so you have the change the sign for one of them
#help-19
silent flax
unkempt pollen
we say that positive direction is upwards, so for the first half of the movement it travels 9.3 meters right, then when fallind down it travels -11.3 meters in negative direction
silent flax
yes
unkempt pollen
so when trying to find total direction you sum these two distances traveled, so 9.3 + (-11.3)
= -2
unkempt pollen
well i have to go now, thanks for discussing it with me. it really helped me understand why s = -2. its fun to discuss because it helps me understand. thank you again 🙂
unkempt pollen
how
unkempt pollen
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odd edgeBOT
silent flax
we are done
odd edgeBOT
Available help channel!
odd edgeBOT
we are done
mellow solstice
@silent flax close it
silent flax
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languid dew
odd edgeBOT
languid dew
I got k to be even for it to be a factor
because it simplifies to (1 ( 1-(2x)^k)) /1-2x
Which simplifies to (1-(2x)^k)/1-2x
Which goes to 1-(-1)^k / 1+1
For 2x+1 to be a factor, the number 1-(-1)^k must be 0
which only happens for even k's
but then putting the question into chat gpt it says it needs odd values of k for it to be a factor
shy smelt
because it simplifies to (1 ( 1-(2x)^k)) /1-2x
the k here should be replaced by k + 1
if you check small values you will find that chatgpt happened to be right this time
languid dew
Howcome sorry?
shy smelt
the formula for a geometric series $$1 + r + r^2 + ... + r^k$$ is $$\frac{1 - r^{k + 1}}{1 - r}$$
clever fjordBOT
Jelle
leaden totem
Evaluate the following limit: (image attached)
I've solved this heuristically to be zero. There is a decrease in the difference caused by -5x/6x, however, this difference is then exasperated by the ^x and thus leads to the denominator being infinitely greater. The base itself has a linear difference but the exponent makes it have the higher rate of growth.
My problem is that I need to find a methodical solution for this.
odd edgeBOT
Show your work, and if possible, explain where you are stuck.
leaden totem
I've done it heuristically but I have no idea where to start
glass trench
You should factor out an x^2
little tulip
notice that 3x^2 - 5x + 11 = 3x^2 + 6x - 2 + (13 - 11x)
divide it (split into 1 + ...) then it looks like "e" limit
leaden totem
Thank you very much but could you elaborate?
I see how it looks similiar but to get it into that form
little tulip
$$\frac{3x^2-5x+11}{3x^2+6x-2}=\frac{3x^2+6x-2+(13-11x)}{3x^2+6x-2}=$$
$$=\frac{3x^2+6x-2}{3x^2+6x-2}+\frac{13-11x}{3x^2+6x-2}=$$
$$=1+\frac{13-11x}{3x^2+6x-2}$$
clever fjordBOT
Modus
leaden totem
I got that far but how do I further it?
leaden totem
How exactly would I get it into the form of (1+1/x)^x?
little tulip
you don't need that form, just
do
$$\lim_{x \to \infty} \Bigg(1+\frac{13-11x}{3x^2+6x-2}\Bigg)^{\frac{3x^2+6x-2}{13-11x} \cdot \frac{13-11x}{3x^2-6x+2} \cdot x}$$
clever fjordBOT
Modus
little tulip
then it's e^(...)
leaden totem
Just one question
I've spent a few days on this problem but with limits, would you know the important ones we have to know
For example
Sin x/x
Or eulers
Actually nevermind
Thank you very much
.close
mystic saffron
Having trouble writing Mathematica code for some physical phenomena
mystic saffron
So far I was able to program a way to visualize point-charges on the xy plane
I think it looks pretty neat 👍
But I'm having trouble creating a vector field that represents a "line of charge"
this is the only youtube video I could find on the subject matter of coloumbs law in cartesian coordinates
i dont really fully understand what r' represents, but I'm assuming that the vector field is going to look something like this:
E(x,y,z) = < some line integral in the x-coordinate , some line integral in the y-coordinate , some line integral in the z-coordinate>
and using this logic the entire thing kind of breaks
also, k = 1/(4*pi*epsilon) so
i used that instead
also i redefined e as the charge-density of the line-of-charge
so it is some very small value
<@&286206848099549185>
odd edgeBOT
@mystic saffron Has your question been resolved?
fast dirge
mystic saffron
tshi channel is already being used
go to help-9
<@&286206848099549185> can u guys delete their message
<@&286206848099549185> I even derived it and it turns out my guess was right
for some reason throwing it into mathematica with some parametric curve doesn't give the result I was expecting
odd edgeBOT
@mystic saffron Has your question been resolved?
mystic saffron
Is no one really able to help <@&286206848099549185>
knotty cobalt
I can't help you I'm really sorry
mystic saffron
Can any other helpers help
odd edgeBOT
@mystic saffron Has your question been resolved?
