First time seeing that
#help-0
indigo saddle
worn fox
[x] usually stands for the equivalence class of x mod n
earnest mortar
[x] usually stands for the equivalence class of x mod n
nah I denote that $\bar{x}$
ocean sealBOT
Silfer
earnest mortar
ok i got 1 mod 6 now what?
You know that $$a\equiv b\ [n] \Rightarrow a^m \equiv b^m\ [n]$$ Right ?
ocean sealBOT
Silfer
fair musk
Ok
earnest mortar
Then just take n = 6, a = 7, b = 1, m = the long thing
earnest mortar
yes
earnest mortar
yes
fair musk
which equals 1
earnest mortar
$$7^{202320232023} \equiv 1\ [6]$$
ocean sealBOT
Silfer
lone heartBOT
@fair musk Has your question been resolved?
subtle coral
Hey I'm looking for some help on Boolean Functions. Got a proof I don't understand
subtle coral
specifically this proof I'm not sure about
I've highlighted the bit that's confusing me. I understand it's a proof by induction, and I understand how the induction hypothesis has to be used (we write f(x_n = 0) and f(x_n=1) in the form of (8)) but I don't understand what that will look like
Couple conventions used in the screenshot above I should clarify:
B = {0,1}
the capital pi for the product is actually a conjunction
<@&286206848099549185>
lone heartBOT
@subtle coral Has your question been resolved?
lone heartBOT
@subtle coral Has your question been resolved?
lone heartBOT
@subtle coral Has your question been resolved?
lone heartBOT
@subtle coral Has your question been resolved?
storm topaz
Hi I need help 🆘
timid remnant
.
lone heartBOT
@subtle coral Has your question been resolved?
alpine sable
specifically this proof I'm not sure about
Try asking this question in Advanced Mathematics Area
stray panther
please helppp
lone heartBOT
please helppp
modern sedge
please helppp
Your solution seems correct to me
stray panther
yess this is the answer but im not sure how to find it
like im not sure how to solve it all i have is the answer
modern sedge
Do you know why is this true?
stray panther
not really
modern sedge
Do you understand this? I subtracted 4x and 42 from both sides
stray panther
yes i understand
stray panther
is that where the 21 came from??
modern sedge
Yep, 42/2
modern sedge
do you know quadratic formula?
stray panther
noo
modern sedge
How do you solve quadratic equations?
modern sedge
ax^2+bx+c=0
modern sedge
Oh nvm :) There is one more step you can do, you can divide both sides by 2. 0/2 is 0 so the right side stays unchanged
Now you have simple quadratic equation where a=1, b=-4, and c=-21
stray panther
right
modern sedge
So is it all or do you have any other questions?
stray panther
please helppp
yess the last part
modern sedge
Do you know this?
stray panther
nope
modern sedge
Okay, and how do you solve equations ax^2+bx+c in school?
stray panther
sum and product
modern sedge
Oh, so find numbers, whose product is -21 and whose sum is 4
modern sedge
Correct
stray panther
is that all???
modern sedge
Yep. These are the solutions
modern sedge
You are welcome :)
stray panther
.close
lone heartBOT
lone heartBOT
Available help channel!
burnt imp
hey
burnt imp
Read that note bit..
My teacher said if it was (x - 30) on LHS there would be a bigger problem, but didnt say what it was/ how to tackle it.. I think he forgot
Could anyone of you say what would that problem be and how we would tackle it??
quasi scarab
maybe its about the 360?
visual temple
it doesn't cause a problem ...
if you get your x=-60° for example you can write is as x=300°
burnt imp
if it was (x - 30) and principle angle was equal/ smaller than it, what do we then do??
visual temple
you add a whole 360°
delicate jacinth
$a^b = 1 \implies (a = 1 \lor b = 0) \land ( a \neq 0 \lor b \neq 0 )$
ocean sealBOT
sopinha
echo socket
b =/= 0 seems weird
delicate jacinth
the secont part is to guarantee that both are non zero
0^0 is one, but only the limit x^x
echo socket
Btw a = -1 and b = 2 (or any even integer) could be a possibility as well
Unless we're talking about real numbers only, then a = i and b = 4 is a solution too
delicate jacinth
real numbers
delicate jacinth
Btw a = -1 and b = 2 (or any even integer) could be a possibility as well
yeah, i forgot about this solution
reef grove
is this true?
