@pure condor Has your question been resolved?
#help-19
odd edgeBOT
odd edgeBOT
odd edgeBOT
Available help channel!
deep lance
odd edgeBOT
deep lance
Can someone please suggest me a graphing website
I need to graph these points for a statistics project tomorrow but the website I'm on isn't really working
I need to make a scatter plot
shy smelt
You could use excel or google spreadsheets, lots of information about them online
odd edgeBOT
odd edgeBOT
Available help channel!
toxic bone
Not sure how to do 3a
odd edgeBOT
Not sure how to do 3a
vale vapor
where are you stuck?
wise idol
notice that 25^x is the square of 5^x
feral halo
25^x
= (25)^x
= (5^2)^x
= (5)^2x
= 5^2x
feral halo
= (5^x)^2
wth
u can't do that
if u log left side
u log right side
and log 0 is undefined
also when u log left side
u can't split each term into logs
it's log all of the left side
wise idol
Idk where to go from here
log isn't distributive
feral halo
Idk where to go from here
try and sub u = 5^x
wise idol
log(a+b) ≠ log(a) + log(b)
wise idol
try and sub u = 5^x
yea
toxic bone
What about this??
toxic bone
idk what you mean by the letter u
wise idol
you know how 25^x is the square of 5^x right
toxic bone
yea
toxic bone
right
wise idol
so how about you replace 5^x = u and convert it into an equation of u
then when you find the values of u you can say 5^x=u and solve for x
does that sound right
odd edgeBOT
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Available help channel!
royal frost
odd edgeBOT
wooden gorge
is the ans h=1 or h does not equal to 1 ?
h != 1. ow you'll have linearly dependent vectors
wooden gorge
h != 1. ow you'll have linearly dependent vectors
|D| != 0 is the condition
royal frost
h != 1. ow you'll have linearly dependent vectors
we had a note in class that says c1v1+c2v2+c3v3=0 in order to be linearly independent
why can't we apply it and solve the system?
wooden gorge
we had a note in class that says c1v1+c2v2+c3v3=0 in order to be linearly indepe...
that implies you missed a crucial piece of addition to this sentence
haughty fulcrum
inconsequential, but check entry 2,2 in the upper triangular matrix
royal frost
I also know that linear indepedncy must have full rank
wooden gorge
add this to your notes -> "...to be linearly independent, must only have c1 = c2 = c3 = 0 as solution"
royal frost
add this to your notes -> "...to be linearly independent, must **only** have c1 ...
so u mean the constants themselves not coeffiecents ?
like c1=c2=c3=0 where v1....vn must be non zero ?
wooden gorge
Yes c1 = c2 = c3 = 0 must be the case, if you have three linearly independent vectors satisfying the equation c1v1 + c2v2 + c3v3 = 0
odd edgeBOT
royal frost
.reopen
odd edgeBOT
✅
royal frost
Yes c1 = c2 = c3 = 0 must be the case, if you have three linearly independent ve...
oh one more thing
it is actually unrelated but I wanna check
is this is the correct formula for Gram schimdt process?
hallow garnet
Someone will have the syllabus of the IMO Olympiad, please, and thanks
wooden gorge
no
what do you mean by dot product of a scalar times vector?
$x_2 \cdot v_1 \cdot v_1$?
clever fjordBOT
Arya
wooden gorge
this is the Gram Schmidt process.
And you can check why projection of v_1 on x_2 is what is written
royal frost
what do you mean by dot product of a scalar times vector?
tbh I don't know my teacher wrote it like that.
But I am not sure whether if | | v| |^2 or | |v|| for v2
royal frost
this is the Gram Schmidt process.
okay
wooden gorge
no, ||v_1|| implies norm of a vector, or simply it's magnitude
(x_2 . v_1) is the size of the projection vector of x_2 on v_1, and (v_1)cap ,i.e., the direction of the projection vector, is given by (v_1)/(its magnitude = ||v_1||)
royal frost
(x_2 . v_1) is the size of the projection vector of x_2 on v_1, and (v_1)cap ,i....
alr
thx
.close
odd edgeBOT
odd edgeBOT
Available help channel!
whole anvil
Do I need to use L'Hôpital's rule here?
odd edgeBOT
Do I need to use L'Hôpital's rule here?
whole anvil
leaden karma
you can directly simplify after this step, there's no need to expand out the denominator
oak crown
3x-9=3(x-3)
odd edgeBOT
odd edgeBOT
Available help channel!
vapid violet
how do i do this (1+r/4)^16 = 3/2 solve for r
odd edgeBOT
how do i do this (1+r/4)^16 = 3/2 solve for r
quasi sparrow
Log 
vapid violet
i cant use log
quasi sparrow
Why not
vapid violet
i dont know how
vapid violet
what u mean
oak crown
something like $\qty(\qty(1+\frac{r}{4})^{16})^{1/16}=\qty(\frac32)^{1/16}$
u
h
pardon the absolute dogshit latex
clever fjordBOT
;(
oak crown
there
quasi sparrow
a * 1/a = 1 for all nonzero a yes
vapid violet
but then i get 1+r/4 = 1.025
quasi sparrow
,calc (3/2)^(1/16)
clever fjordBOT
Result:
1.0256653964664
Rounded incorrectly, but sure
odd edgeBOT
odd edgeBOT
Available help channel!
molten skiff
teacher has given us a bonus question that we have until the end of the year to solve, and we will get bonus points for solving it.
it is a riddle.
it goes something like this:
"A king of an ancient land asked his engineer to build him a bridge to replace the knotted up bridge which makes the crossing of the river difficult, with the proper measuring tools missing, the engineer can only measure the width of the river using steps of the kings servants.
how could the engineer calculate the width of the river (AB) using 4 of the king's servant?"
i dont have an answer to this question available, so anything goes, i guess.
molten skiff
if something doesnt make sense, i translated this on my own, so feel free to ask.
