why not?
a_n = a_1*r^n-1 is the nth term formula for gerometric series
#help-17
strong grove
warped relic
you don't need succeeding terms though
for r>1
sum of first n terms = a(r^n - 1)/(r-1)
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tribal holly
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tribal holly
Can I simplify it to 2 x 10^5 x 8 x 10^3 x 1 x 10^2?
And add the exponents togheter and multiply 8 by 2 and get 16 x 10^10
My book says answer is 2,5x10^9
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@tribal holly Has your question been resolved?
hasty pulsar
Can I simplify it to 2 x 10^5 x 8 x 10^3 x 1 x 10^2?
how did u get that
dark kiln
you can't
tribal holly
how did u get that
they was ^-x
so i put them from division
to top
and positive ^x
dark kiln
1 / 8(10^−3) doesn;t become 8(10^3)
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@tribal holly Has your question been resolved?
tribal holly
.close
manic prism
i have this excel data. the hours have different column than the date month and time.. the excel have about 130445 values. i want o calculate daily , weekly and monthly data. please enlighten me with a formula
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i have this excel data. the hours have different column than the date month and ...
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ivory trail
I have a question regarding improper integrals on a range on let's say 0 to 1, and where the integrand is not integrable by hand. How would you approach this? Let's say, is the integrand (sin x)/x^2 convergent or divergent on the range 0 to 1?
vocal sleetBOT
I have a question regarding improper integrals on a range on let's say 0 to 1, a...
hard atlas
try to compare it to a function you know about
here for example it probably helps to write it as sin(x)/x * 1/x
where sin(x)/x is continuous on the whole interval
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@ivory trail Has your question been resolved?
ivory trail
where sin(x)/x is continuous on the whole interval
That's great advice, however how do I decide whether it is divergent or convergent over such a short span ?
hard atlas
if sin(x)/x is continuous over the closed interval, then its also bounded. so the important part here is the 1/x
what do you know about the integral of that
ivory trail
Not sure what you're getting at, as x approaches 0 then 1/x approaches infinity, and vice versa
The integral is ln |x|
Which isn't defined at 0
hard atlas
so the integral of 1/x from 0 to 1 diverges
I just realized you dont even need to write it as sin(x)/x * 1/x, writing it as sin(x)*1/x^2 also works
but whatever
sin(x)/x is bounded from below. lets say sin(x)/x > c for all x in [0,1]
which means that sin(x)/x * 1/x is always at least c*1/x
storm forum
I need a set of example proofs for limits that do not exist.
ivory trail
bruh
ivory trail
sin(x)/x is bounded from below. lets say sin(x)/x > c for all x in [0,1]
Ah I don't understand : (
ivory trail
so the integral of 1/x from 0 to 1 diverges
This however made a lot of sense
I think
I am clearly missing something abt improper integrals
hard atlas
have you graphed the function
ivory trail
I have
hard atlas
do you know what it means if the integral diverges
ivory trail
But I wanna learn to solve them without the graph
hard atlas
well for 1/x you can just integrate it. like you did
ivory trail
do you know what it means if the integral diverges
I only know that if x approaches infinity and y(x) approaches a number L then it converges
If it does not approach a number L then it diverges
I guess the same is true as it approaches any number
Would you take a look at another integral and tell me how you would solve it ?
hard atlas
dont ask to ask
hard atlas
hmm
the sin(x) like before is bounded, so intuitively we can ignore it a bit
then its roughly about 1/(1+x)
ivory trail
sso your answer is converges ?
hard atlas
well does the integral of 1/(1+x) converge?
ivory trail
No it ddiverges
But I can't for the life of me understand the reasoning behind it
This is how the answer is explainedd: For all x => 1.
