My homework Is done
#help-26
empty sail
Because the common factor is everyone here enjoys math
empty sail
Why the fuck would you do this 🤣
If you enjoyed something enough and wanted to help someone learn, you would teach them for fun
empty sail
My homework Is done
.close If you are done
sterile laurel
No bro fuck them they can learn by them selfs I can hardly answer my questions
Bye bro
Thanks a lot bro❤️ ❤️ ❤️
empty sail
No bro fuck them they can learn by them selfs I can hardly answer my questions
Then you could have learned by yourself
sterile laurel
Then you could have learned by yourself
Well.am not them 😂
empty sail
All of that was just simple Google searches
subtle temple
can someone explain plz 👀
topaz sinewBOT
can someone explain plz 👀
subtle temple
also am i abusing this server, i feel like im in here 5x a day 😭 i apologize guys i have a test to pass and im stupid
chrome hinge
How many things do you have in that test
subtle temple
How many things do you have in that test
ok so basically, i havent done some of the math on there in quite some time, so im refreshing a lot and theres few things i havent learned really in depth
math portion is 16 questions
vry short test, but i want to be rly good at that because the other portion is reading, 10 questions, pretty easy, and then theres the physics portion and i havent had a physics class ever in my life lmao
in short, my prep game plan looks like, try to perfect the math, review some reading practice tests, and then learn the physics portions they're askign
deft mirage
can someone explain plz 👀
Hi again, so what we need to note is that x^4+1 will always be positive, but x^4-1 will be negative for -1<x<1. We are looking for the intervals of x when P(x) is positive in inequality A. Regardless of what these intervals are, they will be the same in inequality B because the denominator does not change the sign of the function at any point. In the case of C, this will definitely reverse the sign of P(x) in the range mentioned as it is negative, so it will certainly add or remove from the solution set, it will not leave it unchanged. So A and B have the same solution sets.
subtle temple
Hi again, so what we need to note is that x^4+1 will always be positive, but x^4...
aaah ok i seee
subtle temple
Hi again, so what we need to note is that x^4+1 will always be positive, but x^4...
thanks again man, sorry for being in here a bit too frequently 😅
deft mirage
No it's fine, that's what the server is here for!
subtle temple
.close
kindred inlet
topaz sinewBOT
kindred inlet
can anyone help?
frosty zephyr
I’ll read it
kindred inlet
okok
kindred inlet
I’ll read it
u get it?
foggy prawn
You roll a 100 sided die, you get to keep the value of your roll. How much would you pay if you can reroll and infinite number of times and pay one dollar per roll?
topaz sinewBOT
```You roll a 100 sided die, you get to keep the value of your roll. How much wo...
foggy prawn
i got $99 since the face from 2 through 100 gives me profit for each roll
worldly tendon
no
worldly tendon
if you pay $99 and $1 per roll you literally cannot profit
you keep only value the end value right
foggy prawn
if i roll 34 i get $34 but to reroll i need to spend $1
worldly tendon
you don’t get $34 plus the new $33
otherwise you would literally have infinite money
foggy prawn
if i roll that than sure
foggy prawn
oh
worldly tendon
and that doesn’t even account for starting pay
foggy prawn
okay
worldly tendon
profit = last roll - starting amount - number of rolls
foggy prawn
we dont start out with any amount
worldly tendon
what were solving for
worldly tendon
that is not a cost
foggy prawn
if we dont roll anything we dont have any value for a die roll
worldly tendon
it’s not agreeing it’s you understanding
you pay $x to play
foggy prawn
we start at $0
worldly tendon
we are finding x
worldly tendon
we start at $0
that’s not the cost to play
foggy prawn
so what is it than?
worldly tendon
what we’re solving for bro
worldly tendon
yes
foggy prawn
we dont know that
topaz sinewBOT
@foggy prawn Has your question been resolved?
topaz sinewBOT
@foggy prawn Has your question been resolved?
shy sage
8 rooks are randomly placed on different squares of a chessboard. A rook is said to attack all of the squares in its row and its column.
Compute the probability that every square is occupied or attacked by at least 1 rook.
topaz sinewBOT
8 rooks are randomly placed on different squares of a chessboard. A rook is said...
shy sage
here's what i tried:
There are 8^8 ways to put one rook per row and 8^8 ways to put one rook per column. This double counts the ways that have one rook in each row and column, which is the classic definition of covering every square. For that there are 8 ways to choose the column for the first row, 7 ways to choose the column for the second row, and so on making 8! in total. Using inclusion-exclusion the final answer is 2⋅8^8−8!=33514112
but i'm not sure if i am correct
Never mind. i got the right answer.
