon
chain rule
?
toxic bane
but wouldnt it be
restive inlet
you didn't account for the derivative of the inner function
restive inlet
doing the sub makes it easier to see
toxic bane
topaz sinewBOT
ionic oar
Do you have a diagram
toxic bane
nope
ionic oar
You should
ionic oar
so is b^2-4ac greater than or less than 0
Can be anything btw
In this case
The discriminant gives us nothing of value this time
Drawing an image should make it very clear
pastel juniper
n should be negative right?
toxic bane
n should be negative right?
yes
toxic bane
Drawing an image should make it very clear
so i draw one?
ionic oar
yes
pastel juniper
is this calculus or just quadratics?
ionic oar
Doesn't have to be a Picasso, just a general sketch
toxic bane
quadratic
ionic oar
Calculus unnecessary
toxic bane
so how do i know if my graph is above y axis or below
ionic oar
And again, it can be both above and below the x axis
there's really only one condition that we care about and Dysrrupt has pointed it out
toxic bane
which is the y coords less than 3
ionic oar
Well the sketch is redundant now that you know the conditions lol
I asked you to sketch it hoping you'd figure out the conditions by looking at it
pastel juniper
no
ionic oar
not necessarily
ionic oar
The graph can be entirely below the axis as well
toxic bane
ionic oar
But surely this causes you to miss out on certain values of n
pastel juniper
you'll get the exact same expression
pastel juniper
But surely this causes you to miss out on certain values of n
no
just do -D/4a < 3
same answer
ionic oar
They did D < 0 though
toxic bane
just do -D/4a < 3
negative discriminant divided by 4a ?
pastel juniper
of the expression formed
ionic oar
Shouldn't it be D < 12a
pastel juniper
yes according to us
they used a different approach
they just took the quadratic < 3
and it becomes < 0 after transposing 3 to LHS
and a quadratic is < 0 if leading coeff is < 0 and D < 0
they just did that
topaz sinewBOT
@toxic bane Has your question been resolved?
toxic bane
oh
analog dome
i need some help with this question
topaz sinewBOT
i need some help with this question
analog dome
its to find the inverse function
simple orchid
What defines an inverse function
analog dome
an inverse function is basically a function that undos what the original function does, right?
im trying to just solve this like how i always solve it
but ive been getting incorrect answers
topaz sinewBOT
Show your work, and if possible, explain where you are stuck.
spare smelt
Just solve the equation for x
analog dome
Just solve the equation for x
for y
spare smelt
Here's a very simple example
analog dome
since id have to switch em around
spare smelt
y = x+1
simple orchid
An inverse function is a function that reflects over the y = x line
analog dome
but i tried to just do that
spare smelt
Can you solve for x
analog dome
and it just isnt that simple
spare smelt
Yeah. Try taking the reciprocal
analog dome
heres the work ive done so far
sorry about the crossouts
but i did try that
and it wasnt the answer
also, that picture has multiple attempts
not 1 working
this is supposed to be the answer
spare smelt
y = -1/(4^(1+x))
analog dome
but how am i even going to get 1/4 as the logarithm base
spare smelt
Lets try rewriting the exponent
long beacon
but how am i even going to get 1/4 as the logarithm base
should be something like ln( -4x)/ ln 1/4
analog dome
first isolate x
but i already isolated it
long beacon
base changing property
spare smelt
y = -1 × 4^(-1-x)
analog dome
in step 2, x is isolated
pastel juniper
but i already isolated it
you didnt
thorny flameBOT
Dyssrupt
pastel juniper
try taking log
analog dome
ok
log_4(-1/y) = 1+x
but the answer had 1/4 as the base
which means that i had to interhcange it in the 2nd step...
is anyone there?
analog dome
both mean the same thing
log_4(-1/x) - 1 and the answer?
frail reef
when you minus the 1, turn that into log_4(4) and divide that
its the same answer
just with 2 different bases
lilac solar
log_4(-1/x) - 1 and the answer?
