im guessing that calculus wasn’t a prerequisite to this course so you will only need to find the area under simpler shapes
#help-41
pseudo crescent
Okay, I see
thick apex
for B you need the displacement
vast spade
you need the displacement without the sign
thick apex
b isn’t a seperate question
they’re two parts of the same question
the point still stands that they’re both parts of the same question
you need the answer from part a to get the answer to part b
you need the displacement and time
distance traveled is displacement
cursive apex
I dont think the displacement is equal to the distance in this problem right?
vast spade
displacement is just distance with direction ,in the first question we find the distance with orientation for the second we ignore the orientation
yes
thick apex
the first thing we have to do is find the displacement, then we can take the orientation out and get the distance
which lets us calculate average speed
sure
vast spade
sure but before that do you know why are we trying to find the area under the cure?
yes thats the method to slove this question
thick apex
the issue here is that we don’t know the distance from t=0 to t=10
the method here would work
if we knew the distance
its a velocity graph
if it was a position graph yes we could do that
but it isnt
vast spade
ohk so in the y axis we have velocity(m/s) aka speed(m/s)with direction and on the x axis we have time(t) .Now to to find displacement ,we know that velocity is displacement/time so velocity x time=displacement this is same as finding the area in this case
vav?
vast spade
oh v_av
grizzled pagodaBOT
Ruby
vast spade
$V_{av}\cdot \Delta t = \Delta x$
use \Vec also to indicate its a vector 
thick apex
ah didnt remember the command for that
not really since thats not the average velocity
not right
ok so
first we need to find the displacement
we can deal with the average speed afterwarss
you remember how the area under a velocity graph is the same as displacement?
if we split the area under the graph into rectangles and triangles, we can calculate the area under the graph
well that’s how you’re meant to find displacement from a velocity graph
cursive apex
Dont complicate things for yourself, do you understand the concept of area under the graph yet or?
What method were you taught?
Thats correct
You are basically doing the same thing here, the only difference that its in the form of a graph
The area under this velocity graph happens to be the displacement, because velocity * time is displacement from the equation you stated above
But in this graph velocity is not constant, there is acceleration over a few intervals of time
So even if the question was in the form of an equation it would still be solved differently from those two formulas
But the graph that he used was a velocity graph correct?
If you want to find the average velocity you need to apply the secant line method to a displacement graph
Not possible
Just start by finding the total displacement, remember area above the graph is positive and the one under the graph is negative
Which is due to the fact that the line under the graph implies velocity in the opposite direction so the bat goes "back"
Well you could get back to us in here, if you want to take some time we can close this channel and open another one later, feel free to ping
Dm is also fine if you dont want to go through the trouble
Good luck with it
amber waspBOT
peak mantle
My bad what my channel ?
tropic wadi
My bad what my channel ?
!help
amber waspBOT
My bad what my channel ?
To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.
tropic wadi
np
amber waspBOT
Available help channel!
vague widget
amber waspBOT
vague widget
,rotate
grizzled pagodaBOT
weak zinc
Work out the bottom three values given the table above?
vague widget
"The table above shows approximate values for some natural logarithms. Use the table to determine the approximate value for:"
vague widget
Work out the bottom three values given the table above?
yes
split sail
yes
You have to use properties of log
All the related values are give u just have to manipulate them to find the ans
dry rampart
i think this problem is like mine too. you might have to find an equation from the table
split sail
Like ln(ab) = ln(a) + ln(b)
dry rampart
and then you can just plug in the valuesof what they're asking for
vague widget
You have to use properties of log
can i rewrite for example ln 8 as ln 2^3 then 3 ln 2 then do 3*0.69
split sail
can i rewrite for example ln 8 as ln 2^3 then 3 ln 2 then do 3*0.69
Yes absolutely
vague widget
wont that be an easier way?
dry rampart
are you not allowed to use a calculator?
split sail
wont that be an easier way?
What
vague widget
are you not allowed to use a calculator?
nope
dry rampart
that is so sad
split sail
are you not allowed to use a calculator?
No calculator is required
For this question/problem
split sail
what was your way?
This was my way too
vague widget
Like ln(ab) = ln(a) + ln(b)
what did you mean with this then?
just an example of a rule ?
split sail
what did you mean with this then?
Oh that was for (b)
split sail
just an example of a rule ?
