im asking u
#help-13
mellow solstice
ik
mellow solstice
OK
royal wasp
AROUND
royal wasp
y=mx+b, U HAVE Y, X, AND M
mellow solstice
OK
royal wasp
WHAT DO U THINK WE SHOULD DO
mellow solstice
MANE
royal wasp
solve for B
mellow solstice
OK
royal wasp
SOLVE FOR B
royal wasp
DUDE
mellow solstice
NOOOOOoOoO
mellow solstice
where IS THE B
mellow solstice
noOOOOoOOoOO
royal wasp
now just put it in slope intercept form
mellow solstice
OONOOONOONONOOONONOOOOoOooOOOoloOOoooooo
royal wasp
y=(number)x plus (what u solved for)
mellow solstice
😦
grave nest
lmao
royal wasp
thats the equation
grave nest
whatis happing
grave nest
is that a bo3 pfp
grave nest
yaya
mellow solstice
w mans
grave nest
best cod game by far
grave nest
im only in 7th grade
grave nest
(outro music plays)
mellow solstice
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cedar kilnBOT
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outer stirrup
cedar kilnBOT
outer stirrup
Where do I go from here?
dire geode
probably use sum angle formulas for tan
it shouldn't be too different from your base case
outer stirrup
ill try
cedar kilnBOT
@outer stirrup Has your question been resolved?
outer stirrup
idk...
dire geode
probably use sum angle formulas for tan
did you look this up
outer stirrup
yeah i cant really figure it out...
i looked at the answer but i still
dont really get it...
it gets up to the same point as me but i dont know wtf happens in the next step
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cedar kilnBOT
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honest spade
cedar kilnBOT
honest spade
Use interpolation to estimate median , why am I wrong?
cedar kilnBOT
@honest spade Has your question been resolved?
cedar kilnBOT
@honest spade Has your question been resolved?
lone garden
is x in the half open interval [x,x)?
cedar kilnBOT
is x in the half open interval [x,x)?
lone garden
(we are working in R with the euclidean metric)
lone garden
i cant really find a concrete answer on google so im guessing my question is ill-defined somehow
lone garden
im listening...
cedar kilnBOT
toxic moat
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radiant jolt
cedar kilnBOT
radiant jolt
I don't know how to do this
south tundra
Part a or part b?
cedar kilnBOT
@radiant jolt Has your question been resolved?
radiant jolt
Part a or part b?
sorry I was distracted, part a
cosmic steppe
You just use the average slope formula
radiant jolt
are you sure?
it's in the topic of differentiation and antidifferentiation of polynomials
.close
crimson sedge
in other words, a function is bounded, or bounded above, or bounded below if f(X) is a linearly orded subset of Y? Since if f(X) was partially but not linearly ordered then not every element would be comparable therefore being impossible to satisfy the definitions of upper or lower bounds.
cedar kilnBOT
@crimson sedge Has your question been resolved?
crimson sedge
<@&286206848099549185>
sacred grail
no
sacred grail
even if a and b are not comparable
crimson sedge
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cedar kilnBOT
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light pine
can someone explain this to me plz
cedar kilnBOT
can someone explain this to me plz
light pine
ie why is not B a subset of not A true?
simple abyss
hello
simple abyss
can i get an explanation as to why the gof domain is that interval?
(ping me if someone is here)
crimson sedge
for g(x) to be defined, whatever is inside g(...) should be in the domain [-1,1]
And so f(x) has to be in [-1,1] for g(f(x)) to be defined
@simple abyss
simple abyss
<@681264295560085523>
hello
simple abyss
for g(x) to be defined, whatever is inside g(...) should be in the domain [-1,1]...
but why is the answer [-2,0]?
simple abyss
shit ngl the [-1,1] through me off
are we discarding that from our solution, and using (-inf,0]?
