#help-17
digital crag
i know this
novel vector
whenever theta becomes larger, the adjacent side becomes smaller and the opposite side becomes larger, correct?
digital crag
i need help
novel vector
Imagine theta at 90˚, then there is not adjacent side, right?
so then tan(90˚) = opposite ÷ 0, right?
novel vector
Because imaging theta gets larger
imagine that theta gets larger, then the adjacent side will become smaller and smaller until it is 0.
the adjacent side does not exist when theta is 90˚
novel vector
its ok let me explain:
so it wants to find tan(-90˚) but
how about this:
open up that desmos graph
and put one of the point on (1, 1)
digital crag
ok
novel vector
wait hold on rq
actually open up this graph
delete the other one i sent open this one
and then set a = 45 on the menu on the left
it's the third one down
digital crag
done
novel vector
so now set a = 75
you can see that the adjacent side gets smaller, right?
then set a = 80
then it becomes even smaller
digital crag
the answer is undefined
novel vector
yes
vast shale
im on the 2nd lesson and theres 4
halfway there king
digital crag
i have to do the review
bro gonna be so honest
ive failed every test this year so
i need to do good on this one and the final just to pass
vast shale
there’s a difference between studying and study effectively
hence why some people spend so many hours “studying” and still get a bad grade
digital crag
idk how to study effectively
digital crag
i dont have time to read a book rn
vast shale
how to become a straight A student by cal newport
digital crag
studying for math sucks
vast shale
read a little bit each day
digital crag
ugh i wanna just jump
and like even if i tried
my grade will be so bad
bro what do i do
i could talk to the teacher
but like im 100% sure she hates me
and i already failed her class one semester
vast shale
are you in uni
vast shale
oh
digital crag
its like ranked as one of the top in the wolrd
digital crag
i dont know enough ppl for that
like idk ppl dont like me
its hs we all basically hate each other
which sucks
vast shale
fair
tbf i didn’t study with others in high school
i didn’t study at all if im gonna be completely honest
digital crag
i didn’t study at all if im gonna be completely honest
prob cause ur smart
vast shale
nah im not
digital crag
idk how to study for math
digital crag
high school is just easy
idk why im struggling
vast shale
u have to have to learn these studying strats
digital crag
i try my best but like my grades suck
vast shale
idk why im struggling
ur in a competitive hs
digital crag
i might have to do an early exist & do community college
like my ecs & sat r like really good but gpa
vast shale
what yr are you?
vast shale
oh that’s weird
vast shale
makes sense
vast shale
7th graders roaming around in a high school 😭
digital crag
anyways my grades are not it like i went for an all a student before i came to the school to a barely passing student
vast shale
i was in 12th last year and the 9th graders were so small
digital crag
i prob well lol ive lived in america my entire life
vast shale
the 7-12 yr high school didn’t seem like an american thing
digital crag
oh its pretty common
anyways
can u help me study
i can usally study till 3-4 and then i start to fall asleep
vast shale
am??
digital crag
yes
vast shale
wtf
no wonder ur studying isn’t working
ur brain comes to a point where it cannot retain anymore information or whatever
so anything after that point is just wasted time
use that time to sleep and if u really need to study
wake up early in the morning
morning is when u retain the most
tranquil charm
what do i do know
50 min of active studying and solving problems and 10 minutes of resting (water break, meditation and stuff ||no electronics btw||)
digital crag
what is active studying
vocal sleetBOT
@digital crag Has your question been resolved?
bronze osprey
what is active studying
where you're actively working on a problem for example
instead of passively reading or copying notes: of course these things are important, but you're not practicing while you're doing that
bronze osprey
i need help
looks like you don't know the identity $\sin \theta = \sin(180^{\circ} - \theta)$
twin meteorBOT
south
digital crag
yeah
bronze osprey
its like when the radius is 1
yes, but do you know the definition of sin and cos using the unit circle
it's radius = 1 btw
digital crag
nah
bronze osprey
https://www.desmos.com/calculator/cno71jmqk2
ah someone did send you this
bronze osprey
there's a version of trig that applies to all four quadrants (SOHCAHTOA only considers 0 < theta < 90 unless you make a few leaps)
bronze osprey
like the test is called "intro to unit circle"
yeah okay
cos theta = x-coordinate
sin theta = y-coordinate
that's the definition of the unit circle
digital crag
yes
bronze osprey
and the height is related to the sin of the angle
bronze osprey
but one triangle has angle theta, and the other one has angle 180 - theta
bronze osprey
yep! so we can conclude
digital crag
exactl
bronze osprey
sin(theta) = sin(180 - theta)
bronze osprey
you know that $\sin 60 = \frac{\sqrt 3}{2}$
twin meteorBOT
south
digital crag
yes
bronze osprey
but from what I said, $\sin(60) = \sin(180 - 60)$
twin meteorBOT
south
bronze osprey
so $\frac{\sqrt 3}{2} = \sin(180 - 60)$ as well
twin meteorBOT
south
bronze osprey
but its wrong
what did you put?