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@mystic saffron Has your question been resolved?
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remote bobcat
need help getting the Intervals of Increasing and decreasing
mystic saffron
What level of math is it?
remote bobcat
precal
mystic saffron
Is there more to the graph or is that all you get
remote bobcat
that was the graph givin for the question
mystic saffron
An increasing function across some interval if both the input values and resulting values of the funciton increase.
remote bobcat
still kinda confused but thank you sir
mystic saffron
Best way to think up it is that it is increasing when it seems to be moving up and to the right/left
Up and to the right/left = increasing
Down and to the right/left = decreasing
Then you gotta find the x values that show the function increasing
You've got the graph increasing from -oo, and then stopping at x = -5, and then decreasing towards x = 0
hollow elbow
I need help with this portion
odd edgeBOT
I need help with this portion
swift rock
well that is wrong
k = 10^3
10^10 Nm
10 . 10^9 Nm
10 GNm
what u have done is get rid of 10^6 which isnt possible
swift rock
So it will stay 10^7
either
10^7 kNm OR
10 GNm
hollow elbow
Thanks
odd edgeBOT
@hollow elbow Has your question been resolved?
desert marlin
How is this theorem true?
If $S\subset \mathbb{R}^{n}$ and $\vec{x_0}\in \mathbb{R}^{n}, \vec{x_0}\in S \iff \exists {\vec{x_n}} \to \vec{x_0}$ of elements in $S$
clever fjordBOT
Austin
desert marlin
I am thinking about the backwards direction
can we not have a sequence of interior points, that converge to a boundary point, and the boundary point not necessarily be in our original set?
this seems to me only true for closed sets.... unles I am missing something
!occupied
odd edgeBOT
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).
summer cradle
@desert marlin
desert marlin
@summer cradle
summer cradle
this seems to me only true for closed sets.... unles I am missing something
yea this condition actually characterizes closed sets
desert marlin
so
if S subset Rn is closed
then the rest
but not just S subset Rn
then it isn't true
ty
.close
odd edgeBOT
summer cradle
but not just S subset Rn
yea
odd edgeBOT
Available help channel!
summer remnant
odd edgeBOT
clever fjordBOT
summer remnant
Why is smallest integer 4 not 2?
tardy lagoon
we need cos(npi/6) be negative
edgy bay
Consider $$A=\begin{bmatrix} 1&1\ 0&0 \end{bmatrix}.$$ I'm looking for $e^A$. Computing powers of $A^k$ I get that $A^k=A$, and so $$I+A\left(1+\frac{1}{2!}+\frac1{3!}+\ldots\right)=I+Ae=\begin{bmatrix} 1+e&e \0&1 \end{bmatrix},$$but this is incorrect. Why?
clever fjordBOT
sunside
edgy bay
The correct answer is $$\begin{bmatrix} e&e-1 \ 0&1 \end{bmatrix}.$$
clever fjordBOT
sunside
hollow jewel
odd edgeBOT
hollow jewel
Why we conjugate with the numerator and not the denominator? But can it possible if we use the denominator to conjugate?
wooden python
you're gonna end up doing the conjugate thing to both anyway!
shell fern
odd edgeBOT
shell fern
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wicked kestrel
Depends on what method you're expected to use to solve them
odd edgeBOT
@shell fern Has your question been resolved?
odd edgeBOT
odd edgeBOT
Available help channel!
pure knot
hi
pure knot
so i'm making a fluid simulation
and using a smoothed particle field
to determine density
and i need to find the integral of my smoothing function
which is currently (s-x)^2
s being the smoothing radius and x being the distance
when i integrate with respect to x between x=0 and x=s i get s^3/3
but the smoothing happens in a circle around each particle
and i want the area under this rotated curve to be 1 so it's all spread out evenly
rotated curve of (s-x)^2 around the y axis
so i though that i could just take the resulting integration and run it through the equation for the area of a circle given its radius
but that doesn't work
what am i doing wrong and why doesnt what im doing work
basically how do i take the integral of a function rotated around the y axis
or the area under a surface in a circle
pure knot
why is there an extra x in there?