$\lim_{x \to 0}x^x = 1$
ocean sealBOT
tobi.
delicate jacinth
0^0 is one, but only the limit x^x
i mentioned the limit here
thorny root
what does limits have to do with this though
delicate jacinth
So, a = 1, b =0, and a = -1 and b =2k
reef grove
oh yeah mb
delicate jacinth
only solutions
echo socket
Yeah
delicate jacinth
I was hoping there would be something like $\left(\sqrt{2}^{\sqrt{2}}\right)^{\sqrt{2}}=2$
ocean sealBOT
sopinha
thorny root
like an irrational solution?
delicate jacinth
yeah
thorny root
a can be irrational and b zero
a can be 1 and b irrational
or did you mean something like a power tower
(x^x^x^...)
delicate jacinth
Yeah, irrational^irrational^irrational
somehow getting to one
(without any of them being zero)
thorny root
hmm
thorny root
maybe you could explore euler's formula and come up with something interesting there
unsure though
like roots of unity
elder plume
Hello, I wrote a program that translates a graph from the Z plane to the W plane, depending on the function. Complex numbers. I got such graphs, can you help explain these graphs from a scientific point of view? The functions shown here are the square root of z, zzz + 1, and z*z + 1
wary stream
.close
dim coral
what do they mean by this
lone heartBOT
what do they mean by this
dim coral
how did they get x=2
whole shell
@dim coral from dy/dx = 0
dim coral
how did they work it out
whole shell
You're left with a quadratic when you factor out x in the derivative @dim coral
lone heartBOT
@dim coral Has your question been resolved?
idle rune
quick question: how do i calculate √x?
for example, what's √48?
idle rune
i am learning the Pythagoras theorem, having a bit of problem
wary stream
quick question: how do i calculate √x?
for example, what's √48?
You can simplify it, that's it
idle rune
please elaborate
wary stream
Like $\sqrt{20} = \sqrt{4 \cdot 5} = \sqrt{4} \cdot \sqrt{5} = 2\sqrt{5}$
ocean sealBOT
dldh06
idle rune
how √4.5?
sullen dome
But if you want estimates just look at closest perfect square
idle rune
ohh
i see
let's say, the area of a triangle is 2 * √48 cm²
what would it logically be?
idle rune
this helps
idle rune
my maths exams are tomorrow and its 8 pm rn lol
idle rune
That's if you want the decimal approximation
will the question specify?
wary stream
Depends on your teacher
idle rune
idk, our papers comes abroad from another state
either that or out teacher does it
i forgot
wary stream
Most exams, from my experience, you just simplify
Decimal approximations are just approximations
wary stream
Like my example of sqrt(20)
idle rune
after simplifying, what do i do exactly?
ocean sealBOT
dldh06
wary stream
You can get a decimal approximation
wary stream
Like sqrt(20), it's greater than 4^2 but less than 5^2, so you know it's 4. something
wary stream
btw quick question, ² = √ right
No
idle rune
hmm?
wary stream
One is squared, the other is square root
idle rune
like s² = 48, s = √48
idle rune
like s² = 48, s = √48
i was talking about this
wary stream
That's if you are solving
idle rune
yeah
wary stream
You straight up said ² = √ and this is not true
idle rune
i didn't really knew how to explain that, sorry
i get the idea now, thanks
may i close this?
wary stream
You can if you are done
alpine sable
Can anyone help me on this?
lone heartBOT
Can anyone help me on this?
alpine sable
Can someone tell me the equation of this word problem?
[ A jar contains N nickels and D dimes. There are 20 coins in a jar, and the total value of the coins is 1.40. How many Nickels and how many dunes are there?]
low quartz
lemme try it
alpine sable
try to make two different equations
alpine sable
A nickel is 5 and dime is 10
worthy bay
Can someone tell me the equation of this word problem?
