knotty kestrel
yea that too
#help-17
misty surge
daring kiln
vocal sleetBOT
daring kiln
In the exercise 6.9
I tried resolving it in 2 different ways shown in the orange color
In the second tried I used change of variables
I know the right answer is 3) a= being any number you want and b<0
But idk if my way of solving it is right
vocal sleetBOT
@daring kiln Has your question been resolved?
vocal sleetBOT
vocal sleetBOT
Available help channel!
dusty siren
how to do chi square?
dusty siren
.close
tawny shoal
vocal sleetBOT
uncut storm
tawny shoal
i need to basically do the opposite of factoring and find out what addition of two fractions made this. I understand it for the most part, but the answer has a C in it and im really confused where the C came from
vocal sleetBOT
@tawny shoal Has your question been resolved?
slate plover
can someone walk me thru this
vocal sleetBOT
can someone walk me thru this
slate plover
.close
vast shale
vocal sleetBOT
drifting jackal
What exactly are you stuck on? As I mentioned before, surface area is just the sum of the areas of the faces
So you need to find the area of each face, then add them
vast shale
I’m thick tho
drifting jackal
Can you find the area of each side?
drifting jackal
It's a triangular prism
So the top face is the same shape as the one on the bottom, the hidden one
drifting jackal
The top face I'm referring to is this
That's a triangle
The bottom face is the same, a triangle
indigo cove
the triangle formula is 1/2b*h
vast shale
9x6
indigo cove
wait sorry i cant even see the picture correctly my eyes are a bit blury 😭
vast shale
22.5
drifting jackal
The 9 and 6 relate to these sides
drifting jackal
22.5
That's the area of 1 of the triangles, you have 2
Then you need the area of the other sides
vast shale
45
drifting jackal
Where is 45 from?
drifting jackal
Also that is not the area of the triangle btw
vast shale
I dont know then
drifting jackal
Do you know the formula for area of a triangle?
You know the height and the base
drifting jackal
The hieght is 5, base is 11
I pointed it out here
drifting jackal
Yes and that equals?
vast shale
27.5
vast shale
X2
drifting jackal
Find the area of the rest of the faces then sum them up
drifting jackal
Why did you multiply by 2?
vast shale
There are two
vast shale
263
drifting jackal
Yes that's it
drifting jackal
You just need to find the areas of each face then add them up, that's it
vocal sleetBOT
@vast shale Has your question been resolved?
vocal sleetBOT
vocal sleetBOT
Available help channel!
tribal pond
sum and difference
vocal sleetBOT
sum and difference
tribal pond
im not sure where to start and/or how my answer is supposed to come out
i know im supposed to make triangles and use x^2+y^2=r^2
if im to do cosa=4/5 with a in QIV then where do i start
is theta the origin on the graph?
if im supposed to find the missing sides then subtract the coinciding answers, then do i need to use a ton of math here?
because wouldn't my answer lie on 0 if the remaining sides equal to 3 and -3 (just a guess)
or am i completely off track
vocal sleetBOT
@tribal pond Has your question been resolved?
tribal pond
by far I have learned that the DMV moves faster than this train
in the meantime, I've been doing other things but i'm still waiting on this
wheat imp
took a crack at it see if this works
tribal pond
took a crack at it see if this works
could you take a snip of it using the snipping tool instead of that?
wheat imp
i can get it in a different format one sec
took a picture from my phone is only problem
tribal pond
ah
wheat imp
tribal pond
so am i taking cosine
and turning the values into triangles
then with the missing side values i use those and throw it into a sine function?