crimson sedge
discarding what
crimson sedge
for g(x) to be defined x has to lie between [-1,1]
simple abyss
yes alright
crimson sedge
And so for g(f(x)) to be defined, f(x) has to lie in [-1,1]
simple abyss
yes
simple abyss
i see
crimson sedge
e^x is always positive it can't be in [-1,0] part of the [-1,1] interval
But it can be in (0,1]
for e^x to be in (0,1]
x can be in (-inf,0]
simple abyss
isnt it from [-2, 2]?
crimson sedge
Yes exactly so we can't take the full (-inf,0] we will only include the part which is common in both which satisfies both the conditions at the same time
crimson sedge
well you can substitute different values for x in e^x to check
crimson sedge
Yes
simple abyss
why do we include the 0?
crimson sedge
Because it is in both the sets
Same reason we include every number in this interval
simple abyss
interesting
simple abyss
x can be in (-inf,0]
okay so when you say x is (-inf,0] is that the intervals we could put into gof or just e^x
simple abyss
okay i see
crimson sedge
that is for gof but didn't came directly at that
simple abyss
so for e^x to be in an interval of (0, 1] x can be -inf to 0?
crimson sedge
Yes
simple abyss
x cant be anything higher than 0 oh yes
ohhh okay interesting
thank you so much!
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cedar kilnBOT
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minor garnet
Can anyone help with this: https://math.stackexchange.com/questions/4553555/error-bound-of-flab-where-a-and-b-are-upper-triangular-matrices
cedar kilnBOT
Can anyone help with this: https://math.stackexchange.com/questions/4553555/erro...
@minor garnet Has your question been resolved?
cedar kilnBOT
@minor garnet Has your question been resolved?
cedar kilnBOT
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hazy frigate
what is the diffrence? i am really confused since the books dont explain
crimson delta
[2,5] is the interval from 2 to 5, including 2 and 5
]2,5[ is the interval from 2 to 5, excluding 2 and 5
the second one is also often written as (2,5)
broken mist
I've never seen that notation before for intervals that's cool
cedar kilnBOT
@hazy frigate Has your question been resolved?
stiff light
I am trying to find E[X|Y] where X is uniform over [0,1] and Y is uniform over [0,x] given X=x
stiff light
I have found the pdf of X|Y but I cannot find the integral
south juniper
you mean you have found f(x|y)?
stiff light
Yes, by first finding f(x, y) and f(y), then using f(x|y)=f(x,y)/f(y)
south juniper
and what is it?
south juniper
Why is x b/w y and 1?
stiff light
Because f(x, y) = 1 / x when x is between y and 1
and this is true because
f(y | x) = 0 for y > x (given by the fact that Y is uniform over [0,x])
south juniper
Okay so for E(X|Y), you need the integral of x f(x|y), wrt x that is
stiff light
and xf(x|y) = x (-( 1 / x*ln(y) ) ) = -1/ln(y) (when x is between y and 1)
so the integral should just be the integral of -1/ln(y) dx from y to 1
which gives E[X|Y] = -1/ln(y) + y/ln(y) ?
south juniper
Or just (y-1)/ln(y)
frail wagon
cedar kilnBOT
rugged palm
What's the question?
frail wagon
Solve & graph
rugged palm
what have you tried?
frail wagon
Idk what to do
rugged palm
Would you be able to graph this if it wasn't an inequality?
frail wagon
yes
rugged palm
Oh ok that's great
Do you know the difference between graphs of equations and graphs of inequalities?
rugged palm
what do you mean?
frail wagon
the inequality signs
rugged palm
Nice
To graph inequalities, the first step is to graph your equation normally, if your inequality includes a = (so ≥ or ≤, like in this case) draw the equation with a solid line, if it doesn't (so for example > or < only, without the equals sign), draw it dotted
Then, if it's < or ≤, color all the area under the equation, if it's > or ≥, color all the area above the equation
With linear equations it helps if you isolate your y, and get your equation to something like y < ...