I have not been able to come up with a solution
dense moth
teacher has given us a bonus question that we have until the end of the year to ...
Butler ?
dense moth
Okk !
tepid pelican
one of the servants could stand at point B and another one (call him C) could move alongside the river until the angle BCA is 45°, then the width of the river is same as the distance between B and C
7
though I dont know what tools exactly are available
low locust
I assume you are really only allowed to count steps somehow
I'm thinking something with having one servant go over the bridge and another mimics the motions or something
odd edgeBOT
@molten skiff Has your question been resolved?
molten skiff
i dont wanna clog up this room, if someone sees this, DM me if you have a question, maybe the C angle approach works, ill have to ask the teacher though, because im not sure how youll be able to measure the angle of ACB
signal carbon
you aren't allowed to directly measure angles
otherwise you don't even need the knotted bridge
odd edgeBOT
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Available help channel!
eternal flower
hi, can someont tell me why this is wrong?
odd edgeBOT
hi, can someont tell me why this is wrong?
clever fjordBOT
oak crown
oh well i guess it a calculator error @eternal flower
odd edgeBOT
odd edgeBOT
Available help channel!
eternal flower
can anyone walk me through finding the asymptote?
odd edgeBOT
can anyone walk me through finding the asymptote?
mystic saffron
can anyone walk me through finding the asymptote?
Sure
So let’s start with
What is an asymptote
eternal flower
an x or y value that the graph cannot be at any point
eternal flower
mhm
mystic saffron
so if we plugged infinity into the equation
we'd have -2(1/4)^infinity
and what can you say about (1/4)^infinity
mystic saffron
we'll get there but
what can you say specifically about (1/4)^(a big number)
as the power gets bigger, what happens to numbers between 0 and 1
for example (1/4)^2 = 1/16
(1/4)^3 = 1/64
..
what do you see happening here
eternal flower
they get smaller
mystic saffron
yes
so if we have the power as infinity
what can we say that (1/4)^infinity is tending towards
eternal flower
zero? or just a smaller and smaller number?
mystic saffron
yeah exactly
its getting smaller and smaller
so will tend toward zero but never reach it
eternal flower
yeah
mystic saffron
so -2(1/4)^(x-2) will tend toward zero
but never reach it
so whats the asymptote
eternal flower
0
eternal flower
but i don't understand how that makes sense with the equation
mystic saffron
could you explain what u dont understand
as x gets very big, (1/4)^(x-2) gets very small, so f(x) -> -2(0) = 0
mystic saffron
yh
eternal flower
okay i think i get it now
im gonna keep working and if i get confused again ill come back
goodbye and thank you !
.close
odd edgeBOT
odd edgeBOT
Available help channel!
devout kayak
Hello! What does absolute value help us with in terms of calculus?
ember oak
Hello! What does absolute value help us with in terms of calculus?
calculating limits
devout kayak
It is my first time learning algebra in preparation for calculus in May. Is there any way you could help me understand a bit more than that?
strange aspen
It is my first time learning algebra in preparation for calculus in May. Is ther...
if i'm not mistaken you are taking functions yea ?
devout kayak
That is correct, I am attempting to learn more about functions, yes!
strange aspen
That is correct, I am attempting to learn more about functions, yes!
absolute value function is known for being a piecewise function you what these functions are ?
devout kayak
Yes! Aren’t they functions that have discontinuity?
strange aspen
Yes! Aren’t they functions that have discontinuity?
not nesseceraly (can't spell it lol)
they are combined functions each with a specific intereval for it
devout kayak
Interval meaning domain values?
strange aspen
yea
devout kayak
What’s important about piecewise functions and why did you bring them up
strange aspen
What’s important about piecewise functions and why did you bring them up
because the absoulte value function is a piecewise function
devout kayak
And how is that important to the calculus
strange aspen
cuz when dealing with problems including absolute value
sometimes you need to how it is defined
specifically in limit problems
devout kayak
Oh! Could you give me an example
strange aspen
Oh! Could you give me an example
this video would help https://youtu.be/y5Wp3RHQ7aQ?si=qsyQFGNJlEJBmEPU
as an example
devout kayak
Let’s talk about derivatives
strange aspen
no problem what do you want to know
ember oak
Let’s talk about derivatives
odd edgeBOT
@devout kayak Has your question been resolved?
devout kayak
Hello
devout kayak
How do we transition from Algebra to calculus?
How should I be thinking about how to learn this
devout kayak
What would you consider the easiest practice problem in calculus
quasi sparrow
Go read books to learn foundations
devout kayak
I have Stewart’s calculus 6e
shell haven
What would you consider the easiest practice problem in calculus
Evaluate d/dx(x)
devout kayak
What do I do with that
devout kayak
Evaluate d/dx(x)
What’s the question asking
shell haven
To evaluate the derivative of x with respect to x
shell haven
What’s the question asking
Frfr
devout kayak
To evaluate the derivative of x with respect to x
I’m not sure I know what that means. Feel like teaching?
odd edgeBOT
@devout kayak Has your question been resolved?
brave torrent
Quick question : Is there a radial formula for an egg shaped curve?
I have heard / found about the universal egg formula, but I need to have a formula using angles theta for a small project.
odd edgeBOT
Quick question : Is there a radial formula for an egg shaped curve?
I have hear...