(2+sin x)/(1+x) => 1/(1+x) => 1/(2x) which means it is divergent
ivory trail
great
hard atlas
and if x>=1, then 1+x<=x+x, so 1/(1+x) >= 1/(2x)
alternatively you could also integrate 1/(1+x)
the point is that they already know either way that it diverges
whether 1/(1+x) or 1/(2x)
ivory trail
and because the integral of 1/(1+x) diverges that means because of the inequality that the first function also ddiverges
It makes a ton of sense
ivory trail
Idk why I haven't run into this
In the calc book
Well I found where I can readd more about it, thanks for your help this was a pain trying to figure out
mellow geode
helo
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lilisworld
mellow geode
[ V = L^T ]
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lilisworld
mellow geode
[ V = D^{-1} U ]
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lilisworld
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@mellow geode Has your question been resolved?
mellow geode
?
scarlet shadow
4
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@mellow geode Has your question been resolved?
faint carbon
what did i mess up?
vocal sleetBOT
what did i mess up?
faint carbon
nvm
math error
why wouldnt this work?
this only gets worse
Differentiate integrate
- e^12x x dx
- e^12x *12 x^2 /2
ohhhhh
i did a typo
1/144
what should i do
diff 64x?
vocal sleetBOT
@faint carbon Has your question been resolved?
faint carbon
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faint carbon
im stuck
wide lance
im stuck
sometimes you need to do integration by parts multiple times over
and sometimes a certain part of the integral keeps coming back
and then you substract that from your original integral
but first work out the integral e^4x 4cos4xdx
faint carbon
but is it good so far?
wide lance
but is it good so far?
lemme do it on a piece of paper rq
faint carbon
ok
wide lance
i don't think the 4 at the front needs to be there
faint carbon
i struggle with picking what to integrate
wide lance
cus you already used it to integrate 4e^4xdx
wide lance
i struggle with picking what to integrate
yeah this can happen at the beginning
if one doesn't work, just choose the other 😭
faint carbon
i don't think the 4 at the front needs to be there
but i factored it?
wide lance
but i factored it?
well you also used it to integrate
so either you factor it or you use it to integrate 4e^4xdx
wide lance
apologies if i'm wrong
faint carbon
apologies if i'm wrong
Factor the 4
4 integral e^4x sin4x dx
Differentiate integrate
- sin4x e^4x
- 4cos4x 1/4 e^4x
4(1/4 e^4x sin4x - integral 1/4 e^4x 4cos4x)
ye i made a error
wide lance
yeah you might as well put the 4 back in now 😭
which makes e^4x sin4x - integral e^4x 4cos4x dx
faint carbon
which makes e^4x sin4x - integral e^4x 4cos4x dx
should i differentiate 4cos4x
?
Factor the 4
4 integral e^4x sin4x dx
Differentiate integrate
- sin4x e^4x
- 4cos4x 1/4 e^4x
4(1/4 e^4x sin4x - integral 1/4 e^4x 4cos4x)
e^4x sin4x - integral e^4x 4cos4x dx
Now do it again
Differentiate integrate
- 4cos4x e^4x
- -16sin4x 1/4 e^4x
- -64cos4x stop
1/4 e^4x 4cos4x + integral 1/4 e^4x 16sin4x
e^4x sin4x - (1/4 e^4x 4cos4x + integral 1/4 e^4x 16sin4x)
it wont end lol
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@faint carbon Has your question been resolved?
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@faint carbon Has your question been resolved?
vast shale
Can anyone give me a hard factorization to practice?
vocal sleetBOT
Can anyone give me a hard factorization to practice?
pale perch
at what level
vast shale
like 5x³ + 2x² + 5x + 5
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@vast shale Has your question been resolved?
livid tapir
vast shale
https://mathnovice.com/algebra/factoring-cubic-polynomials-methods-examples/#que...
Thx
sterile thorn
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sterile thorn
Is this correct?
vocal sleetBOT
@sterile thorn Has your question been resolved?