Yes you can also say that
vague widget
Oh that was for (b)
wait when i think of it
how do you do b and c
your way works for b nvm
but for c?
split sail
Remember these rules as well
Don't apply and forget 😆
split sail
ln 12 = ln 4 *3 = ln 4 + ln 3 = 1.39 + 1.10
Yes
Since ln6 is also give u can also do
ln 6 + ln 2
vague widget
Remember these rules as well
Don't apply and forget 😆
is it called rules in english?
in norwegian we say regneregler so
split sail
is it called rules in english?
!done
amber waspBOT
is it called rules in english?
If you are done with this channel, please mark your problem as solved by typing .close
vague widget
.close
amber waspBOT
vague widget
thanks for the help btw
amber waspBOT
Available help channel!
livid iris
how would I identify these as even or odd or neither
amber waspBOT
how would I identify these as even or odd or neither
livid iris
I know the definition of even and odd functions but i dont know how to diagnose them in this context
shadow stump
use the definition and what you know of which trig functions are even/odd
livid iris
ok so to determine if its even i would just change t to (-t) but what would I do to determine if it's odd
livid iris
what would i do to the function to make it -f(x)
shadow stump
multiply it by -1
livid iris
The entire function?
shadow stump
yes
livid iris
for 101 isn't -1(t^2 * sin(t)) not equal to t^2 * sin(t)
i know -t^2 = t^2 but -1(sin(t)) doesnt equal sin(t) does it
shadow stump
so we want to first do f(-t), which means replacing t with -t
so f(-t) = (-t)^2 sin(-t)
livid iris
oh I see what I'm doing wrong
to check if it's odd I was comparing -f(x) to f(x)
instead of comparing -f(x) to f(-x)
thank you for the help 🙏
split sail
can someoen explain proof by contradiction?
with some examples?
amber waspBOT
can someoen explain proof by contradiction?
with some examples?
@split sail Has your question been resolved?
full elk
The main idea behind proof by contradiction is called the law of excluded middles.
It's fairly "simple" : what it says is that statements in mathematics are for all intents and purposes either true or they are false, i.e. there is no "maybe" or grey area.
Usually, PbC goes like this with statements p and q :
- we want to prove p -> q
- we suppose p holds, but q doesn't. (in other words (not q) holds )
- we do a bunch of steps that lead to a contradiction (something that is clearly not true)
- we conclude that if p is true, then the only way this can work is if q holds (this is where the excluded middles come into play. Since (not q) brings a contradiction, q must hold, there is no "other option".
split sail
ok so for example in this case.. we r making it less than 2
full elk
The way you find the contradiction depends on what you want to prove, but the important bit is that you get some nonesensical statement like 1=0 at the end.
charred estuary
So you assume that
split sail
ohh i see
charred estuary
[
\frac{a^2+b^2}{ab}\leq 2
]
grizzled pagodaBOT
🌸Anthea of the Flowers🌸
full elk
So assume <= 2, then try to get a contradiction
split sail
$$
a^2+b^2 \leq 2ab
$$
grizzled pagodaBOT
da
charred estuary
$$(a-b)^2 \leq 0$$
grizzled pagodaBOT
🌸Anthea of the Flowers🌸
split sail
So assume <= 2, then try to get a contradiction
thanks!
wait a minute.. if a = b
that it wouldn't be contradiction
full elk
wait a minute.. if a = b
Yeah that's what I was going to point out
But it says
Distinct
Actually
So it's fine
split sail
oh alr so it has to be bigger than 0
full elk
Yep
amber waspBOT
amber waspBOT
Available help channel!
strong brook
Hello
strong brook
Can anyone explain 4b)?
shadow stump
use the piecewise definition of absolute value
strong brook
use the piecewise definition of absolute value
What's that?
shadow stump
,, \abs x = \begin{cases} x & x \ge 0 \ -x & x < 0 \end{cases}
grizzled pagodaBOT
cloud
strong brook
,, \abs x = \begin{cases} x & x \ge 0 \\ -x & x < 0 \end{cases}
Then will I have four cases?
Because the answer is showing two
shadow stump
why 4 cases?
strong brook
There's two absolutes
When the upper |x-2| is positive and negative
When the lower one is positive and negative
shadow stump
both of them have the same thing inside
x - 2 can't be positive and negative simultaneously
strong brook
both of them have the same thing inside
You there
strong brook
They’re both x-2
What about the intervals?
spare belfry
Same
strong brook
But that's not piecewise?
spare belfry
Wdym
strong brook
What do you mean by same
spare belfry
It’s either "they are both positive" or "they are both negative"
You just need to discuss the condition when x-2>0, x-2<0
strong brook
You just need to discuss the condition when x-2>0, x-2<0
Can orders change?
spare belfry
What do you mean by orders?
strong brook
What do you mean by orders?