@brave torrent Has your question been resolved?
brave torrent
.close
brazen raptor
How do you do this question?
odd edgeBOT
How do you do this question?
brazen raptor
I'm not sure where to start
brazen raptor
how would you find g"?
brazen raptor
that would be f(x)
brazen raptor
f'(x) ig
brazen raptor
well cuz how would I find the 2nd derivative if I don't have a function
f'(x) would be the derivative tho...
but idk how to move on from there...
amber schooner
of f sure
but it’s also the second derivative of g
and the question asks for g concave up
hence we need to find the intervals where g’’ > 0
but since g’’ = f’
this is no different than finding where f’ > 0
what does f’ > 0 mean graphically
brazen raptor
the function is increasing
amber schooner
and where is that graphically
brazen raptor
-4 to 1
amber schooner
no
brazen raptor
huh
amber schooner
try again
brazen raptor
so would it be -4 < x < 1 ?
amber schooner
sure that’s one part of the answer
brazen raptor
-4 < x < -2 and 2 < x < 6
just to make sure
f' > 0 is the same as f is concave up?
amber schooner
nope
f’ > 0 implies f is increasing
but in this problem f’ = g’’ hence f’ > 0<—> g’’ > 0
brazen raptor
o ok
amber schooner
so if f’ > 0 then g’’ > 0 so g is concave up
odd edgeBOT
odd edgeBOT
Available help channel!
hallow kraken
odd edgeBOT
pastel orbit
mostly with part b
what have you tried?
hallow kraken
i'm completely lost
for the first part
i use the cross product right
and then ijk then the derivative of x , y and z then lastly function and make it equal to 0
but for B
what does the question even mean
pastel orbit
i use the cross product right
yes, for the first part, you can check if the curl of F is zero
pastel orbit
what does the question even mean
so a conservative vector field can always be written as the gradient of some function f(x, y, z)
the problem is asking you to find such a function f, if F is conservative
hallow kraken
what would be the first step
i know i have use the derivative for the function
but it's asking for the whole rate of change of the function
pastel orbit
what would be the first step
so the gradient of a function comes with three pieces of information
the gradient of a function $f$ is $\grad f = \left(\pdv{f}{x}, \pdv{f}{y}, \pdv{f}{z} \right)$
clever fjordBOT
fallenstars
pastel orbit
therefore, you are looking for a function $f$ such that $$\pdv{f}{x} = \mathbf{F}_x = 2xy, \pdv{f}{y} = \mathbf{F}_y = x^2 + 2yz, \pdv{f}{z} = \mathbf{F}_z = y^2$$
hallow kraken
i think i have an idea but i think it's wrong
clever fjordBOT
fallenstars
hallow kraken
i use the deriviate of fx on each right then make it equal to 2xy?
then i apply derivate of y on all of them and make it equal to x^2 +2yz
but like
what am i solving for
pastel orbit
sorry, I'm back
cold sage
if you look at Fx
then i find f(x,y,z)=x^2y+g(y,z)
and youll get similar for the other components
once you have them youll have to look at them all to determine what those functions like g are
hallow kraken
does it matter the order?
clever fjordBOT
fallenstars
pastel orbit
is our first equation
hallow kraken
2y right
pastel orbit
you can integrate both sides to find part of what f is
hallow kraken
OH
pastel orbit
plus a function that depends only on y and z
then you repeat with the other variables
hallow kraken
plus a function that depends only on y and z
how do you know?
so it would be x^2 * y + K?
pastel orbit
how do you know?
you know how when you integrate, you always have a constant at the end?
and when you differentiate back, you kill the constant?
hallow kraken
you know how when you integrate, you always have a constant at the end?
yes but the depends of y and z
pastel orbit
when we differentiate in terms of x, any function solely in terms of y and z is just 0
pastel orbit
**fallenstars**
so when we integrate this, we can safely assume that the integration constant is in terms of y and z
that is, it is a function of y and z
hallow kraken
ahhh
i see tysm
wait so what does this mean
cause i have the constant K
but what does it change with my methods
pastel orbit
you will use the other two equations to solve for the constant of integration g(y, z)
,, \pdv{f}{y} = x^2 + 2yz \ \pdv{f}{z} = y^2
clever fjordBOT
fallenstars
pastel orbit
these two
pastel orbit
you will use the other two equations to solve for the constant of integration g(...
once you have that, you're done!
you've found an f such that grad f = F
hallow kraken
wait can you give me like 2 mins please
pastel orbit
sure!
hallow kraken
let me try and come up with an answer
I got this right
and I have to solve for the constants?
pastel orbit
and I have to solve for the constants?
hmm, you don't need to integrate all three
just one is enough for now
we're going to do this one step at a time
so like, you know that f(x, y, z) = x^2y + g(y, z) now, right?
you're gonna use the equation $\pdv{f}{y} = x^2 + 2yz$ next to find what $g(y, z)$ is
clever fjordBOT
fallenstars
pastel orbit
and the way to do this is to recognize that since we know $f(x, y, z) = x^2y + g(x, y)$, we have that $\pdv{f}{y} = x^2 + \pdv{g}{y} = x^2 + 2yz$
clever fjordBOT
fallenstars
pastel orbit
so $\pdv{g}{y} = 2yz$
clever fjordBOT
fallenstars
pastel orbit
and now you integrate again, to find g as a function of y and z, plus an integration constant that only depends on z: h(z)
and do that one more time, and you're done 
does that make sense? 
hallow kraken
okay i think i understand it now
let me try one more time
just for confirmation
i'll be fast
pastel orbit
hallow kraken
<:thumbsupanimegirl:1203420374243610665>
okay i think i did it
is the answer 2xy + (y^2)*z - (y^2)z + K?