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river spear
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river spear
!status
vocal sleetBOT
What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
1
sage wind
First what are all the roots of f'(x) that lie in the interval [0,10]
river spear
the roots are the critical points right
sage wind
Yes
Not always
The roots of f' are the critical points
The roots of a function g(x) in general are the values of x that satisfy the equation g(x)=0
river spear
yea
sage wind
So the roots of f'(x) are the values of x that satisfy f'(x)=0 which are critical points of f
river spear
so i have to have find what x make f'(x)=0
river spear
since the question is allowing calculators
i can use a graphing calculator right
it would be 0, pi, 2pi, 3pi
sage wind
Correct
Now what is the variation of the sign of f'(x) according to the graph in your hands
river spear
wdym?
i dont understand your question
you mean the slope of the graph
from [0,10]
?
sage wind
My question is when is f' positive and when it is negative
Check this for the interval [0,10]
river spear
its positive from (0,1.84) (4.82,7.92)
and negative from (1.84,4.82) and (7.92,10)
idk if that answers your question
sage wind
❌
What is the meaning of a function being positive or negative graphically
You still there
@river spear
river spear
yea
river spear
What is the meaning of a function being positive or negative graphically
the slope?
sage wind
The slope of what
sage wind
You mean to say the slope of tangent so the derivative ??
river spear
yea
sage wind
Wrong
The sign of the derivative determines if the function is increasing decreasing or having a critical point
If you want to find the sign of f'
Then you should look when it is above the x-axis ,when it intersects it and when it is below it
Why because the x-axis has equation y=0
here y=f'(x) right
river spear
yes
sage wind
Ok
So when is f'(x) positive and when it is negative ?
in other words when is f'>0 and when is f'<0
Use the graph
river spear
isnt that what i put earlier tho
i put the intervals of when it was increasing and decreasing
sage wind
No what you put earlier was when f' was increasing and when f' was decreasing
So you basically got when the slope is positive and when the slope is negative
river spear
yea
sage wind
You don't want the sign of the slope of f'
You want the sign of f' itself
So go to the graph check when the curve of f' is above x axis and when it is below it
Then tell me if it is the same as before or no
river spear
so it would be (0,pi) and (2pi,3pi) for positive and (pi,2pi) and (3pi,10) for negative right?
sage wind
Yes
Ok now
we know that the critical points of f are the points with abscissas x=0,π,2π,3π right
And we know the sign of f'
river spear
what is abscissas
sage wind
x coordinate
a point in xy plane is determined by (x,y) x is called abscissa and y is called ordinate
sage wind
From the sign of f' we know the sign of the slope of the curve of f right
river spear
yea
sage wind
So we know when f is increasing and when it is decreasing
river spear
yes
sage wind
so it would be (0,pi) and (2pi,3pi) for positive and (pi,2pi) and (3pi,10) for n...
Ok over these intervals when is f increasing and when it is decreasing
river spear
thats what i put earlier right
increasing from (0,1.84) (4.82,7.92)
and decreasing from (1.84,4.82) and (7.92,10)
sage wind
so it would be (0,pi) and (2pi,3pi) for positive and (pi,2pi) and (3pi,10) for n...
I want it for f over these intervals
river spear
how do i do that if i dont know the function of f
sage wind
You don't need to
You need to know sign of f'
f is increasing when f'>0 and f is decreasing when f'<0
And f has critical points when f'=0
Thats why I asked you to get sign of f'
sage wind
so it would be (0,pi) and (2pi,3pi) for positive and (pi,2pi) and (3pi,10) for n...
Use this along with what I just said
river spear
isnt it what you just said
sage wind
What did I say
river spear
f is increasing when f'>0 and f is decreasing when f'<0
this
sage wind
Yes
When does that happen
Tell me the intervals where f is increasing and the ones where f is decreasing
@river spear
Sorry for the ping but I gtg soon it's too late in my time and battery if phone is dying
river spear
its alr
sage wind
So what did you get
river spear
wouldnt the intervals where f' is increasing be the same intervals where f is increasing?
sage wind
No
river spear
but f' is the slope of f
sage wind
The intervals where f is increasing are the same intervals where f'>0
The slope increasing doesn't mean the slope is positive
It can increase from -10 to -2 for example
sage wind
It can increase from -10 to -2 for example
It is increasing here but it is negative
To know whether f is increasing or decreasing we care for the sign of f'
We care if f'>0 or f'<0 not whether f' is increasing or f' is decreasing
sage wind
Exactly you need to check if f' changes from positive to negative or from negative to positive
In either case it will pass through a 0
But the difference is whether it is a minimum or maximum
If it changes from negative to positive then it is minimum for curve of f
If it changes from positive to negative then it is a maximum for curve of f
Now I gtg sleep byee
gentle flint
vocal sleetBOT
gentle flint
i need help on #3 and #5
ebon rapids
Were you able to solve #4? Because solving #3 is basically identical
gentle flint
i did, but i got 14 and it was marked wrong.