Can x ≤ 2 go down and x > 2 go up
@spare belfry
.close
amber waspBOT
amber waspBOT
Available help channel!
low summit
What is area of circle □ABC while height of triangle ABC is 9 and area of radius of circle ABC is 3
velvet steeple
Area of a circle = $\pi r^2$ where $r$ is the radius, so it would be $9\pi units^2$
grizzled pagodaBOT
solaris
low summit
It is area of circle □ABC and not circle inside of triangle
The circle with area of 9𝜋 is inside the triangle ABC but the problem says to get area of bigger one
amber waspBOT
@low summit Has your question been resolved?
low summit
Radius of naejeob circle is 3 while problem asks for area of oejeob circle
amber waspBOT
@low summit Has your question been resolved?
amber waspBOT
@low summit Has your question been resolved?
amber waspBOT
@low summit Has your question been resolved?
formal sorrel
What is area of circle □ABC while height of triangle ABC is 9 and area of radius...
do you know if the radius is equal to the base or do u have a visual representation of the problem?
hidden wraith
what is naejeob and oejeob circles ?
low summit
It is alternative word for 내접원 and 외접원
amber waspBOT
@low summit Has your question been resolved?
true trench
hii have u ever learnt linear algebra?
hidden wraith
Is there any other information about the triangle?
If not, there is no answer. To illustrate,
Case A: ABC is equilateral, then the circumradius is double the inradius, so circumradius = 6
Case B: ABC is right-angled with height 9; then some calculations show the triangle has lengths 9, 12, 15 - to make in radius 3, whereas the circumradius = 7.5
amber waspBOT
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Available help channel!
unreal mesa
Need help solving it
amber waspBOT
Need help solving it
unreal mesa
Don't know where to begin
My class is going to start soon tho so I won't be able to reply for like an hr
amber waspBOT
@unreal mesa Has your question been resolved?
civic spindle
I format my responses for clarity and precision. Please do the same with your responses.
Please answer the questions within the order they are provided otherwise I will be forced to close the channel due to sidetracking.
Current understanding:
Factoring is finding smaller combinations of terms to generate the larger term with simpler components.
I understand that the sqrt of (x+1)^2 is x+1 but am asking at the operational level how these work as seen below.
(x^2+1x) (1x 1)
1. I do not understand how 1x and 1x affected by sqrt would entirely dissapear from the equation.
2. I do not understand how you would factor this any further.
3. I understand that because (x+1)^2 reuslts in that that the sqrt should be x+1 but the question i asked is inquring regarding how that would actually work at the operational level or if it ONLY works because it was established that (x+1)^2 is x+1```
civic spindle
.close
amber waspBOT
patent raptor
> ```lua
> I format my responses for clarity and precision. Please do the same w...
The sqrt of (x+1)^2 is not simply x+1 it's |x+1|
amber waspBOT
Available help channel!
split sail
amber waspBOT
quick ridge
inverse?
split sail
which part of this is confusing first
the part where u find a
quick ridge
wack
split sail
just put in the area my man
alrr
split sail
just put in the area my man
sir
quick ridge
da
split sail
i got different answer 💀
quick ridge
what get
split sail
28.4556
oh nvm
i had to do 1-0.22
but why?
oh wait its the same thing but in different direction
quick ridge
ahh you don’t have the tail right command
split sail
ahh i see
split sail
yup now i know
cunning birch
Yeah with the P
split sail
yup
split sail
Yeah with the P
can u explain what the standard normal distribution is?
like whats the difference between just normal distribution and that
quick ridge
i mean you don’t really plot it in the cartesian plane
so i wouldn’t call it "y axis"
but sure it’s symmetric about the line going through the mean
split sail
i mean you don’t really plot it in the cartesian plane
alrr thanks
split sail
but sure it’s symmetric about the line going through the mean
so in snd, its denoted into Z~N(0,1^2)?
why do we even need that?
amber waspBOT
Available help channel!
real plinth
Help plz
misty trail
full elk
What was the original problem they were solving?
amber waspBOT
@real plinth Has your question been resolved?
noble coral
<@&286206848099549185>
amber waspBOT
@noble coral Has your question been resolved?
amber waspBOT
@noble coral Has your question been resolved?
noble coral
Any <@&286206848099549185>
proper burrow
can someone pls help me with this?
amber waspBOT
can someone pls help me with this?
