Yeah let me read the question
#help-36
astral thunder
yes, line K cuts the x-axis at (2 * radius, 0 )
tranquil pine
Okay
final saddleBOT
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tranquil pine
Is it the answer?
r = +√12 or -√12
Where OFC radius can't be negative if we consider real circle
astral thunder
Hi how did you do the first step? Not sure how that comes to place
tranquil pine
Length of perpendicular to the line from point (0,0) i.e. radius
astral thunder
My bad, how did you get
|-8r| / sqrroot (16+4r^2)
astral thunder
I’m going to bed I’m not sure what happens to this channel now
tranquil pine
My bad, how did you get
|-8r| / sqrroot (16+4r^2)
Like eqn of line touching the circle is 4x+2ry-8r=0 if you calculate
so now length of perpendicular will be
r = | 4x + 2ry -8r evaluated at (0,0) | / sqrt(4^2 + (2r)^2)
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heavy laurel
How would I solve this?
final saddleBOT
How would I solve this?
heavy laurel
what is f(a) equal to?
<@&286206848099549185> f(a) is equal to a^2e^-a?
sweet summit
yep!
soft zealotBOT
MellowDramaLlama
sweet summit
and $f'(x) = 2xe^x - x^2e^x$
soft zealotBOT
MellowDramaLlama
sweet summit
so, in relation to these two points, how do we find the tangent line?
heavy laurel
**MellowDramaLlama**
You got this by plugging in..?
soft zealotBOT
MellowDramaLlama
sweet summit
<@&286206848099549185> f(a) is equal to ```
a^2e^-a```?
which you gave me the answer for here 🙂
heavy laurel
**MellowDramaLlama**
and we also got this by manipulating the derivative of the original function?
sweet summit
and we also got this by manipulating the derivative of the original function?
yeah it's the same as what you gave me here
heavy laurel
yeah it's the same as what you gave me here
we find the tangent line by doing limit definition, right?
heavy laurel
it's `y = mx + b`, where m is f'(x)
so its y = 2xe^x-x^2e^x+b?
sweet summit
so its y = 2xe^x-x^2e^x+b?
I don't recommend doing this lol
instead realize that we can create a line with the point slope formula as well: y - y1 = m(x - x1)
heavy laurel
Oh okay so point slope form
sweet summit
so in this case, x1 = a, y1 = f(a), and m = f(x1)
so we get $y - f(a) = f'(a)(x-a)$. This is the tangent line at $x = a$
soft zealotBOT
MellowDramaLlama
sweet summit
**MellowDramaLlama**
so we know f(a)
sweet summit
**MellowDramaLlama**
what would f'(a) be?
heavy laurel
what would `f'(a)` be?
Right, so y-(x^2e^x)= (2xe^2-x^2e^x)(x-a)?
sweet summit
Right, so y-(x^2e^x)= (2xe^2-x^2e^x)(x-a)?
see I don't recommend doing that just yet
you'll get lost in details
keep them separate for now
heavy laurel
alright
sweet summit
so we know f(a), what is f'(a)
heavy laurel
so we know `f(a)`, what is `f'(a)`
a is a constant here?
sweet summit
this is when x = a which comes from the original problem statement
heavy laurel
is this 0?
sweet summit
no
we're looking for a tangent line that passes through (0, 0)
through a tangent line at x = a
sweet summit
**MellowDramaLlama**
correct. so what is f'(a) if this is our derivative?
heavy laurel
correct. so what is `f'(a)` if this is our derivative?
So wait, were not finding the derivative of a^2e^-a but rather 2xe^x-x^2e^x?
heavy laurel
**MellowDramaLlama**
If I'm following you're saying we plug in the function of f'(a) into the f(x)?
soft zealotBOT
MellowDramaLlama
sweet summit
we're just plugging in x = a here
heavy laurel
**MellowDramaLlama**
What value does a have here?
sweet summit
okay
so
$f(x) = x^2e^{-x}$ is a function. We can take a derivative of this. $f(a) = a^2e^{-a}$ is a constant, just like $f(1) = (1)^2e^{-1} = e^{-1}$. We can't take the derivative of $f(a)$ no more than we can take the derivative of $f(1)$.
soft zealotBOT
MellowDramaLlama
sweet summit
so we need to find $f(x)$ (which we did), and then plug in $x = a$. So $f'(a) = 2ae^{-a} - a^2e^{-a}$. That's what I was trying to get at
soft zealotBOT
MellowDramaLlama
heavy laurel
**MellowDramaLlama**
By f(x) do you mean f prime x?
sweet summit
yeah sorry that was a typo
sweet summit
yes!
heavy laurel
the "then plug in f prime a for x = a" was throwing me off. I thought we had to find the derivative of f(a) and do something with that.