pastel orbit
is the answer 2xy + (y^2)*z - (y^2)z + K?
this doesn't seem right to me 
hold on
if you differentiate that wrt z, do you get back y^2?
hallow kraken
ah...
pastel orbit
okay, g(x, y) step looks good
g(x, y) = y^2z + h(z)
that's good
I can't really tell what you did at the end
hallow kraken
the end was so confusing im sorry
clever fjordBOT
fallenstars
pastel orbit
you omitted the final = y^2, for some reason
pastel orbit
**fallenstars**
does it make sense where this is coming from? 
hallow kraken
where did that extra y^2 come from
clever fjordBOT
fallenstars
pastel orbit
pastel orbit
h(z) = a constant K, yes!
hallow kraken
oh my
pastel orbit
it happens to not depend on z at all
hallow kraken
it happens to not depend on z at all
how do we know that for certain
pastel orbit
and you can verify that $f(x, y, z) = x^2y + y^2z + C$ indeed has your gradient
clever fjordBOT
fallenstars
pastel orbit
how do we know that for certain
because $\pdv{f}{z} = y^2 + \pdv{h}{z} = y^2 \implies \pdv{h}{z} = 0 \implies h(z) = C$
clever fjordBOT
fallenstars
pastel orbit
no problem 
pastel orbit
so sorry this took so long but i appreciate you so much 🫶
don't worry about it, and have a nice day too!!
you may close the channel if you want to now 
odd edgeBOT
pastel orbit
odd edgeBOT
Available help channel!
primal ruin
odd edgeBOT
primal ruin
This is a test question that we get at home, help is needed 🙏
sage harbor
This is a test question that we get at home, help is needed 🙏
First, you have to find one zero with the Rational Root Theorem
x0 = p / q, where
- p is a factor of -72, the independent term of the polynomial equation
- q is a factor of 1, the coeficient of x^7
So, x0 could be $\frac{\pm1 , \pm2, \pm3, \pm4, \pm6, \pm8, \pm9, \pm12, \pm18, \pm24, \pm36, \pm72}{\pm1}$
clever fjordBOT
carp
sage harbor
You have to test each value and then if it results 0, you found a zero x0
Then, you can divide the polynomial by (x - x0) or use the Briot Ruffini method to factorize the polynomial
primal ruin
wait, but what would happen if I divide that entire equation by x+1
sage harbor
You will have a polynomial of degree 6, that is, the highest value of all the monomials is x^6
And then, you can apply the same thing again
Find a root of the polynomial -> Divide by x - x0 / Briot Ruffini -> Repeat
If you find more than one root, you can describe as (x - x0) . (x - x1) and divide the polynomial, so you will have less work to do
sage harbor
it's different since that x-int is a multiplicity of 2
you mean (x+1)² ?
primal ruin
yes!
sage harbor
Well, then you can divide the polynomial by that, (x+1)² = x² + 2x + 1
It will be a lot of work, but factorizing that polynomial is not simple without tricky methods 
sage harbor
my teahcer hasnt taiught me that yet
Your teacher hasn't taught you the rational root theorem?
primal ruin
no
odd edgeBOT
Available help channel!
low cradle
odd edgeBOT
low cradle
Where is the mistake
undone jay
low cradle
Why should it be 1/ sqrt 2?
quasi sparrow
Why should it be 1/ sqrt 2?
sqrt(sqrt(2)^2) = sqrt(2)
verbal owl
Anyone here who has studied mechanical engineering
odd edgeBOT
Anyone here who has studied mechanical engineering
verbal owl
<#406129911992942593> for engineering servers
Are you good at engineering bro
quasi sparrow
Are you good at engineering bro
Help channels are for math questions
quasi sparrow
https://discord.com/channels/268882317391429632/406129911992942593/9006332800539...
Go ask here
odd edgeBOT
@verbal owl Has your question been resolved?
odd edgeBOT
dense moth
A parabola facing the negative y axis, with vertex at (2,48)
the eqn is given by,
(x-h)² = -a(y-k)
Where (h,k) are coordinates of the vertex, a is the length of latus rectum, and the -ve sign before (y-k) represents it is facing negative y axis.
odd edgeBOT
odd edgeBOT
Available help channel!
acoustic karma
Hi I need help getting started on answering on solving this equation
acoustic karma
|x-9| = |x+6|
I just don't know what to do, I flip the signs of both equations? I create branches of either or or what:(
Plus when I try isolating the variable they cancel out so I'm just left with my sum equaling nothing
signal carbon
|x-9| = |x+6| means that x-9 = x + 6 or x - 9 = -(x+6); convince yourself that this is the correct enumeration of possibilities
the first possibility doesn't really work, so you're left with the second
acoustic karma
but how does the rest of the equation look like?
when i try isolating the variable it just cancels out completely
$\x-9
$\x-9$
clever fjordBOT
oswaldo_something
$\x-9$
```Compilation error:```! Undefined control sequence.