.close
topaz sinewBOT
topaz sinewBOT
Available help channel!
graceful sparrow
Is it possible to calculate the minimum of something given the standard deviation, average and max?
topaz sinewBOT
Is it possible to calculate the minimum of something given the standard deviatio...
graceful sparrow
oh right-
im so dumb
wait no cuz what if theres like 20 different scores
cuz if it were only 2 scores, then finding min given max and average is easy but with 20, stuff can vary
thats why standard dev is useful I believe, dont know if its possible to find min tho
as it can give the range sorta?
<@&286206848099549185>
odd pagoda
probably not. but I can't come up with an example
graceful sparrow
im able to provide some numbers?
standard dev of 8.11, max of 88.89, average of 75.44
20 like scores
odd pagoda
just intuitively there should be a lot more choices for x1,...,x20 than for stdev, min, max, avg. so surely some choices give the same values for stdev, max, avg but not for min
for example it's not possible to calculate stdev from avg, min, max. see 1 2 4 5 and 1 3 3 5. all min=1, avg=3 and max=5. but stdev of first is 1.58 and second 0.70
graceful sparrow
I see
odd pagoda
fixing the stdev is kinda annoying so you can't as easily play around with different values
but there are probably examples
graceful sparrow
but as you're given the stdev, would it be possible to substitute it?
odd pagoda
given any set X, we can modify X so that is has specified mean and stdev by calculating aX+b for some smart values a, b. so there are a lot of datasets which have the same mean and stdev
sure those might not have the same max but with some extra work you can probably also get the max to be the same
but the min of them very very likely won't always be the same.
but finding an explicit example is just annoying
topaz sinewBOT
topaz sinewBOT
Available help channel!
timber tartan
hi guys for part b
topaz sinewBOT
hi guys for part b
timber tartan
i dont get why is there a x^2 at the last line of the solution
past kayak
They multiplied the top and bottom by x
That way, you don't have to worry about whether or not x is positive or negative
Well, you do, but it's now built in to the thing
valid forum
A quadrilateral with perimeter 52 has an insribed circle with radius 5. What is the area of the quadrilateral?
topaz sinewBOT
A quadrilateral with perimeter 52 has an insribed circle with radius 5. What is ...
chrome hinge
draw
keen venture
Has a picture of it afaik
topaz sinewBOT
@valid forum Has your question been resolved?
valid forum
slate raven
"If the inscribed circle of a polygon with area A and perimeter c exists, then the radius of the incircle has the value 2A/c"
→A = c*r/2
= 130
valid forum
ohhh, so is the area 52x5/2?
slate raven
yep
valid forum
and that's the area?
slate raven
yep
topaz sinewBOT
loud ingot
can you do any of the forms?
topaz sinewBOT
@fast dome Has your question been resolved?
chrome hinge
kinda skipped parabolas
clear wadi
um, you can write the factorized form by looking where the graph cuts the x axis, which in this case is at -8 and 12, so the factors will be (x-12) and (x+8) so the factorized form will be (x-12)(x+8)
and the vertex form is given by (x-h)^2+k just put in the vertex coordinates to get the eq
foggy prawn
You roll a 100 sided die, you get to keep the value of your roll. How much would you pay if you can reroll and infinite number of times and pay one dollar per roll?
topaz sinewBOT
```You roll a 100 sided die, you get to keep the value of your roll. How much wo...
foggy prawn
Wrong
You pay $1 if you want to reroll?
You don’t know how to solve this question
Dude you’re asking stupid questions
That was in the question
Lol
As many as you want
That’s irrelevant
We want to know how much we want to play this game
Okay
Ty for your efforts
topaz sinewBOT
Available help channel!
broken patio
topaz sinewBOT
broken patio
I need help for this proof
topaz sinewBOT
@broken patio Has your question been resolved?
broken patio
well after 15 minutes so <@&286206848099549185>
sweet shard
draw a picture
ashen eagle
Yes, it is the Pythagorean Theorem.
broken patio
okay, i understand geometrically, but how would the proof look?
like what to I write
odd pagoda
calculate the norms explicitly. bit annoying with all the inner products but doable
sweet shard
is it okay that once i'm finished later tonight i can dm?
just repost your question in a new help channel.
iron halo
I can't figure out how to approach this limit, any ideas?
topaz sinewBOT
I can't figure out how to approach this limit, any ideas?
sturdy oracle
I can't figure out how to approach this limit, any ideas?