timber dome
Where you are rotating the function f(x) from x=0 to x=r around the y axis and then compute the volume beneath it
pure knot
where did that come from
pure knot
Where you are rotating the function f(x) from x=0 to x=r around the y axis and t...
yes thats what im trying to do
timber dome
Good question. Intuitively, the x means that the value of f(x) for larger x matters more.
pure knot
why wouldnt it be the integral of the function between 0 and r
and then squared
times pi
timber dome
Then you are rotating about the x-axis
timber dome
Np
pure knot
The volume of which depends both on their hight and radius
but wait why couldnt u just take the area under the curve
and use that as the radius of a circle
like
the area under the curve is the same when viewing from the y axis or the x axis if the part of the function you're looking at is only in the first quadrant
mystic saffron
how to prove that this is true
odd edgeBOT
how to prove that this is true
fallen remnant
Try to find the gcd of (n,n+1)
mystic saffron
wooden python
if you mean ∉ then write ∉ the first time around lmao
mystic saffron
teacher told us its better to write as if thats equal a/b
mystic saffron
if you mean ∉ then write ∉ the first time around lmao
yes i forgot im sorry
wooden python
well yeah assume $\sqrt{\frac{n}{n+1}} = \frac{a}{b}$ with $a, b \in \bN$
clever fjordBOT
Ann
mystic saffron
yes
wooden python
anyway you might now want to multiply both sides by (n+1)b^2
mystic saffron
im not too familiar with typing expressions on jeyboard sorry
wooden python
$nb^2 = (n+1)a^2$
clever fjordBOT
Ann
mystic saffron
ohhh yeah i tried that too
fallen remnant
It's better to assume a and b to be coprime
wooden python
yeah, was gonna say.
wooden python
you can then isolate n from this maybe
mystic saffron
so n=( (n+1)*a^2)/b^2
wooden python
do not use the letter x for multiplication
fallen remnant
Then u get a²+1=b²
n and n+1 are coprime
a² and b² are coprime as well
Now a²/b²=n/(n+1)
The only possible case is
a²=n
b²=n+1
wooden python
ah. hm/
fallen remnant
If a and b r coprime ..
Then yes
mystic saffron
you can then isolate n from this maybe
what do i do after
wooden python
undo this step because it was not helpful
also write your 1 in a way that doesn't make it look like a 4
mystic saffron
If a and b r coprime ..
Then yes
sorry i dont learn in english but if im guessing correctly coprime means they dont have any common divider except 1
mystic saffron
also write your 1 in a way that doesn't make it look like a 4
ok i will sorry
so was what junang said correct?
fallen remnant
sorry i dont learn in english but if im guessing correctly coprime means they do...
Yep
HCF or gcd of those numbers is 1
mystic saffron
aa yes we studied gcd
wooden python
sorry i dont learn in english but if im guessing correctly coprime means they do...
yes coprime means exactly that
sometimes people also say relatively prime
mystic saffron
ohh okay thanks for the info
mystic saffron
n and n+1 are coprime
a² and b² are coprime as well
Now a²/b²=n/(n+1)
The only ...
it looks so easy when u look at it but its hard to think of for some reason
for me at least
anyways thanks for the help, how do i close this?
im blocked
if n belongs to N, are n and n+1 always coprime?
weary pelican
if n belongs to N, are n and n+1 always coprime?
use bezout's theorem
mystic saffron
use bezout's theorem
we didnt do tbat i need to use smth we did which is only absurd reasoning and that every number that belongs to Q can be written a/b with gcd=1
weary pelican
this works as well
weary pelican
yeah really bezout is much better
mystic saffron
what does bezout say
weary pelican
basically : gcd(a,b) = 1 if and only if there exists u,v such that au + bv = 1
mystic saffron
o
weary pelican
so in order to show that n and n+1 are coprime...
mystic saffron
ill see
serene urchin
odd edgeBOT
serene urchin
How to know these triangles are similar?
opaque crane
Two triangles are similar if they meet one of the following criteria: Two pairs of corresponding angles are equal; Three pairs of corresponding sides are proportional; Two pairs of corresponding sides are proportional and the corresponding angles between them are equal.