@proper burrow Has your question been resolved?
proper burrow
<@&286206848099549185>
amber waspBOT
@proper burrow Has your question been resolved?
long shard
If the mix runs out at a certain rate at what rate will reach individual salt run out
amber waspBOT
@proper burrow Has your question been resolved?
lime jasper
Hi why is the 1 inside the bracket in the correct answer
amber waspBOT
Hi why is the 1 inside the bracket in the correct answer
grizzled pagodaBOT
faiyrose
lime jasper
The 1 remains outside
Does ((x-a)+1) = (x-a+1)
Oh
Is this something I need to remember every time I see a question like this
lime jasper
I mean remembering distributive property applies to this question
gloomy tide
yes, factoring is at its core applying the distributive property
amber waspBOT
amber waspBOT
Available help channel!
pale shadow
can some one help me
amber waspBOT
can some one help me
pale shadow
!close
amber waspBOT
can some one help me
No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/
pale shadow
!close
strange field
its .close
pale shadow
.close
amber waspBOT
pale shadow
its .close
ty
amber waspBOT
Available help channel!
thorny terrace
call ‘n’ the number of 2s needed
nova crater
$2 \times n = 2^{99}$
grizzled pagodaBOT
Newt
thorny terrace
Yea
amber waspBOT
amber waspBOT
Available help channel!
runic cypress
amber waspBOT
runic cypress
how do i solve this using transformation of roots?
amber waspBOT
@runic cypress Has your question been resolved?
runic cypress
<@&286206848099549185>
quick spoke
if we let u = 1/(x^2 + 1)
then if x^20 - 7x^3 + 1 = 0
(1/u - 1)^10 - 7(1/u - 1)^(3/2) + 1 = 0
rearrange to make that a polynomial
runic cypress
and if i wanna solve it by taking log and then differentiating?
i keep getting stuck
quick spoke
(1/u - 1)^10 - 7(1/u - 1)^(3/2) + 1 = 0
u wanna turn this into a polynomial
cus then the problem is just asking to find the sum of the roots of ^
amber waspBOT
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runic cypress
amber waspBOT
runic cypress
i am told that the solution to this is by assuming a function
i tried f(x)=(x+x1)(x+x2)....(x+x2022)=2^x but idk what to do after that
is this acceptable?
amber waspBOT
@runic cypress Has your question been resolved?
runic cypress
<@&286206848099549185>
celest tree
amber waspBOT
neat wind
<@&268886789983436800> name
warm glacier
What did u try?
strange field
celest tree
im getting jumped by the same question
tulip tapir
<@&268886789983436800> name
also desc
celest tree
i legit just need the method yk
celest tree
36?
tulip tapir
...
pallid canopy
can you close the channel too since it's in the name
serene wagon
.close
clever ether
x^2 - 36 = 0, x^2 - (6)^2 = 0, ( x -6 ) ( x-6 ) = 0 so there either x =-6 and x =6
pallid canopy
how does your function u(x,y) relate to your graphs
amber waspBOT
@opal kestrel Has your question been resolved?
amber waspBOT
@opal kestrel Has your question been resolved?
amber waspBOT
@opal kestrel Has your question been resolved?
amber waspBOT
proper burrow
If the mix runs out at a certain rate at what rate will reach individual salt ru...
hi sorry i saw this after this channel was closed
@long shard i think the salt should run out at the same rate coz the question says that the salts do not interact with each other
proper burrow
can someone pls help me with this?
here's my question if someone else wants to help me out, thanks!
<@&286206848099549185>
amber waspBOT
Available help channel!
proper burrow
here's my question if someone else wants to help me out, thanks!
^
weak zinc
copied down for convenience
proper burrow
thank you!
amber waspBOT
@proper burrow Has your question been resolved?
jaunty shale
thats right
amber waspBOT
@timber snow Has your question been resolved?
hasty token
the definition of acceleration is the change in velocity over time
so the question you want to ask yourself is, is the velocity changing over the last 4 seconds?
just based on the graph, the velocity doesnt change over the last 4 seconds, i know this because the slope doesnt change (curve) over the duration of the last 4 seconds
if velocity doesnt change or is constant, then acceleration has to be zero by the very definition of acceleration
sand anchor
@amber wasp
amber waspBOT
<@805217272087838750>
sand anchor
[17/9+(-5/36]+4 1/4
sand anchor
[17/9+(-5/36]+4 1/4
@amber wasp how do I do this?
spare belfry
I’m pretty sure the bot will not answer to your question
stable token
[17/9+(-5/36]+4 1/4
im a little confused, is the last number a mixed number 4, 1/2
anyways, start with whats in the brackets
amber waspBOT
@sand anchor Has your question been resolved?
tough barn
😦
rapid relic
whats the question here…
turbid pebble
Question: For variation of parameters, we often assume that v_1'y_1+v_2'y_2=0, but what if instead it equaled some phi(x). I'm required to show that the particular solution can still be shown as the first image.