wheat imp
basically the formula you need is sin(a-b) = sinacosb - cosasinb
so you need to use the cos you are given
to find sin
tribal pond
so one quick question
I have a sum and difference thingy
if you have any knowledge on this please do tell
wheat imp
sorry mate i know i learned this at one point but im completely blanking
tribal pond
it's like the secrets of the pentagon to me
wheat imp
i'll give it a shot but someone may need to tag in lol
tribal pond
ive been tryin
that bottom part needs to be -sinx so i can do an odd/even thing to it and then quotient it to make it cotx
that part might not make any sense
wheat imp
sorry give me a sec
okay figured it out
so basically i figured out the value of both cos(pi + x) and cos(3pi/2 -x)
cos(pi + x) is -cosx (you found this)
for cos(3pi/2 - x):
use the formula cos(A + B) = cos(a)cos(b) - sin(a)sin(b)
subbing 3pi/2 in for a
and -x for b
tribal pond
wheat imp
yeah so at that stage its pretty simple
you literally just calculate what cos(3pi/2) is and what sin(3pi/2) is
and multiply
tribal pond
then simple stuff is always too complex for me
wheat imp
its what always trips me up as well
tribal pond
this all must equal cotx
wheat imp
yeah trust me on this
cos(3pi/2) = 0
sin(3pi/2) = -1
so the bottom simplifies to -sinx
tribal pond
ooooooh
wheat imp
and then you just do what you said earlier
wheat imp
good job : )
tribal pond
basically same thing
wheat imp
go for it
wheat imp
i feel like this is basically the same lol
if u just use sin(a+b) and sin(a-b) formula and follow that through you should get there in the end
wheat imp
do you still need help with this?
tribal pond
yah
wheat imp
just to make sure csc(x) is 1/sinx right?
tribal pond
yes
wheat imp
never seen it written like that
wheat imp
lol
tribal pond
okie
wheat imp
next you need to get the number on the bottom the same so you can add them to make one fraction
so you end up with sin^2x/sinxcosx + cos^x/sinxcosx
which makes sin^2x + cos^2x/sinxcosx
do you think you can figure it out from there ?
tribal pond
so cosx = sinx+1 and sinx = cosx+1
wheat imp
if i split it up better it may become clearer
tribal pond
my meds are wearing off
tribal pond
im becoming more defocused by the minute but im trying
wheat imp
its alright take your time
it may help to think about it like this
you are trying to find cosecx * secx
this is equal to (1/sinx)(1/cosx)
which multiplies to 1/sinxcosx
so we need to go from (sin^2x + cos^2x) / (sinxcosx)
to 1 / (sinxcosx)
what rule can we use
tribal pond
ive just used quotient so then i have to use pythagorean
wheat imp
thats correct
tribal pond
but how do i apply it to the two separate fractions?
do i make them all applied to pythagorean or just the top
wheat imp
okay basically
the theorem you need to use is sin^2x + cos^2x = 1
i might write out the question to make it clearer
tribal pond
so
sinx/cosx + cosx/sinx
sinx+cosx=1
or no
because im getting wrapped around this part
how do i get sin^2x from sinx
wheat imp
give me one sec im just writing it out
wheat imp
thats right
tribal pond
thamk
screw you math gods
i spoke too soon
i need this
^this must equal "siny"
vocal sleetBOT
@tribal pond Has your question been resolved?
icy cedar
I want to know what I'm doing wrong/how to work out the total time
pale perch
7.25 isnt a length of time
oh wait
i see i see
its the .25
25 minutes isnt .25 of an hour
.25 of an hour is 15 minutes
icy cedar
So then would I say that the total time is 7.40?
pale perch
,calc 25/60
twin meteorBOT
Result:
0.41666666666667
Do I calculate what that is and then put that in?
pale perch
if youre using a calculator, you could just type (600)/(7+5/12)
unless your calculator can store answers from the previous line to use, in which case you could, sure
icy cedar
if youre using a calculator, you could just type (600)/(7+5/12)
So I calculated this and it came up with 80.8988764045
pale perch
,calc 600/(7+5/12)
twin meteorBOT
Result:
80.898876404494
seems so
icy cedar
Don't I have to round it out?
pale perch
3 significant figures seems safe
icy cedar
Alright, so that means the total time is 80.8 right?
pale perch
.9
icy cedar
Oh! Okay mb-
so then if 600 divided by 80.9 is 7.416563658838072, thats the average speed?
pale perch
the 80.9 is the average speed
icy cedar
Wait so whats the total time???
