how do you think we can get negative values?
#help-26
crimson iron
shut sand
i thought c was negative infinity
but when i put that it said infinity isn't defined in the context.
crimson iron
well, 8 is a positive number
what values can we raise it to that get us negative numbers?
shut sand
wym?
thorny flameBOT
倧ιι倧 π»
crimson iron
i put it in mathway and got (-inf, 0)
well
lets say we raise 8 to -infinity
what is $8^{-\infty}$
thorny flameBOT
倧ιι倧 π»
shut sand
0?
thorny flameBOT
倧ιι倧 π»
shut sand
wouldnt that just be inf
thorny flameBOT
倧ιι倧 π»
thorny flameBOT
crimson iron
if you look at the graph, you'll notice that it only increases as x increases
shut sand
yes i see
crimson iron
right
so if the function is 0 at -infinity
and it only gets bigger
can it ever get below 0?
shut sand
no
crimson iron
exactly
so what is the range of the function?
or rather, what is the smallest value we can get?
crimson iron
is it one?
are you sure?
we just found that we can get 0 at -infinity
and that we cannot get smaller than that
shut sand
so wouldnt it be infinity since it keeps going
crimson iron
so wouldnt it be infinity since it keeps going
well
thats the maximum
but whats the smallest value we can get
shut sand
0
crimson iron
mhm
shut sand
thank you so much
crimson iron
np
shut sand
you think you can help me with one more?
crimson iron
sure
shut sand
thorny flameBOT
倧ιι倧 π»
crimson iron
im not sure if it's right but I got something that looks like 256 = 1/256*b^3
hm
not quite, but youve defnitely got the right idea
thorny flameBOT
倧ιι倧 π»
crimson iron
following so far?
shut sand
mhm
crimson iron
and what do we know f(2) is equal to
shut sand
1/256
shut sand
how you get -1/256?
shut sand
oh
thorny flameBOT
倧ιι倧 π»
shut sand
so wouldn't f(-1) be 256=ab^2
crimson iron
so wouldn't f(-1) be 256=ab^2
well
shut sand
wait mb
crimson iron
**倧ιι倧 π»**
look back at this
shut sand
256 = ab^-1
crimson iron
we want the argument of f and the exponent of b to be equal right
thorny flameBOT
倧ιι倧 π»
crimson iron
how can we get a on its own
thorny flameBOT
倧ιι倧 π»
crimson iron
how would we make it so that $a$ was on its own
thorny flameBOT
倧ιι倧 π»
shut sand
divide by B
thorny flameBOT
倧ιι倧 π»
crimson iron
so instead of dividing, we should...?
shut sand
multiply
crimson iron
exactly
crimson iron
**倧ιι倧 π»**
so what equation do we get if we multiply both sides of this by $b$
thorny flameBOT
倧ιι倧 π»
shut sand
256*b=a?
crimson iron
**倧ιι倧 π»**
so now what can we do since we also have this equation
shut sand
apply it to f(x)?
crimson iron
**倧ιι倧 π»**
how do we get $a$ on its own in this equatin
thorny flameBOT
倧ιι倧 π»
shut sand
on which ?
crimson iron
**倧ιι倧 π»**
remember how we isolated $a$ earlier? lets try to do the same thing inthis equation
thorny flameBOT
倧ιι倧 π»
crimson iron
$\frac{1}{256}=ab^2$
thorny flameBOT
倧ιι倧 π»
shut sand
to isolate A in this we would just divide by b
crimson iron
to isolate A in this we would just divide by b
well
wouldn't that get us $\frac{1}{256b}=ab$?
thorny flameBOT
倧ιι倧 π»
crimson iron
how would we isolate it?
well
we got a little closer
now there's only one $b$ on the right side
thorny flameBOT
倧ιι倧 π»
crimson iron
how can we get rid of that last $b$?
thorny flameBOT
倧ιι倧 π»
shut sand
divide it twice?
shut sand
(1/256b)/b=a?
thorny flameBOT
倧ιι倧 π»
crimson iron
so what to things can we say are equal now?
shut sand
?
crimson iron
**倧ιι倧 π»**
if both things here are equal to a
are they equal to each other?