Are you familiar with L'Hopital's?
iron halo
I am not
sturdy oracle
Aight so you can multiply by the conjugate
gimmie a sec
this is gonna be a pain to write in latex lol
iron halo
my apologies for the trouble, our textbook seems to have left a few things out
sturdy oracle
lmao np
i've dealt with worst things to type out
$$\lim_{t\to 16} \frac{t-16}{\sqrt{t}-4}$$
$$\=\lim_{t\to 16} \left(\frac{t-16}{\sqrt{t}-4}\cdot\frac{\sqrt{t}+4}{\sqrt{t}+4}\right)$$
$$\=\lim_{t\to 16} \frac{\left(t-16\right)\left(\sqrt{t}+4\right)}{t-16}$$
$$\= \lim_{t\to 16} \sqrt{t}+4$$
thorny flameBOT
Umbraleviathan
iron halo
thank you so much, idk how i didn't think of multiplying by the conjugate
sturdy oracle
try conjuguates if you get any fractional indeterminate forms
iron halo
I will definitely keep me in the mind in the future, you may have just saved my whole calc career 😂
iron halo
our textbook doesn't seem to show anything about it, but its missing a few things that are showing up on our homework anyways
sturdy oracle
yeah because L'Hopital's utilizes derivatives
grave finch
Hi.
I'm trying to help someone with some python code to find how many digits 2 floating points have in common. (so they can discover precision of accuracy in estimating π). Converting them to strings and just comparing them is slow, but accurate. Trying to use logbase10 to count the 0's of their difference is fast, but not entirely accurate. Is their a common math trick for doing this?
topaz sinewBOT
Hi.
I'm trying to help someone with some python code to find how many digits 2 f...
cursive abyss
do you mean first digits or any digits?
grave finch
for example:
3.141583 is 0.000009653 off from π, log10 of the difference is -5.01 but there are 4 digits after the decimal in common.
3.14159 is 0.000002653 off from π, log10 of the difference is -5.57 and there are 5 digits after the decimal in common.
ashen eagle
What is usually done is log
grave finch
do you mean first digits or any digits?
basically what level of precision is this estimate correct, so just the first.
looking for something like: accuracy(3.141583, π) is 4 digits the same after the decimal.
grave finch
What is usually done is log
log base 10 is what we've been trying. but hard to account for carry digits in the difference.
I'm supposed to be installing a doorbell, not helping this guy play with numbers. but it feels like there should be an answer here and I'm just missing it. 🙂
cursive abyss
yeah, log10 doesn't help here
imagine comparing 0.999999 and 1.000001
grave finch
like I trust log 10 to tell me how many 0's there are in the difference, but i don't trust the difference to be correct when what I really want is just a "per digit comparison."
ashen eagle
No, that exactitudness not with log
cursive abyss
how about a loop where you look at the whole part and then multiply each number by 10 mod 10
i'm not sure about the accuracy though, the digits can change in theory
grave finch
That's certainly viable, but sadly no faster than just converting to a string and comparing.
I think I'm satisfied that log10 gives me an accurate enough count of the 0s, but it's not going to work for them because the number we're passing to it is not an accurate difference.
I'm going to write a library that does xor on digits in a floating number. I'm not convinced that will be any faster than the string compare either. Maybe I should install the doorbell.
cursive abyss
i'm pretty sure you can't do that with loop
it should be cheaper than building a string though
but I'd probably look into how float-to-string conversion is usually implemented for better precision
so that we can do it manually without actually using strings
long stirrup
it's python code, you want to avoid doing stuff
grave finch
it's python code, you want to avoid doing stuff
very true.
long stirrup
you can't outpace converting to string, because you need to write code for that
cursive abyss
well, yeah, talking about speed in python doesn't make sense
grave finch
well, yeah, talking about speed in python doesn't make sense
to a certain extant it does. I've cut this guys project down from 20 minute calculations to 1 handful of milliseconds per search, I could make it faster in C, but not that level of faster. Better algorithm > swapping language or hardware.
