Now that's the expanded form
#help-0
last aurora
can i factor 2 out?
i can right?
if we work on the first part
just d/dr(2r * dz/dx)
rocky atlas
It works
rocky atlas
Yes
rocky atlas
Np
last aurora
:D
rocky atlas
Also s was a constant
rocky atlas
Because it wouldn't make sense otherwise on how they factors s out
last aurora
z, is dep var
got it
i will keep in mind
and keep studying through the ntext book
thank you for your time :)
lone heartBOT
Available help channel!
empty spade
six people, four rooms. how many ways can these people be distributed amongst the four rooms, given that each room could accommodate at most four people?
empty spade
i just know that its 4^6 ways without restrictions
timid lion
You can subtract the cases that arent possible
lone heartBOT
@empty spade Has your question been resolved?
empty spade
well how many ways are there when u put 5 people in a room
so would this be 6C5 * 4 * 3
shadow pebble
how to solve this problem
linear programming
The dietitian at a local penal institution is preparing the menu for tonight's light
meal. Two food items will be served at the meal. The dietitian is concerned about
achieving the minimum daily requirements of two vitamins. Table below summarize
vitamins content per ounce of each food, the minimum daily requirements of each, and
cost per ounce of each food. Formulate the linear programming model for determining
the quantities of the two foods which will minimize the cost of the meal while
ensuring that at least minimum levels of both vitamins will be satisfied
shadow pebble
.close
lone heartBOT
lone heartBOT
Available help channel!
alpine sable
3 boys and 2 girls are stanting in a queue, probability that number of boys ahead of every girl is aleast one more than the number of girls ahead of her.
exotic canopy
hint: it's an equation of a semicircle
craggy drift
I need help ... what's the formula I confused
sweet igloo
Hi could I please have some help with 7 C. I don't know how to start the question
opal jolt
Distance is the function given.
The maximum distance requires that the first derivative of said function is 0.
Do you know how to differentiate that function?
sweet igloo
yeah
opal jolt
go ahead
sweet igloo
-0.33te^-1.1t right?
sweet igloo
oops
one second
yeah so I got that as e^-1.1t (0.3-0.33t)
and do I equate that to 0?
which I got t = 0.909
opal jolt
so now you check if that's a maximum or a minimum
for that, you either check the sign of the second derivative, or values close to on each side, and on the point, for the function
sweet igloo
ok so I got it as a maximum but why does taking the derivative to velocity and equating to 0 allow you to find the time?
opal jolt
because derivative = 0 means the tangent to the function is horizontal. Which means the function is at a peak or a valley (maximum or minimum)
craggy ruin
hello is my answer (the one in purple) relevant to the book's answer? i don't know where i'm doing wrong 
fickle sandal
your quotient rule looks okay, but confused on what happened here
looks like you need to simplify the purple further
and if (x+y)^2 is supposed to be (x-y)^2 then you'll get the answer
lone heartBOT
@craggy ruin Has your question been resolved?
craggy ruin
ah yes it's meant to be (x+y)^2 in purple but i forgot to write it as a "+" π³ , for the arrow one it's the idk some people write it like this
also i tried to simplify the answer and i didn't get it the same as in the book , i think i simplified it wrong cause i kept getting different answers and here's an attempt...... i probably forgot a rule or something
fickle sandal
try bringing the minus into the numerator for a start
and then factorise the 2 out
craggy ruin
try bringing the minus into the numerator for a start
wait that will cause the numbers signs to change right?
fickle sandal
yes that's what the minus does
craggy ruin
it worked! :O
fickle sandal
brackets!
small flame
hi, i wanna find $\lim_{x->0} \frac{\cos (\pi/2 \cos x)}{\sin (\sin x)}$
What I've tried to do is:
$= \sin x / \sin (\sin x) \cdot x / \sin x \cdot \cos (\pi / 2 \cdot \cos x) / x$
But then I'm stuck. I shouldn't use de l'Hospital
ocean sealBOT
Clippy
fickle sandal
$\lim_{x\to0}\frac{\cos(\frac{\pi}2\cos x)}{\sin(\sin x)}$
ocean sealBOT
chlamydia
lone heartBOT
@small flame Has your question been resolved?
eternal blaze
@small flame Still there?
small flame
Yep
small flame
I know that sinx/x -> 1
eternal blaze
True.
eternal blaze
means they are equivalent and can be replaced when calculating the limit of a ratio of two infinitesimals
Sry for my poor English cannt explain well
small flame
I think I understand
lament wyvern
when sin x is very small, it's approximately equal to x
eternal blaze
$\lim_{x\to0}\frac{\cos(\frac{\pi}2\cos x)}{\sin(\sin x)} = \lim_{x\to0}\frac{\cos(\frac{\pi}2\cos x)}{\sin x}=\lim_{x\to0}\frac{0}{0}$
ocean sealBOT
ιΆδΈδΈεΊ¦ζε―
eternal blaze
Then try use Hopital again.