shut sand
yes
thorny flameBOT
倧ιι倧 π»
shut sand
(1/256b)/b=256b
crimson iron
(1/256b)/b=256b
right
so now, how do we get all of those b's out of the denominator on the left
shut sand
multiply
shut sand
1/256 = 256(b^3)
shut sand
divide by 256
thorny flameBOT
倧ιι倧 π»
crimson iron
what should our last step be
shut sand
find b
shut sand
square root it
crimson iron
right
thats called the cube root
so what happens when we take the cube root of 1/256^2?
shut sand
2^5 cuberoot2
crimson iron
2^5 cuberoot2
well
we were taking cube root of 1/65536
so it should be 1/that
but yes
thorny flameBOT
倧ιι倧 π»
crimson iron
there we go
shut sand
so that what f(x) is?
crimson iron
so that what f(x) is?
remember, that's what b is
thorny flameBOT
倧ιι倧 π»
crimson iron
we have b
shut sand
256b
crimson iron
**倧ιι倧 π»**
so what is 256b if this is b
shut sand
256(1/32cuberoot4)
shut sand
4cuberoot2
shut sand
4cuberoot2?
thorny flameBOT
倧ιι倧 π»
crimson iron
so put in a and b
shut sand
4cuberoot2^x
shut sand
so what would our function be?
crimson iron
so what would our function be?
well
$ab^x=(4\sqrt[3]{2})b^x=4\sqrt[3]{2}\left(\frac{1}{32\sqrt[3]{4}}\right)^x$
thorny flameBOT
倧ιι倧 π»
crimson iron
do you follow that?
crimson iron
and puting cuberoot in is very confusing
thats fair
crimson iron
no because this is one webwork
oh
well
i think that this was a little slower because we couldn't use substitution
but its fine
shut sand
now that ik the answer i just dont know how to put it in
crimson iron
now that ik the answer i just dont know how to put it in
it might let you use $a^{1/3}$ instead of cube root
thorny flameBOT
倧ιι倧 π»
crimson iron
those mean the same ting
crimson iron
or 4 *2^1/3?
$\sqrt[3]{4}=4^{\frac{1}{3}}=(2^2)^{\frac{1}{3}}=2^{\frac{2}{3}}$
thorny flameBOT
倧ιι倧 π»
shut sand
can you put the entire function that way for me?
I just hate webwork so much because it's so complicated
crimson iron
**倧ιι倧 π»**
well
i showed you how to do it for the one in the fraction
try doing it for the one outside the fraction
shut sand
2^-17/3?
thorny flameBOT
倧ιι倧 π»
shut sand
i just got confused again
shut sand
this is way too confsuing
crimson iron
this is way too confsuing
sorry, its kind of hard to teach this if you don't at least know exponents well
you might want to ask your teacher about this
shut sand
yeah i already did
its cuz im taking a online course
so im trying my best to learn by myself
thank you though
.close
topaz sinewBOT
topaz sinewBOT
Available help channel!
limpid mica
i need to find the laplace of this function
topaz sinewBOT
i need to find the laplace of this function
limpid mica
i get the interval of 0 to 1 is just 0, but im lost on how to handle the other portion
limpid mica
yeah i was overthinking it, realized its just t
its a straight line with slope of 1, so itd just be t
i still messed up somehwere though, this answer is not right apparently
sweet shard
,w int x * exp(-cx)
thorny flameBOT
sweet shard
Your antiderivative looks wrong
twin pollen
Hello
twin pollen
If 100m sprinters accelerate from rest for 3.5seconds at 2.8metres/second squared, how long will it take them to complete the 100m sprint, assuming they maintain their speed the rest of the way.
drifting swift
!status
topaz sinewBOT
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
radiant temple
If 100m sprinters accelerate from rest for 3.5seconds at 2.8metres/second square...
maybe use this formula?
twin pollen
maybe use this formula?
I used it to find displacement and then calculated velocity final from here
drifting swift
maybe use this formula?
careful.
twin pollen
```
What step are you on?