gentle flint
twin meteorBOT
CST (please ping when replying)
ebon rapids
You’re good
gentle flint
okay! what about #5?
for that one i got three but i think its because i forgot how to find the inverse of a function
ebon rapids
What inverse did you get
gentle flint
i just said -(2*-2+1)
twin meteorBOT
CST (please ping when replying)
ebon rapids
show your work
ebon rapids
not how inverses work
ebon rapids
if y=f(x), and f is one-to-one, then $f^{-1}(y)=x$
twin meteorBOT
CST (please ping when replying)
gentle flint
okay i tried putting it into desmos because i couldn't do it algebraic
but i got -1
ebon rapids
**CST (please ping when replying)**
Well, you can use this if you don’t want to solve for the inverse formula
twin meteorBOT
CST (please ping when replying)
gentle flint
OH
okay i got -1.5
is this correct?
if its not im going to do a backflip into the atlantic ocean
ebon rapids
It is correct
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tranquil lodge
fallen sandal
vocal sleetBOT
fallen sandal
Idk how to make the system of equations
hasty lark
!show
vocal sleetBOT
Show your work, and if possible, explain where you are stuck.
hasty lark
You should have a diagram to work from!
hasty lark
Draw a picture of the situation described
hasty lark
Label key elements with variables
fallen sandal
Seabed on other
hasty lark
List what you know
fallen sandal
Idk how to lable
hasty lark
You should send this to me
You know how to label. You just give a letter to a quantity of interest
fallen sandal
You know how to label. You just give a letter to a quantity of interest
Plz help
Do o lable the average speeds
hasty lark
Mhmm, you are missing air-water interface
fallen sandal
Idk how big to make each section
hasty lark
It doesn't matter
hasty lark
Look at your diagram. Are there distances that you don't know but want to know?
Times? etc
just start naming stuff
hasty lark
good! now write down letters for each of those on your diagram
fallen sandal
Idk
fallen sandal
those are the times?
Yes
hasty lark
name em and come up with a relationship
fallen sandal
In seconds
hasty lark
good
fallen sandal
IDK how to name them
twin meteorBOT
Xenophon
hasty lark
this is the straight line distance of the air segement of the fall
fallen sandal
Uhhh i think I'm only supposed to use 2 variables idk
hasty lark
no!
Use as many variables as you need
They will be eliminated as you solve the problem
fallen sandal
ok so d_water too I guess
hasty lark
yes!
fallen sandal
distances
hasty lark
You have an equation with time and an equation with distances
fallen sandal
ok now what
fallen sandal
hasty lark
If you can solve the problem with two variables, then more power to you
ok, speed is distance travelled over a timeframe
fallen sandal
So cool
fallen sandal
Yes
hasty lark
$s=\Delta d / \Delta t$
twin meteorBOT
Xenophon
hasty lark
there
fallen sandal
So wat
hasty lark
delta means change in
fallen sandal
Ik
hasty lark
Now, you have two distances, and two times
If you look back at the question, you're also given two speeds
You can use the speeds to write two new equations
fallen sandal
Again😭
hasty lark
How old are you?
fallen sandal
15
hasty lark
Ok, so you may not know, but math is kinda full of equations
it's almost the point of it
fallen sandal
ok wat the next step
hasty lark
You can use the speeds to write two new equations
do you have the equations with speeds?
fallen sandal
No
hasty lark
hasty lark
which one?
hasty lark
On your diagram, did you write down the speeds next to the relevant section?
fallen sandal
Yes
hasty lark
so $s_{air} = ?$
fallen sandal
So like
twin meteorBOT
Xenophon
fallen sandal
Ok
hasty lark
You should soon have 4 total equations
fallen sandal
What does this equal
hasty lark
**Xenophon**
this?
fallen sandal
Idk what to make equation of
fallen sandal
we know s_air
No
hasty lark
yes, the problem gives it
fallen sandal
Wait what is s
hasty lark
speed in the air
hasty lark
yep, so that would give you 16m/s = d_air/a
where a is the time in the air
Write a similar equation for the water and send me a picture of all your equations
and your diagram
hasty lark
ok, you are like 90% of the way there
The key thing before you start trying to solve is to count your equations and your unknowns
How many equations do you have?
fallen sandal
Oh accidentally wrote s with the 16m
fallen sandal
How many equations do you have?
