Available help channel!
#help-19
odd edgeBOT
Available help channel!
uncut fern
help
uncut fern
how would you solve for x, if x^x^x = e
i have searched online, and used multiple resources in attempt to find an answer
steady tide
this $x^{x^x}$ or this $(x^x)^x$
clever fjordBOT
odd edgeBOT
@uncut fern Has your question been resolved?
split gyro
Yo
Here for the help
listen if it's x^(x^2)=e
Then take ln
We have x^2.ln(x)=1
Now see
ln(x)=1/x^2
We have to find their intersection poinys
Points*
Plot the curve
lusty helm
PS: it's x^x and not x^2
split gyro
,w ln(x)=1/x^2
clever fjordBOT
split gyro
This uses the Lambert W function
As for the case of tetration of x
We have
ln(x)=x^-x
,w ln(x)=x^(-x)
clever fjordBOT
clever fjordBOT
split gyro
So for the first case x^x^x we have x approximately equal to 1.60108 and for 2nd case x^(x^2) we use Lambert function and get solutions
@uncut fern
uncut fern
So for the first case x^x^x we have x approximately equal to 1.60108 and for 2nd...
is there an exact answer though, like there being solution using product logarithms when dealing with 2nd tetration, but in this case, 3rd tetration?
uncut fern
$x^{x^x}$ = e
clever fjordBOT
「 Sloko 」
amber junco
,w graph 21x^x*e^x
clever fjordBOT
odd edgeBOT
@uncut fern Has your question been resolved?
odd edgeBOT
@uncut fern Has your question been resolved?
odd edgeBOT
@uncut fern Has your question been resolved?
odd edgeBOT
@uncut fern Has your question been resolved?
proper solstice
,w x^x^x = e
clever fjordBOT
Requested by anshulyolo121
proper solstice
,w solve x+3 = 2
clever fjordBOT
proper solstice
,w solve x^x^x = e
clever fjordBOT
Requested by anshulyolo121
proper solstice
,w 1.601^1.601^1.601
clever fjordBOT
faint knot
is there an exact answer though, like there being solution using product logarit...
doesnt look like theres any
the product log was useful only because it was defined to be used, you have a special "function thats the inverse of xe^x" that you got to treat as "exact"
unless you want to invent the inverse of x^x^x as a function g(x) then have the answer be g(e), there isnt any accepted or widely known function that does what you need here
alpine jetty
Can someone help me with this? I got a as my answer and I want to know if I got it right
odd edgeBOT
Can someone help me with this? I got a as my answer and I want to know if I got ...
@alpine jetty Has your question been resolved?
alpine jetty
No
split gyro
Yes sure
We gotta integrate
as acc is not constant
And is a function of time
See and we know
acc =dv/dt
So we get
Wait waig
Wait*
Yes 👍
so
dv/dt=3e^(2t)
,w int 3e^(2t)
clever fjordBOT
alpine jetty
Which one would it be?
split gyro
!noans
odd edgeBOT
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.
wanton bison
Let $a \geq 0, f : D = [0,a] \to \mathbb{R}, : x \mapsto f(x)$ a continuous twice differentiable function.
$\$
If $f'(0) = 0$ and $f''(x) \geq 0 : \forall x \in D$ can we conclude intuitively that $f$ is increasing?
elfin zodiac
I suspect no too
clever fjordBOT
𝔸dωn𝓲²s
wanton bison
My thoughts are it has a minimum and is linksgekrümmt
dawn tiger
am i tripping, that intuitively feels true (assuming you consider increasing to be whenever the derivative is nonnegative)
ivory dock
Well we know it's not increasing at 0 right, so it's got like an extreme there, question is what does the second derivative tell us about what happens right of that extreme
wanton bison
curving to the keft
pastel orbit
Well we know it's not increasing at 0 right, so it's got like an extreme there, ...
it doesn't have to have an extremum there
wanton bison
Why
pastel orbit
could be an inflection point
dawn tiger
x^3
ivory dock
isn't the domain from 0 to a though?
pastel orbit
why does that change anything
ivory dock
like, there's nothing going on left of 0, or am I tripping?
wanton bison
Ok I see where I went wrong
dawn tiger
how is the derivative even defined at 0?
wanton bison
I was too hasty
wanton bison
could be an inflection point
thanks for the carry
elfin zodiac
Non decreasing
ivory dock
can you even call something an inflection point if there's nothing to the left of it though?
dawn tiger
x^3 is increasing lol
no i didn't mean that as a counterexample, i meant as an example of when 0 is an inflection point
dawn tiger
how is the derivative even defined at 0?