1. I don't know where to begin.
2. I have begun but go...
3
Im dont know what to do next
I*
drifting swift
that's called status 2 not 3
9.8 m/s is correct for the final velocity
can you make a velocity vs. time graph?
twin pollen
Do i need to?
drifting swift
it'll help you
but if you're deathly allergic to that sort of stuff you don't have to
drifting swift
your answer is wrong bc you're not done + you didn't find what was asked for.
what was asked for is the total time of the sprint,
not the top speed achieved on it
drifting swift
no, that'll only be the average velocity for the part where the runner accelerates.
it won't be the average velocity for the entire sprint.
twin pollen
But it says assume velocity is same throughout
drifting swift
i still think making a velocity-time graph is (a) not hard and (b) fairly helpful
twin pollen
I got it
I got it
Thx
Wait
How come I cant use this formula
:
Velocity final= velocity initial + (acceleration) (time)
And solve for time
drifting swift
the motion of the runner is not uniformly accelerated throughout...
you already know the time for which she accelerates
topaz sinewBOT
@twin pollen Has your question been resolved?
topaz sinewBOT
topaz sinewBOT
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final garden
topaz sinewBOT
final garden
can someone give me a hint
topaz sinewBOT
@final garden Has your question been resolved?
lapis siren
hand of five cards chose from standard deck
probability that the hand contains a three of a kind AND a pair? example 555JJ
topaz sinewBOT
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
i mean the worksheet might not assume youve ever played poker
drifting swift
"three of a kind" and "pair" are also poker terms.
though granted they are more understandable to an outsider.
long stirrup
it's almost exactly like the previous one
instead of 2 suits you have 2 numbers
and instead of four cases, there's 2
lapis siren
if i were to choose 3 5's, that would be 4c3 right
and if i were to choose 2 jacks, that would be 4c2
but im pretty sure im missing something and idk waht
and total is just 32c5
crimson iron
so what do you think the final expression should be
lapis siren
(13 * 4c3 * 12 * 4c2) / 32c5
lapis siren
yes
crimson iron
why?
is it a different hand if i get 3 5's before i get 2 jacks vs 2 jacks before 3 5's?
crimson iron
right
long stirrup
it's not different from the suits problem
crimson iron
so if we are choosing 2 ranks from 13
and order does not matter
how many ways are there to do that
lapis siren
13c2
lapis siren
(13c2 * 4c3 * 12 * 4c2) / 32c5?
long stirrup
what's 12
crimson iron
(13c2 * 4c3 * 12 * 4c2) / 32c5?
why is the 12 there if we've already chosen ranks
lapis siren
wait so
13c2 is choosing both ranks
4c3 is choosing three identical cards in the rank
and 4c2 is choosing two identical cards in the other rank?
crimson iron
right
lapis siren
so (13c2 * 4c3 * 4c2) / 32c5?
crimson iron
that looks correct
topaz sinewBOT
long stirrup
it's not
topaz sinewBOT
Available help channel!
timid marten
Do you need to expand polynomial func when looking for real zero
timid marten
Currently the function is factored as -2x(x^2 - 36) (x^2 +9)
Im wondering since the expanded versionβs numbers are quite large
odd pagoda
no you dont want to expand
from the factored form it is very easy to find the roots
in fact, finding the roots is basically equivalent to factoring
if you have -2x ( x^2-36) ( x^2+9) = 0, that means you have a product of numbers which equals 0, so at least one of the numbers is 0
timid marten
if you have -2x ( x^2-36) ( x^2+9) = 0, that means you have a product of numbers...
Oh!! I see
Thank you for the help denascite 
Should i input the possible real zeros into the function as it is?
And expand afterward?
edgy quail
you can do that as checking ig lol
topaz sinewBOT
topaz sinewBOT
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dapper obsidian
topaz sinewBOT
dapper obsidian
so iβm finding the deriviative of y using this ancient method, using the deriviative cheat sheet is not allowed
the -2x-6 part was easy but iβm stuck at the sin bit
apparently it turns into 2cos(2x+5) but i have no clue how
topaz sinewBOT
@dapper obsidian Has your question been resolved?