chilly moss
∠DBT is common, ( ∠DBT = ∠TBC )
opaque crane
You also have one common side
serene urchin
CT
So we can always take the two triangles and make it into the big one
And just show one angle is common there
.close
glass juniper
hello
glass juniper
does any one know what’s happening here
with the chart of roman numerals
and how i can do it with XXXVII times XIII
pls
he said somethint about halfing the left side or something
idk i was here last class but its extra credit due in a couple hours
odd edgeBOT
@glass juniper Has your question been resolved?
glass juniper
no
odd edgeBOT
@glass juniper Has your question been resolved?
glass juniper
no
odd edgeBOT
@glass juniper Has your question been resolved?
glass juniper
no
odd edgeBOT
@glass juniper Has your question been resolved?
glass juniper
no
hollow carbon
$\mathbb{F}_{\text{un}}$
clever fjordBOT
sakka ismail
odd edgeBOT
@glass juniper Has your question been resolved?
finite flare
<@&268886789983436800> Please delete this message because it is offensive. Rule 4: "Do not insult, attack, troll, gaslight other people. Do not publish people's private information without their consent. In general apply common sense, be respectful to others, and act in good faith."
real trellis
odd edgeBOT
Available help channel!
fickle fractal
help
odd edgeBOT
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golden summit
simple terms u can say in a quadratic equation of type ax^2 + bx + c the sum of solutions is given by -b/a so the ans here is going to be -(-(16a+4b))/64
which is 16a+4b/64
taking 4 common from numberator and cancelling it out we get 4a+b/16
check the equation type ax^2 + bx + c is general form of a quadratic equation
so coefficient of x^2 is a
x is b
and constant is c
generally speaking its something to remember like a formula but it isnt hard to derive im pretty sure
a quadratic equation is formed like this (x-s1)*(x-s2)=0 (here coefficient of x^2 is 1 note that
expand this equation by multiplying we get x^2 -s1x-s2x + s1s2=0
ah alr
so p is one and q is another solution then
so we get x^2 -(p+q)x + pq=0
im not too sure what latex format is tbf im not a mod on this server just someone passin by
hmm..
not sure if that worked
welp anyway i gtg so try to understand rq if u can otherwise u can ping helpers
as coefficient of x^2 =1 we divide the normal equations like ax^2 + bx + c=0 by a and get x^2 + b/ax + c/a = 0 compare this to original equation in terms of p and q and we clearly see sum of solutions is -b/a and product is c/a
odd edgeBOT
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odd edgeBOT
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deep scroll
A new roller coaster park called Seven Flags has decided to open up in the booming city of Frisco, TX. The owners of the park want to ensure that each roller coaster provides their customers with an amazing and unique experience. Your task is to design reasonable blueprints for a roller coaster by writing and sketching a piecewise function that consists of at least a linear piece, a constant piece, a quadratic piece, a square root piece, and an absolute value piece. You may include more than one of each piece if you’d like.
In addition:
a. Your domain should be [0,50].
b. At least one of the quadratic pieces must have a vertex of (3,4).
c. At least one of the absolute value pieces must have a vertical stretch as one of its transformations.
d. At least one of the square root pieces must have a horizontal compression as one of its transformations.
i need help with the square root piece and absolute value piece
this is what i have so far
deep scroll
odd edgeBOT
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deep scroll
<@&286206848099549185>
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agile crow
in expansion of (1+4px)(1+qx)^n, find the values of p and q. the coefficient of x^2 is -40 and x = 0
odd edgeBOT
@agile crow Has your question been resolved?
violet ether
Hey everyone. why the mid-interval of this:
98 < V ≤ 104
would be 101 and not 100.5?
Is it because the symbol before V is < and not ≤???
violet ether
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odd edgeBOT
plain lagoon
?
violet ether
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violet ether
Hey everyone. why the mid-interval of this:
98 < V ≤ 104
would be 101 and not 100.5?
Is it because the symbol before V is < and not ≤???
.close
deep scroll
odd edgeBOT
sonic nova
Did they say anything about p?
pallid tinsel
you can think of transforming the graph of |x| so that it intersects the x axis at 12 and 2009, ig
deep scroll
no he wants an equation
sonic nova
Yea p much that structure
sonic nova
Well it should be greater
Because the intervals are disjoint
Two different pieces
One on the positive infinity side and the other on negative infinity side
Thats an | x | > c
deep scroll
no equal to?