i am curious how this works if the left hand limit doesn't even exist
clever fjordBOT
𝔸dωn𝓲²s
wanton bison
Since x is defined positive or 0 and f" is positive or 0 that means the first derivative is greater or equal to 0
@pastel orbit wyt
pastel orbit
I don't know, is my best answer, but I feel like it might be true 
wanton bison
like the integral tells us about the area so which is height * width
f" ≥ 0 and x ≥ 0
pastel orbit
Since x is defined positive or 0 and f" is positive or 0 that means the first de...
no, this is not true in general I believe
consider 1/x
f''(x) is also positive, but f'(x) is not
however, the function you have in question is continuous, and defined at 0
so 1/x is not a valid counterexample under those restrictions
in this case, I do not know
wanton bison
1/x is continuous in its defined domain tho
pastel orbit
you can't extend it's domain to 0 continuously, though
pastel orbit
yes, that's a good example
but f'(0) is still not 0
which is a restriction we must have
oh.
hold on.
e^-x + x would satisfy all the conditions necessary
but it is indeed increasing
on [0, a], that is
hmm
@wanton bison I'm starting to think the answer to your question is "yes", but I feel insecure because analysis always has counterexamples
wanton bison
Maybe the fact that's it's tangent
horizontally
at x = 0
whether saddle or minimum or maximum whatever
and then turns to the left
indeed i think f'(0) = 0 is very important
pastel orbit
I agree
god, this is taking me back to my RA days where I would lose sleep over potential counterexamples 
always that paranoia
wanton bison
I was just checking a proof
wanton bison
**𝔸dωn𝓲²s**
So I wasn't sure if this was enough
pastel orbit
**𝔸dωn𝓲²s**
on second inspection, I think this is actually enough
f''(t) is always positive, so the integral is positive
and then FTC it, f'(0) = 0, so f'(x) >= 0
I think I am convinced
wanton bison
f''(t) is always positive, so the integral is positive
hmm but that conclusion is kinda wack as we already investigated
the f'(0) = 0 is kinda missing
wanton bison
because of these counter examples
pastel orbit
which ones?
wanton bison
We know $\int_0^x f''(t) : \dd t = f'(x) - f'(0) = f'(x)$
clever fjordBOT
𝔸dωn𝓲²s
pastel orbit
right.
clever fjordBOT
higher!
pastel orbit
because f''(t) >= 0 by assumption
wanton bison
f'' >= 0 and x >= 0 is not enough for exampple
e^(-x)
So where is the other condition included
pastel orbit
no, it is enough, no?
wanton bison
Geometrically it makes sense
pastel orbit
positive area
wanton bison
but I would like to know how to show it algebraically
pastel orbit
on e^-x
pastel orbit
but I would like to know how to show it algebraically
hmm
elfin zodiac
What are u discussing guys, tldr?
wanton bison
but f'(0) neq 0
yea i know but how do we show this for all functions
wanton bison
**higher!**
i dont see where that is included in this
pastel orbit
hold on. I'm confused, isn't f'(0) = 0 an assumption?
wanton bison
yes it is
wanton bison
**𝔸dωn𝓲²s**
but where and how is it being used in this proof
pastel orbit
i dont see where that is included in this
right, it's not related to this
pastel orbit
but where and how is it being used in this proof
I did not prove this fact btw
wanton bison
yea haha
pastel orbit
I asserted it without proof cause I don't remember the proof 
I think it's not that bad though?
elfin zodiac
**𝔸dωn𝓲²s**
Can we say f(x) = c to counterexample? Or was already discussed?
pastel orbit
I'd have to check my book
let me see
I cannot find it in my notes, but it seems like MSE has an answer
https://math.stackexchange.com/questions/3026434/how-do-you-prove-the-integral-of-a-positive-function-is-also-positive
wanton bison
Can we say f(x) = c to counterexample? Or was already discussed?
I don't see how that is a counterexample because it says increasing not strictly increasing and increasing means f'(x) >= 0
pastel orbit
all I see are epsilons and deltas though
elfin zodiac
I don't see how that is a counterexample because it says increasing not **strict...
My bad
wanton bison
but you got me thinking for a moment haha
pastel orbit
I will now run away from this conversation, since it is eps-delta 
(kidding, but I don't expect to be able to be of much use from here 
)
pastel orbit
that's fine by me 
mystic saffron
odd edgeBOT
@wanton bison Has your question been resolved?
wanton bison
**𝔸dωn𝓲²s**
This is the proof they made but I don't see how they concluded this and where f'(0) = 0 is being used properly to deduce this.
lyric marlin
becaus the integrand is non-negative, the integral is also non-negative
wanton bison
Geometrically it makes sense, whether we have a max/min or a saddle point at x = 0 the tangent is horizontal and due to the 2nd derivative it's curving to the left which would kinda imply increasing
sand horizon
wanton bison
becaus the integrand is non-negative, the integral is also non-negative
What about f(x) = 1/(x+1) as a counter example to your statement?