(I used the < sign, but of course that can be any inequality symbol)
Keep in mind that since this is an inequality, if you multiply or divide on both sides by something negative, you have to change the direction of the inequality symbol
frail wagon
so I can change the signs to a equal sign
rugged palm
I don't recommend it
rugged palm
isolate the y
frail wagon
so subtract 2 from both sides?
rugged palm
You should get something like y ≤ ...
rugged palm
?
frail wagon
y ≤ 0?
rugged palm
you should start from one of the inequalities you were given
rugged palm
x + 2y ≤ 2
Subtract 2 on both sides
x + 2y - 2 ≤ 0
Instead you want to have y only on one side
frail wagon
im confused
rugged palm
What exactly is the hard part?
frail wagon
I had subtracted under the x
rugged palm
what do you mean?
rugged palm
I don't understand
frail wagon
I subtracted from both sides
rugged palm
what do you get?
frail wagon
-1x+2y
rugged palm
what happened to the inequality
frail wagon
but wouldnt it be x = 0
rugged palm
why?
rugged palm
Like this I can't understand what you are doing
Can you write your steps as equations?
frail wagon
Im just guessing
rugged palm
don't, that's not a good idea
So if you remember how equations work, you can do something to an equation, as long as you do it on both sides
You can add numbers on both sides, you can multiply or divide (all terms at the same time!) on both sides, and so on
Here's an unrelated example
If you have something like a = 5, if you add 2 on both sides, you'll notice what you get is still true
a + 2 = 7
You can do whatever you want to this equation, as long as you do it on both sides
Here I divide it by 3, and it still remains true
(a + 2)/3 = 7/3
In this case, you are starting with x + 2y = 2, and you want to get to something like y = ..., so you have the y on one side, and on the other side all the other terms
frail wagon
In this case, you are starting with x + 2y = 2, and you want to get to something...
I assumed doing that i would get y ≤ 0
rugged palm
That doesn't happen (btw, I kinda left the inequality part out, for now it's important to understand how equations work)
So what would you do?
frail wagon
subtract 2?
rugged palm
Yes that will help, what is the equation now?
frail wagon
( x +2y) -2 =2?
rugged palm
Oh mb I forgor what the equation was 
but you only subtracted 2 on one side
frail wagon
so ( x + 2y ) -2 = 2-2?
frail wagon
-2x-4y?
rugged palm
no, you can only add or subtract numbers with the same literal part
So this becomes (spoilers ahead) ||x + 2y - 2 = 0||
frail wagon
okay i see
rugged palm
So you want to get y to be the only term on one side, what can you do now?
Something that I remember helped me was thinking that when you add or subtract a term on both sides, you are just moving that term on the other side and changing it's sign
like (unrelated examples)
beginning: x + 3 = 5
3 = 5 - x (moved the x on the other side, and changed it's sign)
3 - 5 = -x (moved the 5 on the other side, and changed it's sign)
If it doesn't help, ignore it
frail wagon
do I add 2?
frail wagon
would it change to x-2=-2
rugged palm
you are forgetting something in the right side of the equation
frail wagon
-2y
rugged palm
Yes that's it! Nice
And now? We have to get rid of that pesky -2, and then we will have our nicer equation
frail wagon
add 2?
rugged palm
we would get x = -2y + 2, but we made a step back, and there are more terms in the side where there's supposed to be the y only
Tip: multiply or divide both sides by something
(reminder: we have x - 2 = -2y)
frail wagon
divide both sides by 2?
frail wagon
x-1=-y?
rugged palm
The right side is good, but you can't simplify like that on the left side, you either simplify all terms in the numerator, or none
so the equation becomes (x - 2) / 2 = -y
frail wagon
why x -1 ?
rugged palm
mb, fixed it
frail wagon
oh sorry, got it
rugged palm
Ok, we are very close now, the only thing left is to get rid of that -, any ideas?
frail wagon
honestly no
rugged palm
What happens when you multiply something by -1?