bronze osprey
yeah and then 60 is the smaller solution so it goes in the first box
digital crag
could be a coding error idk
digital crag
lets do another one
bronze osprey
okay
digital crag
okay this one is hard
ima atempt it first'
lwk dont get it
helperes
helpers
come and help
<@&286206848099549185>
novel vector
hi
so tan(theta) = opposite ÷ adjacent
so either the opposite side is negative or the adjacent side is negavite but not both
novel vector
ok so you have 60˚, you can add 360˚ to that angle
which is the same thing as 60˚
360˚ is a full rotation so you end up where you started
so in this case, 60-360
digital crag
its marking it wrong
novel vector
it should be 120˚ and 300˚
digital crag
YES THATS WHAT I GOT
novel vector
still not correct
digital crag
mhm
novel vector
just move on for now because that answer should be correct
digital crag
i forgot to put degrees
im so stupid
i lowk would rather die than fail two semesters in a row
digital crag
digital crag
ik i didnt know what else to put
paper depot
bump it up by a full turn (360°)
digital crag
wdym
paper depot
add 360° to your out-of-range solution -150°
digital crag
sorry
paper depot
it's kinda annoying to read that way
digital crag
got it
paper depot
anyway, sine is a periodic function
it repeats every 360°
kinda its whole DEAL
with the circles and shit
digital crag
offtopic but does anyone know how to hack aeries
steep crater
offtopic but does anyone know how to hack aeries
...
steep crater
academic dishonesty
steep crater
i havent actually done
ogay sure
paper depot
like at least doubly so
digital crag
oh mb
in this server
okay i take it back
sorry
like i always jst joke abt it with my friends
digital crag
ogay sure
i would have if i could have but unfortunately i dont have those skills
neither do i know any1 who does
guys
i was just kidding
delicate dawn
how do I slove this and can someone tell me each step to sloving it
paper depot
how do I slove this and can someone tell me each step to sloving it
we don't solve things for you
paper depot
well ok explanation it is then
delicate dawn
like give me the answer and explain how you got that answer
paper depot
no
novel vector
simplify it?
delicate dawn
bruh nevermind
paper depot
!noans
vocal sleetBOT
The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.
paper depot
do you know:
- how to work with fractions
- exponent laws
delicate dawn
do you know:
- how to work with fractions
- exponent laws
no
paper depot
we're trying to simplify that thing
flat python
ah
paper depot
presumably
novel vector
$\frac{2a^{2}bc}{30ab^{2}c}=\frac{c}{c}\cdot\frac{2a^{2}b}{30ab^{2}}=1\cdot\frac{2a^{2}b}{30ab^{2}}=\frac{2a^{2}b}{30ab^{2}}$
twin meteorBOT
hello
vocal sleetBOT
**hello**
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.
novel vector
that sthe first step
delicate dawn
As a helper, please do not give out answers that could be copied as a homework s...
BRO
delicate dawn
"no" as in you don't know either one?
the question is js asking me to simplfy it
but idk how
and i want to know how to
steep crater
but idk how
do you know that you can cancel terms from numerator and denominator
delicate dawn
its not homework or cheating i js want to knwo the steps to doing it and the answer to put an example
paper depot
ok but now im asking you what you do and dont know
delicate dawn
do you know that you can cancel terms from numerator and denominator
thats what i dont knwo what the hell is cancel out
paper depot
and im trying to make it clear to myself
delicate dawn
ok but now im asking you what you do and dont know
i dont know anything
paper depot
ok then go to khanacademy lmfao
steep crater
thats what i dont knwo what the hell is cancel out
smth like what @novel vector did
paper depot
if you know absolutely nothing then you will have to start all the way from basic arithmetic
graceful abyss
but idk how
Think of the fraction like this:
$\frac{2a^2bc}{30ab^2c}$, can you seperate all coefficient and variables into their own fractions?
twin meteorBOT
pix
novel vector
you can pull out the "c"
paper depot
Think of the fraction like this:
$\frac{2a^2bc}{30ab^2c}$, can you seperate all ...