lyric marlin
what do you mean?
wanton bison
Or an easier e^(-x)
the 2nd derivative is e^-x
the integrand would be positive
or hmm bad example
lyric marlin
counter example to what statement
the integrals in question are non-negative?
f'(x) is not the integral in these cases though
we use f'(0) = 0 to say the integral which (by fundamental theorem) has value f'(x) - f'(0) equals f'(x)
wanton bison
You are saying it's sufficient that if the integrand is non-negative then so is the integral
lyric marlin
yes
(as long as it exists, which it does because we have a continuous function on a closed interval [0,a])
wanton bison
Intuitively it makes sense what you say because an integral is nothing more than adding a bunch of areas (width x height) and since the integrand and the domain are positive or 0 then so must be the area
lyric marlin
what's your definition of integral
wanton bison
If I recall correctly it was something like a limit
lyric marlin
whatever you're taking the limit of is always non-negative for a non-negative integrand
wanton bison
with some sum that adds the product of function value and input
lyric marlin
and limits preserve weak inequalities (i.e. 'or equal to')
wanton bison
becaus the integrand is non-negative, the integral is also non-negative
I kinda doubted this even though it's so trivial actually
because higher came up with 1/x as a counter example
lyric marlin
so 1/x is not a valid counterexample under those restrictions
?
wanton bison
yea then i was wondering how we deduced that f'(x) >= 0
lyric marlin
well it isn't for f(x) =1/x
because f'(0) isn't 0
so while yes $\int_0^xf''(t) = f'(x)-f'(0)$ is non-negative, we can't say anything about $f'(x)$
clever fjordBOT
Edward II
lyric marlin
in your question we then have $f'(x)-f'(0)=f'(x)$ (because $f'(0) = 0$)
clever fjordBOT
Edward II
wanton bison
Yea
clever fjordBOT
𝔸dωn𝓲²s
lyric marlin
because the integral is non-negative
wanton bison
yea
lyric marlin
because the integrand is non-negative
which is given in the question as an assumption
wanton bison
this is what i doubted the whole time
but it must be non-negative
given the domain and f'' is non negative
we are summing up positive pieces of little areas
at least that's how i think about it
the product of two positive numbers yields a positive numbers so does the addition
thanks
.solved
odd edgeBOT
odd edgeBOT
Available help channel!
gleaming topaz
I need help with long division. I don't know how to long divise this: 6x^3+29x^2+x-36
Maybe if someone hops on call with me or shows me on paper I can try to understand how to do it more
sterile blaze
what do u want to divide it by
odd edgeBOT
@gleaming topaz Has your question been resolved?
gleaming topaz
what do u want to divide it by
x-1
viscid flint
$\polylongdiv{6x^3+29x^2+x-36}{x-1}$
clever fjordBOT
hayley 🥥 🌴
viscid flint
it's very similar to regular long division
gleaming topaz
yeah, I was homeless last year
I got kicked out of home
so I probably missed that lesson on long division
gleaming topaz
I'm just trying to fix my life up
sterile blaze
very sad
odd edgeBOT
odd edgeBOT
Available help channel!
hidden patrol
is this proof ok? (The text is in french but it's understandable without it)
hidden patrol
a = 0 then |a_n - a| < ε
odd edgeBOT
@hidden patrol Has your question been resolved?
analog light
Can someone help me understand derivatives better? We can use f(x) = 2x^2 as an example. Derivative formula is f'(x) = f(x+h) - f(x) / h right?
icy kindle
the limit of that, yes
icy kindle
this is often taught so that you compute the derivative in steps.
Compute f(x+h)
then f(x+h) - f(x)
then f(x+h) - f(x) / h
Then take the limit as h -> 0
analog light
yeah h is approaching 0.
If you simplify it down you get f'(x) = (2x + h)^2 - 2x^2 / h right? I'm not familiar with derivatives, the first one I did was today. I had to find the derivative of f(x) = x^2
icy kindle
that's correct, again you need the limit
analog light
right sorry
icy kindle
well, it should be 2(x+h)^2
analog light
Oh ok thanks for clarifying that!
f'(x) = lim h -> 0 2(x + h)^2 - 2x^2 / h
f'(x) = lim h -> 0 (2x + 2h)^2 - 2x^2 / h
icy kindle
Order of operations, exponents first
analog light
Oh yeah
f'(x) = lim h -> 0 2x^2 + hx^2 - 2x^2 / h
oh wait
Don't I need binomial theorem?
icy kindle
yes
analog light
f'(x) = lim h -> 0 2x^2 + 4hx + 2h^2 - 2x^2 / h
f'(x) = lim h -> 0 4hx + 2h^2 / h
f'(x) = lim h -> 0 4x + 2h^2
take the limit
f'(x) = 4x + 2
is that right?
icy kindle
the h should reduce out of every term
$\frac{4hx + 2h^2}{h} = \frac{h(4x + 2h)}{h} = 4x + 2h$
clever fjordBOT
Zybikron
analog light
It is only h^1, in Algebra 1 I learned it will only take 1 of the h, so if you were to take all the h you would have to have h^3
Oh
You simplify before dividing because PEMDAS, Multiplication goes before division... @icy kindle
icy kindle
multiplication and division have the same level of importance in the order of operations
P E (MD) (AS)
analog light
Let me ask Microsoft CoPilot what the answer is.
icy kindle
So, if we do it your way, you know 4/2 = 2.