[ A jar contains N nic...
heh only if i knew what nickels, dimes and dunes were then i could help 
alpine sable
Set up a system of equations in two variables
I forgot 💀
kindred anchor
alpine sable
This is the equation?
alpine sable
It’s alr
wind cloak
N + D = 20
5N + 10D = 140
alpine sable
5x+10y=140
wdym
low quartz
oops srry
wind cloak
cross revoked
alpine sable
also, it's usually good that you know how to come up with equations in context of word problems
low quartz
x is N y is D
alpine sable
not have people come up with them for you
in the problem
[ A jar contains N nickels and D dimes. There are 20 coins in a jar, and the total value of the coins is 1.40. How many Nickels and how many dunes are there?
low quartz
" it's usually good that you know how to come up with equations in context of word problems" ---STARLIGHT 2023
BEST quote of the day
alpine sable
try to come up with two equations, one regarding the amount of coins, and one regarding the value of the total of those coins
N + D = 20
5N + 10D = 140 so this one is right?
low quartz
yes
alpine sable
10D= 100+ 5N=25, 100+25=125? It’s suppose to be 150
Because nickels are worth 5
each
the variable N refers to the AMOUNT of nickels
not the value of nickels
the variable D refers to the amount of dimes as well
Oh
wary stream
" it's usually good that you know how to come up with equations in context of wo...
I like to come up with the word problems in context of equations
low quartz
lol
lone heartBOT
@alpine sable Has your question been resolved?
dim matrix
Que: The 5th, 8th and 11th terms of a GP are a, b, c respectively. Show that a, b, c are in GP.
dim matrix
It is given that 5th, 8th and 11th term of a "GP", then what if I take the 4th term instead of 5th, won't it be a GP too ?
gray isle
wdym
gray isle
you're being asked to show that
$$a_1,a_2,a_3,a_4,\red{a_5},a_6,a_7,\red{a_8}, a_9,a_{10},\red{a_{11}}$$
are in GP, then
$$\red{a_5}, \red{a_8}, \red{a_{11}}$$
are also in GP \
you could try seeing if
$$a_4, a_8, a_{11}$$
are in GP if you really want.
ocean sealBOT
ℝamonov
gray isle
not sure if that's what you're trying to ask
dim matrix
you're being asked to show that
$$a_1,a_2,a_3,a_4,\red{a_5},a_6,a_7,\red{a_8}, a...
If I take a_4 I won't be able to prove it, it is what confusing me.
gray isle
well yeh, that's because it those specific terms won't form their own GP (unless in special cases of stuff like r=0 or r=1)
a_5, a_8, a_11
have a common ratio of r^3
a_4, a_8, a_11
do not have a common ratio and aren't in GP
dim matrix
yes, but the whole sequence is a GP
gray isle
yes...
a new sequence with consecutive terms
a_5, a_8, a_11
is in GP (because there's a common ratio which you've shown to be r^3)
a new sequence with consecutive terms
a_4, a_8, a_11
is not in GP (because there isn't a common ratio)
dim matrix
a new sequence with consecutive terms
> a_5, a_8, a_11
is in GP (because there's...
okay so the question is asking if the terms chosen are in a "new" GP or not, is it?
dim matrix
ahh okay
I got confused as the question is already stating that it is a GP then I should be able to prove this for every terms no matter what is given in the question.
Thank you so much @gray isle 🙂
.close
edgy gull
hi there i'm really lost on how to do this question using matrices,
the answer is u1 = 4 and v1 = v2 = 3
plain flame
$v1 \neq v2 - 3$
ocean sealBOT
heavy
ocean sealBOT
heavy
edgy gull
yes sorry
plain flame
alright you can rewrite it
since v1 = v2 you obtain the system of equations
$\frac{4}{u_1}+\frac{6}{v_1}+\frac{9}{v_2}=6 \newline \frac{15}{u_1}+\frac{11}{v_1}+\frac{2}{v_2}=8 \frac{1}{12}$
ocean sealBOT
heavy
plain flame
and v1 = v2 hence this is equivalent to
$\frac{4}{u_1}+\frac{6+9}{v_1}=6 \newline\frac{15}{u_1}+\frac{11+2}{v_1}=8 \frac{1}{12}$
ocean sealBOT
heavy
plain flame
$\frac{4}{u_1}+\frac{15}{v_1}=6 \newline\frac{15}{u_1}+\frac{13}{v_1}=8 \frac{1}{12}$
ocean sealBOT
heavy
edgy gull
so the adj(A) would be 0 which wouldnt make sense
distant cove
$\lim _{x\to \infty }\left(\left(1+x^2\right)\cdot \left(\frac{\pi :}{2}-arctan\left(x\right)\right)^2\right)$
why does it equal 1 i couldnt figure it out
and how to calc this
ocean sealBOT
Kingo
thorny root
do you know the "identity", $arctan(x) + arctan(\frac{1}{x}) = \frac{\pi}{2}$
ocean sealBOT
biggboy
thorny root
oh alr
distant cove
.close
fair bay
help
fair bay
please
fair bay
the points which divide internally and externally the line segment joining the points (1,7), (6,-3) in the ratio 2:3 is
yea
thorny root
is the question cut off
tacit arch
Do you know how to calculate the length of a line given coordinates
fair bay
yes
tacit arch
What's the length of your original line segment
lone heartBOT
@fair bay Has your question been resolved?