small flame
**Clippy**
We haven't learnt de l'Hospital yet and we are asked not to use it tho π
eternal blaze
@small flame OkWe can try another direction
$$\lim{x\to0}\frac{\cos(\frac{\pi}2\cos x)}{\sin(\sin x)} = \lim{x\to0}\frac{\sin(\frac{\pi}2 - \frac{\pi}2\cos x)}{\sin x}$$
ocean sealBOT
ιΆδΈδΈεΊ¦ζε―
eternal blaze
$$=\lim{x\to0}\frac{\sin(\frac{\pi}2(1- \cos x))}{\sin x}$$
ocean sealBOT
ιΆδΈδΈεΊ¦ζε―
eternal blaze
And the equivalent infinitesimal of $1- \cos x$ is $\frac{x^2}{2}$, and the equivalent infinitesimal of $\sin x$ is $x$, so we have
ocean sealBOT
ιΆδΈδΈεΊ¦ζε―
eternal blaze
$$=\lim_{x\to0}\frac{\sin(\frac{\pi}2 \frac{x^2}{2})}{x}=\lim_{x\to0}\frac{\frac{\pi x^2}{4}}{x}=0$$
ocean sealBOT
ιΆδΈδΈεΊ¦ζε―
lone heartBOT
@small flame Has your question been resolved?
small flame
Thanks, this makes sense if I believe that lim sin(pi/2(1-cosx) / sinx = lim sin(pi/2 x^2/2) / sinx
keen mulch
If y = x cos u, prove that
π₯^2(π^2π’/ππ₯^2) + 2π₯π¦(π^2π’/ππ₯ππ¦) + π¦^2(π^2π’/ππ¦^2) = 0
lone heartBOT
If y = x cos u, prove that
π₯^2(π^2π’/ππ₯^2) + 2π₯π¦(π^2π’/ππ₯ππ¦) + π¦^2(...
keen mulch
can anyone help with this question
pure jasper
don't take multiple help channels
i suppose take partial derivatives of u with respect to x and y, and then substitute back into the equation tho
@tall topaz agreed?
keen mulch
anyone else?
lone heartBOT
@keen mulch Has your question been resolved?
pale canopy
Hello, given a table of some sort, i found the mean and standard deviation. I need to find the probaility of hitting one interval standard deviaton from the mean. Do i use a nomral curve and get zscore?
tacit arch
Hello, given a table of some sort, i found the mean and standard deviation. I ne...
Show the original question
lone heartBOT
@pale canopy Has your question been resolved?
last walrus
Hello, given a table of some sort, i found the mean and standard deviation. I ne...
If you assume a normal distribution, then you're always 68% likely to land within one standard deviation of the mean (this is a statistical rule for a normal distribution). However, if your data does not follow a normal distribution you may have to be a bit more careful
alpine sable
Why are these formulas the same? how is h calculated?
L = Face length h = Body height
alpine sable
Why is the volume a third of the area of one face multiplied by the height?
severe bear
Why are these formulas the same? how is h calculated?
L = Face length h = Body h...
the formulas arnt same
one has $\sqrt{3}$ and the other has $\sqrt{2}$
ocean sealBOT
anshu
severe bear
Why are these formulas the same? how is h calculated?
L = Face length h = Body h...
if you take h side, the L side joined with h side on the upper corner and 3rd side with bottom point of h side and the triangle base corner
you get a right angled triangle
alpine sable
if you take h side, the L side joined with h side on the upper corner and 3rd si...
I tried calculating h before with pythagora's theorem, and it didn't word
But I assumed the length of side below was β3/4 l
severe bear
But I assumed the length of side below was β3/4 l
no
thats the length of altitude for a normal triangle
alpine sable
no
thats the length of altitude for a normal triangle
that's half of the altitude
severe bear
you have to calculate from the centroid of the triangle to the corner of the triangle
severe bear
that's half of the altitude
oh yea sorry, still wrong
it will not be half of the altitude
alpine sable
you have to calculate from the centroid of the triangle to the corner of the tri...
how
severe bear
actually centroid in a triangle divides the altitude in a 1:2 ratio
alpine sable
how
severe bear
its divided into 1:2 ratio
so you gotta multiply 2/3 to you length of altitude
from the centroid to corner of the triangle
severe bear
do you think its half??
just assume the point in the middle where all the dotted lines are meeting up is called "x"
alpine sable
so you gotta multiply 2/3 to you length of altitude
why is it two thirds
severe bear
why is it two thirds
oh you want a proof?
severe bear
um, its like asking the question "Why volume of the cone with same height and radius as a cylinder is one third of the volume of cylinder"
its just how it is
if you wanna see how the ratios came, you can look into it by seeing proofs
alpine sable
but I get that lenght is 2/3 x β3/2 l = β6/3 l
severe bear
but I get that lenght is 2/3 x β3/2 l = β6/3 l
it will be actually l/β3
alpine sable
if you wanna see how the ratios came, you can look into it by seeing proofs
mm with axioms?
and theorems
severe bear
mm with axioms?
axioms too basic
severe bear
and theorems
um you can say it as a theorem
here is a proof of it
if you just wanna read it real quick and tell me if you think your doubt is cleared up
alpine sable
it will be actually l/β3
somehow photomath gave me first that answer (the one I gave) and now β3/3 l
alpine sable
somehow photomath gave me first that answer (the one I gave) and now β3/3 l
which is the same as yours
severe bear
somehow photomath gave me first that answer (the one I gave) and now β3/3 l
bro but.... you shouldnt just use photomath for just simple calculation π
alpine sable
https://www.vedantu.com/question-answer/the-centroid-of-the-triangle-divides-eac...