OP said she knows absolutely nothing
graceful abyss
OP said she knows absolutely nothing
Wow
delicate dawn
ann you dont need to do me like that 💔
graceful abyss
@delicate dawn for context, what grade is this question in?
delicate dawn
man i was just confused
paper depot
wdym "do you like that"
delicate dawn
<@1017990703994908714> for context, what grade is this question in?
yr 8
paper depot
i am doing nothing but repeating your own words
delicate dawn
Think of the fraction like this:
$\frac{2a^2bc}{30ab^2c}$, can you seperate all ...
i have never been so confused
paper depot
delicate dawn
i am doing nothing but repeating _your own words_
okay
graceful abyss
i have never been so confused
2, 30, a, b, and c are coefficient/variables
novel vector
$\frac{x^{a}}{x^{b}}=x^{a-b}$
twin meteorBOT
hello
delicate dawn
2, 30, a, b, and c are coefficient/variables
yes yes i get those
novel vector
use that
paper depot
ok lets maybe everyone calm down and i try to actually narrow down where OP is at
paper depot
i will ask everyone except OP to please stop typing
delicate dawn
but seprate what fraction
paper depot
i will ask everyone except OP to please stop typing
paper depot
ok lets start from some basic basics
and build up from there
cause i wanna meet you where you're at
delicate dawn
wait so 2a2 over bc?
novel vector
yea
graceful abyss
but seprate what fraction
Classify the whole fraction so that it becomes multiple of them with it being number/number, a/a, b/b, etc
paper depot
ok so here is a fraction: $\frac{6}{8}$
twin meteorBOT
Ann
paper depot
can you simplify this fraction
delicate dawn
Classify the whole fraction so that it becomes multiple of them with it being nu...
ohhh okok
paper depot
ok good
paper depot
you recognized it as $\frac{2 \cdot 3}{2 \cdot 4}$ and then cancelled out the twos
twin meteorBOT
Ann
paper depot
So what does it become?
i was clear the first 2 times
graceful abyss
After you've done this, you can use the fundamental basic @paper depot is teelling you
paper depot
i am helping OP. please do not interfere.
paper depot
im spelling out what you did
delicate dawn
do i js find the hcf of 2 and 30 then divide it??
novel vector
how do I slove this and can someone tell me each step to sloving it
$\frac{2aabc}{30abbc}$ = \frac{2a^{2}bc}{30ab^{2}c}
paper depot
no, hold on, we are not going to jump back to the problem
paper depot
$\frac{2aabc}{30abbc}$ = \frac{2a^{2}bc}{30ab^{2}c}
i was clear the first 3 times i told everyone else to stop typing
delicate dawn
no, hold on, we are not going to jump back to the problem
okay okay
paper depot
$\frac{2aabc}{30abbc}$ = \frac{2a^{2}bc}{30ab^{2}c}
i was clear the first 4 times i told everyone else to stop typing
graceful abyss
🍿
brazen gulch
are u a nba plater
paper depot
god damn it
delicate dawn
are u a nba plater
no
paper depot
@delicate dawn shall we continue
delicate dawn
god damn it
so its a/15b
delicate dawn
<@1017990703994908714> shall we continue
yes ma'am
paper depot
well, ok, yes, $\frac{a}{15b}$ is correct actually.
twin meteorBOT
Ann
paper depot
i guess reminding you of "cancellation" jerked your memory enough to recall it all.
and in fact your "i don't know anything" was a result of momentary confusion
delicate dawn
u should become one ur name is destined for greatness
yesss thats my inspiration
delicate dawn
i guess reminding you of "cancellation" jerked your memory enough to recall it a...
thanks ann for helping me
paper depot
as opposed to you being actually ignorant of all this
ok, do you have anything else to ask or are we done
if we're done you can .close this channel
vocal sleetBOT
vocal sleetBOT
Available help channel!
peak yacht
Hello! 👋
How do I get the ui and uj on the second step of the stepping-stone-method here? 
"c^-ij = cij − ui + uj" i know this fomula for the c^-ij (by c^-ij i mean the c with the - over it)
vocal sleetBOT
@peak yacht Has your question been resolved?
sharp pilot
vocal sleetBOT
twin meteorBOT
sharp pilot
Implies
AB²=(3+x)²-(5-x)²
=9+x²+6x-25-x²+10x
=16x-16
twin meteorBOT
sharp pilot
Implies
CD²=(4+x)²-(4-x)²
=16+x²+8x-16-x²+8x
=16x
CD=4√x
EA=CD=4√x
AB=EB-EA
=4√3-4√x
=4(√3-√x)
AB²=16(3+x-2√3√x)
.