safe basin
I can help you.
hazy totem
lone heartBOT
hazy totem
The answer is -1/6
hazy vortex
wanton nova
hazy vortex
Ok that’s my third time I get the # help why?
thorny root
did you actually read the channel
hazy totem
The answer is -1/6
I solved but got -2. What I did:
h(x^3) = f(x).x
h'(x^3) = f'(x).x + f(x)
h(-8) = -2.f'(x) + f(x)
We have a tangent line. It passes through points (-3, 0) and (0, 6)
We calculate its function: 2x + 6
We put (-2) and we get f(-2) which is 2
And we also know f'(-2) = (tangent line)'
So (2x + 6)' = 2
f'(-2) would also be 2
h(-8) = -2 * 2 + (-2) = -2
<@&286206848099549185>
lone heartBOT
@hazy totem Has your question been resolved?
hazy totem
<@&286206848099549185>
lone heartBOT
hazy totem
.reopen
lone heartBOT
✅
hazy totem
My question got to the bottom of the list. Maybe now some people actually notice it hopefully?
hazy totem
Here is the question new people
hazy totem
I solved but got -2. What I did:
h(x^3) = f(x).x
h'(x^3) = f'(x).x + f(x)
h(-8) ...
And what I did
😔
<@&286206848099549185>
visual temple
hummm
tacit arch
I solved but got -2. What I did:
h(x^3) = f(x).x
h'(x^3) = f'(x).x + f(x)
h(-8) ...
I don't see where you computed chain rule correctly
hazy totem
I don't see where you computed chain rule correctly
How should I use the chain rule?
I don't know how to use chain rule when I don't have f(x)
and it's f(x^3) or something
So I also tried something else meanwhile:
$h(x) = f(rad(3, x)) * rad(3, x)$
ocean sealBOT
rubicminer
hazy totem
$h'(x) = f'(rad(3, x)) * rad(3, x) + f(x)/(3 * rad(3, x^2))$
ocean sealBOT
rubicminer
hazy totem
And then put the values, x = -8, f(-2) = 2, f(2) = 2
And got:
$-4 + 2/(3 * 4) = -4 + 1/6 = -23/6$
ocean sealBOT
rubicminer
hazy totem
Which step did I do wrong...?
tacit arch
How should I use the chain rule?
you're plugging in -8 to h(x), but the question asks for you to plug in -8 to h'(x)
so you need chain rule to compute h'(-8)
hazy totem
**rubicminer**
I calculated it here?
$h'(x) = f'(rad(3, x)) * rad(3, x) + f(x)/(3 * rad(3, x^2))$
ocean sealBOT
rubicminer
tacit arch
$\frac{d}{dx} h(x^3) = ?$
ocean sealBOT
riemann
hazy totem
h'(x^3) * 3x^2
...
But when I turned h(x^3) to h(x), then I shouldn't have needed a *3x^2
So why did I still miscalculate it?
hazy totem
h'(x^3) * 3x^2
And I got h'(x^3) = -2
-2 * 12 = -24
So it's still wrong?
tacit arch
hard to piece random parts of your work. can you write it all out in one format
hazy totem
Alright. So I used two methods:
1st method.