Uhh 4
hasty lark
and how many unknowns?
fallen sandal
6
hasty lark
no, only 4
hasty lark
a, w, $d_{water}, d_{air}$
twin meteorBOT
Xenophon
fallen sandal
Dwater
hasty lark
m and s are units of measure
fallen sandal
e
hasty lark
meters and seconds
hasty lark
no
fallen sandal
ok now what
hasty lark
they are just like miles or hours
now, since the number of unknowns and the number of equations is equal, you can solve for everything using algebra
You want A and w, so try to solve for them
fallen sandal
How this look so weird
hasty lark
The speed equations can be used to write the distances in terms of speed*time
hasty lark
yes
fallen sandal
Why didn't we just use that in the first place😭 😭 😭 😭 😭
hasty lark
You could have, but did you know that just by reading the question?
You still need to solve for a and w
hasty lark
use the two remaining equations
and the d_air=16a relationship
and the d_water=3w equation
fallen sandal
but mine doesn't say that
It says d_air/a=16a
I meant
ok that
NO
WHY
oh
ok
It has that
Not wat u wrote
Fr
fallen sandal
i don't have thar
hasty lark
yes, you do! it's the same as 16 = d_air/a
fallen sandal
u just said speed*time is the same as the distance thingy
So I changed it
Cuz it was same
I didn't know we got rid of the a divisor thing
hasty lark
It's one equation, I just wanted you to solve for the distance
Then you can plug the distance into the other equation involving the distances
fallen sandal
So does 16a+3w=127
hasty lark
yes
now you have two equations with two unknowns
You can solve by elimination or substitution
hasty lark
why are you sad, you're almost done
hasty lark
I think it's 91 instead of 90
fallen sandal
oh
hasty lark
but you don't need to simplify further
fallen sandal
Yeah I messed up fr
hasty lark
fallen sandal
Is the w correct
hasty lark
12-7=?
hasty lark
a+w=12
hasty lark
yep
hasty lark
sigh
Slow is smooth. Smooth is fast.
And slow is better than never.
The way I showed you is the same as this solution. I just showed every step so that you actually learn the method
fallen sandal
Uhh only thing I learned was speed*time is distance
I knew everything already but I didn't know how to write the distances as like into an equation
That's y I kept saying idk how to label it
hasty lark
Honestly, you're young so I won't take it personally, but if someone takes 30-40 minutes to help you, you should probably not then go on to talk about how slow their method is.
If you don't know how to label it, you're very far from worrying about how fast the solution is
craggy mango
vocal sleetBOT
craggy mango
So, I did the work and got c = 3/16
But Im not sure if thats right?
I had the same problem earlier just different numbers, and did the same process, but that answer was wrong, so thats why Im confused
tribal pumice
I had the same problem earlier just different numbers, and did the same process,...
Can you show your work
craggy mango
So what I did was
f'(x) = 2cx - 2x^-3
Then I differentiated again for f''(x):
f''(x) = 2c + 6x^-4 or 2c + 6/x^4
After this, I plugged in 2 into the second derivative for x
And solved for c
2c + 6/x^4
2c + 6/(2)^4
2c + 6/16
2c = -6/16
c = -6/16/2
c = -6/32
c = -3/16 ```I are not sure this be right
tribal pumice
I are not sure this be right
This looks good, please watch out for the 
vocal sleetBOT
@craggy mango Has your question been resolved?
vestal mango
How do i calculate a by hand (question is attached)
vocal sleetBOT
How do i calculate `a` by hand (question is attached)
twin meteorBOT
PajamaMamaLlama
soft walrus
simple letting A=90, gives you the Pythagorean Theorem :)
vestal mango
simple letting A=90, gives you the Pythagorean Theorem :)
Thank you! That was on my reference sheet, now I now were to apply it!
soft walrus
Thank you! That was on my reference sheet, now I now were to apply it!
it's an important one too, and remember if you have three piece of information about a triangle (one angle and two sides) you can get everything else :)
including all the other sides/angles/area/perimeter
vestal mango
it's an important one too, and remember if you have three piece of information a...