cyan mesa
heya
cyan mesa
here's a tip, use $\sin\left(a+b\right)=\sin\left(a\right)\cos\left(b\right)+\sin\left(b\right)\cos\left(a\right)$
thorny flameBOT
Combustion
cyan mesa
where a is 2x+5, b = 2delta(x)
cyan mesa
cyan mesa
you're not dumb lol it's somewhat hidden
try splitting that whole limit into two limits
solve each one on its own
here's another tip: these two have a common factor
$\frac{\sin\left(2dx\right)}{dx}\cos\left(2x+5\right)+\sin\left(2x+5\right)\frac{\left(\cos\left(2dx\right)-1\right)}{dx}$
thorny flameBOT
Combustion
dapper obsidian
thanks for all the help <3
topaz sinewBOT
@dapper obsidian Has your question been resolved?
dapper obsidian
@cyan mesa iβm stuck π₯Ί
cyan mesa
ah alright
for the left limit
sin(2dx)/dx
as dx->0
you should know sin(ax)/x as x->0 = a
and for the right limit (cos(2dx)-1)/dx, you should just multiply by (cos(2dx)+1)/(cos(2dx)+1)
$\frac{\cos^{2}\left(2dx\right)-1}{dx\left(\cos\left(2dx\right)+1\right)}$
thorny flameBOT
Combustion
cyan mesa
$\frac{-\sin^{2}\left(2dx\right)}{dx}\cdot\frac{1}{\cos\left(2dx\right)+1}$
thorny flameBOT
Combustion
cyan mesa
$\frac{-\sin\left(2dx\right)}{dx}\cdot\frac{\sin\left(2dx\right)}{\cos\left(2dx\right)+1}$
thorny flameBOT
Combustion
cyan mesa
and -sin(2dx)/dx as dx->0 is -2, while sin(2dx)/(cos(2dx)+1) is 0/1 which is just 0
and the only thing left should be $2\cos\left(2x+5\right)$
thorny flameBOT
Combustion
cyan mesa
thank you
autumn wraith
What is set A? Is it the borel sets of the form (-inf,x] such that the pre image of it is in F
topaz sinewBOT
What is set A? Is it the borel sets of the form (-inf,x] such that the pre image...
sweet shard
What is set A? Is it the borel sets of the form (-inf,x] such that the pre image...
yes
sweet shard
What did you try
autumn wraith
I considered an arbitrary set in A which has the form (-inf,a], Iβm stuck with showing that the complement is also in A
autumn wraith
What did you try
^
sweet shard
do you know what it means for $B \in \mathcal{B}$ ?
thorny flameBOT
riemann
sweet shard
and the definition of script B?
autumn wraith
B is in the Borel sigma algebra
Do I assume F is a sigma algebra so that if (-inf,a] in A this implies X^-1(-inf,a] complement must also be in F hence (a,inf) is in A?
autumn wraith
do you know what it means for $B \in \mathcal{B}$ ?
^
sweet shard
Do you know what $\mathcal{F}$ is in a probability space?
thorny flameBOT
riemann
sweet shard
you're given that F is a sigma algebra yes
unless your book defines it differently, you should double check it matches https://en.wikipedia.org/wiki/Probability_space.
topaz sinewBOT
@autumn wraith Has your question been resolved?
jolly onyx
My assignment:
1: Find the definition scope of the function
- this was easy
and find her limits in every points of R- including the infinites
I then shall "justify", give grounds , why my calculations are correct ( this is not a proof )
2: Verify that the function is defined on the given point's domain and numerate the function. Again justify.
What I tried so far:
I am sending down my assignment so far and what I tried. I am not sure if I have the limits in +/- inf correct.
my justification there is : a/b -> where a:= sin(inf) is a large number / {divided} by a larger number , hence 0
Then for when the x approaches -2 I have no clue how to proceed , what kind of simplification ,
modification of the formula I shall apply.
Thanks!
arctic bluff
Hi there, I would be really grateful if you could help me with this question. Thank you π
jolly onyx
Hello! This is my first plead for help here! Thanks for answering
arctic bluff
topaz sinewBOT
Hi there, I would be really grateful if you could help me with this question. Th...
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).
@jolly onyx Has your question been resolved?
topaz sinewBOT
@jolly onyx Has your question been resolved?
topaz sinewBOT
@jolly onyx Has your question been resolved?
topaz sinewBOT
@jolly onyx Has your question been resolved?
reef fjord
!status
topaz sinewBOT
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
!showwork
topaz sinewBOT
Show your work, and if possible, explain where you are stuck.
jolly onyx
Have you learned Lhopitals Rule?