$h(x^3) = f(x).x$
Derivative of $h(x^3) = h'(x^3) * 3x^2$
$h'(x^3) = f'(x) * x + f(x)$
Based on graph $f'(-2) = 2$ and $f(-2) = 2$
I put them in the $h'(-8) * 3(-2)^2$ and I get: $(2 * (-2) + 2) * 12) = -24$
ocean sealBOT
rubicminer
hazy totem
2nd method.
$h(x^3) = f(x) * x$ so $h(x) = f(rad(3, x)) * rad(3, x)$
And now $h'(x) = f'(rad(3, x)) * rad(3, x) + f(x)/(3 * rad(3, x^2))$
And again, $f(-2) = 2$ and $f'(-2) = 2$ based on graph. So:
$h(-8) = 2 * (-2) + 2/(3 * (4)) = -4 + 1/6 = -23/6$
ocean sealBOT
rubicminer
hazy totem
@tacit arch those are what I did in two messages. Hope it helps
tacit arch
so use $h'(x^3) 3x^2 = xf'(x)+f(x)$
ocean sealBOT
riemann
hazy totem
so use $h'(x^3) 3x^2 = xf'(x)+f(x)$
I used it in the first method
hazy totem
So instead of multiplying by 3x^2 I should devide by 3x^2
-2/12 = -1/6
Oh wow
Well thank you very much
I've been on this question for more than an hour now
And I also learned something new
.close
ionic hearth
yo so I have a question asking me about the value of k
The equation is 4x^2 + 4kx + 9 = 0 and k > 0
I've used the discriminant to figure out that I need to find 4^2 -4(4)(9) but from this point on im kind of lost
ionic hearth
because if I use that I will get 16 - 144
ionic hearth
huh?
ionic hearth
what do you mean
ionic hearth
yeah
whole shell
not b = 4
whole shell
so why do you have 4^2
ionic hearth
I just didn't include the k
whole shell
then do it?
ionic hearth
but yeah 4k^2 - 4(4)(9)
ionic hearth
well I get 16k - 144
whole shell
yo so I have a question asking me about the value of k
The equation is 4x^2 + 4...
wait
this question
is supposed to tell you
how much solutions you have
ionic hearth
one
whole shell
16k^2 - 144 factorises into 8k(18k - 1)?
ionic hearth
oh wait
glossy bluff
you need to make it into a k^2
ionic hearth
9
glossy bluff
16k^2 - 144
ionic hearth
idk how I got 18
glossy bluff
and solve it
ionic hearth
16k^2 - 144 factorises into 8k(18k - 1)?
is it 16k(9k-1)?
whole shell
is it 16k(9k-1)?
still no
all your numbers are correct but they are in the wrong order
ionic hearth
what do you mean?
ionic hearth
this certainly isnt what you started with
so 16k(1k-9)?
ionic hearth
ok
ionic hearth
i dont
ionic hearth
cause you bring itover right?
whole shell
thats 16 + k
whole shell
16 times what equals 0 @ionic hearth
whole shell
yh
ionic hearth
and thus k is 9
whole shell
yh
lone heartBOT
Show your work, and if possible, explain where you are stuck.
weary wyvern
alpine sable
which part of avxss's steps are you stuck on
draw a diagram
draw B,C and D as well
sly mantle
@elder steppe you asked me a question but the channel moved before i could reply. from #❓how-to-get-help
While asking questions, make sure to mention all relevant details, including what you have tried and what you're stuck at. Do not expect others to simply solve your questions for you.
so asking for a full step by step process as you did in the original channel wont fly
alpine sable
...AB=BC... line through B perpendicular to AC passes through D...
sly mantle
we're not chegg. if you expect immediate answers then this isnt the place for you
a handful of mods obviously cant watch everything on a 100k+ server. though if thats your pattern of behavior here then we're not going to entertain it anymore
.close
final mural
Hey
alpine sable
i need help
final mural
i need help
What do u need
final mural
Youre in the wrong channel 😭but ill try
final mural
Np
alpine sable
its the last collum under themari berhan chrome-extension://bpmcpldpdmajfigpchkicefoigmkfalc/views/app.html
final mural
Is that a link?
alpine sable
yeh
chrome-extension://bpmcpldpdmajfigpchkicefoigmkfalc/views/app.html
189
186
172
196
173
186
182
174
198
149
229
162
192
184
207
175
154
188
213
195
136
153
142
145
146
115
144
118
133
154
139
144
121
126
133
109
130
117
136
114
these are the numbers i need squaring can u dm me the asnwers
@final mural
final mural
Why dont you just use like a calculator
Or do you need a program?