So we get f prime a by substituting in a into the derivative of f(x)..
sweet summit
yep that's the next step
$y - f(a) = f'(a)(x - a)$ is equal to $\y = (2ae^{-a} - a^2e^{-a})(x - a) + a^2e^{-a}$
soft zealotBOT
MellowDramaLlama
sweet summit
now, we want to pass through the origin, aka the point $(0, 0)$, we get $\(0) = (2ae^{-a} - a^2e^{-a})(0- a) + a^2e^{-a} \implies \ 0 = (2ae^{-a} - a^2e^{-a})(-a) + a^2e^{-a} \implies \0 = -2a^2e^{-a} + a^3e^{-a} + a^2e^{-a}$
soft zealotBOT
MellowDramaLlama
sweet summit
which simplifies to $0 = -a^2e^{-a} + a^3e^{-a}$. Now you can just solve for $a$
soft zealotBOT
MellowDramaLlama
heavy laurel
$y - f(a) = f'(a)(x - a)$ is equal to $\\y = (2ae^{-a} - a^2e^{-a})(x - a) + a^2...
So now I can just factor?
final saddleBOT
@heavy laurel Has your question been resolved?
heavy laurel
So the answers are:
final saddleBOT
So the answers are:
heavy laurel
0 and 1?
sweet summit
just 1
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velvet niche
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thin leaf
hello can anyone please join the 384kbps please
final saddleBOT
hello can anyone please join the 384kbps please
torn thicket
post it here
thin leaf
well
yes
but actuall no
i cant
if anyone can join
please do so
its genuinely difficult to type it out
tired walrus
picture?
timid tulip
there is none
thin leaf
fine
thin leaf
Literally screensharing this to an empty class
i gotta go take the fattest shit known to mankind
ill be back
tired walrus
T = 2pi sqrt(L/g)
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next pagoda
How do you summarize axioms like this?
final saddleBOT
How do you summarize axioms like this?
next pagoda
I want to make notes on all the axioms but I'm not even sure what to write first.
thin leaf
.close
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thin leaf
<@&286206848099549185> ^^^
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thin leaf
<@&286206848099549185> 💀
<@&268886789983436800> helpers aren't doing anything, may you assist please
opaque ember
pls dont ping mods for math help
we're volunteer run, we cant guarantee immediate help 24/7, so pls sit tight til a helper comes along
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<@&286206848099549185>
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fast shuttle
How do you summarize axioms like this?
there's no real set way to summarise it, just make sure you understand it and then write it out so that, when you read your notes in future, even if you've forgotten what the textbook says it will give you enough information to understand it again
it will vary from person to person it's really up to you
for that kind of thing i just draw a diagram label it and write a short sentence about the implications
next pagoda
for that kind of thing i just draw a diagram label it and write a short sentence...
That sounds like a great idea.
The book had a lot of examples with triangles
Are there circumstances where you would have to memorize a proof?
final saddleBOT
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autumn flax
Hey I could use help with integrals calcs
final saddleBOT
Hey I could use help with integrals calcs
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autumn flax
<@&286206848099549185>
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autumn flax
i give up
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tranquil bone
How to show this without multiplying out?
final saddleBOT
How to show this without multiplying out?
oblique portal
id think to amplify each fraction with their conjugate in terms of abc
tranquil bone
Like I don’t want to just simplify it
But show this in a more complicated way (for problem solving purposes)
oblique portal
i guess you could split each term from the fractions into 2
for instance $\frac{b-c}{a} = \frac{b}{a} - \frac{c}{a}$
soft zealotBOT
Kel.plush
tranquil bone
In the end it just boils down to simplify no?