<recently read> \x
l.49 $\x
-9$
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.```
vale vapor
$x-9$
clever fjordBOT
Bonk
acoustic karma
$\ x-9=-x-6$
clever fjordBOT
oswaldo_something
vale vapor
when i try isolating the variable it just cancels out completely
then it means that for that case there is no x
if you were to look at the graphs of |x-9| and |x+6|, then you can see why
we have 3 cases
x>9
-6<x<9
and x<-6
odd edgeBOT
odd edgeBOT
Available help channel!
verbal owl
Help channels are for math questions
Sorry sigma
odd edgeBOT
Sorry sigma
verbal owl
.close
odd edgeBOT
steady tide
odd edgeBOT
Available help channel!
obtuse raven
how do I find F (ping when answer)
odd edgeBOT
how do I find F (ping when answer)
vale vapor
how do I find F (ping when answer)
!status
odd edgeBOT
how do I find F (ping when answer)
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
vale vapor
clever fjordBOT
Arjuna
obtuse raven
At first find the value of $a+(1/a)$
I got 3 for that
vapid kayak
than find $a^3+(1/a^3)$
clever fjordBOT
Arjuna
vapid kayak
Its the value of (1/f) . than find F .
obtuse raven
**Arjuna**
I'm stuck on how to find this
obtuse raven
than find $a^3+(1/a^3)$
$a^3 + 3(a^2)(1/a) + 3a(1/a)^2 + 1/a^3 = 27$
clever fjordBOT
chocolate
obtuse raven
$a^3 + 3a + 3/a + 1/a^3 = 27$
clever fjordBOT
chocolate
vapid kayak
$a^3+(1/a^3)+3(a+1/a)=27$
clever fjordBOT
Arjuna
vapid kayak
you have the value of a+(1/a)
obtuse raven
**Arjuna**
What do I do next from here
vapid kayak
whats the value of $a^3+(1/a^3)$?
clever fjordBOT
Arjuna
obtuse raven
whats the value of $a^3+(1/a^3)$?
$a^3+(1/a^3)=27-3(a+1/a)$
clever fjordBOT
chocolate
vapid kayak
$a^3+(1/a^3)=18$
clever fjordBOT
Arjuna
obtuse raven
$a^3+(1/a^3)=18$
Where did you get 18 from?
vapid kayak
I got 3 for that
dont you get 3?
vapid kayak
$(a^6+1)/a^3=18$
clever fjordBOT
Arjuna
vapid kayak
$a^3/(a^6+1)=1/18$
clever fjordBOT
Arjuna
odd edgeBOT
odd edgeBOT
Available help channel!
mystic saffron
!status
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
!show
odd edgeBOT
Show your work, and if possible, explain where you are stuck.
vale vapor
ah, mb
verbal cobalt
since when is $\sqrt{\frac{\sin ^2 \theta}{\cos ^2\theta}} = \frac{\sin \theta}{\cos \theta}$?
clever fjordBOT
fastrack_and_backtrack
verbal cobalt
this is in reference to your 4th step
viscid flint
always (well, absolute value)
verbal cobalt
precisely my point
it is in fact not always true. so there should be an absolute value there
mystic saffron
I was taught to not consider absolute values in indefinite integration
Only in definite integration
viscid flint
generally we assume the limits of integration are such that those don't matter
verbal cobalt
generally the point of indefinite integration is to provide formulas to use when you are definitely integrating. anyways, if you assume some convenient conditions , what you have written looks right
odd edgeBOT
@mystic saffron Has your question been resolved?
odd edgeBOT
ember oak
This is an application of net forces
You have tension, gravity, and centripetal force
So you should know what the net acceleration should be
You can choose any arbitrary $\theta$, and if you know the height, you can get the radius of travel.
clever fjordBOT
SWR
ember oak
Since your only acting forces are tension and gravity, the acceleration can be calculated
And with acceleration and radius, you get velocity
Then period follows right after
Centripetal acceleration
odd edgeBOT
ember oak
odd edgeBOT
Available help channel!
high sandal
Why do we always to add a limit instead of just integrating straight away?
rapid reef
Sometimes direct substitution leads to an indeterminate form
echo ginkgo
wdym by integrating straight away in the first place ?
how do you do that with an infinite bound ?
high sandal
Without adding a limit, creating an extra variable, replacing it with x and finally replacing it with infinity
@echo ginkgo
echo ginkgo
that's pretty much computing the limit in my book
high sandal
Oh so is it because we dont know exactly what the area will be?
rapid reef
In what kind of situations
E.g. Sin(x) / x
echo ginkgo
Oh so is it because we dont know exactly what the area will be?
well the area might not even exist in some cases if you have an infinite bound yes
rapid reef
Because no limit suggests direct substitution i.e. sin(0)/0 = 0/0 which is indeterminate
echo ginkgo
and how do you substitute directly infinity anyway ?
high sandal
@echo ginkgo By replacing it with x after integration
@rapid reef why 0 and not infinity?
echo ginkgo
<@177516015033384960> By replacing it with x after integration
and how do you evaluate the result you get ?
high sandal
?
You would end up in the same exact situation when using a limit as when you dont use a limit anyway
(F(infinity))
echo ginkgo
yeah so you're just using limits without saying it
rapid reef
<@301654480804642816> why 0 and not infinity?
For the example I gave, inf doesn’t work at all bc of sin
high sandal
@echo ginkgo oh Is it some kinda thing that you cant use infinity in cases where you dont have limits
@rapid reef I get it, but lets say you added a limit, you wouldnt still be able to replace x with infinity
rapid reef
No, but you can employ other methods to determine what the function will converge to as x tends to infinity
echo ginkgo
<@177516015033384960> oh Is it some kinda thing that you cant use infinity in ca...
F(infinity) is just bastardized notation for a limit is what I'm saying
but yeah if the limit doesn't exist, you'll have trouble getting a value out of that
high sandal
So really its a notation problem
Guys I learnt a lot, thx both of you
@echo ginkgo and @rapid reef
.close
odd edgeBOT
odd edgeBOT
Available help channel!
fiery patio
hey anyone can teach me
odd edgeBOT
hey anyone can teach me
fiery patio
I need help in understanding 'Solving algebraic equations' i cant understand some of it
fair summit
I need help in understanding 'Solving algebraic equations' i cant understand som...