You could try this on excel
alpine sable
he said we have to use a calc
final mural
You need to square every number?
final mural
35721
34596
29584
38416
29929
34596
33124
30276
39204
22201
52441
26244
36864
33856
42849
30625
23716
35344
45369
38025
18496
23409
20164
21025
21316
13225
20736
13924
17689
23716
19321
20736
14641
15876
17689
11881
16900
13689
18496
12996
Here
Use excel in the future, it comes in handy
<@&286206848099549185>
Need some help with the exercise above
alpine sable
ok
alpine sable
35721
34596
29584
38416
29929
34596
33124
30276
39204
22201
52441
26244
36864
33...
wait h=tis is it
thx
final mural
Np
lone heartBOT
@final mural Has your question been resolved?
visual temple
humm
fluid rampart
how do I find the 6 trigonomic functions of 5pi/6
tacit arch
this is just a special angle on the unit circle
visual temple
draw ur circle and memorise the main ones
tacit arch
so how do I find the trig functions?
depends on your class
fluid rampart
college trig
tacit arch
does your teacher give you this?
tacit arch
use that to first find sin(5pi/6) and cos(5pi/6). then the other 4 trig functions can be derived from those 2 numbres
coordinates are
$(\cos(\theta), \sin(\theta))$
ocean sealBOT
riemann
fluid rampart
so cos would be -root3/2?
tacit arch
,calc cos(5 pi / 6)
fluid rampart
thank you
ocean sealBOT
Result:
-0.86602540378444
,calc -sqrt(3)/2
ocean sealBOT
Result:
-0.86602540378444
.close
lone heartBOT
tacit arch
cam i have help
!help
alpine sable
<@&286206848099549185>
lone heartBOT
<@&286206848099549185>
alpine sable
pls
visual temple
yes
alpine sable
dm
lone heartBOT
@alpine sable Has your question been resolved?
lone heartBOT
lone heartBOT
Available help channel!
dark fern
can every single qudratic be put into factorerd form by using the quadratic equation and a(x-r)(x-s)? (Assuming they have at least a single root)
spring plover
Yes. Also, quadratic always have two roots. There is no case where a quadratic can have one root.
spring plover
Also, complex and irrational roots always come in conjugate pairs.
spring plover
It still has two roots. It is just that the two roots are equal.
dark fern
but how come the factored form when applying a(x-r)(x-s) + quadratic equation doesn't hold true?
nvm
spring plover
but how come the factored form when applying a(x-r)(x-s) + quadratic equation do...
Wdym
I can write say (x-4)^2 as (x-4)(x-4).
dark fern
I made a mistake. I understand now. So there will never be an instance where a(x-r)(x-s) + quadratic formula is unable to create the factored form of a quadratic?
ok thanks
alpine sable
<@456226577798135808> Has your question been resolved?
Yes
calm willow
i swear my teacher is gaslighting me
lone heartBOT
i swear my teacher is gaslighting me
last ether
It doesn't exist
calm willow
if its x greater than or equal to
last ether
You wrote down 4/7
ok ok
last ether
In order for a limit to exist, the sided limits must be equal
earnest coyote
hi, i dont know if this is allowed but i've been chipping away at this forever and i don't feel like i'm understanding what i'm doing or why. i know i need to initially set u=2x and go from there but setting v and dv and everything is confusing to me.
earnest coyote
if anyone can take the time to basically hold my hand it will be hugely appreciated. i've spent like 3 hours almost getting somewhere and then nowhere.
gloomy knoll
No problem
First substitute $u = 2x$, then $du/dx = 2$ if follows that $dx = 1/2 \cdot du$
ocean sealBOT
Jυяαנ
earnest coyote
right ! i have gotten that far at least.
gloomy knoll
We can now simplify the integral to:
earnest coyote
(also thank you so much)
gloomy knoll
$1/2 \Integ{ }{ }{ln^2(u) } du$
ocean sealBOT
Jυяαנ
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
earnest coyote
so far so good.
earnest coyote
take all the time you need brother.