Anyway, I think I've got the answers I came looking for, so thank you very much for your time and help.
cursive abyss
of course i wasn't talking about algorithm complexity, it surely matters
grave finch
And if you ever need any python help come over to the python discord and ask some questions. 🙂
cursive abyss
i'm actually a c++ TA :)
grave finch
Ah cool. I did c++ for a couple decades before I learned python. I'm happy with both, but python is actually "fun", similar to how perl is fun, but without the maintenance issues.
cursive abyss
i'm not happy with either
there're no perfect languages
grave finch
No. Although rust and nim look interesting.
grave finch
It's a surprisingly popular language on the python discord. Although I've barely looked at it yet.
ok thanks!
!close
.close
dense trail
topaz sinewBOT
dense trail
Bottom is supposed to be (3x+5)^2
grim jacinth
Bottom is supposed to be (3x+5)^2
h -> 0
You need to carry the limit part down each step 👍
warm finch
You are doing the formal definition of the derivative
Which is the lim of that as h goes to 0
jaunty quiver
Well, I can't get this method to tell me both the inequalities
topaz sinewBOT
Well, I can't get this method to tell me both the inequalities
lime zealot
when
$$x-1>0, x+1>0$$
you get $x>1$
thorny flameBOT
秋水
lime zealot
when
$$x-1<0, x+1<0$$
you get $x<-1$
thorny flameBOT
秋水
lime zealot
so the result is {x: x<-1 or x>1}
jaunty quiver
I don't understand the how you get parts
$x-1 > 0 = x > 1$ but $x+1 >0 \neq x > 1$
thorny flameBOT
আত্মদর্শী
jaunty quiver
I have a similar problem with the second part
lime zealot
It's their intersection
jaunty quiver
What intersection?
jaunty quiver
**秋水**
It seems like these have different points when they are both >0
(0,1) and (1,0)
lime zealot
x has to satisfy both x>1 and x>-1, so x>1
jaunty quiver
Oh okay
And for the second one it has to satisfy both $x<-1$ and $x <1 $ so it is just $x<-1$
thorny flameBOT
আত্মদর্শী
torn mica
i need dhelp
topaz sinewBOT
i need dhelp
past kayak
Yep
torn mica
lol really?
cursive abyss
why not
torn mica
i thought it might have been 13
cursive abyss
you can't get a negative number when you square something (unless you deal with complex numbers which you are not)
so subtracting a non-negative number from 4 you can't get something greater than 4
torn mica
i need help
topaz sinewBOT
i need help
lime zealot
$\tan \theta = \frac{120}{235}$
thorny flameBOT
秋水
thorny flameBOT
topaz sinewBOT
@torn mica Has your question been resolved?
neon iron
hello
neon iron
I need some help with tally and frequency tables for math
I have to turn this
i have to get all these numbers
And put them into this
Idk where to put any numbers
please help
/close
close
.close
topaz sinewBOT
steady ocean
<@&286206848099549185>
just basic z scores
somoene help
lol
i have no idea
why i am getting this wrong
wheat grove
dont ping helpers before 15 minutes
topaz sinewBOT
steady ocean
fading glacier
use a calculator, you have your standard deviation and mean
you also have your lower bound and upper bound
should work out
otherwise you can use the painful formula by hand
fading glacier
it says between
as ive said
your upper bound should be 1088
and your lower bound should be 1003
topaz sinewBOT
Available help channel!
subtle timber
Define the value of the parameter "a" so that the function will be continuited, "continuity ". True result is 9. I know the way, but somehow i dont understand lim=lim. How to get that lim. For example i have lim (x goes to 0) 2x+a.
topaz sinewBOT
Define the value of the parameter "a" so that the function will be continuited, ...
subtle timber
this is example on how i think it should be done
then a = 2
got to that point
I think i can manipulate it
soo i put everthing on one side and it = 0
then i remove x and put back to a = 4+5
fading glacier
Define the value of the parameter "a" so that the function will be continuited, ...
your limit from the left should be equal to the limit from the right
topaz sinewBOT
topaz sinewBOT
Available help channel!
solemn bolt
what does this notation represent?
topaz sinewBOT
what does this notation represent?
long stirrup
composition usually uses round brackets, i think this has square just for aesthetics
daring geode
how would i convert this sequence into a non recursion one or equation?
a₀ = 1;
aₙ = a₍ₙ₋₁₎ + 2* n
long stirrup
for this specific one i would write how it starts, it's probably something obvious
generally idk
daring geode
Thats wat I was thinking it looked obvious
this is what it looks like on desmos
but i cant seem to pinpoint an equation
ive tried quadratic , logarithmic, exponential
idk
its just a bit off
maybe its impossible?