oblique portal
then try to do this for all of them and maybe something happends
i dont think you can really do anything to it other than that tbh
wraith crater
I don't really get what you're trying to do but you can define a function and use factor theorem
tranquil bone
Can you eloborate I think that’s what I’m kind of looking for
crisp plover
The easiest way to do this is to observe that when put under a common denominator, the left hand side's numerator is bc(b-c) + ac(c-a) + ba(a-b)
Suppose what I wrote is a function of a, i.e., f(a ; b, c) = bc(b-c) + ac(c-a) + ba(a-b) (note the semicolon in f)
Then f(a ; b, c) has two roots as it is a quadratic in a
You know from the right hand side those roots occur at a = b and a = c and by evaluating f at b and c you can see that is clearly true
Then consider a similar function as a function of b, i.e., g(b ; a, c) and repeat this. By cycling through the three variables you conclude that the factored form must be (a-b)(b-c)(a-c)
"easy" being a loaded phrase because if you could see this you could have multiplied it out
tranquil bone
Yeah thanks this is what I’m looking for
Because the question says don’t multiply it out
crisp plover
This is a common "trick"
To change your equation into a function depending on a single variable holding the rest constant
and making conclusions about the roots of this function to give you more information
quiet forge
I was hoping someone could explain to me what this question is actually asking
quiet forge
Find a recurrence relation for a_n, the number of n-digit ternary sequences (sequences of 0's, 1'a and 2's) without any occurrence of the subsequence “012”.
Is it asking me to omit any substrings which contain those three digits directly adjacent to each other and in that order (123 exactly)
Or, any string of those three digits directly adjacent to each other, but in any order (such as "102")?
sturdy cypress
it means this order
the actual ambiguity is if they have to be adjacent
believe it or not
quiet forge
Now, that is weird
sturdy cypress
just assume yes i guess
quiet forge
I'm still a bit lost though
The few solutions I've been able to find online for this take a "what is the first digit approach"
Something along the lines of "there are T(n-1) ways to make a valid string of length n - 1. You can extend this into a string of length n by adding a 0, 1, or 2 to the (front?) end"
Then, if the digit you add to the front end is a zero, there is potential to form an invalid string. You must subtract the T(n-3) strings which start with 12 from the T(n-1) valid strings in the case you're adding a zero
The result is 3T(n-1) - T(n-3)
The first part makes sense. I'm not sure why there are T(n-3) strings which start with 12
sturdy cypress
for every valid string of length n-3 you add "12" and you get a valid string of length n-1 starting with 12
quiet forge
Ahhhhhhh
sturdy cypress
and you can't get a valid string in some other way
small lance
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severe dawn
i hate discrete math help pls
well
severe dawn
we all do
quiet forge
Discrete math = pain
severe dawn
you know how to do the problem for 2 numbers?
its just a multiplier on that same formula
Also mind you that the task is a little bit bait, its more like
'in how many ways can I choose 5 numbers from 1 to 50 without duplicates'
small lance
no sir i was hungover on all 3 previous lectures
severe dawn
just dont care about the order
severe dawn
ok but legit im sry pls help 💀
what do you have so far and what exactly are you stuck on
again, try it with something small first, like 2 numbers from 1 to 5
severe dawn
why consecutive?
small lance
wasnt that the qs
severe dawn
only 4 of them
small lance
ok yes 47
and i need to fill the ends of the 4consecutives with an integer on th efront or the back
severe dawn
seems like you got it
small lance
ok so like 50 options
small lance
yes
severe dawn
now just get the amount of options for single
small lance
allah says 144 is he correct
small lance
ok can the conseq be backwards
severe dawn
no
small lance
can you use exclusion and inclusion
severe dawn
how would you do that
severe dawn
i have no idea
we had the solution already I think
and you overcomplicate it
50x47x2
fathom walrus
<@&268886789983436800>
small lance
ok im so sorry i actually need help
severe dawn
ok im so sorry i actually need help
what did you not understand?
small lance
involving exclusion and inclusion
small lance
i guess so
sturdy ocean
inclusion-exclusion applies because of potential double counting
for example, the sequence (1, 2, 3, 4, 5) would be counted twice if you tried a naive approach of looking at sequences of the form (integer, {4-sequence}) and those of the form ({4-sequence}, integer)
i dont think youve eliminated this issue
unless i missed something
your full work should be:
- Count the number of sequences of the form (integer, {4-sequence}). Call this number A
- Count the number of sequences of the form ({4-sequence}, integer) [should be same as above]. Call this number B
- Check for double-counting: some sequences fit both of these categories. Which ones? ||5-sequences.||
- Count the number of those sequences. Call this number C [sanity check: C should be much smaller than A and B]
- By inclusion exclusion, the number of sequences of the desired form should be A + B - C
can you follow this reasoning? do you see where the A+B-C comes from and why it's necessary?