I knew that, thank you for the help
.close
vocal sleetBOT
soft walrus
I knew that, thank you for the help
craggy mango
This looks good, please watch out for the <:PARENS:371658456215584789>
Thank you!
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shell schooner
Need to learn unit of circle
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Need to learn unit of circle
shell schooner
,help
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soft walrus
$\frac{2}{15}$?
twin meteorBOT
PajamaMamaLlama
shell schooner
,list
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shell schooner
,help cmd
twin meteorBOT
You really shouldn't take it literally :upside_down:. Please type ,help ping, for example!
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shell schooner
,tex
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soft walrus
shell schooner
bro wtf how i write equation
soft walrus
can you send an image?
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vagrant vapor
I was under the impression you had to find two radiuses to do this?
vagrant vapor
or is that only when rotating around a non axis?
outer pendant
In the case of the "washer method" your f(x) and g(x) is your 2 radii if that's what you're asking
vagrant vapor
In the case of the "washer method" your f(x) and g(x) is your 2 radii if that's ...
alright so its only when rotating around a line you need to modify the radii?
outer pendant
Nah basically because since when you rotate it there will be a hole in the middle
vagrant vapor
Nah basically because since when you rotate it there will be a hole in the middl...
nah as in it was right?
or wrong
outer pendant
Oh yea that's right
You'll always be rotating around a line but you'll only have 2 radii when you're given 2 functions
vagrant vapor
Okay
vagrant vapor
Oh yea that's right
btw do you know how i would do this?
vagrant vapor
you forgot to substract the 3 on y=3 I think
wdym?
would i tnot be like this
for the two radii
round ridge
it would just be (3-tan^2(x))^2
round ridge
?? what big radius
as dx tends to zero, the radius is equal to 3-tan^2(x)
then you integrate over every radius
vagrant vapor
?? what big radius
as dx tends to zero, the radius is equal to 3-tan^2(x)
wait so theres only two radii if theres two intersecting functions?
ok
round ridge
picture the volume of revolution around that line
isn't the radius always the difference between 3 and tan^2(x)?
round ridge
you're missing pi
round ridge
np
vocal sleetBOT
@vagrant vapor Has your question been resolved?
plush roost
vocal sleetBOT
plush roost
so s(t) = r(t) - r(0), right?
worthy sparrow
well
worthy sparrow
let me check arc length formula
proven garden
s(t) is a number while r(t)-r(0) is a vector
plush roost
oh wait, it would just be the integral of two bounds of sqrt(149), right?
worthy sparrow
yea
worthy sparrow
maybe
plush roost
proven garden
just evaluate the given integral
plush roost
just evaluate the given integral
doesn't the integral evaluate to r(t) - r(0)?
proven garden
how
mild flower
there's an absolute value sign
plush roost
oh didn't even see that
proven garden
also it's v(t) not r(t)
plush roost
wait im a little confused on what to do now because of the absolute value.
so the antiderivative of v(tao) is r(tao), right?
plush roost
there's an absolute value sign
how would i deal with the abs sign in the integral? I kinda having trouble evaluating it now
mild flower
find v, then find its magnitude
plush roost
find v, then find its magnitude
oh i see. So the magnitude of v is sqrt(149), right?
plush roost
v(t) = < -10sin(t), 10cos(t), 7 >, right?
just the derivative of r(t) given in the question
mild flower
i didn't expect it all to drop out lol
mild flower
so is s(t) = sqrt(149) * t?
ya
plush roost
ya
so then to length of the curve r(t) from 0 to pi/6 is just the integral of of sqrt(149) t from 0, pi/6, right?
plush roost
i hope im not bothering you too much, but what did i do wrong?
oh wait, is the answer 149pi/6?
nvm i got it. thank you so much!