Above and below imply
16x-16=16(3+x-2√3√x)
x-1=3+x-2√3√x
-4=-2√3√x
2/√3=√x
x=4/3
So option B is correct
@stable basalt
bronze osprey
so much Spanish maths recently
sharp pilot
Since #help-6 is closed for some reason, I can't message there, I opened another help channel to inform him about this and know if my answer is correct or not.```The question is: Given 3 circles of radius 3, 4, x. If all 3 are touching each other, find x.
vocal sleetBOT
@sharp pilot Has your question been resolved?
strong isle
```This channel is from #help-6 about @dielle3 's question. He was told there t...
The same problem was I believe to be asked by the same person here: #help-9 message. I think you should have specified that the circles were in a rectangle with the big circle and small circle touching the same side, then it makes sense. You’re solution is also pretty long, but I checked it and it seems fine. Indeed the answer is || 4/3 || which corresponds to || option B ||.
sharp pilot
Circles don't need to be in a rectangle. I mean atleast the way I did it, circles being in rectangle or not has no effect on the solution.
strong isle
Circles don't need to be in a rectangle. I mean atleast the way I did it, circle...
No they kinda have to be
strong isle
For example here you assumed that the smaller circle and bigger circle are tangent at the same top line
Which is the length of the rectangle
vocal sleetBOT
vocal sleetBOT
Available help channel!
vocal timber
If the sum of coefficient of a quad eqn is 0 then it's 1st root is unity and vice versa
How to prove it
vocal sleetBOT
If the sum of coefficient of a quad eqn is 0 then it's 1st root is unity and vic...
rugged orchid
what does it mean its first root is unity
vocal timber
It's one root is one
rugged orchid
so you're saying that if ax^2 + bx + c = 0 has that a + b + c = 0 then x = 1 is a solution?
vocal timber
Exactly
quiet echo
If the sum of coefficient of a quad eqn is 0 then it's 1st root is unity and vic...
Uhh, just plug in x=1 into the quadratic?
rugged orchid
i dont know about you but 0x^2 + 0x + 1 doesn't look like it has a solution at x=1
vocal timber
That will make it zero but that is to verify this
quiet echo
i dont know about you but 0x^2 + 0x + 1 doesn't look like it has a solution at x...
But the sum isn't 0
it is 1
odd helm
i dont know about you but 0x^2 + 0x + 1 doesn't look like it has a solution at x...
a+b+c is not 0
rugged orchid
oh im stupid
quiet echo
You're good
rugged orchid
Uhh, just plug in x=1 into the quadratic?
do this
vocal timber
i dont know about you but 0x^2 + 0x + 1 doesn't look like it has a solution at x...
It's ax2+bx+c not 1
rugged orchid
a * 1 + b * 1 + c = 0
quiet echo
I remember doing this a long time ago, you can prove this for any polynomial (and also find a few neat tricks for factors in other ways)
rugged orchid
so it reduces to the same restriction
vocal timber
Yes there's this one also
odd helm
never thought of this before
rugged orchid
plug stuff in and see i guess
quiet echo
I remember doing this a long time ago, you can prove this for any polynomial (an...
^
Putting it in sigma notation helps
vocal sleetBOT
@vocal timber Has your question been resolved?
sharp pilot
Consider ax²+bc+c=0.
Let 1st root be unity and second root be r.
Then, 1+r=-b/a, r=c/a
So, 1+c/a=-b/a
a+c=-b
a+b+c=0
@vocal timber
You can prove conversely,
If a+b+c=0
Then, 1+c/a = -b/a
1+(r1r2)=r1+r2
1=r1-r1r2+r2
1=r1(1-r2)+r2
1-r2=r1(1-r2)
1=r1
vast shale
Consider ax²+bc+c=0.
Let 1st root be unity and second root be r.
Then, 1+r=-b/a...
Did u do 1+ sum of roots? In step 2
sharp pilot
I am assuming we know sum of roots = -b/a and product of roots = c/a
Is there anything wrong with that?