🤯
analog dome
when you minus the 1, turn that into log_4(4) and divide that
turn '-1/x' in 'log_4(-1/x) - 1' into '4'? i dont get how we'd do that though
i know we can change the base but
not whats inside the log
long beacon
idts
analog dome
-1 = -log_4(4)
not really
analog dome
Does this question have smth to do w derivative
no
analog dome
-1 = -log_4(4)
i just dont get how we change the inside of the log
because i dont know where the -1/x went
analog dome
oh wait
i understand it now
since a fractional base can make it a negative log right?
frail reef
yeah
frail reef
thats the -1 part
frail reef
do you understand that loga - logb = log(a/b)?
analog dome
yes
frail reef
well we have a log_4(-1/y) - 1
we want to make that -1 into a log form so that we can apply that rule
so that we can combine it
frail reef
1 doesnt equal log1
remember log_a(b) is what power do we have to raise a by to get b
log_4(4) means what power do we have to raise 4 by to get 4
hence its 1
sweet spire
topaz sinewBOT
sweet spire
how do i solve for C
dusk lava
!status
topaz sinewBOT
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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
@sweet spire
sweet spire
i dont know where to begin
sweet spire
we can't prove that they are parallel
dusk lava
I think that’s what it wants you to do
sweet spire
i tried using exterior angle theorem
dusk lava
That’s the one weird thing
sweet spire
and a bunch of angle addition
but you have to be able to prove that they are parallel
dusk lava
Ok I did it
I think
@sweet spire I used exterior angles and variable to solve
And it worked out well’
dusk lava
I labeled angle A as X, and then used the properties of bisectors and the exterior angle theorem
Can you show me your work
sweet spire
a picture?
dusk lava
Ok
dusk lava
I labeled angle A as X, and then used the properties of bisectors and the exteri...
I would start here
dusk lava
Gotchu
sweet spire
did you get angle C is 80?
dusk lava
Yep
topaz sinewBOT
topaz sinewBOT
Available help channel!
quiet yoke
solve quadratic equation by completing the square 2 + z = 6z^2
topaz sinewBOT
solve quadratic equation by completing the square 2 + z = 6z^2
quiet yoke
2 + z = 6z^2
6^z2 +z = -2
6z^2 + z + (1/2)^2 = -2 + (1/2)^2 I dont know what to do from here
vocal sorrel
2 + z = 6z^2
6^z2 +z = -2
6z^2 + z + (1/2)^2 = -2 + (1/2)^2 I dont know what ...
the approach you took wouldnt lead you anywhere. First divide by 6
then try to get it to the form i got it (x^2-2ax+a^2) where a in our case is 1/12
quiet yoke
ok yea I see
vocal sorrel
do you understand everything?
quiet yoke
I need a min
topaz sinewBOT
As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.
@quiet yoke Has your question been resolved?
Available help channel!
neon iron
How should I put
$$ W = \frac{1}{2}m(v_f^2 - v_i^2) = F_x d$$ into my head
Specifically the middle part
$$\frac{1}{2}m(v_f^2 - v_i^2) $$
thorny flameBOT
neon iron
mainly confused about this part $$v_f^2 - v_i^2$$
thorny flameBOT
neon iron
How do i say it?
The change in squared velocity?
So $$\frac{1}{2}m(v_f^2 - v_i^2) $$ would be
half of mass times the change in squared velocity?
thorny flameBOT
neon iron
could i rewrite it as
$$\frac{1}{2}m(\Delta v^2)$$
or does that just mean $\frac{1}{2}m( \Delta v)^2$
thorny flameBOT
topaz sinewBOT
@neon iron Has your question been resolved?
vivid flame
wouldn't rewriting it as $\frac{1}{2}m( \Delta v)^2$ imply $\frac{1}{2}m(v_f - v_i)^2$=$\frac{1}{2}m(v_f^2 - v_i^2)$?
thorny flameBOT
Judgemental Snail
vivid flame
i apologize if im not correct im not used to delta notation as of right now
urban grove
(Delta v)^2 and Delta (v^2) are not the same
thorny flameBOT
vivid flame
yeah, i believe so 👍
topaz sinewBOT
vivid flame
no prob
topaz sinewBOT
Available help channel!
pale hawk
topaz sinewBOT
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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
plush vector
I found these videos on youtube in case it helps:
https://www.youtube.com/watch?v=WMws-edk3gg
https://youtu.be/lJ1XTbE4kcU
Just search up "solving inequalities through case analysis" or "solving inequalities through sign analysis" for more videos
hope it helps!
young tinsel
When learning a proof in mathematics my approach as of right now learning calculus 1 is to learn the proof to the best of my ability and if I am confused instead of just pondering over it due to time. I first complete numerous practice problems using the formulas and then afterwards I come back to understand the proof. Any advice that can help me when it comes to grasping math proofs? I take detailed notes, try to explain it to a 5 year old and always try to justify the reasoning for each and every step, but it is tedious at times.
topaz sinewBOT
When learning a proof in mathematics my approach as of right now learning calcul...
vernal vale
When learning a proof in mathematics my approach as of right now learning calcul...
whats wrong with the process youre using now?
young tinsel
There is nothing wrong its just that I am a person who takes time to comprehend proofs.