oh okay, thanks
alpine sable
bro but.... you shouldnt just use photomath for just simple calculation π
I am insecure
severe bear
I am insecure
oh, if you wanna check then its fine, but you gotta do it by yourself in the head,
I have seen people using calculator for litreally everything... I MEAN EVERYTHIGN
they cant solve 2x = 8
well
just read the thing I sent you
and lemme know
alpine sable
https://www.vedantu.com/question-answer/the-centroid-of-the-triangle-divides-eac...
oh I kinda get it
Now I'm doubtful whether in math I need to accept things like these and just know that there is a proof out there
alpine sable
oh, if you wanna check then its fine, but you gotta do it by yourself in the hea...
oh I just use it when I am also thinking about something else or talking with someone, because I don't want to waste their time
severe bear
oh I kinda get it
Now I'm doubtful whether in math I need to accept things like ...
you can always see the research paper for these proofs
no need to blindly accept anything
severe bear
oh I just use it when I am also thinking about something else or talking with so...
oh I see
alpine sable
you can always see the research paper for these proofs
no need to blindly accept...
mm that's right, I have been trying to find proofs for properties in math, and I find it helpful for remembering the properties
mm what would h be? @severe bear
severe bear
mm what would h be? <@731534864268132492>
did you got an answer?
alpine sable
I suppose it's incorrect h = β3
alpine sable
$(l/β3)^2+h^2 = l^2$
ocean sealBOT
ale.r
severe bear
Why are these formulas the same? how is h calculated?
L = Face length h = Body h...
now just put that relation in this formula
alpine sable
yes
It's correct
thanks for the help, I learned that the segment inside a equilateral triangle gets divided into a ratio of 1:2 when it forms a centroid with heights
In this case, heights and midpoints are the same?
severe bear
thanks for the help, I learned that the segment inside a equilateral triangle ge...
heights and midpoints?
severe bear
in this case
what do you mean? I dont really get it
heights are lines and midpoints are points, how can they be same?
alpine sable
what do you mean? I dont really get it
heights are lines and midpoints are point...
oh I meant heights and mediums
and also mediatrix
severe bear
medians?
alpine sable
maybe they are the same in equilateral triangles
severe bear
oh yes, I am translating them
oh yes
for equilateral triangle all the lines like medians, angle bisectors, height (altitude), and perpendicular bisectors are the same
alpine sable
and also mediatrix
and also the bisector
alpine sable
oh yes
for equilateral triangle all the lines like medians, angle bisectors, he...
oh yes, it makes sense, thanks for this
so what's exactly the centroid
is like the barycenter?
severe bear
oh yes, it makes sense, thanks for this
so what's exactly the centroid
centroid is a point where all the medians from all 3 sides meet up
alpine sable
oh okay, so the barycenter is an alternative way of saying centroid
or maybe it is only valid in spanish
I'll search up why the volume of a tetrahedron is a third of the area of one face times the height
thanks again (:
.close
burnt spoke
lone heartBOT
severe bear
idk why this step exist here
ocean whale
can someone tell me which ones i did wrong
Wouldn't you factor first before finding c?
So those two are flipped
And I think that was it
burnt spoke
So those two are flipped
the bottom two in the image u sent right?
severe bear
Wouldn't you factor first before finding c?
am so confused rn, what are c and b exactly?
ocean whale
the bottom two in the image u sent right?
Yes
ocean whale
am so confused rn, what are c and b exactly?
y = ax^2 + bx + c
General form for quadratic
ocean whale
Should be
severe bear
I understand it now I guess
ocean whale
photomath doesnβt even do the same steps π
Because that question is babying you, making you do it one step at a time
Photo math does multiple steps at a time
lone heartBOT
@burnt spoke Has your question been resolved?
shut oar
is this the help channel i use?
lone heartBOT
is this the help channel i use?
tacit arch
yea read this
shut oar
okay so how do i add or subtract these radicals
frail grove
$\sqrt{x^2}=|x|=x$ $(x\geq 0)$
ocean sealBOT
Adam Chebil
rustic hill
r
shut oar
i dont think i might actually need the help, i just have terrible read with so much numbers
ty though friends
.close
lament mantle
lone heartBOT
lament mantle
Is the awnser to B, Height= 160cm and Area=14,640?
hard aspen
urban hazel
need help with this.
Prompt: Perform a regression on the provided data. Identify which mathematical model best represents the relationship between intensity and magnitude. Record your regression equation below. Round decimals to nearest thousandth.