long stirrup
it's sqaure +1 minus n
foggy prawn
Given a six-sided die, what's the expected value of the difference between two die rolls?
topaz sinewBOT
```Given a six-sided die, what's the expected value of the difference between tw...
foggy prawn
wouldnt this be 0, since the ev of 1 die roll would be 3.5
which would make the difference be 0 since each die roll has a ev of 3.5
sick hazel
no
u would need to sum the p(d=0) * 0 + p(d=1) * 1 .... + p(d=5) * 5
where d is difference between rolls
snow lake
@daring geode
foggy prawn
<@560213366178840632>
?
daring geode
l love ui thanks
foggy prawn
this channel is occupied
foggy prawn
u would need to sum the p(d=0) * 0 + p(d=1) * 1 .... + p(d=5) * 5
what is "p(d=0) * 0 + p(d=1) * 1 .... + p(d=5) * 5"
sick hazel
like probability difference is 0 times 0
plus probabibility difference is 1 times 1
and so on until probability difference is 5
times 5
foggy prawn
why?
sick hazel
by definition of expected value
foggy prawn
ic
so for this problem since the ev of a fair die is 3.5
the prob difference would be 12.25 right?
foggy prawn
wdym
sick hazel
if u roll 2 dice
foggy prawn
difference for what?
sick hazel
u cant get the differnece of their values to be equal to anything more than 5
the max difference is if 1 roll is 1
and the other is a 6
foggy prawn
difference for what?
foggy prawn
how do we calculate the values per roll?
foggy prawn
wouldnt that just be ev tho?
sick hazel
what ur doing is subtracting 2 expected values
which wont give u the expected value of this
foggy prawn
what would be the solution?
sick hazel
well
the solution is
to find the probability the difference is 1
plus
ur refering to the 1 in this right?
sick hazel
probability the difference is 2 times 2
plus (probability difference is 3) times 3
and so on
until
(probability difference is 5) times 5
so probability difference is 1
is 10/36
foggy prawn
those numbers basically symbolizes the die rolls right?
foggy prawn
we would only count the situations where we have the same outcomes right?
sick hazel
no?
sick hazel
the probabibility of getting a difference of 1
cause u can have 1-2, 2-3, 3-4, 4-5, 5-6
and reverse
long stirrup
you're both sure it's not absolute difference?
or you're both sure it is?
i can't tell
foggy prawn
im not sure
foggy prawn
the probabibility of getting a difference of 1
which is what the q is asking when it says whats the ev of the difference between two dice right?
long stirrup
it would be my first assumption
but it makes sense with normal difference too why not
sick hazel
u need to calculate probabilities of getting 2,3,4,or 5
foggy prawn
which is what the q is asking when it says whats the ev of the difference betwee...
@sick hazel
sick hazel
only the probability of difference of 1 is not what the question was asking
cause that's not the only case
foggy prawn
what are the other cases?
foggy prawn
up to 5?
foggy prawn
2 - 5 right?
sick hazel
yeah
foggy prawn
who wouldnt 1 or 6 be a difference?
sick hazel
1 is also a difference
foggy prawn
for 6 we cant have a difference of 6 between 2 dice
sick hazel
yeah
foggy prawn
so 10/36 would be wrong than
foggy prawn
why cant we have a difference of 0?
sick hazel
that wont affect the expected value
foggy prawn
ah
sick hazel
cause u end up multiplying the probability by 0
foggy prawn
so i made the mistake earlier by taking the difference between the ev of both dice
sick hazel
yeah
foggy prawn
but what i shouldve done is count the number of dice that has differences between 1 to 5 right?
foggy prawn
and divide it by 36
sick hazel
yeah
foggy prawn
multiply it by the difference
wdym
sick hazel
the difference
foggy prawn
of what?
oh snap
so lets say the differenc eof 1
is 10/36
it would just be 1 * 10/36 right?
sick hazel
yeah
foggy prawn
makes sense ty this all makes sense
lets say i wanted to make both dice seven instead of six
it would be the ev of the dice outcomes of 1 - 6 times the outcome?
neon iron
topaz sinewBOT
neon iron
I got this but I have no idea what to do after
topaz sinewBOT
@neon iron Has your question been resolved?