I did sum of roots = -b/a
Since one root is 1 and other is r we get
1+r=-b/a
vocal sleetBOT
vocal sleetBOT
Available help channel!
mint siren
is anyone able to help me with my statistics final exam? if ion get like an 80 i fail the class😭
vocal sleetBOT
is anyone able to help me with my statistics final exam? if ion get like an 80 i...
wanton bloom
!da2a
vocal sleetBOT
No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/
paper depot
is anyone able to help me with my statistics final exam? if ion get like an 80 i...
you're not asking someone to help DURING the exam are you
mint siren
you're not asking someone to help DURING the exam are you
no i didn’t start it yet b it’s online not on a meeting or anything so i cud cheat
paper depot
so you're still trying to get someone to cheat on the exam for you.
mint siren
so you're still trying to get someone to cheat on the exam for you.
i don’t want to fail so correct
paper depot
<@&268886789983436800> yeah we got an exam cheater in here
quiet echo
W
tawny nacelle
that's against server rules
quiet echo
free moderator ping
wanton bloom
Get rekt.
mint siren
i ain’t know that ngl
grave flame
LOL
paper depot
receipt
quiet echo
i ain’t know that ngl
I ain't know that you need to use logic ngl
cedar kernel
😭😭😭
grave flame
i ain’t know that ngl
Was written in the rules
mint siren
i didn’t read them😭
peak matrix
you chose too large server for this my man
quiet echo
I ain't know that you need to use logic ngl
^
spiral turtle
.close
vocal sleetBOT
quiet echo
Impending doom awaits
quiet echo
The verdict has been delivered
cedar kernel
Gl belive in yourself
flat whale
it'll be funny when we get some statistics questions and a helpee in a rush
spiral turtle
He left the server.
cedar kernel
Oof the embarassment
grave flame
<@&268886789983436800> yeah we got an exam cheater in here
So if anything happens or like now do i have to call the moderators?
quiet echo
Womp womp
wanton bloom
Can you still ban him from coming the server?
cedar kernel
Atleast he won't ask to cheat again so openly 🙏😭
grave flame
So if anything happens or like now do i have to call the moderators?
Just asking cuz i dont know
quiet echo
Wdym
paper depot
So if anything happens or like now do i have to call the moderators?
there's no mandatory reporting rule but like
yes if you see something blatant like this then a mod ping or a DM to @drowsy igloo is appropriate
grave flame
Alr thx
vocal sleetBOT
Available help channel!
grave flame
vocal sleetBOT
grave flame
,rotate
twin meteorBOT
cedar delta
whats b = ?
grave flame
Beta
peak matrix
beta = 1.1°
peak matrix
There are 2 right triangles there, one with angle alpha and one with angle alpha + beta
so from those, make the 2 equations
twin meteorBOT
cedar delta
try substituting now
vocal sleetBOT
vocal sleetBOT
Available help channel!
glacial trellis
I need help
vocal sleetBOT
I need help
hollow pendant
I need help
!da2a
vocal sleetBOT
I need help
No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/
vocal sleetBOT
No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/
hollow pendant
Dividing by 0 is not possible. What happens here when you plug the given x values into the function?
oak magnet
which one isn't 0?
hollow pendant
But it isnt 0 when it’s divided
We don't care what happens after division.
hollow pendant
Also, is this problem typed wrong?
oak magnet
its cubed ?
hollow pendant
$$\frac 1{(x - 2)^3}$$
twin meteorBOT
@hollow pendant
hollow pendant
<@751533372890677398>
That's what I see.
oak magnet
the thing is that its a different issue than 0 division
glacial trellis
All the questions dont make sense
hollow pendant
the thing is that its a different issue than 0 division
But how else is this function discontinuous?
oak magnet
But how else is this function discontinuous?
nothing its probably typoed and they meant x = 2
oak magnet
the other one aren't wierd
hollow pendant
Dividing by 0 is not possible. What happens here when you plug the given `x` val...
glacial trellis
The 7th one i did
oak magnet
saying that limit from right and left aren't finite and the same
glacial trellis
Bru im in precalc and my teacher is teaching calculus and i missed one day and i dont get it
Also how do i do the 8th one
oak magnet
same way the other
oak magnet
redo calculations
careful to parentheses
x² - x -2 at x = -1
so 1 - (-1) -2 = 2 - 2 = 0
oak magnet
yeah but it would have been like x = 2
and the same argument for everyone
limit from left and right at x = smth are infinite so can't be continious (even if same sign of infinity)
vocal sleetBOT
Available help channel!
long patrol
I need help with this plz. Sorry for bad english.
vocal sleetBOT
I need help with this plz. Sorry for bad english.
cyan shadow
I need help with this plz. Sorry for bad english.