small lance
yea, but i dont think its what they want
it has to be the form of factorials or combinations/permutations i think
instead of this abstract thing
sturdy ocean
it will involve factorials once you actually do the work
i just gave an outline of the approach
you need to figure out the numbers yourself
sturdy ocean
let's think it through
first lets consider sequences that look like (integer, {4-sequence})
for example, (1, 47, 48, 49, 50) or (30, 21, 22, 23, 24) or (17, 14, 15, 16, 17)
small lance
yep
sturdy ocean
how many choices for the lone integer are there?
small lance
50
small lance
47
small lance
ok
sturdy ocean
now the exact same logic applies to ({4-sequence}, integer)
so A = 50 * 47 and B = 47 * 50
i guess this doesnt involve factorials actually lmao
anyway, now we need to get rid of double counting
since if we have like
(3, 4, 5, 6, 7)
this actually fits both "forms"
small lance
YES
sturdy ocean
we could see it as a 3 followed by the sequence 4, 5, 6, 7
or as 3, 4, 5, 6 followed by 7
small lance
yes
sturdy ocean
so we need to use inclusion-exclusion to "eliminate" this double-counting
small lance
great
sturdy ocean
to do that, how many 5-element sequences are there?
the minimum is, of course, (1, 2, 3, 4, 5)
small lance
46
sturdy ocean
and yeah, the maximum is (46, 47, 48, 49, 50), so there's 46 total as you said
so C = 46
and now our result should be 50 * 47 + 50 * 47 - 46
which you can throw into a calculator or whatever
do you follow that?
small lance
yes
sturdy ocean
so there's your answer
tranquil pine
Is this correct?
final saddleBOT
Is this correct?
manic prism
Just write arcsin(ON/OM)=m angle [ or say ON=a and OM=b and write
arcsin(a/b)=m angle]
Which would do for the equation
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@tranquil pine Has your question been resolved?
vale light
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vale light
how do you solve this?
sonic crystal
Do you know how to do substitution?
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oak kraken
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tranquil pine
Yes
oak kraken
Ty
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hoary kraken
9 classmates could not agree on who would stand in the group photo along with the teacher for the yearbook. How many possible groups can be made such that there is at least one student with the teacher in the photo?
final saddleBOT
9 classmates could not agree on who would stand in the group photo along with th...
hoary kraken
I guess you would somehow use combination here but idk what the question really means
hearty zephyr
Basically you want to count every photo that has a student in it.
There’s only one way there can’t be a student in the photo
final saddleBOT
@hoary kraken Has your question been resolved?
sturdy cypress
the question doesn't make sense sorry
hoary kraken
Basically you want to count every photo that has a student in it.
There’s only ...
there is?
hoary kraken
the question doesn't make sense sorry
ikr
sturdy cypress
zybikron means you do 2^9 − 1
sturdy cypress
there's 2^9 total ways to pick any amount of students, and you don;t want the one where you picked nobody
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rare belfry
can anyone help me with this question?
final saddleBOT
can anyone help me with this question?
soft zealotBOT
ruiz
rare belfry
but at some point i got 3=2???? maths crisis
void crest
wait
rare belfry
cuz the sum of a and b are equal (they subtract each other and get 0)
void crest
what do they mean by A n B r subtracted we get 0
rare belfry
like $S_{A}-S_{B} = 0$
void crest
but at some point i got 3=2???? maths crisis
ikr
soft zealotBOT
ruiz
void crest
so sus
void crest
i think is just bad wording
mayb they mean the sum of all terms in A
= sum of all terms in B
void crest
nani
rare belfry
i don't get it
rare belfry
did you mean the infinite sum?
void crest
omg their spacing is so sus
rare belfry
FR
rare belfry
the wording is bad asf
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obsidian sundial
Can someone help pls
final saddleBOT
Can someone help pls
obsidian sundial
Ik how the first parts works it’s just long division and I got 6 as remainder
But then am stuck after that
<@&286206848099549185>
hasty pulsar
What is your query?