Hi! No we have not had it yet. Although I have heared of it
jolly onyx
**My assignment:**
1: Find the definition scope of the function
- this was easy...
New here, so I don"t know how to quite react to the bot prompt, here is my work. I got stuck at the last written thing .
topaz sinewBOT
@jolly onyx Has your question been resolved?
neon iron
when i reached ln(x+x^2) - integral (1+2x)/(1+x)dx
I split the integral to 1/1+x and 2x/1+x and dx = du
i will get ln(x+x^2) -ln (1+x) - 2 integral (x)/(1+x)du
what i did next is: let u = 1+x , x = u-1 and i substitute then also split
ln(x+x^2) -ln (1+x) - 2 integral 1du - 2 integral -1/u
lin(x+x^2) + ln(1+x) - 2(x+1)
i am having everything correct but i am getting -2 extra than the markscheme
neon iron
what did i do wrong pls help
woeful drift
where is your extra -2? if you're just subtracting 2 then it can be absorbed into the +c
neon iron
where is your extra -2? if you're just subtracting 2 then it can be absorbed int...
xln(x+x^2) +ln|1+x| - 2x - 2 + c is what am getting
its correct bec -2 is consdiered as c?
woeful drift
yeah a constant - 2 is still just a constant
neon iron
oh...
so i resolved the thing for 5times+
\wasted an hour just to know that its correct
lol
well thanks alot
woeful drift
it happens
neon iron
how do i close channel?
woeful drift
type .close
neon iron
.close
topaz sinewBOT
neon iron
it happens
for some reason the channel didnt get closed so ama just ask another question if u dont mind
integral sin^2 (x) = integral (1/2)(1-cos(2x))
do i have to know why or do i just memorize?
woeful drift
the channel did get closed, you'll want to open a new one since this will lock shortly
neon iron
oh ok
topaz sinewBOT
Available help channel!
wild frost
topaz sinewBOT
wild frost
I am confused again
lime zealot
use the definition of logarithm
topaz sinewBOT
@wild frost Has your question been resolved?
wild frost
use the definition of logarithm
?
lime zealot
$a^x = b$, then $x= \log_{a} b$
thorny flameBOT
η§ζ°΄
wild frost
Oh wait
The equation becomes (5-x)Β² = xΒ²-2x+6 right??
I know I am probably right but I need confirmation
topaz sinewBOT
@wild frost Has your question been resolved?
lime zealot
The equation becomes (5-x)Β² = xΒ²-2x+6 right??
yes, and +65 not +6
neon iron
\textbf{Question:} Let $X_1$ and $X_2$ be two independent random variables with Poisson distributions with parameters $\mu_1$ and $\mu_2$, respectively. Find the distribution of the random variable $Y_1 = X_1 + X_2$
\vs{5 mm}
\textbf{My attempt:} Since $X_1$ and $X_2$ are independent: [
\m f{x_1,x_2} = \f{\m\exp{-(\mu_1 + \mu_2)}\mu_1^{x_1}\mu_2^{x_2}}{x_1!x_2!}
]
topaz sinewBOT
\textbf{Question:} Let $X_1$ and $X_2$ be two independent random variables with ...
thorny flameBOT
neon iron
but where the hell am i meant to go from this
odd pagoda
sum means convolution
neon iron
those variables in my question are discrete though
odd pagoda
well there is a discrete convolution
pseudo jetty
but where the hell am i meant to go from this
calculate the probability of X1 + X2 = k for every single k
pseudo jetty
that's a multivariate transformation
odd pagoda
that would maybe work but is much more complicated
pseudo jetty
R^2 -> R^2
odd pagoda
you would need to come up with some u_2
pseudo jetty
you're considering an R^2 -> R function
odd pagoda
and then later be able to get rid of the u_2 again
pseudo jetty
(x, y) -> (x+y, y) would work
but it's more direct to just consider when X1 + X2 = k
neon iron
i see okay i think i got this
another question tho
Show that $Y =\ff{(X-\mu)^2}{\sigma^2}$ has a chi-squared distribution with 1 degree of freedom when $X$ has a normal distribution with mean $\mu$ and variance $\sigma^2$
thorny flameBOT
pseudo jetty
what's your definition of chi^2
neon iron
pseudo jetty
i was hoping it would be chi^2(1) ~ Z^2 where Z is standard normal
then you wouldn't have to prove anything
pseudo jetty
i was hoping it would be chi^2(1) ~ Z^2 where Z is standard normal
prove this first
show that when Z is standard normal then Z^2 is chi^2 degree 1
just calculate the density explicitly
neon iron
okay one second
i get like
an integral with no closed form
oh wait okay nvm i think i got the answer thanks
.close
wild frost
topaz sinewBOT
topaz sinewBOT
@wild frost Has your question been resolved?