I don't want a specific answer, just some observation
frail wagon
stays the same?
rugged palm
That only happens with 0 · -1, try doing with a calculator 5 · -1, or something like that
frail wagon
its just -5
rugged palm
yes, but we started from 5
we multiplied 5 by -1, and we got -5
So multiplying by -1 changes the sign of what you multiply it with
Here are a few examples:
2 · -1 = -2
-1 · -1 = 1
x · -1 = -x
(h · x) · -1 = -(h · x)
And so on
rugged palm
why?
Last step: (x -2) / 2 = -y
If you multiply everything by 2, that denominator cancels out nicely, but then you get -2y on the right side, but you only want to have y
Maybe we can multiply both sides by || -1 ||, and it will change the signs on both sides, making that -y on the right side a y, which is exactly what we need
frail wagon
what about the left
rugged palm
That's a great question
The quick way is just to leave it as it is, but with a - before
so
- (x - 2) / 2 = y
And we can say that we are done
But generally, a - before a fraction means that you can change the signs of all the terms either the numerator or the denominator, but not both at the same time
You get to pick if you want to change the signs of the numerator or the denominator
This is because if you change both of them, it's like you multiply by -1 two times (the -1 cancel out), like this
(unrelated example)
a + b
(45)
Multiply both the numerator and the denominator by -1 (→ which doesn't do anything to the fraction because of what we said before)
(-1) · (a + b)
(-1) · (45)
But now the -1 cancel out, so it's like we didn't do anything
You can cancel those -1s because the numerator and the denominator are "factored", which is a way of saying that everything is being multiplied
frail wagon
oh i see
rugged palm
Do you have any questions about what we did so far?
frail wagon
Im not good at this topic
rugged palm
If you do have questions about anything we did so far feel free to ask them
frail wagon
its fine, thank you for your help
rugged palm
Ok, awesome
Now it's kinda late in my country, I have to go to sleep
I suggest stopping here for now, at least take a break, this is already a lot of information
You should take smaller steps, it's very important, otherwise it will be unnecessarily hard to learn new topics
With equations you can do some very cool stuff
Keep the good work up 
trim crescent
Hello, i have a fairly easy question i think. When you divide 2 small o’s and try and find the limit, do i just say that they both approach 0 ? Let me send a pic it’ll probably be clearer
trim crescent
I used the Taylor expansion to end up with both o(1) and o(t)
Can i just say that lim o(1) = lim o(t) = 0 when t approches 0 ?
cedar kilnBOT
@trim crescent Has your question been resolved?
trim crescent
.close
ocean cloak
cedar kilnBOT
ocean cloak
hi
hollow minnow
Hello
ocean cloak
ik how to do this question but im sort of stuck on the factoring after setting the derivative to 1/2
ocean cloak
yes
velvet mortar
*6x^2
wraith daggerBOT
Pure
hollow minnow
There we go
ocean cloak
mhm
hollow minnow
Don’t think you can solve this analytically
Can you use a calculator for this?
Well you can discard A and D quite easily
ocean cloak
Can you use a calculator for this?
no
well yes
u have to cuz of the answer choices
solemn torrent
well
aye
then
trial and error
ez
just plug in
every multiple choice
and see
hollow minnow
1.777^3 
crude quest
Out of a class of 20 students, how many ways are there to form a study group that contains at least one of Bob, Sue, and Alicia? A study group must have at least two students.
hoary notch
is that the full question?
crude quest
yes
hoary notch
The question writer needs to be fired
solid juniper
lolll
raw kernel
i think it means bob sue and alicia are in a study group out of the 20 students and the chances of getting at least one of them in a random chosen group of 2+ people
solid juniper
what makes you think it's asking for a probability?
cedar kilnBOT
@crude quest Has your question been resolved?
hoary notch
Anyways I would just find the number of ways neither Bob, Sue, nor Alicia are in a study group
find how many arrangements are possible excluding Bob, Sue, and Alicia
hint: assign each student a boolean (in study group or not)
make sure to exclude single student cases
minor garnet
.repost
trail bridge
cedar kilnBOT
trail bridge
I tried to do part (b), but I kept on getting long answers which are not expected
<@&286206848099549185>
cedar kilnBOT
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trail bridge
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cedar kilnBOT
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heady salmon
How would I correctly solve this?
cedar kilnBOT
How would I correctly solve this?
cosmic steppe
How would I correctly solve this?