Cause I just asked if 80.9 was the total time and you said yes
pale perch
the total time was the 7+5/12
icy cedar
So then the total time is 7.41666666667 so what would I round that to?
pale perch
3 is also fine again
icy cedar
So I round it to 7.41?
pale perch
.42
icy cedar
Okay so dividing the 600 by the 7.42, I get 80.86253369272237
rounding it off would make it 80.9?
pale perch
i mean yeah, but why would you use a rounded value in your calculations when you have the exact value
icy cedar
I figured it would be too long, wouldn't it?
pale perch
why? the exact value is literally (7+5/12) thats not that long to write
using rounded values will screw up your answers in the future if you make that a habit
icy cedar
Wait okay okay okay, so what do I put as the Average speed? Exactly 80.86253369272237?
pale perch
no you can round when you have your answer, i just mean dont round mid working
pastel herald
if youre using a calculator, you could just type (600)/(7+5/12)
What is 7+5/12?
icy cedar
I apologise I believe we were done and that was the answer
pale perch
the time in hours from 11:50 am to 7:15pm
pale perch
Okay so dividing the 600 by the 7.42, I get 80.86253369272237
yeah the answer is the 80.9, im more referring to using '7.42' here
pastel herald
yeah but why? i counted the hours and got 7.416 hours and i used that value
pale perch
when you get to questions that are longer in the future, if you use rounded values during your working theres a possibility for huge discrepancy in your final answers
so its generally good practice to just keep things exact until youre done
pastel herald
the time in hours from 11:50 am to 7:15pm
yeah but why? i counted the hours and got 7.416 hours and i used that value
pastel herald
i know. my question is why did you write time by meand of 7+5/12
pale perch
7 is the number of whole hours, 5/12 represents the additional 25 minutes
pastel herald
i first counted minutes and divided by 6o to get th time
how 5/12 is 25 minutes? whats does it refer to?
pale perch
,calc 25/60
twin meteorBOT
Result:
0.41666666666667
ah i see, think i may have understood your question, my bad
but yeah, its just the 25/60
icy cedar
Sooo.. Where do I go from here??
icy cedar
So this is the right answer?
pastel herald
ah i see, think i may have understood your question, my bad
thanks
pale perch
So this is the right answer?
pretty much
icy cedar
Pretty much? So that means it isnt?
pale perch
its just my way of saying theres not much else you could be expected to do
thats the answer
pale perch
sure
icy cedar
The answer would be census, right?
I just want to double check
Then I'll be out of your hair
pale perch
statistics
icy cedar
I assume you're not good at them? Thats totally fine-
icy cedar
Alrighty, please, no rush
pale perch
seems more like a sample
if the population is the class
and she is surveying only the year 9's in said class then thats a sample of a population
(idk why there would be more than one year group in a class though)
pale perch
no worries
icy cedar
Have a good one
pale perch
you too
icy cedar
.close
fallen sandal
vocal sleetBOT
fallen sandal
vocal sleetBOT
fallen sandal
idrk
vast shale
WHY
fallen sandal
😭 😭 😭
vast shale
WHY DID YOU KILL THAT WOMAN
fallen sandal
Cuz the n and n prime look kinda right
vast shale
*slams desk* FACE THE REALITY
vast shale
Cuz the n and n prime look kinda right
huh?
fallen sandal
Idk
It just looks
Correct
I think it wouldn't shifted down
If it were something else
vast shale
Should've called them N and M and the right point L, that would've been an easy question 💯
vast shale
depends
It can be either
Technically not doing anything is also a dilation
But I digress
fallen sandal
Wahr
vast shale
It's, like... You dilate, but the amount you dilate is nothing
vast shale
It's not relevant just forget about it
"dilation" is actually often used to clarify that it can either make things bigger or smaller
But in this case N' is bigger than N
So it must be outward
vast shale
Why C?
vast shale
That's the gist of it, yeah
Looks like A, B, and D have been strategically placed to confuse
Interesting
@fallen sandal Do you get the idea now?
fallen sandal
Soo it's C
vast shale
Dilation just scales everything in or out (or not at all, which technically counts) from a point without any change in shapes or any rotation
So yeah, C
You can figure out the point by drawing lines like I did
mellow geode
hello, what's the least upper bound of $\frac{x+y}{1+xy}$ when x and y in $]-1, 1[$?
vocal sleetBOT
hello, what's the least upper bound of $\frac{x+y}{1+xy}$ when x and y in $]-1, ...
twin meteorBOT
lilisworld
dull bear
Does it have a finite one? 
mellow geode
Does it have a finite one? <:catThink:1073406415575728200>
?
dull bear
Well just looking at it, seems like the closer you choose x to 1 and the closer y is to -1 that you'd get something that just grows, no?