You divide like terms until you are left with nothing to divide.
Also the factorisation is basically the same, even better in some cases.
You just have to equate the two together.
obsidian sundial
You just have to equate the two together.
What?
So I divide (x+1)(ax+b)+c by x+1?
<@&286206848099549185>
Sry I have to @ again bc that guy is now offline
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tranquil pine
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tranquil pine
Help
broken mantle
bro
echo bough
tranquil pine
SAVE THEM
broken mantle
so the definition of ratio is edge : edge'
here you can take |SR| and divide it by |S'R'|
then you'll get ratio
tranquil pine
So the answer is 5
broken mantle
wait
i messed it up
because
edge * ratio = edge'
in this case $6 * \frac{1}{5}=1.2$
soft zealotBOT
ta
tranquil pine
So the answer is 1/2
broken mantle
so ratio should actually be $\frac{1}{5}=\frac{1.2}{6}$
soft zealotBOT
ta
broken mantle
answr is $\frac{1}{5}$
soft zealotBOT
ta
tranquil pine
I won’t
broken mantle
good
tranquil pine
Thanks for the help besties
broken mantle
youll be excellent
broken mantle
Thanks for the help besties
np 
broken mantle
sure this is what im here for
tranquil pine
broken mantle
well look
broken mantle
edge * ratio = edge'
can you find 2 sides to plug into this equation
tranquil pine
Uhh 90 ? 😭
broken mantle
my brother in christ
tranquil pine
😖
broken mantle
you were close, just divide instead of multiplying
tranquil pine
0.9
tranquil pine
Is the answer 6…
broken mantle
this is werid cause there's no correct answer or im just dumb
tranquil pine
My teacher messed up this exam so hard
Just like the last one 😭😭
He added a different topic to the exam and didn’t tell us
soft zealotBOT
ta
broken mantle
yeah that's exactly the same
yeah your teacher should go work in mcdonalds
instead of teaching
this guy
what a dummy
tranquil pine
The whole class fails his exams
broken mantle
bruh
tranquil pine
He can’t even teach properly
tranquil pine
I can file a complain
broken mantle
yeah
tranquil pine
I don’t think they would change him tho
broken mantle
tranquil pine
I give up on math
broken mantle
it's AA rule
tranquil pine
Is the answer A ?
tranquil pine
83°
tranquil pine
HE EVEN MESSED UP THIS QUESTION 😭😭???
broken mantle
idk it seems to be wrong
im not sure tho
ok there's a correct answer
its rule SAS
try to find ratio
tranquil pine
16/3 ?
broken mantle
yes exaclty
tranquil pine
I refuse to believe
broken mantle
youre the best
tranquil pine
I still failed the exam tho
broken mantle
can u retake it
tranquil pine
My teacher doesn’t allow retakes 🙄
broken mantle
tranquil pine
This was a bonus so that I can up my grade ugh
broken mantle
☠️
tranquil pine
A win is a win
broken mantle
and if the last you scored 0 its around 50
tranquil pine
The bonus doesn’t count if it’s lower than the first exams grade
And now my final is 65% of the grade 💔
broken mantle
its good tho
my average currently is 50 and im like very good at maths
or at least i think i am
broken mantle
yeah exactly lol
tranquil pine
anyways I think I’m gonna play msm and cry myself to sleep tonight thanks for the help girlies 💋
Byee
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tranquil pine
I've got the option to raise a number to another, then take the result mod a third. But I don't need the mod, what could I do such that the effect of the mod wouldn't be perceptible?
It's for a function in libgmp, so I don't really have the option to simply not use it.
final saddleBOT
I've got the option to raise a number to another, then take the result mod a thi...
tranquil pine
I'm not sure of the notation, but all I need is for $x^n \textup{mod} y = x^n$.
soft zealotBOT
3317
tranquil pine
The trivial result would be to set $y$ to be $x^n + 1$, but I need $y$ to calculate $x^n + 1$, it goes in a circle.
soft zealotBOT
3317
tranquil pine
.close
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pseudo cairn
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sullen mauve
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sullen mauve
this contains the question and what I have tried so far. it is fairly simple but I am confused if the base case would be n=1 or n=5 since it fails for values in between
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sullen mauve
<@&286206848099549185>
dark marten
If n = 1 were the base case, and your induction were correct, then you would have shown that it works for n = 2. But you know that this is not the case, so something must be wrong.