Equation: y_{1}\sim a\ln\left(x_{1}-c\right)+d
a = 0.290334
b = -0.571732
d = -0.792673
pure jasper
$y{1} = 0.290 * ln(x{1} + 0.572) - 0.793$
ocean sealBOT
Pure2
pure jasper
agreed?
lone heartBOT
@urban hazel Has your question been resolved?
lone heartBOT
lone heartBOT
Available help channel!
jagged relic
What is difference between the sinΒ²(x) and sin(x)Β²?
lone heartBOT
What is difference between the sinΒ²(x) and sin(x)Β²?
tall topaz
yeah should be the same thing
echo socket
The latter may be more ambiguous though I think
pure jasper
du=cosx(dx)
echo socket
Have you done u-substitution before?
jagged relic
Have you done u-substitution before?
nop
pure jasper
$\frac{u^3}{3}+C$
ocean sealBOT
Pure2
pure jasper
triVIAL
tall topaz
chill out chris
jagged relic
i am trying to understand where the cos(x) went lol
pure jasper
The idea is to substitute a part of the integral with a new variable u
jagged relic
The idea is to substitute a part of the integral with a new variable u
Oh I can see this, its useful
jagged relic
okay sin^2 is 1/3 * sin^3
echo socket
It's spelled derivative, yes
pure jasper
okay sin^2 is 1/3 * sin^3
not realy
pure jasper
U substiuttion is like, u first define U, find derivative, substitue
integrate with respect ot u
BACK SUBSTITUTE LAST
jagged relic
du is the derivate of u?
ocean whale
I suggest viewing that video for a better idea of how u sub works
opal fulcrum
lone heartBOT
opal fulcrum
i am having trouble setting up this question
lone heartBOT
@opal fulcrum Has your question been resolved?
lone heartBOT
@opal fulcrum Has your question been resolved?
opal fulcrum
<@&286206848099549185>
i got 111 mph roughly can someone check my answer please?
.close
proven mantle
Using Rstudio, this question is based on confidence interval.
lone heartBOT
Available help channel!
marble ocean
how would i solve this?
basically there are two piles of knives and forks and the fraction paired are 2/5 1/2, how can i find the amount for the total pile thats been paired?
the equation i need to solve is 2/5x + 1/2y over x+y
alpine sable
are bots not working?
Iβm so lost on this problem
Everything after the 4th line is my work
The 5th line was a hint given to me
Iβm still confused as to how it helps
I know the ranks of the two matrices are different
lone heartBOT
how would i solve this?
alpine sable
Bro these bots are not working
queen harbor
Let $A$, $B$ and $C$ be three different types of bars produced in proportions of $25%$, $25%$ and $50%$ respectively. The length of each bar is a continuous random variable and its pdf depends on the bar type. Type $A$ bars have $U[0,1]$ distribution. Type $B$ bars have $U[0,2]$ distribution. Type $C$ bars have $f_C(x)=(1-\frac{x}{2})1_{[0,2]}(x)$ density. Let $M_n$ be the mean of the lengths of the first $n$ bars.\
Find a lower bound for the probability of $M_n$ being in $[\frac{15}{24}, \frac{19}{24}]$ if $n=100$.
ocean sealBOT
Casiel368
queen harbor
Well I thought the bot was back :yikes
alpine sable
same, it poped on for a bit
sharp harness
Hi guys
alpine sable
?
queen harbor
yes
sharp harness
isnt it
queen harbor
id(f(x))=f(x)
queen harbor
no because id(z) = z for any z. That includes f(x)
sharp harness
(id x β¦ f) (x) = f(x)
(f β¦ id x ) (x) = f(x)
queen harbor
Yes
queen harbor
id(f(x)) = f(x)
f(id(x)) = f(x)
tall topaz
How do i use Lβhopital there?
Do e^log(β¦)
analog pumice
Do e^log(β¦)
Like that?
tall topaz
analog pumice
Ok but im still left with troubles no?
I can bring out the 1/x^2
But now i have log of 1
analog pumice
Right, im guessing twice or ill still have 2β’0
tall topaz
Well once will suffice
analog pumice
But now i have log of 1
Also nvm you can have log(1), i got confused
analog pumice
So itβs log(1)/0^2
But thats all the power of e
I can apply Lβhopital to just that?
tall topaz
Using the continuity of e^x
We can pass the limit to the exponent
So itβs really e^[limβ¦]
This is a common trick
tall topaz
lone heartBOT
vapid shuttle
The owner is missing ??
lone heartBOT
Available help channel!
chrome mirage
lone heartBOT
chrome mirage
is it possible for the terms of an to be small such that it diverges?
alpine sable
woahh banana cat
chrome mirage
im not sure
alpine sable
I need help on all of these
lone heartBOT
tall topaz
!status
lone heartBOT
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
#close
chrome mirage
#close
alpine sable
@vapid shuttle @chrome mirage the bot died for the 4th time again
alpine sable
its killing us
chrome mirage
is it possible for an to converge then cause 1/1+an^2 to diverge
since the lim of the 2nd sum goes to 1 not 0\
rose sigil
more than just possible, sum 1/(1 + a_n^2) never converges if sum a_n converges
a simple example is just to let a_n = 0 for every n
lone heartBOT
Available help channel!
crude marten
Hello
I need help setting up the boundaries for the hyperboloid
I did this, and it didnt work out
lone heartBOT
@crude marten Has your question been resolved?
lone heartBOT
@crude marten Has your question been resolved?
cursive edge
Hi guys heres a question that I need to do for hw
Create and antidifferentiate a function for which the trig sub is sin(theta) = (3x/2)
Ik how to do trig sub but I'm unsure how to do this
pure jasper
solve for cos theta first
cursive edge
why
pure jasper
easier for integration
fervent timber
why is this the last channel in the list
cursive edge
what u mean
Hi guys heres a question that I need to do for hw
Create and antidifferentiate a function for which the trig sub is sin(theta) = (3x/2)
Ik how to do trig sub but I'm unsure how to do this
fervent timber
think about what kind of function would require a trig sub
cursive edge
ik it requires a square root
do i just put a square root
and then
square root ( 2^2 - 3x^2)
and then integreate hat?