Though I may be missing something
vast shale
i also might be wrong but i guess it's 1 cause it implies inequality (x+y)/(1+xy) <= 1 or (1-x)(1-y)>=0 which is obvious from x, y <= 1
twin pumice
i also might be wrong but i guess it's 1 cause it implies inequality (x+y)/(1+xy...
That's what I was thinking
dull bear
~~Well just looking at it, seems like the closer you choose x to 1 and the close...
Oh no my brain's gone, thought of the numerator as x - y 
mellow geode
Consider what would happen if you pick x and y to be as close to 1 as possible
i don't really know
mellow geode
i also might be wrong but i guess it's 1 cause it implies inequality (x+y)/(1+xy...
i don't get the "it implies inequality"
mellow geode
Consider what would happen if you pick x and y to be as close to 1 as possible
if it's the limit then it's 1
vast shale
i don't get the "it implies inequality"
if sup=1, then for any -1 <= x, y <= 1 inequality (x+y)/(1+xy) <= 1 holds and there exist such (x, y) that (x+y)/(1+xy) = 1
mellow geode
if sup=1, then for any -1 <= x, y <= 1 inequality (x+y)/(1+xy) <= 1 holds and th...
so it's 1?
.close
vocal sleetBOT
mellow geode
.reopen
vocal sleetBOT
✅
vast shale
can someone walk me through the algebra for this step please? Thank you!
ancient knoll
$(n^2+n-2)=((n^2+n)-2)$
twin meteorBOT
IV
velvet cove
is $\frac{\infty}{\infty-\infty}$ an eligible form to use lhopitals rule
twin meteorBOT
Jash
vocal sleetBOT
@velvet cove Has your question been resolved?
velvet cove
@spice sun
flat whale
vocal sleetBOT
Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.
vocal sleetBOT
@velvet cove Has your question been resolved?
spiral frost
vocal sleetBOT
spiral frost
I honestly have no clue; if someone could help me going through these four problems I would be super appreciative!
hoary blaze
do you see the pattern of the function
so the period would be the distance between the same points on two successive "patterns"
vocal sleetBOT
@spiral frost Has your question been resolved?
golden dagger
Ask
golden dagger
can someone help me with these math problems
vocal sleetBOT
@golden dagger Has your question been resolved?
karmic crane
Do you know what a gcf is
golden dagger
Greatest common factor
karmic crane
Do you know how to do that for Q24
golden dagger
Would the Gcf be 12?
karmic crane
Can you divide 28 by 12 without remainder
golden dagger
No
karmic crane
So it can’t be 12
golden dagger
2?
karmic crane
Yeah 2 sounds good
golden dagger
Alright then what
karmic crane
Actually 4 is the hcf
golden dagger
Alright
karmic crane
It becomes 4(3x^2+7x-6)
golden dagger
Ok
karmic crane
Now do you know how to factorise that quadratic
golden dagger
No
karmic crane
Multiply 3 by -6, now find numbers that multiply to give -18 and add to give 7
golden dagger
Ok
karmic crane
What are they
golden dagger
3x-6 like u said?
karmic crane
What do you get when you sum them though
golden dagger
-18
karmic crane
Sum as in addition
golden dagger
How do you sum them ?
karmic crane
3 + -6
karmic crane
So it can’t be those two because they don’t add up to 7
golden dagger
So can it be any numbers?
karmic crane
Yes as long as their product is -18 and their sum is 7
golden dagger
4x-8?
karmic crane
4 x -8 is -32 and they add up to -4 so both the conditions are not met
List out all the factors of 18, that should help
1,2,3,6,9,18
golden dagger
Ok now what
karmic crane
Rewrite the first and last terms like this:
3x^2 -6
And inbeteeen you put the two numbers you found multiplied by x
3x^2+9x-2x-6
Now group them:
golden dagger
So is it 3x^2+9x and -2x+6
karmic crane
There will be one for each group
golden dagger
So I think for -2x+6 the factor is 2 and for the other is 1?
