#help-23
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strangely worded question
3 + 5lambda = 0 obviously has one and only one solution
i'm not sure what more there is to say on the subject
idk i was gonna say like
since it's parametric
lambda like the constant which ties the equation together for all the points on the line
kind if like a replacement for the X in a normal 2d function
but like how do i put that into words idk im dumn
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<@&286206848099549185>
Helppp š
How you do this proof
@stray warren help
@lament bluff
I know them bro
Ye
How do u set the problem up
Like the basis step
base case
can you explain in your own words what proof by induction is
Yea
what n should you select for the base case
You prove itās true for n=1 then assume itās true for n=k
Then use induction hypothesis
you need to prove that assuming n=k holds then n=k+1 also holds
this is the full inductive step
dont split it so that "assume f(k) is true" is lumped into the base case
also note that your base case n is not necessarily always 1 its just the smallest n possible
Hm so itās 0?
there is no a_0
Iām confused
your sequence starts at a_1
Ye
so n=1 is your base case this time
But does n start at 0
its asking you to prove that the formula is true for all natural numbers n
by definition natural numbers start at 1
^ may be a controversial opinion but whatever
Hm true
absolutely controversial, i do combi and i think it SHOULD start at 0
š
Nah 1 š
but im not here to debate definitions and semantics
LOL since they provided a_1 i assumed their opinion was natural starts at 1
Real
for this problem yes
are you comparing a_2 to a_1
Yes thatās the problem
The other equation starts at a_2
a_1 = -4 as you typed yourself
Ohhhhh
Huh
Math aināt mathing rn
Ok base case is true then prove it for n=2 because Iām skeptical
how come youre not just
when you compute this you're using n=2
simply substituting n
when you compute this you have to use n=3
do it step by step
Wdymmm
š
and then dont do anything else
copy the equation on its own, sub n on a new line under it
dont compute anything
But this is comparing n=1 to n=2
take it one step at a time
you are not comparing anything
you are merely showing that
if you plug n=2 into the equation
it works
Because Iām plugging in different numbers for n
Yea what abt the second line
you had to EVALUATE a_2
š
by using a_1
but that has nothing to do with the original equation
you plugged in n=2 there
so youre checking that n=2 works
thats it
Ok
ok so
plugging in n=1 to show its true
thats the base step
the next part where you assume that plugging into any k is true
you are too quick to want to assume it
you are too antsy to get to the next step
After we prove the bases
start with "Assume ..."
dont put it on the same line
its a different step entirely
it doesnt matter to the professor
it matters to YOU because right now you are confused about the inductive step
because you dont know what is inductive and what is base
if you dont want my help ill go somewhere else
I didnāt say that
ok
Iām looking at the notes and he did start a new line for the assume but never explicitly told us to do so
well IM telling you to do it so you can organize your ideas better
Ok
so lets first explain how induction works
imagine youre standing in the back of an infinite line
i want to prove the following statement: Every person on the line is capable of touching the person in front of them.
base case: you can touch the person in front of you
Ye
inductive case: ASSUMING you can touch the person in front of you, then that person can also touch the person in front of them
Yes
you can replace "assuming" with "if" or "in the case that"
so think about how that works
since you can touch person 2
person 2 can touch person 3
and since p2 can touch p3
what does that imply
P3 can touch p4
can you see how this creates a domino effect to infinity
Ye
thats induction
thats why the "assume" stuff starts on a new line
it is separate from the base case
Ok
putting assume on the same line feels like you
broke the line at a weird place
like i did just now
its not wrong its just weird
I see
Weāre assuming that
Ok then where do I go from there
you have a true statement by plugging in k
write that first
then write the statement you want to prove under it
first write that
good, plug in the k+1
so like write
"we will now show that:"
followed by the equation
good
now start algebraically manipulating this equation
so that it looks like the n=k case we are assuming
for example, can you see what to do with a_k+1?
on the lhs
no you have k+1 in the subscript
we need to rewrite $a_{k+1}$ into something with $a_k$
CosmoVibe
Why a_k
because you have this equation you need to prove to be true
but the only thing similar to it that you know is true
is the statement you assumed earlier by plugging n=k
youve got nothing else similar, so you have to use it
you need to turn it into that form
did you forget the definition of the sequence a
from the original problem?
look at the original problem
here
cant respond for a while
no signal
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we pull a 3^(x-3) from both sides
divide?
yep we are essentially dividing since we are factoring it out
3^(x-3) divided by 3^(x-3) is just 1
for the next term,
3^x divided by 3^(x-3)
remember the laws of exponent when dividing?
we subtract the powers
it becomes
3^[x - (x -3)]
woah
we can divide single parts of a equation??
the ratio in the equation would literally change
its just factoring, we are still multiplying 3^(x-3) in the left side
can you show as images?