In your induction you have the additional assumption that 2k + 1 < 2^k. This does not follow from k^2 < 2^k, see k = 1 as a counterexample.
If you find a way to fix the induction step, then it will probably be clearer which base case works / makes sense. :-)
fast nova
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fast nova
Can someone tell me how to do the e part of this question
am I supposed to put m=tan theta/2 into the results obtained in part c?
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fast nova
<@&286206848099549185>
waxen briar
am I supposed to put m=tan theta/2 into the results obtained in part c?
why not?
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pulsar wind
pulsar wind
Do both these two values of N work?
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pulsar wind
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dry ruin
We will show that if $f(n)=22n^{2}+19n-63$ is $O(n^{2})$ then we must show that for all $n^{2} \times C \eqslantgtr f(n)$, $g(n)$ will overtake the function.\
Devide both sides by $n^{2}$\
$\frac{f(n)}{g(n)}=\frac{22n^{2}+19n-63}{n^{2}} < [\underbrace{\frac{22n^{2}+19n^{2}-63n^{2}}{n^{2}}}_{\text{-22}}<C]$\
For all $n \eqslantgtr\ n_0$, if we choose $n_0$ to equal 1, then we need a value of c such that: $-22 \eqslantless C$\
Thus, $22n^{2}+19n-63$ is $O(n^{2})$ because $22n^{2}+19n-63 \eqslantgtr\ -22n^{2}$ whenever $n > 0$\
final saddleBOT
We will show that if $f(n)=22n^{2}+19n-63$ is $O(n^{2})$ then we must show that ...
soft zealotBOT
Nurech
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
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@dry ruin Has your question been resolved?
quiet token
Assume that this is known
final saddleBOT
Assume that this is known
quiet token
Prove that this is true:
If you know that F is differentiabele in an open 'smooth?' surface and projectable on one of the coordinate-planes
I tried brute-forcing some things, but I feel like it won't get me anywhere.
I'm stuck as to how I go from an equation in vectors, to an equation in scalars. A friend gave me a tip to look at [F1,0,0] But i don't see how that would help me here either.
(nk is the normal vector using the right hand rule)
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quiet token
<@&286206848099549185>
final saddleBOT
@quiet token Has your question been resolved?
final saddleBOT
@quiet token Has your question been resolved?
final saddleBOT
@quiet token Has your question been resolved?
final saddleBOT
@quiet token Has your question been resolved?
final saddleBOT
final saddleBOT
Available help channel!
vernal hearth
final saddleBOT
vernal hearth
I need help with the set upo
everything else should be fine
Is this the right set up
and then you would combine like terms and go from there
the area equation would be length x width x height
young bobcat
um okay yeah so its mainly the right setup
except you aren't given h
you are given the volume is 10. so what is the volume in terms of h and w
@vernal hearth
vernal hearth
yea that makes sense
young bobcat
yeah so just plugin that for h and yeah do your thing
vernal hearth
okay also in the time it took you to repsond I also thought of this
young bobcat
wait another thing
young bobcat
yeah this is actually the right way your previous way is wrong
except the box doesn't have a lid
so like there are only 5 sides
so it would just be 15 times w times 2w
not 2 times 15 times w times 2w
vernal hearth
Ohhh okay
That piece of the problem was throwing me off
It was kinda of hard to visualize
young bobcat
okay
young bobcat
um yeah it looks like a box idk what else to say
vernal hearth
okay lol
final saddleBOT
@vernal hearth Has your question been resolved?
young bobcat
are you good
vernal hearth
uh
I think I got stuck?
My final answer is approximately 313.5
but the site says its wrong
@young bobcat
The cost equation I ended up with was this
vernal hearth
yep
vernal hearth
which one?
young bobcat
the second part of the RHS is 2(9h2w)
vernal hearth
Why is that
Is it literally only the bottom piece that gets the 15
and everything else is a side even though its a rectangle
young bobcat
and everything else is a side even though its a rectangle
yeah its a side thats why it should be a 9
you wrote it as 2(15*2hw)
vernal hearth
damn okay
let me re try
and then Ill let you know
do you have an apporx final answer?