karmic crane
Always take out the negative, so it would be -2 for that one, but for the other group it’s not 1
golden dagger
Oh
golden dagger
Would it be -2x? For the factor
karmic crane
3x(x+3)-2(x+3)
This becomes
(3x-2)(x+3)
And don’t forget toe 4 from before
4(3x-2)(x+3)
vocal sleetBOT
Available help channel!
atomic zephyr
I was wondering how this question (attached below, #8) was solved, given all the information provided. Mainly, my brain is breaking up on the explanation "The area beyond z for Zx=-.83 is .2033". How is that figured out? What set of numbers can you use to figure this out? My mind is shattered I have been staring at this for like an hour now.
vocal sleetBOT
I was wondering how this question (attached below, #8) was solved, given all the...
atomic zephyr
Sorry for the low quality pictures.
Can repost the pics to be more clearer if needed
<@&286206848099549185>
vocal sleetBOT
@atomic zephyr Has your question been resolved?
vocal sleetBOT
atomic zephyr
.reopen
vocal sleetBOT
✅
vocal sleetBOT
@atomic zephyr Has your question been resolved?
proven garden
for z score you have a standardized normal distribution
Using integration gives area, or you can use a z table instead
atomic zephyr
Using integration gives area, or you can use a z table instead
wouldn't Table B be the z table?
proven garden
?
z table tells you the area given a z value
table B is just a table of z values, it doesn't tell you the area
atomic zephyr
table B is just a table of z values, it doesn't tell you the area
Ah, I'm sorry, missed a couple classes and I feel lost regarding z-scores lol. So, say I figure out the z-score of -.83, what exactly would be my next step? Where should I be looking?
Omg I didn't know z table was just like something I could look up lmao
I'm so dumb
I'm sorry
safe cove
vocal sleetBOT
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
1
thin vale
have you ever solved an equation like this before
safe cove
ik quadrants and like
how to do it
i just need a refresher
and the way i remember doing it i keep getting it wrong
thin vale
!show
vocal sleetBOT
Show your work, and if possible, explain where you are stuck.
thin vale
, rotate
twin meteorBOT
thin vale
okay well one thing is
safe cove
-0.444
thin vale
you shouldn't be rounding probably
safe cove
ik its -0.444 mbmb
thin vale
and that is another thing
thin vale
0.4444....44...?
that's still rounding if you leave it as 0.444
but if it is 0.444000..
then that's fine
anyways
thin vale
,w -6.4/14.5
twin meteorBOT
thin vale
it is definitely rounded
safe cove
thin vale
why did you think that was -0.44 repeating?
safe cove
the dot above the 4 😭
thin vale
no clue why there is a dot
safe cove
yeah same
thin vale
but ignore it
safe cove
that was why i was cvonfused okok
thin vale
so try without rounding see if that works
safe cove
i got
-26.19191972
so that = 5x+12
i got
x = -7.638383945
and then i add 180
for the 3rd quadrant
worthy citrus
Find the other dot, it means that whole part from dot to dot repeats
safe cove
so try without rounding see if that works
what i do wrong?
safe cove
however
waxen cobalt
it says there all answers
safe cove
yeah ik that part with the period adding and all that
so i got
x = 29.856751
and then
bc its negative
180-29.856...
= 150.143...