My attempt is the second image. I am stuck on the next step where I am supposed to use the product rule to combine a phi(x)y'+phi(x)'y so I can integrate by parts but I am unsure where to get it.
amber waspBOT
Question: For variation of parameters, we often assume that v_1'y_1+v_2'y_2=0, b...
@turbid pebble Has your question been resolved?
turbid pebble
<@&286206848099549185> Could I get some help with this? Thanks in advance
amber waspBOT
@turbid pebble Has your question been resolved?
amber waspBOT
@turbid pebble Has your question been resolved?
civic spindle
Anyone here willing to help?
amber waspBOT
> Anyone here willing to help?
civic spindle
if 2 was multiplying the whole then how come they can factor it into addition and simply add it to 5 by combining like terms?```
I dont even really understand at a conceptual level how they added 2 because if 2 is multiplication then it should be fundamentally different to the number 2 itself.
calm oriole
```lua
if 2 was multiplying the whole then how come they can factor it into addi...
So
Do you understand how we take common? For eg: 4x²+6x can be written as 2x(2x+3)
civic spindle
Do you understand how we take common? For eg: 4x²+6x can be written as 2x(2x+3)
yes
because its equivalent
and sure thats equivalent
but i dont understand how operations done AFTER equivalency work
because they defy logical rules
and they are extremely vague
regarding how they keep equality
civic spindle
like literally it isnt explained anywhere from multiple sources
calm oriole
What we do here is exactly what we're doing all along
amber waspBOT
Available help channel!
random halo
I'm having trouble understanding what they meant by using step 2
random halo
how exactly did they use the assumption in the induction?
aren't we still missing (k-2)!
strange field
I'm having trouble understanding what they meant by using step 2
so $k! + (k-1)! = k^2(k-2)! - (k-2)!$
grizzled pagodaBOT
Astar777
amber waspBOT
amber waspBOT
Available help channel!
split sail
4^x+x=260
crisp stratus
solve for x?
split sail
yed
plain coral
no youre not
plain coral
now think about 4^x
plain coral
but that is guessing
sucks for you then that that's your only option
whats next is to prove that x = 4 is the only real solution
you can think that 4^x is increasing
and so is x
so 4^x + x is increasing
so when you find that 4^x + x becomes 260 when x = 4, that x = 4 will be the only solution
storm sentinel
have you done logarithms yet @split sail
split sail
yes
plain coral
have you done logarithms yet <@456226577798135808>
its (4^x) + x = 261, not 4^(x + x) = 261
plain coral
its not possible to get an exact answer for 4^x + x = 261 without resorting to the lambert W function
storm sentinel
i was about to say that
crisp stratus
,w 4^x + x = 261
plain coral
even then the answers dont look pretty
storm sentinel
i want words with whoever wrote that question
grizzled pagodaBOT
split sail
yes
plain coral
it sounds like you were intended to guess that x=4 looking at the 260
split sail
i'll leave it then
plain coral
you know that 4^4 = 256
storm sentinel
where did this question come from
split sail
where did this question come from
yt
split sail
okay
crisp stratus
even then the answers dont look pretty
it's actually a bit simpler. the big number is 2^(523)
split sail
ur in high school still right?
yes
storm sentinel
yeah stay away from that question
split sail
ok bro
storm sentinel
guessing is the best you can do at a high school level
amber waspBOT
amber waspBOT
Available help channel!
thick marlin
How to solve this with only u-sub?
amber waspBOT
How to solve this with only u-sub?
plain coral
How to solve this with only u-sub?
choose u-subs of inside expressions, such as trying u = 1 + 1/x
if a u-sub doesnt do enough, do another u-sub
thick marlin
I tried using u = 1+ 1/x, or 1/x which just ended up getting ln(x) that cant be cancelled out by other terms using another layer of u sub doesnt help too
Or am i doing something wrong?
amber waspBOT
@thick marlin Has your question been resolved?
distant quartz
.
distant quartz
How to solve this with only u-sub?
Try substituting 1+ 1/x = u^2
amber waspBOT
thick marlin
.reopen
amber waspBOT
✅
thick marlin
Try substituting 1+ 1/x = u^2
Like this?
distant quartz
Like this?
How'd you get lnx?
jade pelican
hey
jade pelican
i need help with math
amber waspBOT
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).
distant quartz
Like this?