1s
actually ill do your method to show how it results to this
we have to subract
yes
yk this right
its x-(x-3)
oh its -(x-3)
its kinda hard to factor that way
np
its wayyyy harder for me to do it the other way
i asked like 3 of my buddies
somehow they got it
couldnt explain it
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How do u graph this?
Desmos
Like without it
How do u find the phase shift and period of this graph?
Would the period be 2pi divided by 2pi/12
?
so you gotta factor a 2pi/12 from 2pix/12 - pi/2
correct
ye you got it right
why does it
So like for example the phase shift is 1 and that + the period is 12
What would be in between
what do you mean by in between
In a phase shift thereās 5 points right?
What would be in the middle
it should be 1 and 13
This is just an example
what you have drawn is for a period of 11, not 12
Like in between 1 n 5 is 3
ye you are essentially finding the midpoint between them
So what would the midpoint between 1 and 12 be?
in the thing you have drawn, the midpoint between 1 and 12 is 6.5
Oh alright
but take note thats for a period of 11
ah
For the help
oki
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Given the sphere $(S): (x-1)^2+(y-1)^2+(z-1)^2=16$ and the plane $(P): x+y+z+2=0$. The intersection of (P) and (S) is the circle (T). CD is a fixed diameter of (T), A is a point on (T). The line passing A and is perpendicular to (P) intersects (S) at B. Calculate $BC^2+AD^2$
FunguDeu
@versed wave Has your question been resolved?
look at the image from this angle as shown in the arrow
i hope its clear
thats like its projection from that angle
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Can anybody help me with a couple grade 12 calc questions?
I can't do any of these 5 questions at all.
Im taking calc while taking advanced fucntions because I got screwed over
So I can't really do calc, and these I can't do at all
Can anybody give me answers in steps?
<@&286206848099549185>
1, the derivative tells you the slope of a function at any point x, and the equation for a line with slope m at (x1,y1) is y-y1=m(x-x1)
2. differentiable means that the derivative changes smoothly, and you have to make sure that happens when the functions meet, so take their derivatives and set them equal at x=pi
3. you're told L'(t)=-0.1999, solve for t
4. you can do the product rule on the whole thing, but 2^x^2 needs a double chain rule, like d/dx[f(g(h(x)))] = f'(gh)*g'(h)*h'(x)
5. take the derivative two or three times and see what happens, it'll continue in this way
Thanks so much for the help and tips, but I seriously know 0 calc. Im basically just asking for answers. Ik I sound like a dick lmao but if nobody can help its alr
!noans
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.
not really how this server works š
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I know I have to use Ramsey Theory, here's what I've tried so far
(ignore the writing in black)
<@&286206848099549185>
@kindred mesa Has your question been resolved?
<@&286206848099549185>
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How can i do these? I have no clue how to do proofs what so ever. And i have a test coming and these are just the easiest/basic proofs...
I dont understand the "proofs" part of the two colum proof
I can easily do the problems themselves of course but the proofs part is just so BS to me.
this and that theory or sum...
Iāll go over question 5
So basically you want to find the angle using the proofs then state the proofs you used
To find x, notice how the 35 degrees and x are on a straight line
Whatās the statement about angles on a straight line
uhh
its gotta do with like 180 right
congruence?
im not sure man, i dont understand the statements.
Can you elaborate
Which part donāt you understand
I dont understand the thereons
like i dont KNOW what stuff to put for the statements area
the two columb proofs type stuff
In order to solve the angles
You used some rules right
Literally just wrote down those rules
Oh
here
i just use like common sense.
Which ones do you remember
lol you sorta just have to remember them
when im writing the two colum proofs i dont
know what to put next?
like i just jump stragith into the answer lol.. idk how im supposed to show step by stepby step..
its so tedious and annoying i just dont understand it
because i cant tell whats neccessaryt to put down or not
i just do everything in my head
Look at the picture
yes
Draw out which angles you need to find to find the answer
Then do through each one one by one and write down the rules to find those angles
Itāll be slower than doing it all in your head but youāll miss marks otherwise
well basically im on all of them..
give me amoment
for this one
116 = 6x plus 32
what rule would i have to put
Ok
i dont need ext?