and then surely thats one
of the answers
waxen cobalt
hmmm
safe cove
but its apparently wrong
waxen cobalt
yes
waxen cobalt
since x is between 0 and 270
waxen cobalt
when u did arccos you shoudve figured out what 134.427004 degrees would be in the first quadrant
waxen cobalt
oh yes
waxen cobalt
may i know what is the correct answer
safe cove
if i reveal the answer i gotta do a new question
waxen cobalt
ohhh
safe cove
waxen cobalt
hold on
waxen cobalt
bitch what
safe cove
yeah fucking exactlt
idk how they get that
bc i feel like i do everything correctly
safe cove
safe cove
so 40.786 = (5x+14)
wtf do i do next bc thats where it seems to go all wrong
i normally take 14
waxen cobalt
subtract both side by 14
safe cove
so i get 26.768 = 5x
safe cove
no this is degrees
we have to keep
in degrees
radian is the other part
wait lemme try convert to radian
how tf i do that
safe cove
wrong
safe cove
i did this
before
and i forgot
and i cant find my fucking notes
for
the
subject
.close
wet tendon
How to solve it? I am probably missing some crucial thing
vocal sleetBOT
How to solve it? I am probably missing some crucial thing
sonic hatch
Hi guys
dull bear
Part b of the question is cut off
Part a seems fine but be careful with handwriting as this looks like $e^{\frac{2t}{2}}$, which isn’t the same as $\frac{e^{2t}}{2}$, which it appears you meant from the following work you did
twin meteorBOT
@dull bear
dull bear
Part c seems fine too, though you might want to show a tiny bit more working possibly
sonic hatch
Part b of the question is cut off
It said hour
sonic hatch
Part c seems fine too, though you might want to show a tiny bit more working pos...
Yes please, how can I do it more detailed
Is this better?
<@&286206848099549185>
dull bear
Yes please, how can I do it more detailed
Just showing [some more of] the manipulations you'd do to get to that final answer I think, though of course it depends on how much they're assigning to that question 
dull bear
It said hour
In that case seems fine to me 
dull bear
Is this better?
And yep, better, less likely to be misinterpreted 
vocal sleetBOT
@sonic hatch Has your question been resolved?
rose pike
Which one is wrong any why?
vocal sleetBOT
Which one is wrong any why?
rose pike
I'm certain the last 4 are right but I don't see how I'm wrong
wraith venture
who makes the choices A, C and D
actually that's fair, but it's disturbing for a second
wraith venture
actually that's fair, but it's disturbing for a second
absolute, convergent, divergent
Debatable but arguable
wraith venture
so why does 1) diverge ?
anyways
Why did you answer D ?
rose pike
anyways
Why did you answer D ?
Well because I used the ratio test for it, to be fair I didn't get that far in so I stoped at a certain point and tried to find the limit as(i used x) approches infinity and found it was greater than 1
Though I tried all options and got them wrong so I assume one of the others is wrong
rose pike
I see, how so
wraith venture
Which one is wrong any why?
2^n / 5^2n
That decreases geometrically
Adding a factor 1/n in front only helps to make it convergent
rose pike
Okay fair, but would that make it converge conditionally?
I need to invest in a new keyboard
wraith venture
Okay fair, but would that make it converge conditionally?
did I need the help of the (-1)^n to assert convergence ?
rose pike
Yes because without it, it decreases gemetrically like you said
Ah, so that's the condition
Hm, okay but I'm pretty certain ono the others, which one else could be wrong
wraith venture
Yes because without it, it decreases gemetrically like you said
No I didn't
wraith venture
2^n / 5^2n
That decreases geometrically
Adding a factor 1/n in front only helps ...
I said it went to 0 remarkably fast
So I don't need it to alternate to converge
rose pike
Okay
Wait, if decreading geometrically means you multiply by a constant to get a lower term
is that constant 2/25?
Wait no
wraith venture
and it decreases even faster because of the leading rational function
rose pike
Oh okay
wraith venture
is that constant 2/25?
that should have been the result of your ratio test
rose pike
that should have been the result of your ratio test
Ah, okay
And because that is less than 1, it's absolutly convergent?
wraith venture
the ratio test can only see the obvious
it will never tell you something is conditionally convergent
that is far too obscure for it
rose pike
Because L=1 is inconclusive?
For the test, you either have L>1 which is divergent or L<1 which is convergent
okay I see
Alright, I understand it now, I just need to try out the others again to see where i went wrong
vocal sleetBOT
@rose pike Has your question been resolved?
rose pike
Well I have one more question
coming back to this, which one(the first one was resolved) is wrong
wraith venture
3
rose pike
ty, redoing it rn
wait, isn't L=1/4
For 3
Cool, so it should be A
YES
cool, finished the worksheet, thank you very much
I'll do more practice to get the hang of both tests
thanks a bunch, I apologize for the trouble I caused
wraith venture
you caused no trouble
vast shale
vocal sleetBOT
vocal sleetBOT
Please don't repeatedly close and claim a new channel with the exact same question. This erases all previous progress made towards your problem and is confusing for helpers, making it more difficult to help you. Please be patient, even if your channel has not received much attention.