The thing is when I see a proof or a formula I try to always figure it out
on my own, unless I can't, but if its something algebraic I always try.
For instance I am in the midst of explaining rn to myself why
d/dx [a^u] = a^u x ln(a) x du/dx
But the thing is it takes a great deal of time. So I guess how can I improve my speed at comprehending proofs? I am heavily against memorizing anything, unless I have to, which is why I always love learning the proofs of stuff.
whole geode
There's an old saying that there is no royal road to math. It takes time and effort. You'll become more fluent in time.
scenic flare
But the thing is it takes a great deal of time. So I guess how can I improve my ...
Proof comprehension speed probably comes from both experience in recreation of proofs which you already do as well as gaining experience in advanced subjects which teach one to think of most concepts more abstractly
young tinsel
Proof comprehension speed probably comes from both experience in recreation of p...
Mhmmmmm.
Even though the proofs take time I do defintely think its worth learning cus like what is the point of even learning calculus if one doesn't know where the proofs originate from.
scenic flare
proofs aren't necessarily written in a way to be easily comprehensible which is why getting used to abstract concepts helps with familiarizing oneself with the less intuitive notations etc
scenic flare
Even though the proofs take time I do defintely think its worth learning cus lik...
Depends on the intent, one could also purely strive for using calculus application-wise, e.g. for programming
young tinsel
Proving it also helps me retain what I learn better. Like I'm given the option to use a formula sheet, but I am trying my best to be my own formula sheet learning the proofs for formulas and theorems.
vernal vale
But the thing is it takes a great deal of time. So I guess how can I improve my ...
to me it sounds like youre doing the work
i cant think of anything obvious that it sounds like you arent already doing
young tinsel
Oh beleive me I am. Each day this summer I've been putting 5-7 hours every day teaching myself calculus, sometimes even 10 hours when I feel like it.
Its not pressure on me at all though, because I love it.
vernal vale
well yea i mean idk theres anything you can do to improve speed
dont forget all the normal exercise addages which also apply here
you know rest, realistic expectations
young tinsel
I just want to ensure in University that I will be able to complete the practice problems and the proofs
vernal vale
being honest with yourself about shortcomings and strengths
young tinsel
cus University is faster pace.
vernal vale
lol i wouldnt worry about uni if you enjoy self studying calculus
im sure youll do great
scenic flare
Proving it also helps me retain what I learn better. Like I'm given the option t...
Formula sheets can be seen as a comprehension of previously acquired axioms and rules to start from when solving new problems. Not ever being given how something was proven or where it originates from is kind of fatal of course
vernal vale
yea me too
and im also dumb in general 
so you probably have that one on me
but if you can work hard you can make it
young tinsel
I hope so. Calculus for me is a love hate relationship lol.
vernal vale
Formula sheets can be seen as a comprehension of previously acquired axioms and ...
this is definitely true i would keep track of derivations and stuff youve already done
you dont need to remember everything
young tinsel
Lots of algebra quite shocked by how much algebra some questions involve.
vernal vale
just convince yourself you understood something and move on
young tinsel
I know you don't need to remember everything.
But just imagine in 5 years time not looking at the book, but being able to recall what you learnt in great depth.
Heck even 10 years.
I know this is unrealistic and probs not feasible but why the hell not anyways?
scenic flare
cus University is faster pace.
yes, whilst the general efficiency in solving is higher, picture it more as an understanding of everything you know so far from a more abstract perspective which in turn lets you solve everything with better approaches as well as understand the intent of an unknown proof better
young tinsel
yes, whilst the general efficiency in solving is higher, picture it more as an u...
yeah.
scenic flare
but don't worry, especially the start won't be too difficult, motivation is key
young tinsel
I am heavily motivated.
I enjoy it.
I love Physics, and seeing its applications in Physics was breath taking for me lol.
scenic flare
Same, if I could recommend something then it may be looking for like-minded people right at the start already, mutual encouragement makes learning harder subjects easier, regardless of your learning speed
(at uni)
young tinsel
Yep I'm gonna find a study group and make friends
I'm doing a degree in engineering
scenic flare
neat
young tinsel
and was expecting it to be competitive, which it is, but I heard from others that a lot of the engineers they congregate forming study groups helping one another.