By your reasoning:
$\frac42 = \frac{2+2}{2} = 1+2 = 3$
clever fjordBOT
Zybikron
icy kindle
by my reasoning: $\frac42 = \frac{2+2}{2} = \frac{2(1+1)}{2} = 2$
clever fjordBOT
Zybikron
analog light
lemme ask google
uneven osprey
bro have so much trust issues
split gyro
Yo
icy kindle
f'(x) = 4x + 2
you may want to look at your answer again....
and the way you got your answer is still not correct.
icy kindle
i haven't taken the limit yet.
analog light
exactly, after the limit is taken you're left with 2x + 2
analog light
**Zybikron**
nvm 4x + 2
icy kindle
still no.
analog light
@split gyro help
split gyro
Yo
analog light
Who is correct
odd edgeBOT
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.
analog light
Can someone help me understand derivatives better? We can use f(x) = 2x^2 as an example. Find the derivative of f(x)' = 2x^2
icy kindle
🙄 you do you bud. I'm trying to walk you through your errors and you've pulled up two calculators that disagree with you and now a new person. Have fun.
split gyro
d/dx of (x)^n=nx^(n-1)
analog light
?
split gyro
see
analog light
I meant f(x) = 2x^2
icy kindle
Can someone help me understand derivatives better? We can use f(x) = 2x^2 as an ...
he's doing the limit definition of derivative.
split gyro
We gonna apply it here
analog light
he's doing the limit definition of derivative.
oh
icy kindle
no power rule here
analog light
I think we have too many people in this. 77^2 had been typing for like 3 mins
split gyro
See definition of derivative says @analog light
That f'(x)=lim h tends to zero f(x+h)-f(x)/h
analog light
yep
split gyro
Ook
analog light
Thats right
icy kindle
🖖 i'm out
split gyro
Now your f(x) is 2x^2
analog light
See ya
split gyro
so what will be f(x+h)?
Tell me
U
@icy kindle is the 🐐
bro
f(x)=2x^2
If I put x=a
f(a)=2a^2
U simply need to do that
Instead of x we put x+h in the function
Now tell me what is f(x+h)
analog light
My Process:
f(x)' = lim h -> 0 f(x+h)-f(x)/h
f(x)' = lim h -> 0 2(x+h)^2 - 2x^2 /h
f(x)' = lim h -> 0 2x^2 + 4xh + 2h^2 - 2x^2 /h (Bionomial Theorem)
f(x)' = lim h -> 0 4xh + 2h^2 /h
f(x)' = lim h -> 0 4x + 2h^2
f(x)' = 4x + 2
Is there any error?
uneven osprey
My Process:
f(x)' = lim h -> 0 f(x+h)-f(x)/h
f(x)' = lim h -> 0 2(x+h)^2 - 2x^2 ...
yup in second last step
analog light
huh how?
split gyro
Yes
uneven osprey
2h^{2}/h = 2h
analog light
u need to substitute h for 0 in second last line
No it's in the last line right?
Too many people are talking
analog light
Check this step again
Hmmm... 4x^1h^1 + 2h^2 / h^1
split gyro
So now simplify it
analog light
So now simplify it
4x + 2h^2
analog light
u cant simplify h^2?
You can't you only have h^1
distant pagoda
You can't you only have h^1
h^2 is h*h
analog light
Yep
distant pagoda
what is h*h/h
analog light
h
distant pagoda
?
split gyro
Yes
distant pagoda
You only have h^1 and there is a h^1 and an h^2
do u not understand indices?
whats h^1
its just h
whats h^2
its h * h
analog light
What is the answer 4xh + 2h^2 / h, 4xh + 2h????
analog light
I have a whiteboard
distant pagoda
do it there and check
distant pagoda
I have a whiteboard
do it there
distant pagoda
ur confused why (2h^2)/h = 2h?
analog light
This is not what I learned in Algebra 1
analog light
ur confused why (2h^2)/h = 2h?
no?