.close
vocal sleetBOT
vocal sleetBOT
Available help channel!
modern steppe
I got a huge problem in my thinking
When having exercice about euclidean Division I don't know what to do each NEW exercice
vocal sleetBOT
I got a huge problem in my thinking
When having exercice about euclidean Divisio...
modern steppe
How i can train myself to this ? I don't want to check Each fuckin time the correction
Ex 84 where I'm blocked
It piss me off because i'm sure if I'm doing a new type of exercice I will flop like shit
paper depot
a = bq + r
modern steppe
I had this problem since September
modern steppe
a = bq + r
I know this but what can I do with this for a exercice ?
modern steppe
i know 0 <= r < b
paper depot
q = 2r
modern steppe
hm yeah ?
modern steppe
Oh
paper depot
and r goes from 0 to 3 inclusive
modern steppe
I just remplace q by 2r ?
modern steppe
wait that it ?
modern steppe
the problem explicitly says this
I got big problem when reading question
i sware
(thanks u)
paper depot
that's pretty much it yes
modern steppe
the problem explicitly says this
so n = 9r ?
paper depot
yes
paper depot
How can I train this ?
dunno, there's no silver bullet
modern steppe
dunno, there's no silver bullet
own... welp
So if I understand your thinking
U translated the exercice into something u can work
then u remplace q by 2r bcs it's what the exercice said
u finish by n = 9r but what It prove ?
how i can be sure it's it ?
hm I will figure it out
thanks u @paper depot
.close
ivory trail
Let's say we have 2(24x-8x^2)^0.5 = 24 -16x
To simplify this statement, apparently I can divide both sides by 4, which leaves me with (6x-2x^2)^0.5 = 6 - 4x.
I do not understand how the division works on the left side. I assume it is (24x-8x^2)^0.5 / 2 = (24x-8x^2)^0.5 / 2^0.5 * 2^0.5.
However I can't remember using this before, where can I read more about this or can someone help explain this to me
vocal sleetBOT
Let's say we have 2(24x-8x^2)^0.5 = 24 -16x
To simplify this statement, apparent...
proven garden
use $a=\sqrt{a^2}$
twin meteorBOT
WhereWolf(ping if needed)
proven garden
so $\frac{1}{2}=\sqrt{\frac{1}{4}}$
twin meteorBOT
WhereWolf(ping if needed)
ivory trail
so $\frac{1}{2}=\sqrt{\frac{1}{4}}$
Makes sense, idk why I am not familiar with it
I have a further question, Let's say I solve 2(24x-8x^2)^0.5 = 24 -16x and find that x is either 1 or 2.
Now I have to plug these values into the function and see if they're true roots, how can if I plug 2 into the function I get the answer 2 = -2?
vocal sleetBOT
@ivory trail Has your question been resolved?
ivory trail
how'd you get 2 = -2
simplify the equaation into (6x-2x^2)^0.5 = 6-4x
Plug in x = 2
2 = -2
proven garden
so x=2 is not a solution
ivory trail
so x=2 is not a solution
Yeah, but I am curious about the idea behindd it
Why is x = 2 popping up as a root if it is not a solution
I assume that x^0.5 creates this issues somehow
proven garden
I didn't see your steps but
squaring create extra solutions
like x=1 when you square it you get x^2=1
ivory trail
alright yeah it was pretty much what I was wondering
so always good to check the answers
left perch
Hello, I need help with integrals understanding
vocal sleetBOT
Hello, I need help with integrals understanding
left perch
I have this question ∫-x^1.5 dx
when I used the power rule, I'm given -(x^2.5)/2.5
However using online calculators, they give me the answer of -(2/5)x^2.5
heavy yoke
1/2.5 = 2/5
hybrid flicker
$\frac{1}{2.5} = \frac{2\cdot 1}{2\cdot 2.5}$
twin meteorBOT
rafilou2003
mild bolt
VOXIOM
mild bolt
Hu
river minnow
What's your question?
vocal sleetBOT
What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
"I got an answer but I'm told it's wrong"
Got what answer to what question?
river minnow
Part a or part b?
mild bolt
Part a
paper depot
just 270?