young bobcat
180
vernal hearth
young bobcat
yeah thats correct
vernal hearth
okay bet
young bobcat
ill get an answer for you
vernal hearth
ill speed run the calculus
young bobcat
okay the answer should be around 245
arctic zinc
why did you make this so complex
arctic zinc
vernal hearth
I just tried setting it up the way my prof tought me
arctic zinc
this question could have been solved easier but now its done its done
arctic zinc
ok so you could have used simple algebra
length = 2x
Width = 1 x
wait ill right the formula and explanation and send in dms
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quiet token
bro i was sleeping
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Available help channel!
tranquil pine
n
tranquil bone
$\sum ^{n}{r=1}\dfrac{\sqrt{r+2}}{2}-\sum ^{n}{r=1}\dfrac{\sqrt{r}}{2}$ what’s the easiest way to do the method of difference here
final saddleBOT
$\sum ^{n}_{r=1}\dfrac{\sqrt{r+2}}{2}-\sum ^{n}_{r=1}\dfrac{\sqrt{r}}{2}$ what’s...
soft zealotBOT
Faq
tranquil bone
It takes a while to do normally
wraith crater
reindex
tranquil bone
How?
wraith crater
for the first one let u=r+2 then $$\sum_{u=3}^{n} \frac{\sqrt{u}}{2} + \frac{\sqrt{n+2}}{2} +\frac{\sqrt{n+1}}{2} - \sum_{r=3}^n \frac{\sqrt{r}}{2} - \frac{1}{2} - \frac{\sqrt{2}}{2}$$
soft zealotBOT
Pure
tranquil pine
they will kind-of cancel themselves
and you'd be left with $\frac{\sqrt{n + 1}}{2} + \frac{\sqrt{n + 2}}{2}$
soft zealotBOT
trololol !
tranquil bone
and you'd be left with $\frac{\sqrt{n + 1}}{2} + \frac{\sqrt{n + 2}}{2}$
Wait only that?
tranquil pine
wait wait wait
i missed something
and you'd be left with $\frac{\sqrt{n + 1}}{2} + \frac{\sqrt{n + 2}}{2} - \frac{1}{2} - \frac{\sqrt{2}}{2}$
soft zealotBOT
trololol !
tranquil pine
can you see why ?
tranquil pine
**Faq**
because the sum on the right kinda cancels everything from the sum on the left
except for the +2 "offset" of the sum from the left
tranquil pine
which is why we're left with that
tranquil pine
Yeah I can see why this works
yeah
oh wait
now i see someone already gave the solution, and far better explained
autumn dust
a = 24(mod 31), -15≤a≤15.
find whole number a
final saddleBOT
a = 24(mod 31), -15≤a≤15.
find whole number a
worldly vale
When does x = y (mod 31)?
autumn dust
for an example ?
worldly vale
What's the rule
autumn dust
there is only one rule a must be a whole number and when we divide something(a)/24 mod must be 31
and we have intervals too that i wrote
i wanna know certain formula to find it out
worldly vale
When does x = y (mod 31)?
I am asking you to answer this question in general
autumn dust
i can't think that much
if i think i should get an answer but i need it to write down
worldly vale
Well then think
autumn dust
i can't get it
final saddleBOT
@autumn dust Has your question been resolved?
tranquil pine
i need help
final saddleBOT
i need help
tranquil pine
Can someone tell me what is section
worldly vale
Context?
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@tranquil pine Has your question been resolved?
shell musk
I am trying to solve this problem but it says incorrect
final saddleBOT
I am trying to solve this problem but it says incorrect
shell musk
My process:
tired walrus
do not forget about the 5 and the 2
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@shell musk Has your question been resolved?
regal tree
Hello! I don't understand how to do thisThere is 3 parts to this
final saddleBOT
Hello! I don't understand how to do thisThere is 3 parts to this
shell mountain
What have you tried
regal tree
I don't understand how to solve for y
shell mountain
It's just algebra
oak kraken
final saddleBOT
oak kraken
Any issues with this?