Alright. Firstly, what do you not understand?
fiery patio
sometimes my teacher uses the sum of the but theres no parenthesis but sometimes too if my teacher uses the sum of the there is a parenthesis
the word "The sum of the"
rapid reef
What?
fair summit
sometimes my teacher uses the sum of the but theres no parenthesis but sometimes...
Sum of the what?
fiery patio
and the question wiat imma give example
The sum of two numbers is 15. If one of the numbers is 7 theres no parenthesis if i write that in Numbers
fair summit
The sum of two numbers is 15. If one of the numbers is 7 theres no parenthesis i...
How would you write it in notation?
fiery patio
𝑥
+
7
15
𝑥+7=15
no parenthesis
even i used the word The Sum
nvm you know what lets just move on the most thing that idk that my teacher gave too me that i dont even know and didint teach to me
3.5p=10.5p can you please give the answer and explain?
btw its still Solving Algebraic Equations
fair summit
3.5p=10.5p can you please give the answer and explain?
3.5p = 10.5p? That's not right.
fiery patio
yep thats right
fair summit
Did you forget something?
fair summit
3.5p=10.5
Oh, I see.
I can tell you how to solve it, and you work out the answer yourself. OK?
fiery patio
okay
fair summit
Now, this is actually quite simple.
To solve:
3.5p = 10.5,
You divide both sides by 3.5.
fiery patio
ye
fiery patio
oh
im wrong ig
lets continue tommorow
im sleepy
sowwy
cuz im answering this 1 to 40 question
fair summit
Oh, I see. But we have to finish this question first...
fiery patio
oh ok
fair summit
3.5p / 3.5 = 10.5 / 3.5
So, what happens when you evaluate this?
fiery patio
the answer will show and it will be 3
fair summit
the answer will show and it will be 3
OK, good job. We'll continue this tomorrow. Most probably won't be in the same channel though.
fiery patio
okie:>
odd edgeBOT
@fiery patio Has your question been resolved?
storm pebble
hello, can anyone help me in this problem?
odd edgeBOT
hello, can anyone help me in this problem?
storm pebble
all that i am sure of is variable a and g
a would be 162 and g would be 55 because of supplementary angles
im really not sure about the rest, i dont know where to go there from now
especially the c, d, and f parts
odd edgeBOT
@storm pebble Has your question been resolved?
karmic stirrup
If i have a coordinate on a circle and i want to find the tangent line to the circle. and i only know the point's location and the radius of circle and its center. How do it do it
mystic saffron
If i have a coordinate on a circle and i want to find the tangent line to the ci...
-
Find the slope of the radius: (y2 - y1) / (x2 - x1)
-
Find the slope of the tangent: -1 / slope of the radius
-
Use the point-slope form: y - y2 = tangent slope(x - x2)
karmic stirrup
Ok yea that makes sense i figured it out. Ty
odd edgeBOT
@karmic stirrup Has your question been resolved?
Available help channel!
Available help channel!
keen lily
anyone help me solve this?
odd edgeBOT
anyone help me solve this?
mystic saffron
anyone help me solve this?
What's the position of the test charge ?
keen lily
What's the position of the test charge ?
there's no given position, is it possible to be just at the origin?
mystic saffron
Yeah?
We can find the electric field if we know that it's position is at origin
keen lily
Yeah?
We can find the electric field if we know that it's position is at origin
I believe it's just at the origin
odd edgeBOT
@keen lily Has your question been resolved?
keen lily
<@&286206848099549185>
odd edgeBOT
@keen lily Has your question been resolved?
desert dome
odd edgeBOT
desert dome
how do you do this
vale vapor
!show
odd edgeBOT
Show your work, and if possible, explain where you are stuck.
vale vapor
can you show how you arrived at your current answer?
desert dome
@vale vapor
vale vapor
<@946543471668379678>
no need to ping, ill see it dw
desert dome
ok
vale vapor
yes, and fill it in
desert dome
vale vapor
so close
remember that 1/5 at the start?
and it looks nicer if you put it into a singular fraction
desert dome
and it looks nicer if you put it into a singular fraction
ok
odd edgeBOT
@desert dome Has your question been resolved?
odd edgeBOT
odd edgeBOT
Available help channel!
minor quiver
Can someone tell me if this is completed? and if it's not what is it showing?
chilly ravine
Can someone tell me if this is completed? and if it's not what is it showing?
Where exactly does the question start
minor quiver
(4+-3-7)/2
chilly ravine
oh mb I didn't see the squiggly lines
real musk
Can someone tell me if this is completed? and if it's not what is it showing?
Ur correct
minor quiver
Thanks, I was looking through my teachers video and not sure if I had to solve
real musk
I like how you solved it step by step to avoid confusion 👍
odd edgeBOT
odd edgeBOT
Available help channel!
vast dawn
Hey guys any help with the following:
I need to find an example for a function g: $R to R$ that satisfies the following conditions:
a. g is bounded, b. $lim_{x\to 0}g(x) doesn't exists$, c. $g(x) \neq 0 \forall x\neq 0$
my example was g(x) = sin(1/x)
the second question is given $f(x,y) = (x^2+y^2)g(x)g(y)$ now i need to show that $\lim_{(x,y) \to (0,0)} f(x,y)=0$ but the limits $\lim_{x\to 0}\lim_{y\to 0} f(x,y), \lim_{y\to 0}\lim_{x\to 0} f(x,y)$
clever fjordBOT
st123
real musk
?
cold swift
XD
the original message got deleted
a guy came on here telling st123 to give him their cashapp or paypal
one sec i'll find the user for you
@low locust do you remember it?
had a yellow discord pfp
gaunt spindle
cold swift
right right
odd edgeBOT
@vast dawn Has your question been resolved?
clear rune
I have a question regarding basic plane geometry.