!status
vocal sleetBOT
I need help with this plz. Sorry for bad english.
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
are you familiar with the concept that $f(x) = (x-h)$ has a zero at h?
twin meteorBOT
long patrol
i know that for example degree 5 means 5 zeros
cyan shadow
it only sort of means that
cyan shadow
it means that there is a term of $ax^5$ in it
long patrol
so yeah
twin meteorBOT
long patrol
yes
cyan shadow
yes
cyan shadow
but for my first question, do you understand this?
long patrol
but for my first question, do you understand this?
idk. then it just means f(x)=x?
cyan shadow
no
long patrol
then idk
cyan shadow
what is the zero of $f(x) = x-5$?
twin meteorBOT
long patrol
5?
twin meteorBOT
long patrol
10?
cyan shadow
and then in general $f(x) = x-h$ for any h
twin meteorBOT
cyan shadow
yes
okay so your problem requests what exactly?
polynomial of degree 5, and a zero at zero, and two other ones, yes?
long patrol
how do i find like a graph with degree 5 that has a zero at (0,0) and 2 in negative and 2 in positive
long patrol
polynomial of degree 5, and a zero at zero, and two other ones, yes?
yes
that's the first one
and then there's also one with degree 6
idk how to find that
cyan shadow
how do i find like a graph with degree 5 that has a zero at (0,0) and 2 in negat...
well lets build it in steps (although your problem doesnt ask for this)
long patrol
i asked AI but it said trash and it's wrong and i can't find videos on youtube
cyan shadow
lets build a polynomial of degree 1 that has a zero at zero
cyan shadow
can you do that?
cyan shadow
thats degree 2
cyan shadow
exactlyu
okay now lets add another root, say we want to add 1
whats a polynomial of degree 1 that has a zero at 1?
cyan shadow
f(x) = x-1 yes
now we need to combine them. Since a number is 0 if any part of it is zero we can just multiply them together
f(x) = x(x-1)
this has a root at 0 and at 1
do you follow this?
cyan shadow
what do you mean
long patrol
where did you take it from
cyan shadow
I did not take it from anywhere. I just combined your f(x) = x and f(x) = x-1
its a second degree polynomial with roots at 0 and 1
long patrol
its a second degree polynomial with roots at 0 and 1
i get that it's second degree
and yeah
i actually get it yeah
i think
so yes i folloewd it
cyan shadow
Okay great! Can you figure out how to add another root?
make it a third degree polynomial with roots at 0, 1, and 2
long patrol
make sure its a function
ok
cyan shadow
now try to answer your question. A fifth degree polynomial with a root at 0 and 2 other roots
long patrol
now try to answer your question. A fifth degree polynomial with a root at 0 and ...
uhm
im a bit confused
because why does the fith degree only have 3 zeros
i know it's possible when it's higher
but
idk how high it gets
cyan shadow
ah heres the trick
it does have to have 5 roots
but they are allowed to repeat
you could have 3 roots at 0
formally called "root of zero with multiplicity three"
so you can make your polynomial have roots of 0, 0, 0, 1, 2 and it would be a 5th degree polynomial with only 3 distinct roots
cyan shadow
f(x) = x^3 is a third degree polynomial and only has a root at 0
long patrol
so you can make your polynomial have roots of 0, 0, 0, 1, 2 and it would be a 5t...
i didn't know that
long patrol
f(x) = x^3 is a third degree polynomial and only has a root at 0
idk how to do it then
cyan shadow
x(x-1)(x-2)
how would you add a root of 0 to this?
and what would you get if you did that
long patrol
how would you add a root of 0 to this?
i would have just added another x but then it would be 2²
x²
cyan shadow
write out the full function please
long patrol
write out the full function please
x(x-1)(x-2)x turns into x²(x-1)(x-2)
cyan shadow
now this is a 4th degree polynomial with roots at 0, 0, 1, 2, right?
its f(x) = x^2 (x-1)(x-2)
long patrol
now this is a 4th degree polynomial with roots at 0, 0, 1, 2, right?
i think yes
cyan shadow
this is very close to what you want
you want a 5th degree polynomal
how do you add another root to get it there?
long patrol
so add another x?
cyan shadow
sure that works
twin meteorBOT
long patrol
so it's correct?
cyan shadow
assuming I read the german correctly its a correct answer for (a)
long patrol
assuming I read the german correctly its a correct answer for (a)
(a)?