Rational function
So it needs a numerator and a denominator
Start with where it is discontinuous
Where is the function discontinuous
cosmic steppe
Yeah
Which one is an asymptotic discontinuity and which one is a removable discontinuity?
heady salmon
im not quite sure what your taking about, all i is that these two numbers are the vertical asymptotes, and they belong in the denominator
cosmic steppe
One of them is not a vertical asymptote
One of them is
The other isn't
Identify which one is an asymptotic discontinuity and which one is a removable discontinuity
heady salmon
oh wow, i didnt read that problem correctly, ya 4 would be the vertical asymptote
heady salmon
Identify which one is an asymptotic discontinuity and which one is a removable d...
oh so the removable discontinuity would be 9 and the asymptotic Discontinuity would be 4
if theres a whole in this function does that mean that there's an imaginary number in here somewhere?
cosmic steppe
No
There's no imaginary number
So the removable discontinuity at 4 would indicate that the numerator would also have (x-4)
And then it also has a horizontal asymptote
What's the horizontal asymptote?
cosmic steppe
Yeah so
We can start with just having an asymptote of y = 1, and then we multiply this function by 2
$$2\cdot \frac{x(x-9)}{(x-9)(x-4)}$$
wraith daggerBOT
Umbraleviathan
cosmic steppe
Removable discontinuity at x=9, asymptotic to x = 4 and y = 2
heady salmon
Removable discontinuity at x=9, asymptotic to x = 4 and y = 2
how would you make the 9 into a hole?
cosmic steppe
**Umbraleviathan**
I mean it's pretty obvious: the (x-9)'s would cancel out
But you would change the function then
So you have to leave it both as factors in the numerator and denominator
hollow briar
1/4×7 + 1/7×11 + 1/11×15 ... 1/47×51 = ?
Please help
cedar kilnBOT
1/4×7 + 1/7×11 + 1/11×15 ... 1/47×51 = ?
Please help
obsidian coral
1/4×7 + 1/7×11 + 1/11×15 ... 1/47×51 = ?
Please help
Is that suppose to be $\frac{1}{4 \times 7} + \frac{1}{7 \times 11} + \frac{1}{11 \times 15} \ldots \frac{1}{47 \times 51}$ or $\frac{1}{4} \times 7 + \frac{1}{7} \times 11 + \frac{1}{11} \times 15 \ldots \frac{1}{47} \times 51$?
wraith daggerBOT
dldh06
hollow briar
First one
1/(4×7)...
$\frac{1}{4 \times 7} + \frac{1}{7 \times 11} + \frac{1}{11 \times 15} \ldots \frac{1}{47 \times 51}$
wraith daggerBOT
C H A C H A M A R U
livid hound
partial fractions should work here
hollow briar
Please explain..
livid hound
also did you copy down the question correctly?
hollow briar
Yes
livid hound
are your sure that first term is 1/(4*7)?
livid hound
express 1/(3*7) in the form
a/3 - b/7
cedar kilnBOT
@hollow briar Has your question been resolved?
oak fossil
I have two unit circles whose centeres are unknown. All I do know about them is that they overlap and the distance between their centers is 2a where a lies between 0 and 1(both inclusive)
oak fossil
How can I find the overlapping area of the circles using integration
I have tried devising a general formula for both the circles using equation of circle with centeres as variables but it doesn't help me reach a solid conclusion. I feel like the question is too vague to be dealt with
Most of the Internet starts of with considering that circumference of one circle lies on center of other circle which opens a lot of opportunities. But this specific case isn't limited to just that
cedar kilnBOT
@oak fossil Has your question been resolved?