I'm competitive, but wish to see my peers do welll as well. I'm not dirty minded like some who wish to see others fail that is just wrong.
vernal vale
no way engineering is very social and collaborative
you could go as far to say interdisciplinary
young tinsel
yeah.
vernal vale
if you make a strong diverse group of friends in uni then you will go far
young tinsel
I hope so.
scenic flare
and was expecting it to be competitive, which it is, but I heard from others tha...
Just keep in mind that in university even though the structure of a school system is partially maintained, professors and lecturers are less focused on grades, their dedication is expanding your horizon, not letting your numbers go up
young tinsel
Yeah.
I still hope to achieve A+'s as I did in hs, but learning is more important to me.
scenic flare
I still hope to achieve A+'s as I did in hs, but learning is more important to m...
Right approach for moving forward :)
young tinsel
I've gotten B's before
so I won't cry if I get a B
heck I got C-'s as a freshman in hs
in hs
but what made me change was my approach to learning
instead of memorizing things I started during my grade 12 year really focusing on the "why" and having fun with what I learnt as oppose to seeing it as a tedious task.
scenic flare
wish thee gl moving forward, many don't have this mental restructuring until they're a few semesters in
so I consider it well suited for starting out
young tinsel
Thank you very much. I wish u the very best with ur future endeavors and hope to see u around some time.
glad cedar
hi i need help finding the answer to 2n1+788
young tinsel
is this algebra?
young tinsel
mk what is it equivalent to?
like what does 2n1 + 788 equal to?
is this general algebra or university stuff just maing sure?
cus 2n1 + 788 by itself is strange.
vernal vale
Im trying to figure it out
theres nothing to figure out, you cant solve an expression
topaz sinewBOT
@young tinsel Has your question been resolved?
weary iron
im trying to find total number of divisors of a number
topaz sinewBOT
im trying to find total number of divisors of a number
weary iron
like this
but i dont understand the logic behind the formula
where is it coming from
toxic grove
consider a divisor D of N
it can be of the same form (p^x)(q^y)(r^z)
note that x can range from 0, 1, 2 .. a
similarly for y -> 0 ... b and z-> 0 ... c
thus there are (a+1) options for x, (b+1) for y and (c+1) for z
total number of possibilities is their product
light heath
help
light heath
hazy pumice
it's a static equilibrium question
light heath
i think so
hazy pumice
recall that the sum of the forces in the x-direction must equal 0, and the same must follow for the sum of the forces in the y-direction
do you understand how to decompose the tension forces into their horizontal and vertical components?
@light heath
I'm going to bed soon
topaz sinewBOT
@light heath Has your question been resolved?
hazy pumice
@light heath I solved your problem but since you aren't here, I'm going to bed.
light heath
recall that the sum of the forces in the x-direction must equal 0, and the same ...
yea i do
but i have only done so using angles
undone flicker
I want to learn the sum of the series
topaz sinewBOT
I want to learn the sum of the series
frosty cape
You want to learn how to evaluate sum, from 1 to inf?
frosty cape
That I'm not sure, but you can use limits and telescoping for evaluating simple sums...
mellow arrow
long time no see basudev
frosty cape
long time no see basudev
Yes my dear frnd
mellow arrow
1 to infinity 1/(n+1)
sum of 1/n 1 to infinity diverges
for a finite n, it is roughly logn
undone flicker
I guess convergent
mellow arrow
1+1/2+1/3+1/4...1/infty is the series you mean right
thorny flameBOT
frosty cape
Oh
mellow arrow
as I said...
undone flicker
1+1/2+1/3+1/4...1/infty is the series you mean right
Divergent
mellow arrow
1/2k converges to 1 for 1 to infty tho
frosty cape
Looks very wired
frosty cape
Alr kul, deal with this I'm out
undone flicker
What is the sum of 1/n+1
N is 1 to infinity
mellow arrow
(1/n)+1 or 1/(n+1)
undone flicker
Last one
undone flicker
1 to infinity 1/(n+1)
See
thorny flameBOT
undone flicker
1/(n+1)^p
P=1
What if we use ratio test here
An+1/an?
n/n+2
Which is 1
<@&286206848099549185>
1 to infinity {1/(n+1)} convergence?