While reviewing lessons for a test, I redid this problem and ran into an issue in understanding my reason for why angle 1 is equal to angle 2, considering the sparse givens only dealing with the lengths of some lines. I double checked it by the official answer source, and it confirmed my answer.
They expected me to give a reason as to why angle 1 was equal to angle 2 by way of vertical angles being equal, yet I couldn’t see why it was reasonable to assume that lines AMB and CMD were straight lines and not broken lines as you see in a hypothetical diagram below
I know they warned me not to make assumptions just by observation of the diagram, but how was I supposed to know that the two lines crossing point M were straight and not broken?
odd edgeBOT
@clear rune Has your question been resolved?
clear rune
http://aleph0.clarku.edu/~djoyce/java/elements/bookI/propI15.html
Thank you for the help, but I noticed that the example stated that the lines are two straight lines as a given, and yet my problem does not elaborate that
The only givens are that line AM is equal to line BM, and that line CM is equal to line DM
NOT that line AB or line CD is straight
ember oak
The only givens are that line AM is equal to line BM, and that line CM is equal ...
I believe you are to assume CD is a straight line. Otherwise, the problem cannot be solved
It does not say anywhere that "CD and AB intersect at M"?
or anything like that?
clear rune
or anything like that?
No, I checked
clear rune
I believe you are to assume CD is a straight line. Otherwise, the problem cannot...
Well, if the answer is that for this problem, I can judge based on visual observation, I can treat this as a clerical error and pretend that they did
This is clearly an exception to the rule
So I thank you for your time
.close
odd edgeBOT
odd edgeBOT
Available help channel!
ebon island
sqrt((x-3)/2)+sqrt(2x)=sqrt(x+3)
odd edgeBOT
sqrt((x-3)/2)+sqrt(2x)=sqrt(x+3)
ebon island
i tried moving sqrt((x-3)/2) and sqrt(x+3) together and using the a^2+2ab+b^2 thingy
vale vapor
$\sqrt{\frac{x-3}{2}}+\sqrt{2x}=\sqrt{x+3}$
clever fjordBOT
Bonk
ebon island
yes
i then got sqrt((x-3)/2) times sqrt(x+3) = (x-3)/-4
I then squared all sides to get ((x-3)/2)(x+3)=(x^2-6x+9)/16
I multiplied to get ((x-3)(x+3))/2 = ((x-3)(x-3))/16
I cancelled and reached the ending of 16(x+3)(x-3)=2(x-3)(x-3)
cancelling the rest out would result in the answer of X= -27/7
Now my answer, when reput into the original equation
is incorrect
Im stuck help
<@&286206848099549185>
dim sandal
i tried moving sqrt((x-3)/2) and sqrt(x+3) together and using the a^2+2ab+b^2 th...
What did you do?
ebon island
What did you do?
well if your referring to my work I described it above
if your referring to that then I tried making a perfect square trinomial on the two terms
if your referring to step 1
It was a^2+b^2=a^2+2ab+b^2
ocean bramble
you have roots. Usually, you want to square both sides when you have roots
in this case, that will result in you having one root instead of 3
then, you get said root in one of the members, and the rest on the other, and square both sides again. Then you wont have roots, and you'll be left with a second degree equation.
Is this enough information?
ebon island
then, you get said root in one of the members, and the rest on the other, and sq...
Im having trouble understanding the correct step to do after finding the root
because If I plug in this root I have then its incorrect
its extrenious
ocean bramble
okay, my mistake.
When i said "root" in my messages here, i dont mean as "root of the equation", i meant it as a square root
you currently have something of the form:
a + b = c
If you square both sides, you will get:
a^2 + b^2 + 2ab = c^2
ebon island
yes
ocean bramble
so there, the only term that will still be a square root will be the "2ab" that i termed there
ebon island
yes
ocean bramble
obviously, that line leads to:
2ab = c^2 - a^2 - b^2
Which when you square again, will have no square roots, and (if i didnt fuck it up somewhere) will be a 2nd degree equation
Can you solve it with this?
ebon island
yes
it turns out I just did my work really messy
my apologies for asking this dumb question
the answer however, is 3?
man this question took a bit of brainpower
.close
odd edgeBOT
ebon island
ok I have another one, for the sake of space I dont want to use another channel
(6xy^3)/5throot(162x^2y^3)
we have to put this into simplest form
I tried rationalizing the denominator
to get 6y^2*5throot(162^4x^3y^2)
But I got it wrong
Help
ocean bramble
.reopen
odd edgeBOT
✅
wanton sierra
(6xy^3)/5throot(162x^2y^3)
$\frac{6xy^3}{\sqrt[5]{162x^2y^3}}$
clever fjordBOT
Karma
wanton sierra
Remember that:
$\frac{6xy^3}{\sqrt[5]{162x^2y^3}} = \frac{6xy^3}{(162x^2y^3)^\frac{1}{5}}$
And:
$(ab)^c = a^cb^c$
clever fjordBOT
Karma
wanton sierra
@ebon island
ocean bramble
i'm not seeing how doing anything there is gonna make it simpler honestly
i would consider the one on the lft the simplest for already
ebon island
i mean
I also dont see a way other than rationalizing the denominator
ill see from my teacher
but in the meantime
I really have no idea if this is the appropriate use for these channels
but I have yet another question I am stumped on
y=(x+1)/(sqrt( x^2-9x^4))
we need to find the domain
and I have identified the critical points of 0,-1/3, and 1/3
however, they all test negatively
I cant find the x's that work with this
cause none of them do
odd edgeBOT
Available help channel!