foggy pecan
yes, i wrote it or you
foggy pecan
moemnt, i do that here, fwe mins plz for latex
cursive edge
kk
foggy pecan
$\int_{}^{}\sqrt{4-9x^{2}}dx=2\int_{}^{}\sqrt{1-\left( \frac{3x}2{} \right)^{2}}dx=2\int_{}^{}\sqrt{1-\left( sint \right)^{2}}\cdot \frac{2}3{cost}dt=\frac{4}{3}\int_{}^{}cos^{2}tdt=$
ocean sealBOT
Joanna Angel
foggy pecan
$=\frac{4}{3}\int_{}^{}\frac{1+cos2t}{2}dt=\frac{2}3{}\left( t+\frac{1}2{sin2t} \right)+C=$
ocean sealBOT
Joanna Angel
foggy pecan
such a problem we can meet when we consider the area of a certain part located udne the certian elipse curve
foggy pecan
$\text{ellipse with the equation: }y^{2}=4-9x^{2}<=>9x^{2}+y^{2}=4$
ocean sealBOT
Joanna Angel
foggy pecan
i took number 4 out of the integral
foggy pecan
moemnt
$4-9x^{2}=4\left( 1-\frac{9}4{x^{2}} \right)=4\left( 1-\left( \frac{3x}{2} \right)^{2} \right)$
ocean sealBOT
Joanna Angel
cursive edge
ooohh i c
foggy pecan
yw)
cursive edge
.close
lone heartBOT
lone heartBOT
Available help channel!
shell orchid
How come y is considered a function for this x? Aren't there two potential variables for x? Can't it be both negative and positive and we will still recieve the same answer for y ?
lapis goblet
Does it pass the vertical line test?
magic dragon
it's not a function if there are multiple y's for one x
here there are multiple x's for one y, so it can still be a function
so yeah, you can receive the same y with two different x's, but it's still a function
shell orchid
so yeah, you can receive the same y with two different x's, but it's still a fun...
Is this something I should just assume for any parabola based question? y = x^2 + b (that its a function?)
magic dragon
yes
well
if you have like y = ax^2+bx+c, that's a function
if that's what you mean by parabola based question
something to that you should note is that square root is assumed to be positive in a question like this
but if i had y^2 = x^2 + 4, that would not be a function
because when you square root both sides you get y = + or - sqrt(x^2 + 4)
shell orchid
do we automatically assume there will be a +/- infront of the (x^2 +4) because of the y^2? does this just mean there are two functions all together?
when i square rooted both sides i ended up getting y = x +2 π΅
magic dragon
square root does not distribute in addition
magic dragon
do we automatically assume there will be a +/- infront of the (x^2 +4) because o...
yeah
shell orchid
ahhh
magic dragon
because it's y^2, when you square root both sides, you do it as +/-
ig you can view it as two functions combined into one equation
shell orchid
square root does not distribute in addition
what do u mean about this?
magic dragon
im assuming the way you got y = x+2 is by doing sqrt(x) and sqrt(4) right
shell orchid
yess
magic dragon
you can't do that :p
shell orchid
π±
magic dragon
happy to help
lone heartBOT
@shell orchid Has your question been resolved?
hard wing
<@&286206848099549185>
jagged cobalt
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lone heartBOT
hard wing
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ocean whale
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blazing charm
Hi
blazing charm
I don't understand why, when we convert A = bh (assuming that A is meters squared) into inches squared, it becomes A = 1550bh. I know that there are 1550 inches squared in one meter squared and that is why it's a conversion factor, but why do we multiply it by the base and height?
Is it because we need to make up 1550 inches squared to make one meter squared? I'm confused.
ocean whale
I don't understand why, when we convert A = bh (assuming that A is meters square...
It's because when you multiply bh, the units are m^2 so to convert from m^2 to in^2, you need to multiply by 1550 as well
blazing charm
so base and height are meters squared?
But how does multiplying that by 1550 get us a smaller unit
ocean whale
Because 1 m^2 is 1550 in^2
blazing charm
Yes
So
A = bh
in m^2
to convert it into inches
we need to set the area to inches squared
we do that
but the base and height are still meters squared
right?
ocean whale
That's why you multiply by 1550
Take something that has 5 m base and 5 meter height. The area is A = bh so A = (5 m)(5 m) = 25 m^2
So to convert from m^2 to in^2, you multiply by 1550
So 25 m^2 * 1550 in^2/1m^2 = 38750 in^2
blazing charm
hmm
ocean whale
The 1550 in^2/1m^2 is the conversion
blazing charm
I think I'm getting it
ocean whale
1550 in^2 = 1 m^2
blazing charm
1550 in^2 = 1 m^2
1 m^2 = (1m)(1m)
? in^2 = 1550(1m)(1m)
So we're essentially disregarding the units of the base and height of the original, and just multiplying it by the conversion factor to get more inches?
ocean whale
I don't get what you mean
Take something like money, 1 dollar = 100 pennies, so if you have 3 dollars and wanted to see how many pennies you have, you multiply by 100
So 3 * 100 is 300 so you have 300 pennies
The reason why you result in a bigger number is because meter is a bigger unit
blazing charm
right and inches are smaller
so to get the # of inches
we multiply the conversion factor by the meters
so like if the area is 21
in meters
21 m^2 = (7m)(3m)
x in^2 = 1550(7m)(3m)
right?