If not then why it's value is log2-1
gentle spear
i could be wrong but wouldnt the answer be calculated as = n^2 - 1 an + 1 = (n + 1)^2 - 1 = n^2 + 2n + 1 - 1 = n^2 + 2n (only a thought)
barren oyster
what maths is this precal or cal
undone flicker
well, that one would too diverge to infty
So you meant that sum of it is infinity
Why they says sum of it is log2-1
distant nymph
Yes, but ratio being 1 doesn't mean than it would converge. Test is inconclusive if ratio is 1.
topaz sinewBOT
topaz sinewBOT
Available help channel!
edgy quail
topaz sinewBOT
edgy quail
i have no idea how to approach this problem, does anyone know?
i want a lil hint or the approach
drifting swift
so N looks like 47**74 where the asterisks stand for two digits?
edgy quail
yeah
drifting swift
@edgy quail i'd try pinning down how many numbers went into the product. there cannot be too many of them.
it is significant that the last two digits are 74, as that tells us something about divisibility (both affirmative and negative)
mellow arrow
Hint:||Look at the unit digit||
edgy quail
well its even
mellow arrow
the numbers multiplied are consecutive
drifting swift
it's even yes but so's the product of any number of ≥2 consecutive ints.
there's something else that can be said from the last two digits being 74 that you COULDN'T say anything about just looking at the last digit.
mellow arrow
Well, that's what I was saying. There exist no two consecutive numbers whose product would end in 4
However I think you can not yet conclude there are ONLY 3 numbers
edgy quail
i got help from a friend
yes we can
via modulus 5
there is no case where product two conseuctiveeceeec numbers are congruent to 4 mod 5
its 0, 2, 1, 2, 0
so it has to be 3 numbers
but what's the next step?
aha
i bounded it so that if n is the smallest number, 70<n<80
then, using modulus 10, the numbers can only end in 234 or 789
issue: 72 is a multiple of 4
so the only possible case is 789
verifiying: answer is 474474
mellow arrow
Yeah
edgy quail
nice
mellow arrow
77*78*79
topaz sinewBOT
topaz sinewBOT
Available help channel!
edgy quail
topaz sinewBOT
fierce sierra
edgy quail
oh this is awkward
fierce sierra
haha dw u can have
edgy quail
thx
neon iron
topaz sinewBOT
neon iron
how does one go about this?
main shale
replace z with a+bi in the two equations and expand the definition of |-| and arg(-)
this gives a pair of simultaneous equations you can try solve for a and b
main shale
that's not the right formula for argument
main shale
yes
set those equal to the values given in the question and solve for a and b
you might get multiple solutions because of the trig/sqrts
but you can throw away the ones that don't match the right argument
topaz sinewBOT
topaz sinewBOT
Available help channel!
sleek remnant
topaz sinewBOT
sleek remnant
Just struggling find out why its ^kt
and how did they get k
and is the models equation something I need to memorise for exponentials
frail reef
they have that equation with 2 unknowns, A and k, so they substitute values for t and v in to be able to work them out
sort of like forming simultaneous equations
sleek remnant
I did that and ended up with 20000/16000 = Ae^-1t
frail reef
how did you get that?
sleek remnant
i formed 2 equations by subbing the 2 values that were given into V
so when t=0 then v is 20000
and when t=16000 t=1
then just divided the V values from eachother
and minused the powers
sleek remnant
cuz 0-1 from the powers give me negative 1 fore the value k
but i have no clue how they got -0.223
frail reef
these should be the equations you get
if you divide it, it should lead you to this
topaz sinewBOT
@sleek remnant Has your question been resolved?
shut obsidian
You can model exponential growth with a function $V$ as [V(t) = A \cdot a^t,] where $A$ is the starting value. We can rewrite $a^t$ with base $e$ by letting $k \coloneqq \ln(a)$. Then, [V(t) = A \cdot e^{\ln(a)t} = A \cdot e^{kt}.]
topaz sinewBOT
topaz sinewBOT
Available help channel!
neon iron
hello
neon iron
if B is that and C is that
what is the B n C
my thought is that B n C is the set of shared numbers between the 3x multiplication table and the 7x multiplication table
but i have no idea how to describe it with descret math language
worthy storm
can you name the first few numbers in the intersection?
neon iron
hmm
worthy storm
it might be helpful to use words to describe what is in B and what is in C
worthy storm
right
neon iron
all natural numbers are included in universe
worthy storm
so B is the set of positive multiples of 3
and C is the set of positive multiples of 7
neon iron
yes
worthy storm
and the intersection is the set of numbers that are in both
neon iron
yes
worthy storm
which is..?