topaz sinewBOT
@wild frost Has your question been resolved?
topaz sinewBOT
@wild frost Has your question been resolved?
jagged wigeon
I do not understand what i am doing in that exercise.
I don't know if it's right or not...
topaz sinewBOT
I do not understand what i am doing in that exercise.
I don't know if it's right...
topaz sinewBOT
@jagged wigeon Has your question been resolved?
topaz sinewBOT
@jagged wigeon Has your question been resolved?
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@jagged wigeon Has your question been resolved?
brave zenith
I need help finding the maclaurin series for the square root function, I know it doesnβt exist at x=0 since the derivative there cannot be evaluated, so Iβll need to start at another point.
Iβm trying to get the answer in sigma notation since I want to code it into a for loop in MatLab (I donβt need help with the code, just this math part).
I canβt believe I spend a full hour on this 
Any answer would be appreciated
topaz sinewBOT
I need help finding the maclaurin series for the square root function, I know it...
brave zenith
I need help finding the maclaurin series for the square root function, I know it...
(Since it doesnβt exist at x=0, I wanna start at 1 instead)
tawny spade
If it starts at 1 its not a maclaurin series π€π€π€π€
mellow venture
,w nth derivative of sqrt(x)
thorny flameBOT
brave zenith
,w nth derivative of sqrt(x)
Thnx, do you know how I can get this in sigma notation
Oh hold on
Lemme take another look at it, srry
topaz sinewBOT
Available help channel!
frail jacinth
.open
prime phoenix
I try to learn this, im like 40% aware of whats going on. Could someone teach me to solve this one? π
a) Determine the equation for the straight line in the figure.
b) In the coordinate system, draw a straight line with the slope k = -1.
c) In the coordinate system, draw a line perpendicular to the line in task a and write its equation.
topaz sinewBOT
I try to learn this, im like 40% aware of whats going on. Could someone teach me...
@prime phoenix Has your question been resolved?
topaz sinewBOT
@prime phoenix Has your question been resolved?
fluid belfry
$P^{H}=-\log_{10} [H^{+}]$\
$[H^{+}]=-10^{P^{H}}$\
topaz sinewBOT
$P^{H}=-\log_{10} [H^{+}]$\\
$[H^{+}]=-10^{P^{H}}$\\
thorny flameBOT
π±!Yajat! γCatfan1398γπ±
chilly fulcrum
- log x = log(1/x)
young tinsel
Its wrong because
pH = -log([H^+]) β> -pH = log([H^+]) β> 10^-pH = [H^+]
pH refers to the potential of hydrogen
young tinsel
βSeven is Heavenβ Its acidic nor basic, its neutral.
chilly fulcrum
I mean okay same thing
young tinsel
not potential
nah pH the meaning is potential of hydrogen
sure it is the power as well
chilly fulcrum
βSeven is Heavenβ Its acidic nor basic, its neutral.
it depends on the temperature too. scale of ph changes with increase or decrease in temperature
young tinsel
but I was speaking abt meaning
chilly fulcrum
yes, ph means power/potential of hydrogen
fluid belfry
pH = -log([H^+]) β> -pH = log([H^+]) β> 10^-pH = [H^+]
yup okay, thankyou
young tinsel
Thanks for the info.
young tinsel
pH < 7 acidic, pH = 7 (Neutral. Seven is heaven) pH > 7 basic
The more acidic it becomes the greater concentration of Hydronium ions H3O^+ if pH < 7
young tinsel
The more basic it becomes if concentration of OH^- ions becomes greater than 7 more basic
7 is an equal ratio of both OH^- and H3O^+
young tinsel
i will now close the channel
kk.