languid pier
odd edgeBOT
languid pier
sorry wrong picture
can someone help me with 17?
so like using the base change formula
it would be log2/log3 * 2log2/3log2 * 3log3/4log2
i got 2log3/4log2
my classmates are saying the answer is 1/2
am i just wrong or is 2log3/4log2 =1/2?
oak crown
it would be log2/log3 * 2log2/3log2 * 3log3/4log2
$\frac{\log 2}{\log 3}\cdot\frac23\cdot\frac{3\log 3}{4\log 2}$
clever fjordBOT
;(
oak crown
yes your classmates are right
odd edgeBOT
odd edgeBOT
Available help channel!
tribal fossil
when is lim f(x)^2 = (lim f(x))^2 ?
odd edgeBOT
when is lim f(x)^2 = (lim f(x))^2 ?
tribal fossil
or for any c not just 2
frigid canopy
If $lim f(x)$ is defined then $limf(x)^2$ is defined assuming this isn't a rational function with denominator being 0
clever fjordBOT
What a wonderful world!
tribal fossil
when can lim f(x) not be defined and lim f(x)^2 be defined?
odd edgeBOT
@tribal fossil Has your question been resolved?
odd edgeBOT
odd edgeBOT
Available help channel!
cursive pewter
How do I find the integral of sin⁴x dx using (1-cos²x)² rather than the usual (1/2(cos2x+1))²
wooden gorge
I'll tell you a trick
cursive pewter
I'll tell you a trick
Ok
wooden gorge
,w int sin^4 x dx
clever fjordBOT
wooden gorge
should be 3/8 x instead of 1/8 x
cursive pewter
should be 3/8 x instead of 1/8 x
Where does it come from
wooden gorge
cursive pewter
Ohhhh let me try again with + and see
So I got -3/16 sin2x+ 3/8x
Is that right @wooden gorge
Is -3/16 sin2x+ 3/8x the same as 3/8x- 1/4 sin2x + 1/32 sin4x for the integral of sin⁴x <@&286206848099549185>
odd edgeBOT
@cursive pewter Has your question been resolved?
wooden gorge
Is -3/16 sin2x+ 3/8x the same as 3/8x- 1/4 sin2x + 1/32 sin4x for the integral o...
No
And if it's so difficult, you could instead go sin ⁴ x = acos 4x + bcos 2x + c
Solve for a, b, c
cursive pewter
And if it's so difficult, you could instead go sin ⁴ x = acos 4x + bcos 2x + c
What is this based on
cursive pewter
No
I thought different methods lead to the same answer
Could I have made an error?
wooden gorge
Yes
cursive pewter
Or maybe the answers are the same but in different forms?
wooden gorge
Clearly, you'd be having a cos² 2x term which then leads to a cos 4x term, but you're missing it
Also, cos² 2x = (1 + cos 4x)/2 not (1 + cos 2x)/2
cursive pewter
cursive pewter
Also, cos² 2x = (1 + cos 4x)/2 not (1 + cos 2x)/2
I didn't have that term anywhere
cursive pewter
I said cos² 2x = (1 + cos 4x)/2
Okay
odd edgeBOT
@cursive pewter Has your question been resolved?
cursive pewter
Thank you so much @wooden gorge
quick sand
Can someone help me quickly prove $\frac{1}{n+1}=\sum^{n}_{p=0}\binom{n}{p}\frac{(-1)^p}{p+1}$?
clever fjordBOT
Felix.5
shy smelt
Try expanding the binomial coefficient and get rid of the p+1 in the denominator
quick sand
I don't see how $\sum^{n}_{p=1}\frac{(-1)^p}{(p+1)!(n-p)!}=\frac{1}{(n+1)!}$
clever fjordBOT
Felix.5
shy smelt
$\sum^{n}_{p=1}\frac{n!(-1)^p}{(p+1)!(n-p)!}=\frac{1}{(n+1)}$ this, right?
clever fjordBOT
Jelle
shy smelt
what you want to prove now
You can multiply top and bottom of the fraction on the LHS with n + 1, and move the (n + 1) in the denominator out of the sum
odd edgeBOT
@quick sand Has your question been resolved?
quick sand
You can multiply top and bottom of the fraction on the LHS with n + 1, and move ...
I don't see how $\sum^n_{p=0}\frac{(-1)^p (n+1)!}{(p+1)!(n-p)!}=1$ helps, maybe doing induction would be easier.
clever fjordBOT
Felix.5
shy smelt
You can change it back to $\sum_{p=0}^n \binom{n+1}{p+1}(-1)^p$
clever fjordBOT
Jelle
clever fjordBOT
Jelle
quick sand
if thats fact I see it. But for a follow up question I need to calculate $\sum^{n}_{p=0}\binom{n}{p}\frac{(-1)^p}{p+2}$
clever fjordBOT
Felix.5
shy smelt
Hmm, not sure. Have you had these types of problems before? Did you do them combinatorically or algebraically?
odd edgeBOT
@quick sand Has your question been resolved?
wispy geode
ive got a question
odd edgeBOT
ive got a question
wispy geode
$f(x) = 1.08x+100000 \overbrace{\to}^{\text{?}} \boxed{f(x,n) = \overbrace{f(f(f(\cdots f\relax(x)}^{\text{n}}}$