sonic nova
Yes equal to as well
sonic nova
Thats an | x | > c
I meant this is the structure
Yours will be >=
Because the intervals are
Closed
Meaning they use this [ bracket
Those closed brackets include the endpoints
So theyre associated with greater than or equal andless than or equal
If they wrote
(-inf, p)
With an open bracket
Then it would be strictly greater/less than
deep scroll
can you remind me how to get midpoint and range i forgot
sonic nova
Should be
Midpoint: (2009+12)/2
Range: 2009 - 12
Midpoint will be their average
Range will be the largest minus smallest
frosty tendon
odd edgeBOT
quasi sparrow
cropping is your friend
frosty tendon
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odd edgeBOT
odd edgeBOT
Available help channel!
sacred swallow
Can anyone help me with number 3
odd edgeBOT
odd edgeBOT
Available help channel!
inner badge
odd edgeBOT
inner badge
,rotate
odd edgeBOT
clever fjordBOT
swift rock
i know that a + b = -2 and ab = a (the one in the quadratic equation)
thats the sum and product of roots
take LCM of the fractions and use those values there
inner badge
i think i found out how to do it
a^2 + 8a - 16 = 0 right?
the a in the quadratic equation
swift rock
no?
inner badge
why ont
swift rock
sum of roots = -2
product of roots = a
inner badge
can i show you my working
swift rock
yeah
clever fjordBOT
swift rock
is the upside down e alpha?
inner badge
yes
wait no
it's the a
in teh quadratic equation
basically the thing im tryna solve for
clever fjordBOT
JustToPro
swift rock
use that instead of the numetaor and then add the values
u have a+b and ab , so u can simplify
inner badge
use that instead of the numetaor and then add the values
because i kinda already substituted in the values
swift rock
oh right , my brain slow work
swift rock
so (4-2a)/a^2 = 1/4?
yeah then it becomes the quadratic and solve that for a
inner badge
but the values are so weird ( i can't use calculator )
are the values 4sqrt(2) - 4 and -4sqrt(2) - 4
swift rock
probably , there isnt any other
swift rock
how do you know there isn't any other
cuz there is a quadratic and i trust u can solve quadratic
theres only that way to find a that i know of
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scenic elm
how to calculate this?
odd edgeBOT
how to calculate this?
scenic elm
wooden python
!status
odd edgeBOT
What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
1
wooden python
do you know how to add fractions normally
wooden python
so if i told you to add 1/5 + 3/7 you could not do it?
wooden python
what did you do
scenic elm
wooden python
how did this happen?
wooden python
bad
you are supposed to add the fractions! not divide the right one by the left one.
wooden python
also you should send your work in full not give it breadcrumb by breadcrumb
it is annoying when every single step has to be pulled out like a rotten tooth
scenic elm
I got it
scenic elm
also you should send your work **in full** not give it breadcrumb by breadcrumb
my handwriting is somewhat bad
but okay Ill write my full calculation in wa next time
its 10 I got it
thank you
.close
odd edgeBOT
odd edgeBOT
@ancient robin Has your question been resolved?
void yew
no
odd edgeBOT
odd edgeBOT
Available help channel!
gleaming hedge
I need help understanding this problem:
Find the module and argument of the complex number z, if z=-1/2
gleaming hedge
so far I know that z=|z|(cos(a)+i(sin(a)))
for the module it's obvious to me it's 1/2
but how do I find the argument in radians?
should be pi (180 degrees)
wooden python
yes
gleaming hedge
but idk why it's so
wooden python
arguments are measured counterclockwise from the positive x-axis
or from the positive real axis
so a complex number that's either real or pure-imaginary has a multiple of pi/2 for its argument
0 for positive real, pi/2 for positive imaginary, pi for negative real, 3pi/2 (or -pi/2) for negative imaginary
gleaming hedge
it's half of a full circle
oh ok, can it be literally just multiplied by the module of z?
wooden python
why not
gleaming hedge
0 for positive real, pi/2 for positive imaginary, pi for negative real, 3pi/2 (o...
idk how to measure this:
for z=1+i
ik it's sqrt(2)
but it becomes pi/4
the argument
gleaming hedge
yes
wooden python
if you join the points 0, 1 and 1+i with straight lines you get a right triangle
with angles 90, 45 and 45 degrees
because both its legs are 1
gleaming hedge
ugh
gleaming hedge
if you join the points 0, 1 and 1+i with straight lines you get a right triangle
why 0, 1?
wooden python
fluid iris
Hello, can I please have some help proving that a function has a left sided inverse if it is injective?
fluid iris
I know that it's actually an if and only if relationship
odd edgeBOT
@fluid iris Has your question been resolved?
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@fluid iris Has your question been resolved?