thick harness
whats h(4x + 2h)
analog light
4xh + 2h
thick harness
why didnt u distribute the h to the 2h
distant pagoda
incorrect
thick harness
right
so then you can divide by h
and take it back to 4x + 2h
since you divide it all by h
analog light
OOOOHOHOHOHOHOHO
thick harness
analog light
That makes more sense
thick harness
fr
analog light
so the answer is 4x + 2!
distant pagoda
no
analog light
What
split gyro
,w (4xh+2h^2)/h
thick harness
h becomes 0
distant pagoda
You get rid of h
u dont get rid of it when u lift the limit
thick harness
you dont get rid of it
distant pagoda
u substituve h for 0
split gyro
Mf
analog light
u substituve h for 0
Thats what i meant
split gyro
What did Wolfram do
thick harness
so its 4x + 2(0)
distant pagoda
Thats what i meant
so whats 2*0?
analog light
so its 4x + 2(0)
oh? 4x?
thick harness
yeppers
analog light
OH
thick harness
analog light
thanks you guys
thick harness
np
analog light
Why did I think this would be harder?
distant pagoda
godbless
analog light
I mean it is calculus right?
distant pagoda
I mean it is calculus right?
basic calc, yes
analog light
basic calc, yes
That'll help me with a year of high school
thick harness
calculus has a reputation of seeming to be very difficult but most of it is algebra if you think about it
shouldnt be terrible if you have a good handle on algebra
analog light
Yeah, and to think I understand derivatives even though I have only passed Algebra 1
thick harness
fr
analog light
To signify a derivative is it f'(x) or f(x)'?
thick harness
first one
analog light
ok
thank you for your help and everyone else that was in this conversation. .close
.close
heady plover
Can we know if $f(x,y)=\frac{e^x}{x-y}$ is differentiable?
clever fjordBOT
riyobi
odd edgeBOT
@heady plover Has your question been resolved?
odd edgeBOT
@heady plover Has your question been resolved?
odd edgeBOT
@heady plover Has your question been resolved?
ember oak
Can we know if $f(x,y)=\frac{e^x}{x-y}$ is differentiable?
I assume it's differentiable everywhere except when the denominator is zero
heady plover
Except x=y?
heady plover
I assume it's differentiable everywhere except when the denominator is zero
Btw how did you know it's differentiable everywhere except that
ember oak
It's clearly not differentiable where it's undefined. And everywhere else, the partial derivatives can be calculated, so it must be differentiable there
heady plover
Wait how did you know that the partial derivatives can be calculated at a glance
ember oak
Wait how did you know that the partial derivatives can be calculated at a glance
Because it's just a ratio of two differentiable functions
heady plover
Why a ratio of two differentiable functions must be differentiable
uncut fern
doesnt look like theres any
the product log was useful only because it was defin...
so though there is a real solution, there is no possible representations without creating your own inversed function f(x)?
heady plover
.close
odd edgeBOT
odd edgeBOT
Available help channel!
fallow adder
odd edgeBOT
fallow adder
Why do I get 2 different results for the c) task
fallow adder
I took what is in the red box and multiplied the upper and lower part of the devision with (3x+9), thats the difference in solving in the lower tab of this screenshot
.close
odd edgeBOT
odd edgeBOT
Available help channel!
signal kraken
I am given this exercise where I have to use logarithm laws/properties, then look for their log by using the log tables etc, but as I have already seen, the numbers have to be positive, so X = AB/-C log X = log AB/-C would be undefined right? I mean not possible? since A,B,C have to be greater than 0. So the only waay to solve this would be by just carrying out the arithmetic operations?
fervent hawk
in such case, i would personally pull out the negative sign before applying log
like to calculate
-log((286.5)(4.714)/(67.84))
signal kraken
in such case, i would personally pull out the negative sign before applying log
...
so I'd pull it out as (-1)? like (-1) log (A)(B)(C)
fervent hawk
yep
and plug back in after the operations with log tables
the outcome will be a negative number.
signal kraken
yeah, I was thinking about that but wasnt sure if it was right :c / so what would the equation be like? (-1) log X = (-1) log (A)(B) / (C) right?
fervent hawk
yeah, I was thinking about that but wasnt sure if it was right :c / so what woul...
yea, if you let
A=286.5
B=4.714
C=67.84
and
X=AB/(-C)
then yea, we can evaluate it by first finding
log(AB/C)
and then multiplying the -1 after all the calucations
signal kraken
yea, if you let
A=286.5
B=4.714
C=67.84
and
X=AB/(-C)
then yea, we can evaluate ...
thanks. I was just making sure (-1) log X = (-1) log (A)(B) / (C) (this of course after taking out the - from C, so you have -1) makes sense
.close
odd edgeBOT
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Available help channel!
latent meadow
If i have a list of points that makes a somewhat makes an imperfect circle and average them( like the average of the X Axis and Average of the Y Axis)
Will i get the center?
short scaffold
If i have a list of points that makes a somewhat makes an imperfect circle and a...
it should be a good estimate
short scaffold
if the points are not more uniform, then the center could drift to the true centroid
latent meadow
like X amount of points will give me the midpoint
so like 8 points
or 1230 points
and they will give me a good midpoint
short scaffold
are they uniform or not?
latent meadow
uniform as in?
short scaffold
cuz if they're not, then it would be a lesser approximation of the center
short scaffold
uniform as in?
if the points somewhat looks like or forms a circle
latent meadow
as an example of how bad it gets
latent meadow
thanks!