neon iron
bro i dont know how to describe it
solid sparrow
multiple of 3 and multiple of 7 is what?
worthy storm
if a number is a multiple of 3 and a multiple of 7 then it's a multiple of 21, yes?
worthy storm
yea, all positive multiples of 21
neon iron
a little slow there hahaha
worthy storm
you can write it the same way they wrote A and B
neon iron
okay so its just B n C = {21x | x in all natural numbers}
worthy storm
yes
topaz sinewBOT
topaz sinewBOT
Available help channel!
rich maple
Hello. Attached is the problem I'm trying to solve and my work so far, I have no clue where I'm wrong
topaz sinewBOT
Hello. Attached is the problem I'm trying to solve and my work so far, I have no...
@rich maple Has your question been resolved?
rich maple
<@&286206848099549185> Hello, just pinging because I still have no response. I just don't know where I went wrong in general
sweet shard
Did you use compounded monthly anywhere
rich maple
I did not, that must be it. Where do I put that in the formula though?
Do I somehow combine it with the 4 years time given?
violet umbra
rich maple
Gotcha, so I was just using the wrong formula from the start
violet umbra
yep well
since you're compounded monthly, just divide the rate by 12
and put it to theh power of (number of years) x 12
if that makes sense in the formula above
rich maple
The formula you posted makes sense, I just need to plug my numbers into it
Got it, thanks y'all!
!close
violet umbra
ok
rich maple
Ah dang I forget the command hang on
violet umbra
Hello. Attached is the problem I'm trying to solve and my work so far, I have no...
oh and just another thing
if you want to remove the power of 1/4
you shouldn't be rooting the 1.04
but puting 1.0^4
sorry
1.04^4
rich maple
You're good
Gotcha. I'm not too sure how I would do that then, but it wasn't required yet. That is an important thing for me to come back to though in the future
Thanks again for the help!
hasty cove
is there any way to solve the following equation
ln(2x-n)/n = ln(n-x)/x
hasty cove
I have tried out running iterative programs to figure out solutions for some values of n, so for example n=1000 gives a solution of x approximately equal to 812
empty falcon
cross multiplication?
hasty cove
Even if i do cross multiply, what do i do after that, I am just left with x * n(2x-n)-n * ln(n-x)=0
empty falcon
im thinking
okay uhm
we do cross multiplication
we end up with xLn(2x-n) = nLn(n-x)
which is the same as Ln(2x-n)^x = Ln(n-x)^n
we have a rule that says if Ln A = Ln B then A = B
so (2x-n)^x = (n-x)^n
and from here...
topaz sinewBOT
@hasty cove Has your question been resolved?
empty falcon
x = 1.58n?
hasty cove
x = 1.58n?
x can't be more than n , because otherwise ln(n-x) would be undefined
it has to be between n/2 and n
empty falcon
is there any way to solve the following equation
ln(2x-n)/n = ln(n-x)/x
oh i think i got it
is the whole Ln divded by n ??
or is the (2x-n) divided by n
hasty cove
the whole of ln(2x-n) divided by n
at this point feels like this might not have a closed form solution
hasty cove
I don't think you can explicitly figure out whether the solution is closed or not, but I don't think there's any way you can get rid of the logarithm. if you do then you are stuck with comparing a polynomial with an exponential, which is as bad, if not worse 💀
topaz sinewBOT
i need help understanding how to factor this
orchid wyvern
where did the 9 coem from
glossy acorn
-9
the 9 is the least common multiple
what is the easiet number to divide 729 with? ||It would be 9||
scenic flare
729 is 9³ so that limits your answers :P
glossy acorn
howd u end up with the quadratic tho
well you get it because (x^2 + 9x + 81) times (x-9) gets you x^3 - 729
orchid wyvern
okay
scenic flare
how do i go down from x cubed - 729
Ofc you need to know it if you want to factor? 🐣
One approach would be looking at the initial term which has a degree of 3
and if you factor out x-9 you'll reduce the degree by 1, since the factored out term has degree 1
meaning after factoring out, the leftover term has a degree of 2
x³-729 = (x-9)*(ax²+by+c)
where a, b, c are yet unknown values you want to figure out
a must be 1, since the initial term x³-729 has a 1 in front of x³
do you think you can figure out b & c? @orchid wyvern
orchid wyvern
nop that was what i was asking
scenic flare
without looking at the solution of course :D
orchid wyvern
i already understand the rest i just couldnt figure out where those values are pulle from