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@fluid iris Has your question been resolved?
meager juniper
Hello, can I please have some help proving that a function has a left sided inve...
Generally, these proofs are worked by starting from definitions. What is the definition of a left-sided inverse?
coarse storm
y = x^2 - 6x + 5 how i rearange to make x in terms of y to get the inverse function
coarse storm
<@&286206848099549185>
reef sandal
It's not invertible unless you restrict the domain
sharp hull
how would I find the mean of this graph?
odd edgeBOT
how would I find the mean of this graph?
sharp hull
(this is in calc II but that might not be relevant)
just need a refresher
I got the answer by guessing but I can't replicate it
crisp wadi
In general the mean of $f(x)$ on $(a, b) \subseteq \bR$ is simply
[ \frac{\int_a^bf(x)\dd{x}}{b - a} ]
clever fjordBOT
A Lonely Bean
crisp wadi
Here it may looks like a problem that the function behaves differently on the intervals (0, 6) and (6, 10)
But thankfully you can simply use the fact that
[ \int_0^{10}f(x)\dd{x} = \int_0^6f(x)\dd{x} + \int_6^{10}f(x)\dd{x} ]
And figure out what expressions $f$ is equal to on each interval
clever fjordBOT
A Lonely Bean
sharp hull
Ah, I see
that makes sense, I didn't look at it that way haha
thank you very much!
.close
flat ocean
how do I write 3e(^2x) + 9e^(−2x) in terms of sinh(2x) and cosh(2x).
worldly current
how do I write 3e(^2x) + 9e^(−2x) in terms of sinh(2x) and cosh(2x).
(1/2(e^2x - e^-2x) = sinh(2x)
So just do a cheeky rearrange
odd edgeBOT
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flat ocean
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opaque fog
can anyone help with epsilon delta proofs?
odd edgeBOT
can anyone help with epsilon delta proofs?
@opaque fog Has your question been resolved?
odd edgeBOT
@opaque fog Has your question been resolved?
fringe bough
looks good but your intervals should be open
( ), not [ ]
no problem 👍
oh wait @raw acorn
in part B you put -4 instead of 4
sorry didn't notice that at first
yeah I agree
signal halo
Why do you think sqrt(6) is a critical number
Or wait
I mean 0
Mb
Uh yeah that looks right to me
Cuz derivative at 0 would be 0
Ohh
I thought you meant like the point (0,sqrt6)
What about in something like
1/(2sqrt(6))x^2-x
sqrt6 would be a critical number there right
I mean I think it’s possible for a square root to be a critical number
halcyon thicket
Topic: Rational Function
odd edgeBOT
Topic: Rational Function
halcyon thicket
can sum1 help me solve rational function?
quasi sparrow
halcyon thicket
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odd edgeBOT
odd edgeBOT
Available help channel!
vague lion
I have a simple question since I'm confused, which is not simple for me, though, since I cannot comprehend it. My brain isn't working at the moment. So take this image for example:
vague lion
could this triangle be named △BCA
or/and △ACB
like would △bca and △acb be the same triangle
tender lagoon
yes for a single triangle its ok
odd edgeBOT
Available help channel!
wheat apex
odd edgeBOT
wheat apex
I had to write a formal proof for this, and i did but my prof never gave any feedback
let me write it up real quick and lmk what should change in it
forgot to finish it off but
clever fjordBOT
Joshii
dim thicket
why does 2(c^2+c)-1 = 2n-1 ?
wheat apex
because c^2+c is an integer
dim thicket
also you dont need 2c plus or minus 1
you can just take one
they both give you all odd numbers
wheat apex
oh right
dim thicket
also you can just argue by saying n^2 + n - 1 = n(n+1) - 1
one of n or n+1 must be even
so n(n+1) is even
so n(n+1) - 1 is odd
if that makes sense
odd edgeBOT
@wheat apex Has your question been resolved?
wheat apex
yes it does ty
hybrid heron
Would you solve this problem with partial fraction decomposition?
dim thicket
i would complete the square in the radical and use trig sub
hybrid heron
Aah so it would be -(x-1)^2 +1
dim thicket
yes
hybrid heron
And then x+1 =sin theta?
dim thicket
youre welcomeà
buoyant jungle
odd edgeBOT
swift rock
If x is negative, |x| = -x
isnt it supposed to be |-x| = x?