Ping me when you're back.
amber waspBOT
@thick marlin Has your question been resolved?
distant quartz
Try it now
amber waspBOT
amber waspBOT
Available help channel!
amber waspBOT
cunning birch
,rotate
grizzled pagodaBOT
cunning birch
Why did we remove the term e^(3x) ?
we just said e^(3x) > 0, so the denominator is bigger than 9x^2
which already goes to infinity
azure valley
Is there a systematic or defined way on eliminating terms in limits?
cunning birch
Is there a systematic or defined way on eliminating terms in limits?
just simplify stuff to the max so that you only have to focus on one term
for example you could have simplified it into
$|f(x) - L| \leq \frac{1}{9x^2+e^{3x}} < \frac{1}{e^{3x}}$
grizzled pagodaBOT
rafilou2003
cunning birch
the last part being e^(-3x)
and you can also use that e^(-3x) goes to 0 as x goes to infinity
you simply need e^(-3x) < epsilon so M = -ln(epsilon)/3 works
amber waspBOT
@azure valley Has your question been resolved?
errant eagle
1+1=？
amber waspBOT
amber waspBOT
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carmine tusk
hey
carmine tusk
can i get some help with this?
i just need understanding of the first question
like an example relating to the 2
i was at a school event, and i missed the discussion my maths teacher gave my class
i asked for an explanation but i didint get it
<@&286206848099549185>
amber waspBOT
@carmine tusk Has your question been resolved?
carmine tusk
<@&286206848099549185> pls help
proud gull
If u want to make a graph of a quadratic equation..first make a perfect square of the equation and adjust with respect the constants added or subtracted
carmine tusk
is this right?
proud gull
What is ?
carmine tusk
proud gull
Have u started differentiation ?
carmine tusk
What class is this ?
Grade 10 maths
proud gull
Okay
carmine tusk
Have u started differentiation ?
im not sure...
proud gull
Okay no then
carmine tusk
i missed our discussion
proud gull
Just follow these steps
carmine tusk
becuz as i said, i was at a school event
proud gull
You understand these terms right ? Vertex and axis of symmetry
carmine tusk
You understand these terms right ? Vertex and axis of symmetry
yep studied them when graphs were introduced to us
but only vertex thi
proud gull
Same way u did the first one ...open up the (x+2)^2 and solve it
carmine tusk
axis of semmetry is new to me
carmine tusk
Same way u did the first one ...open up the (x+2)^2 and solve it
how tho?
proud gull
Axis of symmetry is basically a line drawn from the vertex and and it mirrors the either side of the graph
carmine tusk
becuz y = ax^2 + bx + c
proud gull
Yes
carmine tusk
how can i find the terms?
carmine tusk
Ohhh
proud gull
Yeah
proud gull
👍
knotty hearth
limpid sun
velvet ibex
Can someone help me
amber waspBOT
Can someone help me
velvet ibex
It’s a multivariable calculus problem
velvet ibex
north wraith
ok wait
north wraith
It’s a multivariable calculus problem
ight lil bro
velvet ibex
?
north wraith
ok wait
To determine the minimum amount of paper required to construct a cone-shaped paper cup of volume 20pi cm^3 you want to minimize the surface area of the cone while maintaining the given volume.
so the formuals we need are
Volume of cone
Surface area of cone (including base)
got it?
@velvet ibex
north wraith
do yk the formuals
north wraith
But we don’t need the base
just wait
velvet ibex
Okay
grizzled pagodaBOT
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north wraith
Step 5: Calculate minimum surface area
Once ( r ) is found, substitute it back into the surface area formula.
Let's perform the differentiation and solve for ( r ) to find the critical points.
The critical value for ( r ) that minimizes the surface area is ( r = 15^{1/3} \cdot 2^{1/6} ). We can simplify this to a numerical approximation to get a clearer value.
Now, let's calculate the exact numerical value of ( r ) and then use it to compute the minimum surface area.
The optimal radius ( r ) for the cone to minimize the surface area, while maintaining a volume of ( 20\pi , \text{cm}^3 ), is approximately ( 2.77 , \text{cm} ). The corresponding height ( h ) is about ( 7.83 , \text{cm} ).
The minimum surface area required to construct this cone-shaped paper cup is approximately ( 96.30 , \text{cm}^2 ). This represents the least amount of paper needed to create a cup with the given volume.
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velvet ibex
Bro it’s lagging
velvet ibex
### Step 5: Calculate minimum surface area
Once \( r \) is found, substitute it ...
You’re not supposed to include the base though
Since it’s a paper cup
?