I forgot to get GCF first
But in the end I have distribution and it feels weird to put a number in between brackets like this
How do you know if 3x is for the first or last factor if you see that fourth line and nothing else?
worldly vale
You can just move the 3x to the front
cloud zephyr
There are no first and last factors
worldly vale
If its bothering you
oak kraken
You can just move the 3x to the front
Wait just the 3x? Or do you mean 3x(2y-1)
worldly vale
Multiplication is commutative abc=cab=bca
cloud zephyr
Multiplication is commutative
oak kraken
But 3x(2y-1) is distribution and the entire thing counts as one term
worldly vale
Multiplication is commutative abc=cab=bca
(Other permutations sold separately)
3x•(2y-1)=(2y-1)•3x
oak kraken
I think it would lead to a different answer if I put 3x at the front of (y+6)
worldly vale
I assure you it will not
oak kraken
Wth
worldly vale
These things are essentially just numbers, they're objects waiting to be told what numbers they are (when you plug in x and y values)
So they satisfy number rules
2*3*4= 3*2*4
worldly vale
I mean, you haven't done anything there
Those brackets you added are purely aesthetic
oak kraken
Woah
I really thought the 3x had to stay with the expression it came from
With this simple example it doesn’t seem to matter if I distribute or not
Interesting
So then why on earth is this entire expression considered one term? 3x(2y-1)
Terms or only separated by + or -, right?
(6)(7)(1) so would this entire expression also be considered one term?
worldly vale
Sure yeah
oak kraken
This is really interesting how brackets can really change the game
I would normally see 2y-1 as 2 terms
But (2y-1) with brackets is 1 term?? Or it depends on the context
worldly vale
Well (2y-1) on its own is literally no different than 2y-1
But like 5(2y-1) is one term
Term is a kind of vague word really
oak kraken
So it’s kind of like saying all squares are rectangles but not all rectangles are squares
That’s why 2y-1 on its own us two terms
But 5(2y-1) is one term
worldly vale
It's more like idk the difference between 2 eggs, and those 2 eggs as part of a cake
oak kraken
Lol so the eggs 🥚 and milk 🥛 are in the cake and on their own they make up two ingredients, but as a whole the cake 🎂 is only one item altogether
oak kraken
Haha
vital crag
just give me a slice of cake when you're done baking
oak kraken
I guess it’s just important to know that terms are only separated by + or -. But sometimes multiple terms can be grouped as a single term too
Like factor by grouping. When you group and find a common factor let’s say (x+2) it becomes one term just like z or 9 or pi
And by adding the parentheses you can treat that group exactly like a single term
Do I have that correct? Of course the (x+2) does carry some special powers too, such as the power of distribution, but in general I hope my analogy is not way off?
worldly vale
Yeah i think you get it
oak kraken
Here is an example, it starts with 3 terms and after factor by grouping is only 2 terms
Do we generally wanna do more factoring than expansion in math?
All are exactly the same just written differently
I could see top polynomial being useful for visualizing a graph, bottom factored form useful for finding x and y intercepts?
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south warren
How do I show that this series converges for p<1? I can show that it diverges for p=1, but dont know how to prove for every p<1
final saddleBOT
How do I show that this series converges for p<1? I can show that it diverges fo...
south warren
well if I did the ratio test correctly I did get 0
well no it doesnt really make sense
as it would be the same for p and p-1 when p>1 aswell
vital crag
well if I did the ratio test correctly I did get 0
the result of your ratio test should depend on p
but i think the algebra to make that work sounds awful
vital crag
oh integral test is a better idea
so do this
tranquil pine
,w convergence sum n/(1+n^2)^p
soft zealotBOT
south warren
alright thanks, will give it a try and come back if I still dont get it to work
.close
umbral crane
how i do this
final saddleBOT
how i do this
umbral crane
integrating by parts
vital crag
integrating by parts
Yes. Show your attempt
umbral crane
i got f prime x * g prime x - integral of g prime x * fdouble prime x dx
but idk where to from there
@vital crag
the
uv- integral vdu
but then idk what im suposed to do
vital crag
uv- integral vdu
Try different combinations for u and v. Let the question guide you
umbral crane
k
vital crag
i got f prime x * g prime x - integral of g prime x * fdouble prime x dx
This sounds wrong
vital crag
Just stick with your uv formula
shell musk
I am having difficulties with the last one
final saddleBOT
I am having difficulties with the last one
marsh temple
What have you tried?
shell musk
Ok
Lemme look real quick
So I have subtracted the amount of outcomes when it flips 12 times
Minus the probabilities of the probabilities of 12/12-11/12-10/12-9/12
marsh temple
That seems right
shell musk
I used symbolab