We're just making up for the said area by multiplying it
since its a smaller unit
blazing charm
right
but the area is originally in meters
and we're converting the area into inches
so we need to multiply the base and height by 1550
to get the same amount of area
just in inches
because its a smaller quantity we multiply
ocean whale
So 25 m^2 * 1550 in^2/1m^2 = 38750 in^2
Base times height is in units of m^2 so to get in^2, you multiply by 1550
You can do the same thing, if you convert m to in first then multiply them
So my 5 m by 5 m
5 m = 196.5 in
So (196.5 in) * (196.5 in) = 38612 in^2, it's off from what I said here because I rounded the conversion. 1 m = 39.3701 in but I just did 1 m = 39.3
blazing charm
hmm
ocean whale
You can convert the units before or after, you just need the correct conversion
blazing charm
Okay
Well
Lets say I have A = bh but in feet
and I wanted to convert it into inches
I know ft^2 = 144 in^2 right
and A is in ft^2
ocean whale
So as mentioned 1 m = 39.3 in
A = bh so (5 m * 39.3 in/1 m) * (5 m * 39.3 in/1 m) = (5 * 5) m^2 * (39.3 * 39.3) in^2/m^2
ocean whale
I know ft^2 = 144 in^2 right
More specifically 1 ft^2 = 144 in^2
blazing charm
So as mentioned 1 m = 39.3 in
A = bh so (5 m * 39.3 in/1 m) * (5 m * 39.3 in/1 ...
Why are you dividing by 1m all the time?
blazing charm
More specifically 1 ft^2 = 144 in^2
Right
So
If I have a larger unit, converting it into a smaller unit
I would need to multiply
ocean whale
Why are you dividing by 1m all the time?
Because it's the conversion
blazing charm
so wouldn't A = 144bh
blazing charm
Because it's the conversion
Okay
ocean whale
so wouldn't A = 144bh
Yes
If you are still having trouble understanding, what you are doing is dimensional analysis, so you can look up videos and practice more
lapis goblet
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placid zinc
You're saying that b) is not antisymmetric. So, provide a counter-example
lapis goblet
alright so {2,3} and {4,5}
placid zinc
Done. b) is not antisymmetric
lapis goblet
is a) correct
placid zinc
You are asserting the properties are true, not showing the properties are true. You'll need to reference the set X somewhere in your proof
lapis goblet
I see
So like for reflexive, i can say for some a element in A
applying the relation
it becomes $\abs{a} \leq \abs{a}$
ocean sealBOT
chef
lapis goblet
so its reflexive
does that work
@placid zinc
my teacher was doing it like this
so i can just slap a general statement in the front of the reflexive statement like this? \ $(\forall A \in X)(A \sim A \iff \abs{A} \leq \abs{A})$. So $A\sim B$ is reflexive.
ocean sealBOT
chef
placid zinc
Seems like your teacher is also pretty lax about asserting these, haha
lapis goblet
i see
placid zinc
But you DO need to mention X in your proof, because whether or not ~ is a partial order depends on X
Something special about X is important here
lapis goblet
**chef**
so is this fine or what else should i do
im not sure tbh
i have that little "addon" i wrote for the antisymettric one for part a)
placid zinc
Why does b) fail? What does a) do differently?
lapis goblet
b has symmetry for some elements, but a has none for all of the elements
/there are no distinct elements in (a) that relate in both diretions
placid zinc
Notably, every element of a) is a different size
placid zinc
That's true for all partial orders though. So you could write that on any partial order proof, and you'd technically be correct
But you're missing the underlying reasoning
WHY can you write that line?
Because every element of X is a different size
Actually, no you are saying that here aren't you
Well, okay we can fix it up. "|A| = |B|" is not a set and you can't have an element in it
You mean "for all A, B β X, |A| β |B|"
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Available help channel!
craggy forge
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craggy forge
,rotate
ocean sealBOT
craggy forge
Iβd like my answer checked please
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jagged cobalt
sorry fellow
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Available help channel!
fading galleon
What does this question mean ?
lone heartBOT
What does this question mean ?
violet urchin
What does this question mean ?
in the sets in 9 and 10, you give the numbers that are real, integers, rational, or irrational
the naturals are 0,1,2...
the integers are ...-2,-1,0,1,2,...
fading galleon
Am I supposed to list them accordingly from the sets ?
violet urchin
Am I supposed to list them accordingly from the sets ?
right
fading galleon
Ok thanks
normal bison
anyone have a copy of the worked solutions for the extension 2 maths in focus textbook?
fading galleon
.close
undone ledge
im not sure where to start tbh.
lone heartBOT
im not sure where to start tbh.
ocean sealBOT
real glen
solve simultaneously with quadratic equation and a + b + c = 0
undone ledge
sorry?
real glen
so you know the quadratic equation right?