neon iron
<@&286206848099549185>
carmine stone
question seems wrong
i graphed all the answers and didn't get a graph that matched the ans
neon iron
i graphed all the answers and didn't get a graph that matched the ans
the answer is A
but doesn't have an explanation
carmine stone
these are the two graphs
if they were equivalent they should match
but they don't which is why i'm not confident that this question is valid
carmine stone
idk i think the questions just wrong
neon iron
what if its y^1/8^y^9/8
instead of multiplying its another exponent?
is that possible
carmine stone
i don't think that changes anything
neon iron
are you sure none of them matches?
carmine stone
yep
carmine stone
yea go for it ig i'm not a helper tho
neon iron
oke
empty sail
Don't ping specific people
neon iron
<@&286206848099549185>
empty sail
That font makes it poorly formatted. It's $$y^{\frac{1}{8}} \cdot (y^{\frac{3}{4}} )^{\frac{3}{2}}$$
neon iron
hmm
thorny flameBOT
dldh06
topaz sinewBOT
topaz sinewBOT
Available help channel!
sonic knot
topaz sinewBOT
sonic knot
can somebody explain this one
the x is positive so it has to be the regular function and the only one i thought it was was b
slow oyster
@sonic knot the ans is A
keen venture
It can help to try plotting a few points. What's f(0)? f(3)?
slow oyster
@sonic knot the value of function goes on decreasing after a certain time
You understant what I meant to say ??...
slow oyster
ok
sonic knot
the only point i know is f(0)
slow oyster
do f(0) , f(4) , f(10)
keen venture
Okay, the only point I was trying to get across is that f(3) is smaller than f(0), so the function is decreasing
That happens when the base is less than 1
Cannot be B, which is increasing
sonic knot
why is it not e, f, or d
keen venture
f(0) = 1, so the function is positive somewhere
neon iron
Can someone help me solve this
topaz sinewBOT
Can someone help me solve this
neon iron
I kinda get confused when the x's arc gets mixed in one place with the others
lofty salmon
So what did you get?
lofty salmon
Wdym 96 and 128?
neon iron
2x - 224
lofty salmon
I kinda get confused when the x's arc gets mixed in one place with the others
You got the answer?
lofty salmon
2x - 224
Wait, the inner angle will be 360 - 2x?
So using the angle sum property we will get 360 - x + 112 = 360?
lofty salmon
sURE
neon iron
then I did what is probably wrong
neon iron
after this
what should I do
I couldn't decide what I was supposed to equalize 2x - 224 to
lofty salmon
0
So, the inner angle would be 360 - 2x
add with the x and the other two angles and equalize them to 360
ripe crane
topaz sinewBOT
topaz sinewBOT
@ripe crane Has your question been resolved?
topaz sinewBOT
@ripe crane Has your question been resolved?
subtle timber
In this case, i dont know, how we got Yo as 9. For Xo and x i know, but for 9 i dont.
topaz sinewBOT
In this case, i dont know, how we got Yo as 9. For Xo and x i know, but for 9 i ...
sweet shard
use that
subtle timber
.reopen
topaz sinewBOT
✅
topaz sinewBOT
@subtle timber Has your question been resolved?
topaz sinewBOT
Available help channel!
river stag
topaz sinewBOT
river stag
can someone pls help me figure out where i am going wrong? im trying to find the area between the curves
.close
proven olive
do you recognize this inverted question mark?? I feel like no one knows anything about it , its under conditional statement
topaz sinewBOT
do you recognize this inverted question mark?? I feel like no one knows anything...
empty sail
Probably an error with the loading of fonts
proven olive
Oh so basically it doesn't mean anything and just the error of the computer?
empty sail
Yes
young vale
topaz sinewBOT
young vale
Hey
neon venture
hi
young vale
Im trying to solve this limit
And I've tried multiplying by (sqrt(x+3) +2x)
And dividing too, ofc
But still getting 0/0
What I've done is here
neon venture
multiply the denominator and the numerator by sqrtx + 1
neon venture
i dont know, try it
neon venture
weird i forgot how to deal with these kind of limit lmao
young vale
I was thinking on doing the conjugate too, but no idea why doesn't work
young vale
Wdym
neon venture
like :
$$\frac{\sqrt{x+3}}{\sqrt{x}-1} -\frac{2x}{\sqrt{x}-1}$$
thorny flameBOT
Ｈｅｒｅｌｓ
topaz sinewBOT
@young vale Has your question been resolved?