gloomy knoll
xD
minor needle
$1/2 \Integ{ }{ }{ln^2(u) } du$
$\int \frac{1}{2} \ln^2 u \ du$
gloomy knoll
ah thank you
ocean sealBOT
Modus
gloomy knoll
$\int \frac{1}{2} \ln^2 u \ du$
now solve this integral with integration by parts
$df/dx = 1$ and $g = ln^2(u)$
ocean sealBOT
Jυяαנ
gloomy knoll
it follows that $ f = u$ and $dg/dx = 2ln(u)/u$
ocean sealBOT
Jυяαנ
earnest coyote
yes this is where i became confused.
gloomy knoll
dont you know how to integrate by parts?
earnest coyote
barely haha. i've done 3-4 other IBP problems before this.
so this is where things were unclear.
gloomy knoll
Okay.
the problem is that we dont know the integral of ln(x) * ln(x), but we know the integral of 1. So we can use integration by parts to integrate 1 and differentiate ln^2(x)
Because differentiation is always the simpler computation.
gloomy knoll
$\int \frac{1}{2} \ 1*ln^2 u \ du$, now set df/dx = 1 (because integrating 1 is easy) and differentiate the other part (ln^2(u))
ocean sealBOT
Jυяαנ
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)
gloomy knoll
then plug your results in the integration by parts formula and you solved the integral
the result should be: $u ln^2(u) - \int \ 2*ln u \ du$
ocean sealBOT
Jυяαנ
earnest coyote
this will be sort of anticlimactic for you because am at the gym now but i am saving this convo and when i get home i'm sure it will be a piece of cake.
thank you so much.
final mural
Hey
final mural
@carmine reef , I put the question I asked a couple hours back into maple, and M = 26 gave a solution?
final mural
Multiples of it too?
carmine reef
not all multiples
final mural
Which ones then
carmine reef
sorry, i dont really have time right now
final mural
Ok np, looking at it, it seems like every M that gcd(M,30)|2014 will give an answer
carmine reef
i could believe that
lone heartBOT
@final mural Has your question been resolved?
carmine reef
thats equivalent to M being not a multiple of 3 or 5
which is what i thought the solution probably was too
it seems like toby's mod switch might have been the way to go
if it was equivalent
idk
south remnant
lone heartBOT
south remnant
on line CD?
desert tusk
And use trigonometric functions to find the angle
desert tusk
on line CD?
not a good one
try drawing a line somewhere
Where it can create a 90 degree angle triangle
south remnant
from C downwards
desert tusk
Sure
south remnant
do i need to use pythagoras now?
desert tusk
No need
south remnant
4cm along the bottom
desert tusk
yeah you need Pythagoras theorem to find one of the side
desert tusk
13 is the product of the square root of the sum of the square of the other sides of the triangle it has
nope wrong
south remnant
oh right
south remnant
5
desert tusk
5
yes
now you should be able to find the angle
I don’t know the actual answer since I don’t have a calculator with me
but if you use the correct trig function then that’s your answer
desert tusk
how do i know which function to use?
do you know how each function gives the formula based on the angle given?
south remnant
yes
desert tusk
i think its tan but im not sure
can you tell me why is it tan
south remnant
because when you have tan you need to divide the opposite by the adjacent angle
and they are the two there
south remnant
would it be tan (5 divided by 4)?
desert tusk
wrong
remember
trig functions only accept angles
tan (angle) = 5/4
you gotta use the inverse of tan
or whatever you call
there’s a name for it
south remnant
tan to the power of -1?
south remnant
ok
desert tusk
Or arctangent
south remnant
so tan to the power of -1 (5/4)?
desert tusk
yes
south remnant
thanks
tacit arch
$\arctan(x) \neq \cot(x)$
ocean sealBOT
riemann
south remnant
.close
red vault
help
keen forum
red vault
sorry i forgot i made this
i got distracted
lemme see what i have to do
the slope is x right
west girder
????
red vault
so m would be the number before x like 5x
carmine reef
is 5x the number before x?
red vault
5 is
red vault
ok let me try this and u can check and make sure did this right
is this the right equation
carmine reef
yes
red vault
ok thank u ill ask again if i am confused
carmine reef
np
carmine reef
yeah
red vault
ok
carmine reef
3 and 5 good
red vault
3 and 5 good
is this good
carmine reef
only the intercept is good
red vault
?