drifting jackal
I'm talking about the exact formula
vast shale
then no
drifting jackal
Like $m = \frac{y_2-y_1}{x_2-x_1}$
vast shale
Check 2 points where line crossing corner and use this formula between those points
twin meteorBOT
CaptainNova22
vast shale
i have no idea what that is sorry
drifting jackal
That's the formula for slope
vast shale
oh ok
feral oxide
drifting jackal
i have no idea what that is sorry
In your class, if you were given a graph, how were you asked to find the slope?
drifting jackal
Were you asked to count the rise over run or to use a formula?
drifting jackal
i have no idea what that is sorry
https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:linear-equations-graphs/x2f8bb11595b61c86:slope/v/slope-of-a-line
This is the method you can use, just by counting the units between two points
vocal sleetBOT
@vast shale Has your question been resolved?
tall shuttle
You have a line with some slope.
Find two places where the line crosses a + on the grid.
Count how many squares up and down you need to go to get from one point to the other in order to get the rise (in this example it is 1) and how many squares to the left or right you need to go to get the run (in this example it is 3).
If the line goes from the top right to the bottom left, the slope will be positive (like in this example), but if it goes from the top left to the bottom right, it will be negative.
The slope is the rise/run.
swift surge
How do you find the derivative of the function f(x) = 4x^3 + 2x + 7
paper depot
do you know how to take derivatives in general?
swift surge
I am trying to learn
paper depot
do you know the power rule?
swift surge
could you explain it?
paper depot
oh boy
ok wait hang on
can you tell me what you DO know about derivatives? im struggling to get a footing here
swift surge
Its about how the value changes
lucid bane
Do you know about finding the slope/gradient of a line connecting two points?
vast shale
<enumitem>
For your information, you should know those two properties of the derivative:
\env{enumerate}[[1.]]{
\ii $\ds\bm[\bigg]{\dv x}{\m fx + \m gx} = \bm[\bigg]{\dv x}{\m fx} + \bm[\bigg]{\dv x}{\m gx}$
\ii $\ds\bm[\big]{\dv x}{x^n} = nx^{n-1}, \q n\in \R$
}
twin meteorBOT
paper depot
did your textbook or teacher show you how to work out derivatives? like did you see any derivative worked out at least once?
the one you came here with isnt terribly tough but for a complete beginner it is not trivial.
swift surge
did your textbook or teacher show you how to work out derivatives? like did you ...
I did, but i understood nothing
vestal comet
Is my answer correct?
vocal sleetBOT
Is my answer correct?
vestal comet
.close
normal badge
ok so first of all I know I over complicated things
vocal sleetBOT
ok so first of all I know I over complicated things
normal badge
but I was studying the subject of average and the tutor says the function for the average of two numbers is $$ \frac{a+b}{2}$$
ok i havent ise this channle for a long time so do I use math here again?
twin meteorBOT
eitiel
normal badge
oh here
so anyway, since this formula is the private case of $$\frac{a_1+a_2+a_3...+a_n}{n}$$
(bacause any two given numbers (0>a<b) i s like adding the whole numbers in between right?
twin meteorBOT
eitiel
normal badge
so if you write it as a function you can say that would be
never mind I'm an idiot
.close
fresh jolt
So I need to find the derivative of f(x)=Cos(x)+x and i’m stuck. My prof hasn’t taught us L’Hopitals and we haven’t learned how do use d/dx. We’ve been using the trig sum formulas and I know I have to use cosine sum formula but after i do and group like terms, I get stuck.
vocal sleetBOT
So I need to find the derivative of f(x)=Cos(x)+x and i’m stuck. My prof hasn’t ...
fresh jolt
and also since i’m doing the top of the fraction I just left out the denominator.
true estuary
so your question is just how to differentiate f(x)?