@north wraith
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velvet ibex
@help
velvet ibex
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limber briar
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marble shoal
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marble shoal
guys pls help
did i put P = correctly?
- the dx in first intgrl forgot but is it good?
amber waspBOT
@marble shoal Has your question been resolved?
pallid canopy
settle down
strange field
the limits are wrong
strange field
you use the points of intersection of two graphs
pallid canopy
this would be right if your lower function were the same for the entire integral
but it changes from y = -sqrt(2x-1) to y=x-1 at x=0
marble shoal
you use the points of intersection of two graphs
Oh so 4 and -1 ?
strange field
wut
marble shoal
that is where they intersect
strange field
find the intersection points of y^2 = 2z-1 and y = x-1
marble shoal
x=4 y= 3 and x=-1 and y=-1
strange field
i think you have wrong points
marble shoal
🤔
strange field
either you used the wrong equations in question or in the graph
marble shoal
strange field
2x + 1.......
strange field
because if u use x axis you will have to split into two
because one part is below axis and one is above axis
marble shoal
Yeah but
what confused me
the part below the axis is
its weird
because above and below is at the same time somehow in 1 shape
but
can you just tell me please
since this is wrong
how should this be put?
strange field
with respect to x axis or y axis
marble shoal
strange field
strange field
no
marble shoal
with respect to y axis i think
strange field
$\int_{-1}^{3} \left(y+1-\frac{y^2}{2}+\frac{1}{2}\right)$
grizzled pagodaBOT
Astar777
marble shoal
and then + the apsolute value from -1 = b to -1/2 =x?
strange field
what?
strange field
**Astar777**
this is the area enclosed by the 2 given curves with respect to y axis
marble shoal
seperately calculate the positive part and negative right?
strange field
thats when you write with respect to x axis
marble shoal
Oh
strange field
strange field
nah
marble shoal
hey
1 question
this was not possible to be calculated with respect to x'
?
please please please plase tell me 
amber waspBOT
@marble shoal Has your question been resolved?
pallid canopy
this was not possible to be calculated with respect to x'
it is. you just need to adjust the subtracting function like i said above
pallid canopy
but it changes from y = -sqrt(2x-1) to y=x-1 at x=0
.
glass sparrow
hii have i done this correctly?
amber waspBOT
hii have i done this correctly?
pallid canopy
,w simplify a^(1/5) * (2a^(-1/5))^(-4) / [ (a^(1/2))^(-3) * (16a^3)^(1/2)]
grizzled pagodaBOT
slim latch
lol
glass sparrow
it doesnt matter what it is, if its the result in my answer or wolfram?
pseudo crescent
it doesnt matter what it is, if its the result in my answer or wolfram?
they are the same, as long as you keep in mind that a must be > 0
pallid canopy
it doesnt matter what it is, if its the result in my answer or wolfram?
your answer is more simplified. wolfram is just not as good as you
glass sparrow
i dont understand why i didnt get the a5/2, have i simplified something earlier
pseudo crescent
Open one of these channels
glass sparrow
your answer is more simplified. wolfram is just not as good as you
hahah
should i convert minus exponents to a fraction first and then multiply , like what i did for A i just multipled directly -1/5 with (-4) without converting it to a fraction, or should it be converted to a fraction, is one way more correct than the other?
pallid canopy
nope. do whatever you're comfortable with, fast at
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fast nova
amber waspBOT
fast nova
The correct answer is +6, I think I’m going wrong in the last few steps where I’m using the identity [a b c]=-[b a c]
but I can’t seem to find my mistake
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fast nova
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patent sierra
need help if i got A right
amber waspBOT
need help if i got A right
devout ledge
looks good to me
amber waspBOT
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split sail
How do I find If this series converges? I tried simplifying the expression to n^3 * (...) but I get an Indetermination of inf*0 If I distribute the limit.
Really dk what to do here.
amber waspBOT
How do I find If this series converges? I tried simplifying the expression to n^...
@split sail Has your question been resolved?
ancient snow
How do I find If this series converges? I tried simplifying the expression to n^...
You can start by rationalising to get $T_n = (\sqrt[3]{n^9+2n}-\sqrt{n^6-7n^3})*\frac{\sqrt[3]{n^9+2n}+\sqrt{n^6-7n^3}}{\sqrt[3]{n^9+2n}+\sqrt{n^6-7n^3}}$
grizzled pagodaBOT
Goran
ancient snow
God that was long to type out
split sail
I tried that too but didnt get anything because of the cubic root
Its supposed I could simplify by rationalising, but because of the dam cubic root I cant :<
ancient snow
Its supposed I could simplify by rationalising, but because of the dam cubic roo...