undone ledge
yes...
real glen
are you using a classpad or anything
real glen
3ax^2 + 2bx + c = a + b + c
3ax^2 - a = 0
sorry no
3ax^2 +2bx - a - b = 0
then you can factorise right
and do the null factor law
undone ledge
dont think that will take me far
real glen
do you want me to go further with that
undone ledge
check if you can actually arrive at an answer with your method
real glen
tbh i dont really have time
undone ledge
understandable np
real glen
but one solution is that a b and c is 0
undone ledge
...
real glen
so A is not true
what im saying is right
or it means that one or two of a, b or c is a negative while the other(s) are postive
bro just use the discriminant formula
B^2 is always positive so it doesnt matter
-4ac
if a and c are both negative, we know that this will be less that 0 ie imaginary (because a + c is gonna be half of b)
undone ledge
what im saying is right
sorry to inform you but the answer in fact is A.
( answer key )
undone ledge
if a and c are both negative, we know that this will be less that 0 ie imaginary...
no? we dont know a and c are negative or not.
honestly first thought i would have to use rolle's theorem but na that didnt work
real glen
a + b + c = 0 either they are all 0 or one or two are negative
idk then
sorry i gotta study for physics
im here for my own question tbh
thats a weird question
undone ledge
np
thanks for trying!
oh wait
OH WAIT i think i got it , what if i consider this as f prime and then find f(x) , and try to see what interval have root of fprime
it was just rolle's theorem , reversed
great
got it thanks!
.close
neat oracle
Using vector space axioms can we prove that if two vectors are equal then their field components are also equal ?
lone heartBOT
Using vector space axioms can we prove that if two vectors are equal then their ...
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sour verge
If we assume that both are written in the same basis
Then yes it follows
From the axioms
Because if a=b, then a + (-b) = 0, so the coordinates are pairwise 0
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inland ocean
I used binomial expansion theorem how on earth do i find out where is the constant on the given numbers???
inland ocean
Like instead of calculating the whole thing
daring rover
The constant term is the one where the x cancels out
gray isle
what's the general term in the expansion?
pastel aurora
The constant term is the one where the x cancels out
to make x's cancel out, power of x in 3x^2 and -1/x should be same
so if you notice in (3x^2)^2, (-1/x)^4 the x's would cancel out
safe tartan
I used binomial expansion theorem how on earth do i find out where is the consta...
Write the general form of this binomial
inland ocean
so if you notice in (3x^2)^2, (-1/x)^4 the x's would cancel out
Ah i see
ocean sealBOT
annyeong
inland ocean
so if you notice in (3x^2)^2, (-1/x)^4 the x's would cancel out
So i saw that and it is 15(3x^2)^2(-1/x)^4
Wait lemme calcu
inland ocean
Do you know how to write that binomial in itβs general form
Like what
safe tartan
Like
Using binomial theorem
The way that the other person said wonβt work properly
inland ocean
Ah ok
safe tartan
Iβll try write it out in latex for you
inland ocean
okay
ocean sealBOT
annyeong
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
safe tartan
Ok I give up
pastel aurora
The way that the other person said wonβt work properly
how doesn't the method work?
safe tartan
It does but it takes ages
pastel aurora
it's just 6C4 * (3x^2)^2 * (-1/x)^4
or 6C2 doesn't rlly matter
safe tartan
Oh I thought you were gonna do another way
I guess I didnβt understand your method
pastel aurora
I guess I didnβt understand your method
oh then sorry mb for the confusion
inland ocean
So basically if i am ever given this type of problem once more I would just try and find the part that cancels out the x's in the expansion right?
pastel aurora
So basically if i am ever given this type of problem once more I would just try ...
If it asks for the constant term then yes
inland ocean
If it asks for the constant term then yes
Ah alr thankz
rotund shoal
Need some understanding with the translation of trig graphs
lone heartBOT
Need some understanding with the translation of trig graphs
rotund shoal
When you add pi/3 it moves the graph left by pi/12
my expectation was that the equation would have had pi/12 in it to move the graph pi/12 left?
In a similar way y=(x+1)^2 moves the graph 1 to the left?
Does the 4x in front have anything to do with it?
lone heartBOT
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neat oracle
If we assume that both are written in the same basis
like polynomials
lone heartBOT
like polynomials
agile grove
Does the 4x in front have anything to do with it?
yes.
You have to factor the 4 out.
the only way you can do that in your content is
(4(x+pi/3))
That way we ensure for whatever the magnitude of the phase shift is it will shift by the exact amount we tell it to.
lone heartBOT
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torpid dirge
A simple example of a pair (X, A) with A closed for which the homotopy exten-sion property fails is the pair (I, A) where A = {0, 1,1/2,1/3,1/4, Β·Β·Β·}. It is not hard to show that there is no continuous retraction IΓIβIΓ{0} βͺ AΓI . The breakdown of homotopy extension here can be attributed to the bad structure of (X, A) near 0. With nicer local structure the homotopy extension property does hold, as the next example shows.
I don't quite understand why this pair doesn't have a homotopy extension
lone heartBOT
A simple example of a pair (X, A) with A closed for which the homotopy exten-sio...
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sly mantle
@torpid dirge this is very advanced for help channels, try #point-set-topology
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@torpid dirge Has your question been resolved?