brisk urchin
First one states that x approaches to 0 through -ive side meaning
x -> -0.1 , -.0.01 , -.0.001 , ... , 0 never actually gets to zero but it gets really close, and as the number gets smaller in the divisor, the result keeps getting bigger
for first lim x -> -0 for g(x)
lets just plug in some negative numbers and see the behavior of the denominator
buoyant jungle
oh i get it , hold on lemme test those values
brisk urchin
try -1, -2, just for the denominator
brisk urchin
because we dont want a zero on the denominator, that'll make ou equation undefined
n/0 = infinity
we have a simple x and an x with the absolute sign as well
so we have to check answers for both +ive and -ive sides
brisk urchin
what about 0
brisk urchin
we can make a claim that for any value < 0 (less than zero) we can get a definite answer
buoyant jungle
so what would i answer
brisk urchin
the equation does not break if we approach zero from negative side
buoyant jungle
oh i get it
brisk urchin
so we get a defined result from -ive side
brisk urchin
for g(0) we get 0/0 which ofc is undefined
buoyant jungle
.
brisk urchin
what would i put as my answer
the whole equation as answer
buoyant jungle
mhm
brisk urchin
now we calculate lim x -> +0 for g(x)
is there a +ive value we can put in the denominator such that it becomes zero?
since we are approaching zero from +ive now, we know both values for x are +ive, and we can remove the absolute from it
the equation will become
3x - 7x
-4x
brisk urchin
for lim x -> -0, we could remove the absolute as well and replace it with -x, since we are approaching zero from -ive side, thus making the equation
3x - 7(-x)
3x + 7x = 10x
and you were getting multiples of 10 for x=-2, -1
brisk urchin
was building some base before it, now for the solution:
for lim x -> -0, for the whole equation now:
7x + 14|x|
----------
3x - 7|x|
replace |x| with -x, since we know we are approaching x from -ive direction and simplify the equation now
buoyant jungle
oh tysm
buoyant jungle
wait hold on'
brisk urchin
was building some base before it, now for the solution:
for lim x -> -0, for the...
7x + 14|x|
g(x) = ----------
3x - 7|x|
7x + 14(-x)
g(x) = -----------
3x - 7(-x)
@buoyant jungle simplify and see the result
we solved for denominator already which was -10x
now solve for numerator wihch is 7x + 14(-x)
odd edgeBOT
@buoyant jungle Has your question been resolved?
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Available help channel!
blazing shuttle
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quaint marten
Hello, I'm struggling with algebraic word problems with two variables.
My current problem I'm working on is Angela has dimes and nickels totaling $3.65. The amount of dimes is 1 less than 2 times the number of nickels. How many nickels does Angela have?
quaint marten
I'm using the substitution property setting x = number of nickels and y = the number of dimes. My equation is:
y = 2x - 1
When substituting, I get:
x + 2x - 1 = 365
I wind up with 3x = 366, or x = 122
That simply can't be correct.
boreal crag
where does x + y = 365 come from?
quaint marten
setting x = number of nickels and y = the number of dimes
My current problem I'm working on is Angela has dimes and nickels totaling $3.65. The amount of dimes is 1 less than 2 times the number of nickels. How many nickels does Angela have?
I just removed the decimal to simplify the equation.
nimble blaze
number of nickels + number of dimes isn't 365
wooden python
setting x = number of nickels and y = the number of dimes
My current problem I'm...
don't confuse the number of coins w their total value
do you know how many cents a nickel and a dime are worth respectively?
quaint marten
It should be 5x and 10y for the variables.
boreal crag
it sounds like you could be on the right track but the specific way you phrased that doesn't make much sense
quaint marten
I'm going to have to ask my professor. I have numbers that are divisible by 5 going into an even number. I'm doing something really wrong here.
nimble blaze
show your updated equations/work
quaint marten
5x + 10y = 365
x = number of nickels
y = number of dimes
y = 2x - 1
nimble blaze
ok so far
quaint marten
So, when substituting back...