You get this and you can seperate it out to 2 fractions where 1 has just the 7n^3 part and the other has the rest which you could maybe then rationalise as cubes
It will be quite a bit of work
Although I think the second fraction will go to 0 then
split sail
You get this and you can seperate it out to 2 fractions where 1 has just the 7n^...
I Will try again and see If I can get somewhere
ancient snow
Actually you can conclude this is 0 because the n^9^(2/3) and n^6 will cancel each other out meaning that the highest powers are in the denominator although to write that as a proof it would take some time
(n^9 +2n) will be equivalent to n^9 for our purposes which is easily provable
split sail
Actually you can conclude this is 0 because the n^9^(2/3) and n^6 will cancel ea...
Alright, will do that then seems reasonable
Ty
.close
amber waspBOT
split sail
Ty very much, I got 7/2 after aproximating to n^9 and n^6
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swift spoke
amber waspBOT
swift spoke
help understanding this
proper bloom
Do u know where to start?
swift spoke
not really, but i thought of setting the function equal to 0
proper bloom
It’s too early to substitute 0
swift spoke
ive never done a problem like this with an integral
proper bloom
Do u know how to find the derivative of f, and relating it to the derivative of its inverse?
swift spoke
isnt the derivative of f(x) just the inside function?
swift spoke
hmm not sure
proper bloom
Although you shld attempt to prove this urself at some point, 1/f’ = (f^-1)’
Is an important derivative theorem
swift spoke
oh yeah ive seen this
proper bloom
Combination of these two facts is sufficient to solve the problem
swift spoke
is the derivative with t or x variable
swift spoke
why is that?
proper bloom
If u do f(t), then the variable shld be t
proper bloom
Since the variable x is used as a limit for the integral, t is used to distinguish between the variable of f, and the integration variable
swift spoke
oh so when i take the derivative of f(x) the inside radicand would be terms of x?
since the integral is gone
swift spoke
Although you shld attempt to prove this urself at some point, 1/f’ = (f^-1)’
isnt this here just the formula for derivative of inverse?
proper bloom
Yes
proper bloom
its 1 / sqrt(28)
This is correct
swift spoke
you have any resource on proving the formula?
and how the function derivative links
with it
proper bloom
swift spoke
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amber waspBOT
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vapid schooner
how do i solve this
amber waspBOT
how do i solve this
vapid schooner
first what do i do
neat wind
expand (2 - x)^2
vapid schooner
expand (2 - x)^2
then i multiply the x^1/3 to the entire equation?
x^2-4x+4 is the expanded form
neat wind
it is expression not equation (but yes that sounds good)
vapid schooner
x^2-4x+4 is the expanded form
i meant this
vapid schooner
it is expression not equation (but yes that sounds good)
alr
grizzled pagodaBOT
labeled4497
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quick spoke
we just need to find the variance of sqrt(1-p^2 y1 hat)
there probably is, but it's late where i am so i'm heading to bed soon
and i can't think of a way to do it
but effectively we wanna find E(sqrt(1-p^2 y1)^2 ) - E(sqrt(1-p^2 y1))^2
do @ helper
grizzled pagodaBOT
labeled4497
quick spoke
i'm tired so i didn't format it properly, sorry
but is this even possible?
yeah i don't think this is possible if you don't have the distribution of y1 hat
but yeah i'm kinda tired rn, @ another helper and see if u get a response
quick spoke
**labeled4497**
Compile Error! Click the <:errors:504266556054962196> reaction f...
actually you might wanna double check the problem cus i don't think you can do it
$1 - p^2 y_1$ could have any distribution
grizzled pagodaBOT
LY
quick spoke
and in general, you cannot work out var(sqrt(X)) from X even if you know the mean and variance
we're square rooting here
what?
how did u get that
yeah i know the variance of 1-p^2 y1 = p^2
but then we still have a square root
what?
that's not how the property works
also yeah there's definitely not enough information
if y_1 = 1 and -1 with probability 1/2
then you get a different variance than with y1 = sqrt(1.5), sqrt(0.5), -sqrt(0.5) and -sqrt(1.5) all with probability 1/4
yeah?
but expectations don't work like that
E(sqrt(X)) is not sqrt(E(X))
if you don't believe me just compute the variance for
quick spoke
if y_1 = 1 and -1 with probability 1/2
this
quick spoke
then you get a different variance than with y1 = sqrt(1.5), sqrt(0.5), -sqrt(0.5...
and this
(take p=1/2 our life easy)
amber waspBOT