rain drift
I have this problem.
cedar kilnBOT
I have this problem.
rain drift
and I have this definition:
I need to see if my proof for 2 is good and then see if I'm on the right track with 3
thick cipher
Okay
rain drift
Is this fine for 2?
thick cipher
The thing on the empty set comes from the fact that everything is true for any element of the empty set by convention
thick cipher
**MellowDramaLlama**
Good
thick cipher
Yes
rain drift
sweet
that's a relief
I was struggling with that
okay so for the final definition
Okay so for the last one, I was kind of thinking that since the finite intersection of open sets is a subset of any of the open sets, and so it's open?
Namely if $U_i$ is open for all $i = 1, 2, ... n$, then $\bigcap\limits_{i =1}^n U_i \subseteq U_i$ implies $\bigcap\limits_{i =1}^n U_i$ is open since any $U_i$ is open. is that true or can I not make that assumption?
wraith daggerBOT
MellowDramaLlama
thick cipher
You need a bit of work there
If p is in your intersection it is in every set
Thus every set has an internal with p
The finite intersection of intervals with p is an interval with p
rain drift
oh huh
so basically that if we have a point p in the finite intersection, then there is a segment around p that has to be in collection of open sets?
and then it's open since that point is in the segment and that segment would be a subset of T_E?
thick cipher
Yup
rain drift
huh nifty
okay let me see if I can write that up in a "proofy" way lol
- $Let ${U_i}{i = 1}^n$ be a collection of open sets of $T_E$. We want to show that $\bigcap\limits{i =1}^n U_i $ is open. Notice that if $\bigcap\limits_{i =1}^n U_i = \emptyset$, then $\bigcap\limits_{i =1}^n U_i $ is open since $\emptyset$ is open. If $\bigcap\limits_{i =1}^n U_i \neq \emptset$, then there exists $p \in $\bigcap\limits_{i =1}^n U_i $ such that $p \in U_i$ for all $i = 1, 2, ... , n$. Without loss of generality, choose $U_m$ for some $m \in 1, 2, ... , n$ and let $p \in U_m$. Since $U_m$ is open, then there exists a segment $r$ such that $\ in r$ and $r \subseteq U_m$. Notice that $r \subseteq \bigcap\limits_{i =1}^n U_i \subseteq U_m$. Therefore $\bigcap\limits_{i =1}^n U_i \in T_E$ so $\bigcap\limits_{i =1}^n U_i $ is open.
Like that?
sorry one second
wraith daggerBOT
MellowDramaLlama
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
thick cipher
Good
random osprey
Dank
thick cipher
My pleasure
rich radish
could someone pls remind me how to fill in the values
cedar kilnBOT
could someone pls remind me how to fill in the values
rich radish
cedar kilnBOT
@rich radish Has your question been resolved?
rich radish
I think it wants it in terms of pi
how would i answer it
crimson sedge
How do I factor something like this?
cedar kilnBOT
How do I factor something like this?
crimson sedge
Not sure where to go from there
And also, is there a faster way of finding the value of n? My way seems quite tedious
You had 5n(n-1)(n-2)=300 => n(n-1)(n-2)=60 i think that's the best you can have
Wdym
(5n(n-1)(n-2))/6=50
solemn torrent
yeye
crimson sedge
$(5n(n-1)(n-2))/6=50$
wraith daggerBOT
Jared
crimson sedge
Oh one sec
crimson sedge
Idk the theorem
solemn torrent
just plug in
values of x
as factors of 60
and see if it =0
if it does
it’s a factor
crimson sedge
I think it's easier to put $\dfrac{n!}{\left( n-3\right) !}-\dfrac{n!}{3!\left( n-3\right) !}=50$ on the same denominator
wraith daggerBOT
Zamarus
crimson sedge
**Zamarus**
Try this maybe
But you can also try n=1,n=2... etc until you find n(n-1)(n-2)-60 = 0
Bruh
Led me to the same outcome
Where do I even go from there
…
You wanted to factor it so
Is there a way without
We told you
try n=1,n=2... etc until you find n(n-1)(n-2)-60 = 0
or try what i said
crimson sedge
**Zamarus**
This?