oops its negative
and i gotta fix something it doesnt match up on graphing calculator
red vault
only the intercept is good
ok i fixed it i think
carmine reef
yeah thats right
red vault
nice
alpine sable
.help
lone heartBOT
Commands:
clopen: .close, .reopen, .solved, .unsolved
consensus: .poll
factoids: .tag
help: .help
Type .help <command name> for more info on a command.
alpine sable
lone heartBOT
alpine sable
Fyi, you just need to post you question, no need to do this
?
coral vector
Fyi, you just need to post you question, no need to do this
u got this
or shud i
ik how this is done
wary stream
?
I mean, you don't need to open a channel doing .help, just post your question and it automatically opens with your name
alpine sable
I mean, you don't need to open a channel doing `.help`, just post your question ...
Ok
But how do I get help?
wary stream
ik how this is done
You can assist
alpine sable
Do I have to ping someone?
wary stream
But how do I get help?
Wait patiently for help
alpine sable
Ok
alpine sable
Kinda
coral vector
so
a percent is
the amount of ppl/ total ppl
so for men dogs
the total men are 56
and dogs are 30
so how would you get a percent from this
alpine sable
If I divided 30 and 56?
alpine sable
53%?
alpine sable
What do you mean?
coral vector
like the rest of the blanks
coral vector
oh shoot i messed up
instead of doing 56 u use 140
because its asking relative to all ppl
alpine sable
So I divide each one by 140 right?
Then I put it in the blank
I have another question
When I do 30÷140
coral vector
yeah
coral vector
so
alpine sable
Like 21%
coral vector
yep
alpine sable
8th and pre Algebra 💀
novel crescent
lone heartBOT
rapid bloom
lone heartBOT
rapid bloom
To find when the concentration decreases, would I have to find the first derivative?
strange meadow
that seems reasonable
oak sonnet
we can help because its in the turkish
rapid bloom
I find it unclear what the original function, first derivative, and second derivative normally tells us
what
i ate a really nice turkey a couple days ago
strange meadow
what does the first derivative tell you
rapid bloom
i’m not so sure
oak sonnet
about that (1/5 + 1/ 1/5)
rapid bloom
i’m confused
i think the first derivative tells us the location of max and min values?
or if we set it to zero, it would tell us where there’s a min or max
oak sonnet
it's about fractions
strange meadow
yes but what exactly does it tell you
rapid bloom
i’m guessing that i should find that, and then do test points around the function
rapid bloom
yes but what exactly does it tell you
i don’t know
rapid bloom
ohhh
strange meadow
you had to have learnt it
ocean sealBOT
ed
oak sonnet
shorter fraction
rapid bloom
like the change of the slope?
rapid bloom
ohh that makes sense
analog falcon
since, if the curve is not a straight line, the we find gradient at different different points, because slope will be diff at diff points
so we take the slope of tangent to the curve at that particular point
rapid bloom
right, i can understand that!
so if the first derivative gives me the slope of the tangent, does that mean a negative value will tell me when the concentration is decreasing
strange meadow
thats correct
rapid bloom
how about the second derivative?
would it be helpful during this question?
this is where i’m at so far
i don’t know if i did this correctly, but i wouldn’t be able to add them together right?
please help anyone
ayuda
candid frigate
It'll be C'(t) = 0, and you want to find when t makes the first derivative = negative, because that would be a decrease in concentration
rapid bloom
It'll be C'(t) = 0, and you want to find when t makes the first derivative = neg...
i have no idea how to isolate t
would i need to use test points at some point in this question?
rapid bloom
i have no idea how to isolate t
oh wait i’ll try using the natural log
i dont know how.. please help
lone heartBOT
@rapid bloom Has your question been resolved?
rapid bloom
<@&286206848099549185>
lone heartBOT
@rapid bloom Has your question been resolved?
buoyant python
@rapid bloom
if you tried to elaborate this expression more, i suggest you should use binomial theorem
median dirge
@buoyant python ???
steel dagger
If y = tan(2x^2 + 4y), find the rate of change of y with respect to x at the origin.
long axle
Yk how to implicitly differentiate?
steel dagger
yeah
long axle
Aight what have u done so far