blazing crescent
topaz sinewBOT
blazing crescent
for part c) and d)
i've calculated that p(x<=8) = 0.9722 which is > 0.95
and also calculated that p(x<=7) = 0.9302 which is < 0.95
shouldn't this mean that the critical region is x>8?
mild hearth
if you've calculated it right, then yes
topaz sinewBOT
@blazing crescent Has your question been resolved?
mild hearth
yeah so you're right
i mean ok
X > 8 is the same thing as X >= 9 when X is only whole numbers
blazing crescent
so i would technically get the mark?
manic swan
limit (ln(x+1)-x) / (x^(2))
X->0
topaz sinewBOT
limit (ln(x+1)-x) / (x^(2))
X->0
manic swan
I try to make x as ln(e^x) but it don't work
I try also to make 1/x as factor and make the limit of ln(x+1)/x Which = 1 but also it's didn't work
chilly walrus
what does ln(x+1) go to as x->0
manic swan
not -inf lol
You broke my brain 
manic swan
Well what should i do then?
.
chilly walrus
um
i mean you can try l'hΓ΄pital after separating the fractions
but idk how that would work
manic swan
i mean you can try l'hΓ΄pital after separating the fractions
The professor say no hospital rule π
chilly walrus
ok
sweet shard
comparison works
manic swan
comparison works
Squeeze Theorem?
chilly walrus
comparison works
yes
manic swan
π€
manic swan
Nah ,
I don't Think they will go for something like that
Well even we didn't study it
manic swan
i mean it will give u -1/2
Yes , using hospital rule
trail heath
no series expansion
will give u minus half
and obv it should be the same as lhopitals
neon iron
it's okay, just carry on
manic swan
,
manic swan
comparison works
Well , how i can use it
@chilly walrus π (sorry for mention and Disturbing you)
chilly walrus
let me think
manic swan
Sure , take your time
chilly walrus
Sure , take your time
basically
these steps are algebra
$\frac{\ln(1+x) - x}{x^2} = \frac{\left(\ln\left(x+1\right)-\ln\left(e^{x}\right)\right)}{x^{2}}$
thorny flameBOT
artemetra
chilly walrus
$\frac{\left(\ln\left(\frac{\left(x+1\right)}{e^{x}}\right)\right)}{x^{2}}$
thorny flameBOT
artemetra
chilly walrus
=$\frac{\left(\ln\left(\frac{\left(x+1\right)}{e^{x}}\right)\right)}{\ln\left(e^{x^{2}}\right)}$
thorny flameBOT
artemetra
chilly walrus
now, by $\frac{\log_c(b)}{\log_c(a)}=\log_a(b)$
thorny flameBOT
artemetra
chilly walrus
we get $\log_{e^{x^2}}\left(\frac{x+1}{e^x}\right)$
thorny flameBOT
artemetra
manic swan
not sure what comparison test to make
As i know, i think we can use comparison test when we have series
But i'm not sure if we can use it here
chilly walrus
oops i meant squeeze theorem
manic swan
oops i meant squeeze theorem
Hmm π€, yea if we can use it ,i it's will be great , but we need to find the two numbers that we will use it in comparison
topaz sinewBOT
@manic swan Has your question been resolved?
manic swan
<@&286206848099549185>
sweet shard
do you know
$\lim_{x\to 0} \frac{\log(1+x)}{x} = ?$
thorny flameBOT
riemann
sweet shard
<@&286206848099549185>
if so, divide all terms in your fraction by x and then take the limit
thorny flameBOT
gkeocog
manic swan
do you know
$\lim_{x\to 0} \frac{\log(1+x)}{x} = ?$
I think it's 1 , right?
log(1+x)^(1/x)
sweet shard
yes if you've proven that result you should use it
$\frac{\log(1+x) / x - x / x}{x^2 / x} = ?$
thorny flameBOT
riemann
manic swan
So , limit log (1+x)/x= 1
Then x/x = 1
So 1-1= 0
Then for The denominator xΒ²-x=x
After if i calc limit it's will be 0/0
manic swan
yes if you've proven that result you should use it
Hmmmm i'm not sure what i should do next
sweet shard
hmm i thought this would become the derivative of log(1+x)/x at x=0, but that's not helpful
topaz sinewBOT
@manic swan Has your question been resolved?