cyan shadow
part a
long patrol
do you meant the first bullet point
cyan shadow
yes
long patrol
bc this whole question is d)
cyan shadow
well okay for the second bullet point, it wants a 6th degree polynomial with "no roots", right?
what it means is that it wants only imaginary roots
for example, what are the roots of $f(x) = x^2 + 1$?
twin meteorBOT
cyan shadow
this is a second degree polynomial with "no roots"
long patrol
this is a second degree polynomial with "no roots"
idk what roots means exactly
m,y english is a bit bad
cyan shadow
Nullstelle
twin meteorBOT
long patrol
this is a second degree polynomial with "no roots"
oh yeah
cyan shadow
try to solve it to find the roots
cyan shadow
it doesnt have real roots
you need a 6th degree polynomial that also doesnt have any real roots
long patrol
you need a 6th degree polynomial that also doesnt have any real roots
oh
what about x^6+1
cyan shadow
yep that works
long patrol
yep that works
but where is the Nullstelle then
cyan shadow
this is what it looks like
cyan shadow
but where is the Nullstelle then
have you heard of "imaginary" or "complex" numbers
it might not be something you have learned yet
long patrol
have you heard of "imaginary" or "complex" numbers
yes but idk it
i shouold know it from calss but idk
cyan shadow
yeah well basically the roots are imaginary
which for the purposes of your exercises you can pretend they dont exist
long patrol
that sounds really weird
cyan shadow
but the roots of $f(x) = x^2 +1$ are $x = i, -i$
twin meteorBOT
cyan shadow
it does still have two roots, they are just imaginary
you will get to it eventually
hopefully you understand this problem here!
long patrol
hopefully you understand this problem here!
i think i
means like 1 or -1
but thank you for your help i already understood a lot of new things but i need to go now
cyan shadow
goodbye!
vocal sleetBOT
vocal sleetBOT
Available help channel!
lethal scarab
hello i need help with both of these equations
vocal sleetBOT
hello i need help with both of these equations
tranquil charm
Just post the question first so it gets pinned
paper depot
image on its way?
paper depot
ok just for my own sake
ok
these are exponential equations
have you done these before
tranquil charm
take log on both sides after simplifying?
paper depot
ok first
lethal scarab
thats what i dont understand with log and what not
paper depot
so you have seen logs as a thing before but your recollection is hazy, correct?
lethal scarab
yes
paper depot
ok
lethal scarab
correct
paper depot
then let's go over that
tranquil charm
send exponential term to one side
paper depot
i first wanna make sure you have a better grasp of logarithms as a concept
lethal scarab
wym
paper depot
so let's set those questions aside for a moment
lethal scarab
Ok what do u want me to do
paper depot
for a start: tell me \textbf{in your own words} what the symbol $\log_a(b)$ means.
twin meteorBOT
Ann
paper depot
it doesn't have to be perfect and i will correct you if/as necessary, but i want you to try your best.
lethal scarab
i mean is it not just log base
i dont know how to explain it
i mean like get some log problems
i get some
?
paper depot
hmm...
ok let's put it another way
how would you explain what log_a(b) means to someone who's not heard of logs before?
for example how do you explain why we say $\log_2(16)=4$?
twin meteorBOT
Ann
lethal scarab
this equation is basically sayinf 2 to the power of 4 equals 16
2 is your base always
and the equal is your power
paper depot
ok thats a step in the right direction
"the equal is your power" is a bit questionable as far as wordings go but whatever.
lethal scarab
im talking abt exponet
paper depot
the core idea is that $\log_2(16) = 4$ because $2^4 = 16$.
twin meteorBOT
Ann
lethal scarab
ye thats what i meant
paper depot
the general way to phrase that which i like to use for explanations is as follows:
lethal scarab
its what ur base is raised to
paper depot
$\log_a(b)$ answers the question ``$a$ raised to \textit{what power} gives $b$?''
twin meteorBOT
Ann
paper depot
which, for example, lets you figure out something like $\log_7(7^{24})$ instantly, without having to do any laborious exponentiation.
twin meteorBOT
Ann
lethal scarab
Ok
paper depot
just so i make sure you've understood this concept:
paper depot
can you tell me what $\log_7(7^{24})$ is
twin meteorBOT
Ann
paper depot
but how wouild i apply this to one of the equations i sent
patience! we'll get there.
lethal scarab
its 24
lethal scarab
i used a calculator tho ngl
paper depot
...................
ok so you used a calculator instead of thinking about this concept yourself?
wtf.