No
can you explain please
Ext is when both angles are outside the āshapeā
hmm
You see how the main part of the picture could be turned into a closed shape
If both angles are inside its interior
If both are outside its exterior
If oneās inside and oneās outside then donāt include any
If you donāt know then just do alternate angles
Twice
Cause itās just one step more
yeah i dont even know what happendd.
lol
Your maths is wrong or your rules are wrong
math
5y-21+116=180
The 6x+32
mhm
5y-21=64
5y=85
5y=85
yeah
17
but then
17x5
-21
64
oh
what did i do wrng in my work tf
ohhh i tried removing the 21 too early
whoopsie.
yeah im fdailing my test tomorrow
its officka
(If thatās how youāre trying to prove it your doing it wrong)
(The proof is literally meant to be (for y) angles on a straight line add to 180)
can you show me how you would do it?>
Ok lemme get to my desk
thank you bro
give me a bit, i will go pray an be right back
ok
if you had a seperate column for the rules then write those there, but make sure its clear for which step youre using the rules for. (At least thats what I was taught)
what is co - res?
coresponding
honostly i think im stupid
nah
i dont get this shit at all man š
used to be that lil nerdy kid
now i dont understand this highchool math
greatttt end of the year so far
cant wait for the test
the proofs ar eeven harder
hurray.
no...
see these are coresponding angles
lol sorry
and the only part i get
nah
thats all i know basically
thanks for helping
but ig my brains just
would you like me to go over the other ones again
alrr
2x and 58?
yeah
you tryna hop on call to make this like
more easier ig
les typing and easier to explain
can but i cant talk unfortunatley
k
i spent an hour earlier tryna lok at youtube videos and shi
did not help
im that dense lol
anyways back to 7
2y and 58 are corresponding
yep
while 58 and 2x are congruent
idk about that lol
can you explain why theyre congruent
cuz wont 58 plus 2x create 180
yeah
wait congruent means the same
whats the term called uhh
i got the wrong name man
š
yeah
both are the same
i could put that?>
i thought proofs neeed like
the right terms and stuff
this and that thereom or sum š
nah not mine
š
like these terms
definitely
thereom
balbalbla.
property
etc
cant even cheat on these things.
i mean those are jst the terms ig
i just dont understand the whole point of proofs
if you can solve it why need to prove that you can solve it
like wtf
welp back to 7 off topic whoops
ima find y first
ik 2y = 58
so y = 29
yes
and then 58 +2x = 180
so x = 66
the finding x and y arent hard forme aslong as i do it right
but i dont know how to like put it in two colums ig
my teacher stopped recording his lectures too
they were mad useful
hmm ok
relatable
yep
nah its like
corresponding angles therem
or vertical angles congruence thereom
those type shi
oh
man.
ok
wait lemme read that agian
(idk the answer, depends on what your teacher thinks)
yeah fuck that
I was taught differently
man i wish i was one of those smart ass kids
but even the smat kids in my class dont get it
so im cooked
theres no cheating on proofs either
honestly
cant just search it up like everythign else
useless
fuck those scientiest
and nasa people
fucking squigly line shit with number
š
xD
i cant even do this with straight lines
lets try y
this what i gfot
ignroer the handwriting
used to always right in cursive and stopped so it kinda messed me u
p
so rn you only have coresponding
which links these two
then you need to link that with 2y
lol
youre getting the hang of it
man i swear every time i study late at it
it never fucking helps
i always end up clueless during the test some hwo
but then i studyt late cuz i dont fucking UNDERSTAND ANYTRHINGAKNGK
UHHH
heres something
as soon as theres something you dont understant
if not im moving on.