Although alternative question
do you know a good algorithm to get the average from a list of 4000 numbers
short scaffold
if the numbers forms a geometric series or arithmetic, it should be way faster
just use the partial summation formula
latent meadow
just use the partial summation formula
could you elaborate?
short scaffold
its just the summation notation lmao, but in a formulaic way
mainly only for geometric and arithmetic series
find the common ratio or difference between the numbers, and then use the partial sum formula
this is a very unlikely scenario tho
i.e., the numbers are a geometric or arithmetic series
short scaffold
np!
latent meadow
.close
odd edgeBOT
odd edgeBOT
Available help channel!
deep prism
Is there a way to calculate theta without a calculator?
deep prism
@orchid torrent
deep prism
and then measure it xD?
you would usually do it with atan(1/sqrt(3))
merry finch
…
Draw it first
If you can do it by hand it’ll either be the 30 60 90 or 45 45 90 triangles
cold sage
there are some standard results you should know, or memorise tools like the unit circle or trig triangles
deep prism
there are some standard results you should know, or memorise tools like the unit...
fair enough. there are no shortcuts in this aspect? ^^
deep prism
Just draw it
im not even sure if we have a geo triangle in this exam
so i cannot even measure it
i just tested it. if it is allowed. it would be huge
cold sage
no one is saying to make a scale accurate drawing and measure it
deep prism
60
smart
this works for this triangle. but if it is -1/2 + sqrt(3)/2 i
like the second question
deep prism
Is there a way to calculate theta without a calculator?
.
one can see that it is in q2.
but i cant see if it is 120 or 130 deg
woeful escarp
These 3
leaden karma
Do you need to prove these?
woeful escarp
Do you need to prove these?
Yes
woeful escarp
how many attempts have you made?
Like 4-5 each problem
urban rose
Like 4-5 each problem
hm
woeful escarp
and what is your take on this
I have to use sinC + sin D or cos C + cos D formula in lhs
urban rose
hm
woeful escarp
I am able to get 4 sin ( alpha + beta /2) but nothing else
And in the cos problem 4cos ( alpha + beta /2)
urban rose
Now?
let me see what I can get it to then
till then, more attempts and see if anybody else gets it first
woeful escarp
till then, more attempts and see if anybody else gets it first
When u get 4 sin ( alpha + beta/2) I can't get thw remaining and When I get the rwmeaning I can't get the 4sin
odd edgeBOT
@woeful escarp Has your question been resolved?
woeful escarp
U gotta use that sinC + sinD formula
I tried I'm unable to do it
odd edgeBOT
@woeful escarp Has your question been resolved?
woeful escarp
what year are you in?
11th grade
elder heron
nvm my schooling system must suck
woeful escarp
It's just starting of trigonometry
woeful escarp
nvm my schooling system must suck
Like the easiest part of trigonometry of this year
woeful escarp
so you just need to prove it?
Ye
elder heron
also what is this topic called
woeful escarp
Ik I need to use sin C + sin D
woeful escarp
also what is this topic called
Trigonometry
elder heron
oh nice
elder heron
im gonna do a bit of googling
but if its for 11th graders
im sure i can figure it out
if not imma just go repeat primary school
woeful escarp
<@&286206848099549185>
lusty helm
for first
assume alpha + beta + gamma = k
and then apply
cos c + cos d
and then tell me what you got
send ur work
(ping me)
odd edgeBOT
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
this would solve first 2 ques
woeful escarp
do you still need help?
Yes
noble solstice
Also do you need help for 1, 2 or 3?
lusty helm
please send your work
woeful escarp
Also do you need help for 1, 2 or 3?
3
lavish jackal
what's the full content
lusty helm
lavish jackal
I meant to solve it in what way?
lusty helm
ohk
woeful escarp
@lusty helm
lusty helm
,rotate
woeful escarp
1st step is from after applying sin C + sin D
clever fjordBOT
noble solstice
Try this: Rewrite cos(A+B+C) as cos(A+(B+C)), in other words: treat b and c as one number, then apply the angle sum identity
lusty helm
how you got 2 beta
woeful escarp
Try this: Rewrite cos(A+B+C) as cos(A+(B+C)), in other words: treat b and c as o...