Yeah
Ho i think you find something similar
But it's faster at least
I just erased everything for nothing… 💀
You're saving on paper
try some value for n(n-1)(n-2)-60 = 0
You'll find easily enough
But then that’s not reliable nor consistent
What if this were to be a question with different numbers
What if the answer is very large
I would have to continuously guess and check
Well that's easy
You pray it doesn't happen
…
Or you learn to solve cube
Idk if it's worth the time
How do I solve cube?
Solving cubic equation
Great
Or you can guess 
cedar kilnBOT
@crimson sedge Has your question been resolved?
cedar kilnBOT
@crimson sedge Has your question been resolved?
crimson sedge
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
dawn moth
Hello!
I'm working with 3d rendering of a cube and i'm quite a noob in this domain.
Let's say I've a cube defined by one point x, y, and z and its side size is 1. Let's say i'm at a point C. What are the sides of the cube I can see ?
My hypothesis : the three or less sides that will be rendered are the three sides that has the lowest distance between their middle (the point at the middle of its diagonal) and the point C, from where I am looking at the cube.
I do not know if this is true, or how to prove it. Any idea ?
cedar kilnBOT
Hello!
I'm working with 3d rendering of a cube and i'm quite a noob in this doma...
@dawn moth Has your question been resolved?
crimson sedge
dumb exponent rule
cedar kilnBOT
dumb exponent rule
crimson sedge
im sorry but im too lazy to ask google
but like all the laws of exponents blah blah
when u add powers, and there is an exponent
do u touch it
like x^2 + x^3 =
livid hound
if you have the time to ask here,
you have the time to look up the relevant exponent laws
dense hornet
crimson sedge
if you have the time to ask here,
you have the time to look up the relevant expo...
google isnt giving me the answer
i dont understand what that equal sign is
livid hound
well is there an exponent law listed that references
$$x^m + x^n$$
?
crimson sedge
google isnt helping me
wraith daggerBOT
ℝamonov
livid hound
ya
which one?
crimson sedge
**ℝamonov**
idk for this
livid hound
post an image
crimson sedge
is it x m+n
livid hound
$\redneq$
crimson sedge
dont u add 5 + 2
wraith daggerBOT
ℝamonov
crimson sedge
or it wont equal that
livid hound
that is the not equal sign
livid hound
which law are you looking at that makes you think that you can?
stiff badge
$\lim_{x\to0} \log(1+3x^2) \sim (1+3x^2-1) \sim 3x^2$
cedar kilnBOT
$\lim_{x\to0} \log(1+3x^2) \sim (1+3x^2-1) \sim 3x^2$
wraith daggerBOT
Umma.Gumma
stiff badge
Hi, is this correct?
cedar kilnBOT
@stiff badge Has your question been resolved?
cedar kilnBOT
@stiff badge Has your question been resolved?
cedar kilnBOT
@stiff badge Has your question been resolved?
raw kernel
ping the helpers
stray plover
Hi
stray plover
stray plover
Yup
stray plover
OMG HI AGAIN
stray plover
I think I explained gradient
solemn torrent
person
stray plover
YES
stray plover
No so what I did is 6.4 to the power of 2 x 3.2 to the power of 2
stray plover
Idk man
solemn torrent
thought process
stray plover
I think when I was doing the unit it told me to do that
stray plover
Nope
solemn torrent
really?
wraith daggerBOT
Springsskateboard
stray plover
The longest
solemn torrent
a hypotenuse is
stray plover
Side
stray plover
So it’s 6.4
stray plover
I had to look at my notes
stray plover
Yup
solemn torrent
ye?