lethal scarab
i mean i get the concept
its quicker typing in the concedpt through the calculator
paper depot
ok then you should be able to spell it out using that concept. this was a non-calculator question.
paper depot
log_7(7^24) answers the question "7 raised to what power gives 7^24?"
paper depot
and the answer to "7 raised to what power gives 7^24?" is quite obvious
paper depot
ok now that that hiccup's gone
the most basic type of exponential equation is something that looks like $a^x = b$, where $a$ and $b$ are raw numbers.
twin meteorBOT
Ann
paper depot
which comes with two points, equally important:
\begin{itemize}
\item to solve an equation in that form, you take $\log_a$ on both sides: the equation becomes $\log_a(a^x) = \log_a(b)$ which simplifies to $x = \log_a(b)$.
\item for most other exponential equations, the strategy is to \textbf{reduce the equation into that form}. (which means isolating the exponential term)
\end{itemize}
twin meteorBOT
Ann
paper depot
i will ask you to read this 2 or 3 times and ping me when done, then we can continue
lethal scarab
i will ask you to read this 2 or 3 times and ping me when done, then we can cont...
ok i read it
paper depot
ok right
so we're gonna get to the equations in your paper in a moment, but right now what i'd like to do is give you a few simpler ones to practice with.
is that ok with you?
lethal scarab
ngl i kind of need to do that equation i have a few more other concepts
but i mean if thats the only way then ig so
im lost on it
like i just want to see the solving steps for an equation like this so i can apply it
do you tho im all ears im learning
paper depot
well im gonna need you to get a piece of paper and solve a few simple exponential equations
which im about to give
in increasing levels of difficulty, but none should be too hard with what we've talked through now
lethal scarab
hit me
paper depot
so here are the equations i want you to solve:
\begin{enumerate}[a)]
\item $5^x = 18$
\item $2^x - 7 = 23$
\item $3^{x-2} = 40$
\end{enumerate}
and for all of these i'll ask for your working and \textbf{exact} answers. this is a \textbf{non-calculator} question.
twin meteorBOT
Ann
paper depot
these all take like three steps to solve at most btw
leave logarithmic terms as-is, too.
lethal scarab
its confusing
paper depot
5^x = 18
this is an equation in the basic form (a^x = b) that i mentioned
paper depot
ok
reading comprehension time
for equations in the basic form (a^x = b), what step did i say to do?
lethal scarab
no idea
lethal scarab
take log a on both side
lethal scarab
5?
paper depot
read the bolded words to me
lethal scarab
but thats the format we are doing on the exam
Ok i understand you but this is how im gonna need to do it on my exam
is the answer correct
?
paper depot
x = log_5(18) is the correct answer for letter a), yes.
but i will ask you once again:
for these other two questions i'm asking you, DO NOT use a calculator. i am asking you NOT TO use a calculator. you MUST NOT use a calculator. DO NOT use a calculator. you SHOULD NOT use a calculator.
lethal scarab
look
paper depot
capisce?
lethal scarab
can i just use the calculator thats the answer i need to give on finals
paper depot
no.
there is a reason i'm asking you not to reach for the calculator immediately.
we will get to the calculator when it is appropriate.
if you insist further, i will stop helping you.
lethal scarab
b is log2 (30)
paper depot
yes, this is correct.
to spell out what you've done:
you added 7 to both sides to get 2^x = 30 -- you isolated the exponential term -- and then took log_2 on both sides.
lethal scarab
yep
paper depot
now do c).
lethal scarab
wait so i did it right
tardy cove
wait so i did it right
Yes that's correct. Well done!
paper depot
wait so i did it right
well, maybe you went through some 5th-dimensional wormhole and your process does not match what i've spelled out here
but if that didn't happen and it does match, then yes, you did it right.
lethal scarab
x=log 3(40)+2
paper depot
underscore for the base of logarithms btw
log_3(40) + 2
but anyway yes ok that's correct
paper depot
yes, i was gonna get to those.
let's do Q15 here. i am aware this is now a calculator question, but i'll ask you to still hold off on that, and show your work leading to an exact answer.
paper depot
once i am sure that your exact answer is correct, then i'll ask you to whip out the calculator and give an answer rounded to 4dp.
paper depot
show your work.
paper depot
did you do it on paper or in your head?
lethal scarab
in my head because first
lethal scarab
you divide the 10 on both sides
paper depot
redo it, but on paper.
lethal scarab
the after wards
paper depot
stop.
lethal scarab
u get the log 8