My maths teacher told us that the first step will be the same as I did and from the 2nd step I have done it myself
lusty helm
noble solstice
whats your first step?
lusty helm
he applied cos c + cos d
noble solstice
ill let vansh help, seems like he has more experience than me in trig (considering i have none)
woeful escarp
whats your first step?
The first line is the step he wrote on board while explaining the homework
noble solstice
ok but what is it
woeful escarp
he applied cos c + cos d
Yea but I did cos c + cos d in cos c + 2 cos d
woeful escarp
what about 2nd step?
I applied cos C + cos D in the 2 middle terms even tho it was cos C + 2cos D
lusty helm
you must not forget BODMAS
^^
woeful escarp
as in its multiplication
No?
lusty helm
yes
woeful escarp
lusty helm
woeful escarp
yes
It got in multiplication after I applied cos C + cos D on the 2nd line but on 1st line both middle terms were in +
lusty helm
see the blaack
they both in multi
you did like
2x3 + 5x6
3x5 and then mult, which is incorrect
woeful escarp
Oh I understand
lusty helm
yup
woeful escarp
So it is not possible to do cos C + cos D of the 2 middle terms?
lusty helm
nop
take cos (alpha+beta)/2 common
and then apply cos c + cos d (on whom which are in bracket)
woeful escarp
take cos (alpha+beta)/2 common
Genius
Now the problem of the extra cos ( alpha + beta /2) is also solved
lusty helm
yup
woeful escarp
U are doing what currently IIT?
lusty helm
in 12th
woeful escarp
Or JEE?
woeful escarp
Like this or I tske 2cos common?
woeful escarp
i am good at maths
Good
lusty helm
,rotate
clever fjordBOT
lusty helm
take 2 common too
and aply cos x + cos d
that would give u the ans
and then try 2 with same logic and lmk if you get it or not
woeful escarp
and then try 2 with same logic and lmk if you get it or not
Okok I'm gonna write this problem in complete first then I'll try
lusty helm
alright
woeful escarp
@lusty helm
I want answer in all sin but for than it should be cos C - cos D but it is cos C + cos D
If for Sin C - sin D = 2cos ( C+D/2) × sin ( C-D/2) we take -Sin C + sin D = 2cos ( C+D/2) × sin ( D-C/2)
We will get the answer we want
woeful escarp
Nope it is like that
If it was cos it would be easy cause cos - A = cos A but sin - A is - sin A
Sin is Negative in 4th quadrant 😭
lusty helm
gimme some time
i am doing some calc ques
yup back
is there anything given alpha, beta, gamma is angles of trianglw>
2 gets cancelled out
as alpha + beta + alpha - beta + 2gamma = 2(alpha + gamma)/2 = alpha + gamma
same with other and will give you beta + gamma
aha wait but its /2
nvm
you have done everything correct till now
yeah you have done + - mistake
here -alpha-beta would come
then applu sin(-x) = -sin x
and you will get ans
odd edgeBOT
@woeful escarp Has your question been resolved?
verbal talon
sat math question
odd edgeBOT
sat math question
verbal talon
don't know where to start for this one
lusty helm
take a/(x²+a²)^1/2 to to other
side
since denominator is same
add them
and then reduce the numerator which you get after addition by denominator and you will be left by:
(x²+a²)^1/2
verbal talon
(x^2+a^2)/sqrt(x^2+a^2)=27
verbal talon
and then reduce the numerator which you get after addition by denominator and yo...
how can we reduce in this case
lusty helm
multiply and divide √(x²+a²)
verbal talon
wait so the denominator is basically (x^2+a^2)^1/2
lusty helm
yes
verbal talon
and using exponent properties we can reduce the left side to (x^2+a^2)^1/2
verbal talon
square each side to get x^2+a^2=27^2
lusty helm
yes
odd edgeBOT
odd edgeBOT
Available help channel!
viral herald
can someone tell me what the value at the line is?
odd edgeBOT
can someone tell me what the value at the line is?
viral herald
like based on the log graph the gray line
pastel orbit
the gray line?
sharp girder
30?
pastel orbit
sharp girder
You probably would have to guess it to an approximate value
viral herald
yeah
sharp girder
I’d say abt 30
sharp girder
So 10^x = 30
viral herald
which is 10
and when i approximate the value to be around 10^0.8 i got a werid answer to my question
sharp girder
Not sure then
Maybe you have to get the value of the gray line though something else,
viral herald
the question just said extimate from log graph
viral herald
it has to be 10^x
sharp girder
Hm don’t really know then
boreal crag
Well, the plot should be linear in x What does it look like x should be here
cinder stirrup
Im trying the quotient rule but im not sure if im doing it correctly and im not sure how to finish the equation
wanton bison
Im trying the quotient rule but im not sure if im doing it correctly and im not ...