young vale
.close
obsidian gale
topaz sinewBOT
obsidian gale
how did step 3 become step 4
honest hazel
how did step 3 become step 4
(n-2) was factored out, and the parenthesis were opened
(n-2)^2 +2(n-1)(n-2) = > (n-2)((n-2)+2(n-1))
grave lava
hi
grave lava
so I'd need some guild for next step
,tex
The solid between the sphere $x^2 +y^2 +z^2 = 19$ and the hyperboloid $z^2 -x^2 -y^2 = 1$,
for $z > 0$\\
Converting to spherical coordination:\\
$\begin{cases}
x=\rho\sin(\phi)\cos(\theta)\\
y=\rho\sin(\phi)\sin(\theta)\\
z=\rho\cos(\phi)\\
\end{cases}$\\
$x^2+y^2+z^2=19 \Rightarrow \rho^2=19 \Rightarrow \rho =\sqrt{19}\\
\begin{aligned}
z^2 -x^2 -y^2 &= 1\\
\Rightarrow z^2&=1+(x^2+y^2)\\
\Rightarrow \rho^2\cos^2(\phi)&=1+(\rho^2\sin^2(\phi)\cos^2(\theta)+\rho^2\sin^2(\phi)\sin^2(\theta))\\
\Rightarrow \rho^2\cos^2(\phi)&=1+\rho^2\sin^2(\phi)\\
\Rightarrow \rho^2(\cos^2(\phi)-\sin^2(\phi))&=1\\
\end{aligned}$
Darkness
topaz sinewBOT
@grave lava Has your question been resolved?
topaz sinewBOT
@grave lava Has your question been resolved?
grave lava
well then
foggy prawn
You roll a 100 sided die, you get to keep the value of your roll. How much would you pay if you can reroll and infinite number of times and pay one dollar per roll?
topaz sinewBOT
```You roll a 100 sided die, you get to keep the value of your roll. How much wo...
@foggy prawn Has your question been resolved?
knotty ledge
uh what, isn't this a bit subjective
people will pay however much they feel they want to depending on how much they want to gamble
foggy prawn
people will pay however much they feel they want to depending on how much they w...
true
its asking how much would you pay to play this game
rugged cradle
hello I'm confused on what to do here was hoping to find some help
rugged cradle
question c
loud ingot
Can you find v at t=5?
rugged cradle
how do I go about doing that?
rugged cradle
ahh I see, I could do that but the questions are based on integration and differentiation so I assume the preferred answer would have to involve those methods
not to mention the entire questions is worth quite a few marks so yeah :/
loud ingot
Aha so do you know that velocity is derivative of distance over time?
rugged cradle
yeup
loud ingot
So to find distance you would need to integrate v
foggy prawn
what calc concept is a derivative before an integral?
topaz sinewBOT
what calc concept is a derivative before an integral?
foggy prawn
is it calc 2 thing?
keen venture
You mean the fundamental theorem of calculus? Yeah calc 2
topaz sinewBOT
Available help channel!
orchid night
topaz sinewBOT
orchid night
how do i differentiate this
drifting swift
quotient and product rules
hope you aren't being asked to do it from first principles
if you are that'll be pain
orchid night
yep i know i have to use quotient rule but what do i differentiate that e
oh ofc not first principles
drifting swift
do you know what the derivative of e^x is?
drifting swift
the derivative of e^x is e^x.
drifting swift
you made mistakes in several places
orchid night
oh
drifting swift
also maybe consider listening to things when someone tells you something
just as a life pro tip
orchid night
ok
so how do i differentiate e^x?
well instead of already knowing the answer i just wanna know the process
drifting swift
you need to know the limit lim[t -> 0] (e^t - 1)/t = 1
drifting swift
loud ingot
which software do you use atomic?
loud ingot
how?
orchid night
ctrl+scroll
loud ingot
how do you take screenshot though?
tame saddle
hey, can i upload pic of problem i need help about?
tame saddle
oh ok sorry and ty
pine forge
and yes you can upload a pic
pine forge
i use a program called greenshots
why do you need a program
?
just do
windows key + shift + S
there's a built in snipping tool as well in windows
orchid night
its stripped from my pc
pine forge
what does that mean
topaz sinewBOT
@orchid night Has your question been resolved?
topaz sinewBOT
topaz sinewBOT
Available help channel!
celest glade
if I apply a function to itself infinity * n times, it's not the same as just applying the function to itself infinity times, right?
topaz sinewBOT
if I apply a function to itself infinity * n times, it's not the same as just ap...