proven narwhal
topaz sinewBOT
proven narwhal
Donβt you get -4/2x if you actually take the square root of the top
Then what do u do
Or if I cube everything I get 9x^3/4x^3 if im just considering the highest power
thorny flameBOT
riemann
thorny flameBOT
proven narwhal
Why cant I do this?
knotty ledge
$\sqrt{9x^2+16} \neq 3x + 4$ if that's what you're trying to do
thorny flameBOT
Ξ£ΞCu
proven narwhal
$\sqrt{9x^2+16} \neq 3x + 4$ if that's what you're trying to do
I squared everything
knotty ledge
Well $(a-b)^2 \neq a^2 - b^2$ either
thorny flameBOT
Ξ£ΞCu
proven narwhal
Does the square not just cancel out the root tho
topaz sinewBOT
@proven narwhal Has your question been resolved?
past venture
what do i put in this
topaz sinewBOT
what do i put in this
neon iron
what do i put in this
alr so
look at the graph
when is the line going up
what interval
neon iron
look at the line itself
past venture
yeah
past venture
x>-3?
past venture
it would be none right
past venture
wait can u hold on like 3 mins please i need to help my brother out
past venture
so when does it stop going down
-3
neon iron
sure
past venture
ty
past venture
lmk when ur back
ok im back
neon iron
given what you already said
neon iron
so i would put x<-3?
yeah
neon iron
for the decreasing part
and then
for the end behavior
read the graph from right to left
because then you are looking at the point of view as x approaches -infinity
what do you think y is doing
past venture
decreasing
neon iron
well no
technically it is but not in this context
read the graph from right to left this time
not left to right
past venture
increasing
past venture
yes
neon iron
so then what would be a reasonable assumption for what y will be approaching
past venture
positive infinity?
past venture
y->+inf
neon iron
yep
past venture
and it would be the opposite for the second part right
neon iron
in some cases yes
but now
change your perspective back to normal
read the graph from left to right
what is y doing
as x approaches infinity
past venture
decreasing and then increasing
past venture
yes
neon iron
does it show any signs of stopping
past venture
no
neon iron
so then what would be the answer
past venture
y->-inf?
neon iron
yep
past venture
ohhh ok
past venture
yeah
past venture
uhh
neon iron
honestly i forgot
past venture
i dont think so ngl
neon iron
hmm
past venture
i think its the function itself
neon iron
the function is always in the realm of positivity
past venture
oh
past venture
yeah
neon iron
so
using process of elimination and logic
since we know the function is always positive
what would we fill the positive box in with
past venture
x < -3 and x > -3
neon iron
yep
past venture
what about negative?
neon iron
and since we know theres no point in the interval we are given that is negative
what would we put in the negative box
past venture
none?
neon iron
yep
past venture
i was struggling hard as hell on this question
past venture
is there anything else u need help with
besides just checking the rest of my questions not really
neon iron
besides just checking the rest of my questions not really
did you solve them already
past venture
its only 6 questions btw
neon iron
1st one is right
past venture
ok
neon iron
2nd one is right
3rd one is right
4th one is right
for the 5th one i think you need to pick an option still
neon iron
the graph of the equation looks good though
neon iron
the first and last ones were wrong
oh yeah mb
i think u woulda had to start at y=6
the slope was fine tho i think
neon iron
np
past venture
btw how do i close the channel
neon iron
.close
i think
something like that
it'll give you a prompt to do it in a little whiles anyway
keen raptor
.close
ivory wave
v
topaz sinewBOT
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
1
acoustic pecan
A=xy and x+2y=600 (corrected by pure)
try get something from there
x and y are the respective side lengths of the rectangle
vale furnace
well it would be x+2y=600
acoustic pecan
true say, didnt notice that
ivory wave
can i sub for x first or y?
ivory wave
this isn't derivatives 
quadratic function
how do you know you need to use derivatives?
vale furnace
this isn't derivatives <:sadcat:547124024585486359>
Really?
ivory wave
yeah
vale furnace
Well itβs an optimisation problem
ivory wave
bruh
vale furnace
Do you know derivatives