$f(x) = \frac{2-x}{(x+2)^3}$ ?
clever fjordBOT
𝔸dωn𝓲²s
cinder stirrup
$f(x) = \frac{2-x}{(x+2)^3}$ ?
Yeh thats it
wanton bison
Ok first thing I notice
the denominator gets squared
So you need a power to the 6 not 4
and you are missing (2-x)
$f'(x) = \frac{-1 \cdot (x+2)^3 - \textcolor{red}{(2-x)} \cdot 3 \cdot (x+2)^2}{(x+2)^{\textcolor{red}{6}}}$
clever fjordBOT
𝔸dωn𝓲²s
cinder stirrup
$f'(x) = \frac{-1 \cdot (x+2)^3 - \textcolor{red}{(2-x)} \cdot 3 \cdot (x+2)^2}{...
Thank u for pointing out those mistakes helps a lot, im still confused as to how u go from this to the answer given
wanton bison
**𝔸dωn𝓲²s**
what common term can you observe in the numerator?
cinder stirrup
what common term can you observe in the numerator?
(X+2)^2?
wanton bison
yes!
wanton bison
yes
cinder stirrup
We need to work on the numerator, right
Yeeh could we factor out the x+2 on the left side too?
wanton bison
what about
expansion
Let's expand the terms
can you tell me what we would get
multiplying it out
cinder stirrup
Let's expand the terms
What does expand the terms mean? Sorry im more used to dutch math terms
wanton bison
multiplying everything out
cinder stirrup
can you tell me what you would get in chat
Should I write it down and then post picture or try to write it
On keyboard
wanton bison
write it on keyboard I can code it
cinder stirrup
-x-2 - 6-3x / x+2^4 ?
wanton bison
yea (dont forget brackets)
clever fjordBOT
𝔸dωn𝓲²s
cinder stirrup
when you multiply the - into it
Oooh yeh that makes sense
cinder stirrup
Now we can add some terms together
2x and -8 right?
cinder stirrup
Nice!
clever fjordBOT
𝔸dωn𝓲²s
wanton bison
last step?
cinder stirrup
last step?
Divide by 2?
cinder stirrup
any common number in the numerator
I dont think I see one
cinder stirrup
do they have something in common
They are both even numbers?
wanton bison
hmm yea that's correct
what else
the plan is we wanna factorize 2
like in the solution
so the 8
cinder stirrup
If u divide it by 2 wouldnt the two dissapear cause it just be x?
cinder stirrup
ok i understood you wrong
No worries
wanton bison
well we really pull out things then that we literally divide
my point was
8 is the same as 2 * 4
what do 8 and 2 have in common
they both have the 2
8 = 4 * 2
2 = 1 * 2
so thats the common term
cinder stirrup
So we can get rid of the two?
clever fjordBOT
𝔸dωn𝓲²s
cinder stirrup
see thats our common factor
Ooh ic ic
clever fjordBOT
𝔸dωn𝓲²s
wanton bison
and thats it
So the goal is to simplify your terms by expanding (mulitiplying everything out) and factorization
recognize patterns and so on
cinder stirrup
and thats it
Shouldnt the 2 be gone cause we factored it out?
cinder stirrup
Oooh im dumb
wanton bison
**𝔸dωn𝓲²s**
like here (x+2)² was outside and not gone first
cinder stirrup
Ok i get what u did now
wanton bison
yea it's called factorization
cinder stirrup
Thanks a bunch!! Ur explanation helped a lot!
cinder stirrup
factorization is basically reversing what's been multiplied out
Yeeh im not used to doing that but I gotta practice it more
wanton bison
that's fine 😄
cinder stirrup
that's fine 😄
.close
odd edgeBOT
odd edgeBOT
Available help channel!
solid smelt
Hi, can someone explain me how do I reduce this expression?
sullen ferry
expand (x-1)^2 :3
solid smelt
expand (x-1)^2 :3
I see, and my second question is about this. The image says:
This expression needs to be reduced
...
For this, the following procedure is proposed
...
Why is the proposed procedure incorrect?
sullen ferry
,tex .exp rules
clever fjordBOT
🫎 Moosey 🫎
odd edgeBOT
odd edgeBOT
Available help channel!
wild spruce
Can i simplify $\frac{n^k}{n^0+n^1+n^2+...+n^{k-1}}$?
clever fjordBOT
Pop
clever fjordBOT
Pop
wild spruce
oh wait no
brittle notch
Correct
brittle notch
Nop
brittle notch
Lemme think
wild spruce
$\frac{n^k(n-1)}{n^k-1}$
brittle notch
Yes
clever fjordBOT
Pop
wild spruce
options?
brittle notch
Is it multiple choice?
wild spruce
no
brittle notch
Then how do I know if it's simplified
wild spruce
actualy i think u can still simplify the lower part