river minnow
I believe there should be a pi in there
river minnow
And what did you get?
river minnow
I can't really see what the height of the cone is indicated to be
Does it say 12cm?
mild bolt
Yeah
river minnow
You shouldn't be adding the surface area of the bottom of the hemisphere in this case
mild bolt
And for the hemisphere i got 243 pi
mild bolt
????
river minnow
See that circle of radius 9 that connects the cone and the hemisphere?
mild bolt
Yes
river minnow
You added its surface area twice
mild bolt
OHH
river minnow
Meanwhile that circle is not even on the surface of the entire figure
So just do (4pir^2) * 1/2 + pi * r * l
low dagger
vocal sleetBOT
river minnow
What's confusing you in particular?
low dagger
the process, i've gone from finding dy/dx with just x's in the brackets
but now its trig
wait sorry, thats wrong
ebon rapids
Do you know chain rule?
low dagger
i got it wrong because they added -ln
i have barely used ln
with derivatives
.close
atomic jetty
vocal sleetBOT
atomic jetty
Hello! I really want someone to explain how to simplify this question
tidal dock
have you tried completing the square?
atomic jetty
have you tried completing the square?
Yes
tidal dock
how did that go?
atomic jetty
I may have messed it up , i didnt get anything
Help!!!
Someone
@tidal dock
Are you there?
upbeat plinth
Yo can anyone help me
tidal dock
Yo can anyone help me
go to an available help channel, this one is occupied
tidal dock
$\sqrt{3-2\sqrt{2}} = \sqrt{2} -1$, btw
twin meteorBOT
artemetra
tidal dock
completing the square
atomic jetty
How you complete square
tidal dock
$(a+b)^2 = a^2 + 2ab + b^2$\
Consider $3-2\sqrt{2}$. $a^2 + b^2 = 3$, $2ab = -\sqrt{2}$, solving this system will get you $(\sqrt{2}-1)^2$
twin meteorBOT
artemetra
tidal dock
this won't work for the first fraction tho
atomic jetty
this won't work for the first fraction tho
I am trying to get it
tidal dock
I am trying to get it
consider the denominator for the first term
$\sqrt{\sqrt{5}+2}+\sqrt{\sqrt{5}-2}$
twin meteorBOT
artemetra
tidal dock
square this and take the square root
atomic jetty
**artemetra**
Hey isnt 1- root 2 also possible here
tidal dock
Hey isnt 1- root 2 also possible here
oh yeah, that's right cuz there's a minus in front
tidal dock
yea
tidal dock
square this and take the square root
but do this
twin meteorBOT
artemetra
tidal dock
then you can factor out root2
atomic jetty
Yes
tidal dock
and from there you can easily get the result
atomic jetty
Hey
atomic jetty
**artemetra**
I will get answer 1 if i take this
But why i get 2root2 - 1 if i take this 1-root2
The problem is still not solved
Which term should be negative and which one should be positive in the 2nd term
@tidal dock
tidal dock
But why i get 2root2 - 1 if i take this 1-root2
what?
you should get $\frac{\sqrt{2}\sqrt{\sqrt{5}+1}}{\sqrt{\sqrt{5}+1}} - (\sqrt{2} - 1)$
twin meteorBOT
artemetra
tidal dock
and you can most definitely simplify that
atomic jetty
and you can most definitely simplify that
I simplified
But i have trouble with this
atomic jetty
Wait let me write and show you
See
If i alternate the values than the values of N also differ
What is the right value of this term
@tidal dock
tidal dock
only the second one is correct
tidal dock
hope this helped
atomic jetty
How do i end this thread?
atomic jetty
hope this helped
You are the best guy i ever met
tidal dock
How do i end this thread?
type ".close"
atomic jetty
.close
vocal sleetBOT
vocal sleetBOT
Available help channel!
cursive fern
Can someone tell me how to solve this without a calculator cos(arctan(1/2))=?
river minnow
First it would be nice tot have cos(arctan(x)) simplified
arctan(x) represents an angle whose tan is equal to x, right?
What does that imply cos to be equal to
cursive fern
I made a mistake btw
river minnow
Hm?
cursive fern
I corrected it now