fresh jolt
Yes. How can i get f'(x)
true estuary
so the adition rule says d/dx f(x) + g(x) = f'(x) + g'(x)
and the derivative of cos(x) is -sin(x)
and the derivative of x is just 1
fresh jolt
Okay so then it would be f'(x)=-sin(x)+1
true estuary
yes
fresh jolt
Okay that makes sense is there any hint you could give me in respect to my paper? I dont know hwta my next step would be im a bit stuck.
but that does make sense that it will be -sinx+1
true estuary
Okay that makes sense is there any hint you could give me in respect to my paper...
what next step do you mean?
fresh jolt
Like im not sure how to get there from where I am right now. You mentioned using d/dx but we havent learnt that yet.
fresh jolt
ohhh okay sorry
true estuary
and you would not take the derivative using limits
fresh jolt
we've just started this unit so im still learning
true estuary
you generally use the derivative rules
old niche
this proof should be super easy
vocal sleetBOT
this proof should be super easy
old niche
but im not sure if im doing it correct
i mean the tldr is that
if you multiply 2 diagonal matricies you get a diagonal matrix
and multiplication of components is associative
is that literlaly i
it
vast shale
yeah just expand both multiplications and then like
old niche
like make 2 abitrary vectors with n and m on the diagonal respectively
and then show that like
idk m x n is the same as n x m
vast shale
you will get something that resolves into axioms of normal multiplication
old niche
because of associativity
vast shale
like make 2 abitrary vectors with n and m on the diagonal respectively
this sentence makes no sense to me sorry
old niche
like this
vast shale
like this
yes you can multiply them out from both ways
then you can show they would be equal
old niche
oh like show M x N and N x M
vast shale
yes
old niche
okay i just had this beautiful moment in math
you use part a in part b
thats so cool
old niche
<@448651226007994380>
does this look ok?
dull bear
I would maybe also suggest stating that the fact that there are the n independent eigenvectors implies that A and B are diagonalisable but otherwise 
noble lily
Looks okay except the fact that you’ve grouped P inv * P = 1, since P * P inv = 1 as matrix multiplication is NOT commutative
Probably someone whose seen this question for longer has better context but that’s something I just noticed
dull bear
Looks okay except the fact that you’ve grouped P inv * P = 1, since P * P inv = ...
However the fact that P^{-1} is the inverse of P, that part is still fine (it's usually shown elsewhere that both P^{-1}P and PP^{-1} are the identity matrix)
noble lily
Matrix multiplication is associative but not commutative, consider that as a clue
old niche
However the fact that P^{-1} is the inverse of P, that part is still fine (it's ...
wait i need to show this?
dull bear
wait i need to show this?
It's likely that either the definition of an invertible matrix $A$ is such that there's another matrix $B$ such that $AB = BA = I$, or that when you create the inverse matrix, you show that either way you multiply them, you get the identity matrix back
twin meteorBOT
@dull bear
old niche
yes this is what i origanlly thought which is why i just moved things around like that
dull bear
Yea that's all fine to do when it comes to a matrix and its inverse
old niche
is it okay if i ask another question?
dull bear
Sure 
old niche
what exactly is lambda and X in this context
is X a matrix containing all the eigenvectors
dull bear
I’m not quite sure, do they not define it somewhere?
dull bear
is X a matrix containing all the eigenvectors
I would think so, but don’t quote me on that one!
I’d guess the other one is the diagonal matrix of eigenvalues
old niche
i dont know if lambda always represents the same thing
old niche
I’d guess the other one is the diagonal matrix of eigenvalues <:catThink:1073406...
this makes sense i think...
A=PDP−1 right
D is the diagonal matrix of values? P is the matrix of eigenvectors?
dull bear
D is the diagonal matrix of values? P is the matrix of eigenvectors?
Yep, if you have P and D as you’ve stated
noble lily
cool
old niche
Yep, if you have P and D as you’ve stated
did i make a mistake here?
noble lily
Take a look at the last line of your calculation
Up until there everything seems fine
old niche
here?
old niche
i think its lambda^2 - 0.7 lambda -0.42
noble lily
No
old niche
noble lily
What’s 0.06-0.36
noble lily
Oui
old niche
so i guess the diagonal matrix of eigen values is
[1 0, 0 -0.3]
i think i am stuck again
.close
bleak rampart
hilpeleepl
vocal sleetBOT
hilpeleepl