odd pagoda
well first clearly define what "applying a function to itself infinity times" means
then we can talk
celest glade
$f(f(f(x)))$ this is applying f to itself 3 times
thorny flameBOT
illuminator3
celest glade
and applying it to itself infinitely many times would be
$\lim_{x \to \infty} a_x, \text{ where } a_k := f(a_{k-1}) \text{ and } a_0 = x$
thorny flameBOT
illuminator3
odd pagoda
ok and we are assuming that this limit exists
celest glade
yes
odd pagoda
then probably the limit is a fixed point of f. so applying f one more time just leaves it fixed
odd pagoda
so now what exactly is your question?
celest glade
if $a_{\infty \cdot n}$ converges to a fixed point, does $a_{\infty}$ too?
thorny flameBOT
illuminator3
thorny flameBOT
illuminator3
odd pagoda
\begin{align*} f(L)&=f\left(\lim_{n\to\infty} f^n(x)\right) = \lim_{n\to\infty} f\left(f^n(x)\right) \&= \lim_{n\to\infty} f^{n+1}(x) = \lim_{n-1 \to \infty} f^{n}(x) \&= \lim_{n\to\infty} f^n(x) = L \end{align*}
thorny flameBOT
Denascite
odd pagoda
assuming f is cont
celest glade
**Denascite**
thanks c:
odd pagoda
$\lim_{x \to \infty} a_x$
well if you mean that, then a_\infty is a number. so asking if it "converges" is weird
celest glade
well if you mean that, then a_\infty is a number. so asking if it "converges" is...
that's like saying asking if $\sum^\infty_{i} a_i$ "converges" is weird as it's a number
thorny flameBOT
illuminator3
celest glade
anyhow
odd pagoda
fair enough
celest glade
\begin{align*} f(L)&=f\left(\lim_{n\to\infty} f^n(x)\right) = \lim_{n\to\infty} ...
can the same trick be applied here? assume I have a $x$ st $f^n(x) = x$ thus $$\begin{align}\lim_{k \to \infty} f^{k \cdot n}(x) &= x\ \lim_{n \cdot k \to \infty} f^k(x) &= x \ \lim_{k \to \infty} f^k(x) &= x\end{align}$$
topaz sinewBOT
can the same trick be applied here? assume I have a $x$ st $f^n(x) = x$ thus $$\...
thorny flameBOT
illuminator3
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
odd pagoda
so, first off, just because $f^n(x)=x$ for some $n$, does not mean $\lim_{n\to\infty} f^n(x)$ converges. do you mean that $f^n(x)=x$ for all $n$?
thorny flameBOT
Denascite
celest glade
so, first off, just because $f^n(x)=x$ for some $n$, does not mean $\lim_{n\to\i...
that answers my question
thx
.close
topaz sinewBOT
topaz sinewBOT
Available help channel!
topaz sinewBOT
jade thunder
What have you tried
gritty compass
I tried changing equating the equation to 0
And trying to find two values of t when h=0
jade thunder
Which equation
jade thunder
This one
That should be equal to what
What is the left side equal to
In general what is it equal to not this specific case you’ve made
jade thunder
No it’s equal to H yeah?
jade thunder
This one
Why is there decimal here
You basically never want to use decimal when dealing with these things in math
gritty compass
I put decimals because part (a) asked for decimal to 3.d.p
jade thunder
Oh yuck
So what happens when you solve for h=0
What answer do you get for the given bounds
jade thunder
dont forget the question is asking for an amount of time
gritty compass
?
jade thunder
And trying to find two values of t when h=0
this only tells you when P is at water level
that aint the question, the question asks for the time P spent under water
gritty compass
So subtract the two values right?
jade thunder
are you sure?
gritty compass
I think so. The two values of t when h=0. So subtracting them would find the total time under zero?
jade thunder
ok so instead of finding for h = 0
what else can you do
h = 0 gives u the points in time at which P is on water level
gritty compass
No idea tbh
jade thunder
what does it mean if it's under water with h
gritty compass
Negative h value
jade thunder
so mathematically that means?
gritty compass
?
jade thunder
h < 0
gritty compass
Is that what you meant
gritty compass
I was so lost lol
jade thunder
it gets hard to convert it into something you can do math with
so i like to keep the things written in math form
gritty compass
Fair enough
jade thunder
because with h < 0 you have an inequality
and then u also know that h = Rcos(something) + c
whatever that equation u had was
so you can solve for that < 0
jade thunder
you would get a range
gritty compass
Yh
gritty compass
But I need total time not a range