go ask the teacher
uhh
yes
me asking
you did it right
and dont go away until you understand
i dont want to be at school
lol
i dont even want to be associated with it that early in the morning
relatable
ok
wait lemme js
run through 10,.3 rq
oki
lets see here
so this is just asking if its parellel
should be decently easy but im not sure if i have to prove it
13 x and y are parellel because they are both perpendicular to z
this part honostly i dont know
oh
i need a thereom
bruhh
whaton haeven is the trasnversal thereom
oh if its perp ig
yep
aight im chil ig
this part is aight
thing is im gonna forget ot put these whe ni take the test
i just absolutely hate this shit man
why first period
i used to sit right in fron tof the teacher till like a mont ago
and now he flipped the class around so im all the way in the bakc so ofc im not paying attention for shit when the hard stuff i have no idea about starts
you can ask him
tell him you're finding it harder to focus
if that doesnt work just say you cant see from back there
ok lol
yes
alr
so
line w and z are perp to x so uising the transversal thereom x and z are parellel
should work
and then same thing for x and y switch it with poerp to
actually
i think i may have done it wrong
because theres only right angles at the bottom left and topright
ah
you can just use coresponding theorum
for either w or z
then since the 90 degrees is on the same line it doesnt matter
(or whatever your teacher told you to do)
i get what ur saying but at the same time i dont know how to interpret that into the sentance
based on everything we've been going over so far do you really think i payed much attention to the teacher š¹
kinda regret it now
but its his fault honostly moving me to the back....
half is his fault
if hes not the guy to give out detentions go up to him and ask him reteach you the topic
hes the type of guy to NOT reteach you it and instead just say go ask your friends
š
"Lines 'x' and 'y' are parallel because the angles marked with single arrows are corresponding angles and are equal. Lines 'w' and 'z' are parallel because the angles marked with double arrows are corresponding angles and are equal. This is based on the Corresponding Angles Postulate."
tryna understand this lol
Corresponding theorem means line w is perpendicular to both x and y
ah
that makes sense
you dont say WHY they are
jsut say they are
:)
like he just said
lines w and z have coresponding angles, and x and y have coresponding angles. this means that [ w and z ] and [ x and y ]are parralell to each other
icic
man
im fucjing failing this test
i hate this so so much
never have i hated math till proofs
always liked it because it easily doable in my head
now i gotta fucking prove this
is this one important?
uhh its just like any other test
but my grades this semester are bad
my grades hav edropped to bs and a
and for math i never have bs
til now
we'll get you an a
does not look like it cuz my brain is just not functioning.
if there are, I find past papers very helpful
š
nop
normally i watch his lectures
but suddenly he doesnt uplaod them anymore
I'll go on you tube and find a guy thats doing it, pasue on each question and do them then watch his working
damn
pasue?
pause
o
dont jduge
lol not judging i just coiuldnt make out what u were saying'
i thought u were tryna say puruse
lol
I think this is more of a youre not getting enough info problem
have you tried writing notes
does NOT work for me
cant read my own handwriting
ok
and it just never works
so amazing
my english teacher gave me a missing
on a test
i did
in her class
said shed fix it like 2 weeks ago
guess what she HASNTN AWI
it just sucks honostly
i used to go to a private school
was in the nerdy advance shit
i was in 4th grade learning stuff
and ive never had to study until this yar
year
and thats just completely fucked me over
idk how to study man.
ask if you can have the paper, ask to take a photo of the paper, of have him post a picture of the paper
hmm will do ig
ill just ask him to record the lectures agian
i think he just thinks nobody uses them
or maybe he thinks no one's watching his lectures. You could also ask him to start recording again'
yeah
ye..
they came in clutch
alot
nobody just raises their hands cuz probably embaressed
i probably didnt speak loud enough ig
well im going to finish this revierw assignment and head to sleep
thanks brother
if you need anything you can ask
probably tripled or quadrupled my knowledge haha
sorry for not providing decisive feedback
from nothing to somthing
cya lol
7pm
its 10 53 for me
Ah lol
Yep
Same as above
State L m n all have co responding angles
Same with a and b
So they must be parallel
) our examples of traversal
Or smth
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2 sinĪø-4cosĪø=0
2sinĪø=4cosĪø
sinĪø=2cosĪø
sinĪø/cosĪø=2
sinĪø/cosĪø=tanĪø
so
tanĪø=2
tan^2Īø=4
and also
what are you trying to do?
well i tried solving it
solve for theta?
and i got 2 different value of tan
well, show the process
ye ok
Well
is it correct till now?
If tan theta = 2
squaring both sides was an unnecessary step
after tan(theta)=2
Then u should get something along the line of n + 2* k *pi
tan=2 is correct right
are you aware of ITF
no
then you shouldn't be solving it
wait see this first
you must have a bit of knowledge of it in order to solve for it
now like so tanĪø=2 is not correct?
i just need that confermation so i can show u the next part
well you need to solve for theta right
well no
tan(theta)=2 is right
im askin that only