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iron vortex
Hi, I'm trying to solve that differential equation, how do i get into a form in which i can integrate? RC is a constant, so is V
round geyser
Hi, I'm trying to solve that differential equation, how do i get into a form in ...
$\frac{\dd V_c}{\dd t} = \frac{V - V_c}{RC}$
ocean sealBOT
nalin
round geyser
can you see what to do now?
iron vortex
Not really, I took a gap year after diff equations and I've forgotten most of it :((
round geyser
$\int \frac{\dd V_c}{V-V_c}= \int \frac{\dd t}{RC}$
ocean sealBOT
nalin
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proper garnet
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proper garnet
i know this server isnt for chem but how do u know which one is + or - x
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delicate knot
lone heartBOT
https://gyazo.com/eb056cd005e338b6950e7f1ce0e4dbd0
delicate knot
So i'm supposed to find all the asymptots to the function above
-1/3 and 5 are the answers i got by myself
And that was taking the denominator = 0
However a friend says i'm missing a vertical asymptote
What does that mean?
ancient ivy
K(x)=(Ln(ax+1))/(Ln(bx+1) ) with 0<a<b and x is strictly positive, prove that K(x) is monotone
tall topaz
have you looked aa the derivative
ancient ivy
Yes
Couldnt know th sign of the numerator
should i calculate the dertivateof the numerator so i can find the sign of it or there is another way more easier
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edgy helm
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mild quail
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mild quail
How do you do this
lone heartBOT
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #βhow-to-get-help for instructions).
tall topaz
U need to learn from dr Chris when he comes back
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sonic ginkgo
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wild umbra
!status
lone heartBOT
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
also close ur second channel
mild quail
.reopen
mild quail
Try writing everything as a power of 3
I had 9 to the power of three inside the square root
And outside was 4
sonic ginkgo
```
What step are you on?
1. I don't know where to begin.
2. I have begun but go...
1
wild umbra
I had 9 to the power of three inside the square root
channel is now occupied by someone else now, open ur new channel
wild umbra
im saying this to steelcow only
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Available help channel!
gray axle
The problem is as follows:
"Eight points are placed on a circle: A1, A2, A3, ..., A8 such that the distance between any two neighboring points is 1 cm. A frog can jump from a given point clockwise either 2 or 5 cm to another point. The frog starts at A1 and wants to get to A8 without stepping on the same point more than once. In how many ways can the frog do this?"
I managed to get 6 by counting every single possibility by hand, and the answer is correct. However, I expect it has a simpler and more elegant solution. I tried writing it as
1 + 2p + 5q β‘ 0 (mod 8)
but I can't think of how to account for the condition of not stepping more than once on the same point.
lone heartBOT
The problem is as follows:
"Eight points are placed on a circle: A1, A2, A3, ......
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gray axle
<@&286206848099549185>
gray axle
Anyone?
lone heartBOT
@gray axle Has your question been resolved?
alpine nacelle
If you start at A1, you can go to A3 or A6
If you end at A8, you come from A3 or A6
so there are two natural paths A1->A3/6->A8
and the ones where you add steps between A3 and A6 or A6 and A3
for A6->A3, I have only one choice which is the direct path, leading to A1->A6->A3->A8
Let's count non direct paths where I go to A3 and don't go to A8 directly, I have to go to A5, and to be on A4 before A6, then I have several choices, A5->A7->A4->A6, A5->A2->A7->A4->A6, or A5->A2->A4->A6
The 3 non direct paths depends on choosing if I use A2, A7 or both
The whole problem is the non direct paths, it's not nicely countable because it depends specifically on the relations between A2, A4 and A7
gray axle
Okay, thanks.
alpine nacelle
ie I can do A2->A4, A2->A7->A4, A7->A4, but not other orders
and it's not depending on your equation altough the idea was good
bc it's related to the nature of the graph
west lance
need to show that there exist bijection between C/ker and C
lone heartBOT
need to show that there exist bijection between C/ker and C
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waxen turtle
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waxen turtle
How to solve without log
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wanton frost
@waxen turtle think how you might equate the two sides through a common base and comparing their powers
waxen turtle
Idk
wanton frost
well first. how would you represent the population decrease in the function?
waxen turtle
<@&286206848099549185>
waxen turtle
well first. how would you represent the population decrease in the function?
Uhhhh
Wdym
The n(t)
wanton frost
yes the equation
if the population of tigers is a certain fraction of what it is initially, then how would that fraction be implemented in the equation?
waxen turtle
if the population of tigers is a certain fraction of what it is initially, then ...
Uhhh idk what the initial thing is multiplying by idk
wanton frost
so do you understand the terms in the equation? like what they represent?
waxen turtle
yes
wanton frost
if not: 710 is the starting number of tigers. over time the population is multiplied by (8/125)^t and t represent the amount of decades
8/125 is less than 1 so the population reduces each time it is multiplied.
so what is happening to the population when that fraction (8/125) is raised to different powers over time?
waxen turtle
Uhh N(1) is like one decade
wanton frost
okay so we know there are initially 710 tigers... and it loses 3/5 of its population every x amount of decades... so every x amount of decades 2/5 of the population remains.
so we are trying to find when will (8/125)^t = 2/5