5x + 10(2x - 1) = 365
5x + 20x - 10 = 365
25x - 10 = 365
+10 to both sides
25x = 375
Divide both sides by 25
x = 14
nimble blaze
375/25 isn't 14
odd edgeBOT
@quaint marten Has your question been resolved?
odd edgeBOT
wooden python
nope
the intersection is actually "at least 16 years"
a circuit breaker that lasts both >=12 and >=16 years is just one that lasts >=16 years
coral cloak
Languages : french, or English
Grade: 1ere(french system), 11th grade
Subject: Math
Help needed: Guidance and explaining why that is that ;-;
Translation:
A) give the missing value in the table
B) give the canonical form of f(x)
coral cloak
<@&286206848099549185> halpos ;-;
odd edgeBOT
@coral cloak Has your question been resolved?
coral minnow
how does the -1 turn into x^2 by simplifying?
odd edgeBOT
how does the -1 turn into x^2 by simplifying?
swift rock
lcm
toxic glacier
1 can be written as x^2/x^2
shut cypress
odd edgeBOT
wooden python
make a probability distribution table
shut cypress
Oh okay
wooden python
generally never a bad idea to do that if you've got a random variable you're working with
shut cypress
Something like this or
Wait but
How do u find a I know what to do from there 😭 but how is “a”found
odd edgeBOT
@shut cypress Has your question been resolved?
odd edgeBOT
@shut cypress Has your question been resolved?
valid marsh
hi, let f : R -> R, if f(R)=R+, then f is not injective
is it true ?
I have no counterexample
valid marsh
yes so this is not a counterexample
lime fog
in general $\mathbb{R}^+ \subset \mathbb{R}$
clever fjordBOT
nadav
valid marsh
wtf
lime fog
hi, let f : R -> R, if f(R)=R+, then f is not injective
is it true ?
I have no c...
it is true. f is not injective. f(x)=x^2 is f: R->R+ and it is not injective.
lime fog
my bad i confused myself
valid marsh
yes it is not injective
no counterexample
hi, let f : R -> R, if f(R)=R+, then f is not injective
indeed x->x² is not injective
lime fog
yeah sorry im a bit tired 😅
in general the cardinality of R is the same as taht of R+ so you should be able to find an injective function
f(x) = e^x @valid marsh
valid marsh
no
lime fog
then what do you mean by f:R->R+
valid marsh
R+ = [0,+oo[
valid marsh
all positive reals
hi, let f : R -> R, if f(R)=R+, then f is not injective
is it true ?
I have no counterexample
lime fog
and what do you mean by R*+
low locust
I cant think of an easy example to write down rn, but you can easily draw a graph that fits
valid marsh
do you think it is true ?
low locust
well they have same cardinality so you can find an injective function between them
valid marsh
so it is not ?
valid marsh
well they have same cardinality so you can find an injective function between th...
what's the name of this theorem
lime fog
definition of cardinality (more or less)
valid marsh
?
low locust
dont know if it has a name
in this specific case
bijection between R and R*+ is clear (exp)
lime fog
sets have same cardinality iff there is a one to one map from one set to another
low locust
and then you just have to add an extra point to R*+
which is a bit technical but not hard
lime fog
which is a bit technical but not hard
wouldnt it just be |R*+ U {0}| = |R| + 1 = |R|
low locust
well if you know that you can just add like that, sure
doing it properly with a bijection is a bit harder
essentially it boils down to showing that {0,1,2,3,...} and {1,2,3,...} have the same cardinality
because the rest of the sets are identical
low locust
that doesnt have R+ has image. 1 is not hit
lime fog
but then you dont have {1}
low locust
essentially it boils down to showing that {0,1,2,3,...} and {1,2,3,...} have the...
try this first
odd edgeBOT
@valid marsh Has your question been resolved?
valid marsh
but that's not true
odd edgeBOT
but that's not true
valid marsh
it may be false
valid marsh
there is no necessaraly bijection beetwen R and R+ ?
uncut remnant
|{0,1,2,3,...}| = |{1,2,3,...}| ?
valid marsh
oh
uncut remnant
there is no necessaraly bijection beetwen R and R+ ?
there is.
uncut remnant
|{0,1,2,3,...}| = |{1,2,3,...}| ?
i thought u were asking about this
valid marsh
hi, let f : R -> R, if f(R)=R+, then f is not injective
is it true ?
I have no counterexample
uncut remnant
there is no necessaraly bijection beetwen R and R+ ?
but I gather from the above, people have suggested how to find this
using that
valid marsh
|{0,1,2,3,...}| = |{1,2,3,...}| ?
that's N not R
uncut remnant
well im not backreading everything
I just assumed you were referring to this
since thats the last thing mentioned
uncut remnant
hi, let f : R -> R, if f(R)=R+, then f is not injective
is it true ?
I have no c...
This is false.
uncut remnant
well I say this because I thought of a counterexample...
uncut remnant
the function which is exp(x) in R* and 0 in 0
didnt you write it
valid marsh
the image is not R+