stray plover
Got it
solemn torrent
now
we have a and b
and there are
2 more sides right
you can let either side be a or b
stray plover
Yes
stray plover
Z can be a and 3.2 can be b?
wraith daggerBOT
Springsskateboard
stray plover
So far so good
stray plover
6.4-3.2?
wraith daggerBOT
Springsskateboard
stray plover
30.72?
solemn torrent
,w (6.4)^2 - (3.2)^2
wraith daggerBOT
wraith daggerBOT
Springsskateboard
solemn torrent
solve for x
stray plover
Yup
solemn torrent
Z*
stray plover
Z is 30.72
stray plover
Half of z?
solemn torrent
nah
stray plover
I’ve never learnt that I thought the opposite was a normal number
solemn torrent
I’ve never learnt that I thought the opposite was a normal number
wdym
stray plover
Oh
stray plover
30.72
stray plover
5.5
solemn torrent
yep
stray plover
?
solemn torrent
nice
stray plover
I have another one but I’ll try to solve it
stray plover
7.8^2+5.6^2= 92.1999
So that makes h= 9.5? - queen because of the square root @solemn torrent
wraith daggerBOT
solemn torrent
npnp
stray plover
I have one last question which I won’t disturb u with so I’ll end this and reply to this
Don’t mind it!!!!
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
stray plover
cedar kilnBOT
stray plover
Just wanted to make sure that was correct
hushed spoke
It’s not
bold lotus
$\frac{14}{2} \neq 6$
wraith daggerBOT
dog.
stray plover
8+6
stray plover
Oh
bold lotus
have you learnt how to factorise
bold lotus
hmm
search it up or smth
there will always be good explanations there
then you can ask if you are confused about something
stray plover
I’ll rather get help from a helper it’s quicker because they can tell me how to solve the equation whilst educating me on how to factorise thanks tho!
stray plover
-2a(4+7y)?
stray plover
There
hushed spoke
That is correct now
stray plover
Thank youu
hushed spoke
Np have a good day
hushed spoke
Okay what can you factor out in this question?
stray plover
B(b-6)
hushed spoke
You clicked on the wrong option
cedar kilnBOT
cedar kilnBOT
Available help channel!
tough aurora
cedar kilnBOT
tough aurora
find the power series of d/D
so far I factored q
then in the parentheses I put (1+d/D)
managed to find the power series of that, but not of that squared
i should end up with juste one power series
<@&286206848099549185>
tbh i just don't know how to progress
and part 2 is "show that E is proportional to 1/D^3 when D is large)
crimson sedge
ig you can use this 1/(D+d)² = D^2•(1+d/D)^-2
tough aurora
I... forgot to take out the D after factoring it
brb
ok so now this
@crimson sedge any idea on how to progress ?
i dont think difference of squares gives any progress here, i'll end up with 2 power series
wolfram alpha gives this
and it would work, as when multiplied by 1/D^2 it would make it proportional to 1/D^3, because all other values will be really close to 0
but how to get there
crimson sedge
You can use (1+x)^n = 1+ nx here ...
tough aurora
wdym
crimson sedge
For small values of x that is true ... as it is given D is much greater than d then d/D is very small you can neglect its higher powers ...
tough aurora
it isn't given in part 1
they want an exact power series
it feels like cheating, but 1/(1-x)^2 = sum of n*x^(n-1)
crimson sedge
Then use binomial theorem here but power will be negative ...
1/(1-x)²= (1-x)^(-2)
tough aurora
time to cheat
1- that is quite easy to calculate and it works fine
use the fact that 1/1-x = sum of x^n, differentiate both sides with respect to x you get 1/(1-x)^2 = sum of nx^(n-1)
will be happy with that
looks good to me
.close
weak berry
How do you answer this without calculus?
cedar kilnBOT
How do you answer this *without* calculus?
bold lotus
How do you answer this *without* calculus?
is it said in the question it should be answered without calculus?