Huh
Would you care to remind me how continuity helps one calculate limits if you manage?
#help-23
tall pumice
lean otter
Huh
Would you care to remind me how continuity helps one calculate limits if you...
A limit exists at a point only if the function is continuous at that point (or at the points right next to it).
Oh, if you asked if you can "decompose" functions in general (not just in the context of limits), then yeah, continuity is not a requirement.
tall pumice
Right, but I remembered some strong trait of continuouty that non-continuous functions didnt have
Or is my memory betraying me?
In the context of calculating limits*
lean otter
Right, but I remembered some strong trait of continuouty that non-continuous fun...
That the both-sided limits are equal ?
I am not aware of anything else.
tall pumice
Huh, alright
I'll go through my notes again, see if I can find anything
Thanks a lot guys
.close
true estuary
safe radishBOT
safe radishBOT
@true estuary Has your question been resolved?
worthy cedar
you can find P(X=0) and P(X=4) easily using combinations, then find P(X=2) by doing 1 - (P(X=0) + P(X=1) +P(X=3)+P(X=4))
worthy cedar
i'd personally find P(X=0) by getting (14/20 * 13/19 * 12/18 * 11/17)
worthy cedar
distrubution
cant rly find that one, and you dont need to find it as well
true estuary
i'd personally find P(X=0) by getting (14/20 * 13/19 * 12/18 * 11/17)
why 14/20
ie why 14
worthy cedar
P(X=0) means that youre catching no trouts at all, meaning the total of fishes that are not trouts are 70% of 20
70% * 20 = 14
for P(X=4), which means youre getting all trouts, you can find it by (6/20 * 5/19 * .....)
worthy cedar
the problem qn is nice enough to give you P(X=1) and P(X=3), and since P(X=5) = 0 because theres no possible way for you catching 5 trouts in your 4 pulls, you can subtract 1 - those
worthy cedar
you already have P(X=1), you dont need to count it again, no?
true estuary
wym
worthy cedar
if you want to prove it again, then sure, but it would be quite long
true estuary
if you want to prove it again, then sure, but it would be quite long
ph sry
i meant
i found x = 0
and 4
worthy cedar
oh, sure
true estuary
2 seems long
worthy cedar
you just need to subtract 1 - P(X=0) - P(X=1) ...
and get P(X=2)
since the characteristic of a pmf/pdf is that the total equates to 1
worthy cedar
ye, usually test qns wont be so nice to give you P(X=1) and P(X=3) and you'll need to count them as well
so just be aware of those in the future
worthy cedar
1/20 * 14/19 * 13/18 * 12/17
14/20 * 1/19 * 13/18 * 12/17
14/20 * 13/19 * 1/18 * 12/17
14/20 * 13/19 * 12/17 * 1/18
then add them all up
got it?
worthy cedar
ah wait yea, i forgot there are 6 trouts
6/20 * 14/19 * 13/18 * 12/17
14/20 * 6/19 * 13/18 * 12/17
14/20 * 13/19 * 6/18 * 12/17
14/20 * 13/19 * 12/17 * 6/18
this is the correct one
worthy cedar
yea, thats the same as 2184/4845 ye
true estuary
kl
worthy cedar
tho faster way to calculate this would be 4(14P3 * 6P1)/(20P4)
true estuary
tho faster way to calculate this would be 4(14P3 * 6P1)/(20P4)
ye
1 final thing
ive done b
for c
how do u show that Y is approximately binomial?
worthy cedar
what did you get for b
true estuary
what did you get for b
worthy cedar
hmm, i would just prove it using binomial's property that the mean = np = 4*0.3 = 6/5 and Var(X) = npq
true estuary
hmm, i would just prove it using binomial's property that the mean = np = 4*0.3 ...
but it says Y is for a million fish tho
worthy cedar
it shouldnt rly matter, the chances of you getting the trout should be the same no matter how many total fishes are there, as long as the ratio of trouts to non-trouts are the same
true estuary
it shouldnt rly matter, the chances of you getting the trout should be the same ...
i see
also is my VAr correct?
i get 21/25 with binomial
for var
but i get something else with the pmf
hmmmmm
worthy cedar
it should be correct hmm
it's probably because the one at a) doesnt replace the fish again, while the binomial distribution do replacements
true estuary
it's probably because the one at a) doesnt replace the fish again, while the bin...
they didnt do this in mS
lemme show u the MS answer
worthy cedar
MS?
worthy cedar
well, i mean
all theyre showing is that it fulfills the properties of binomial distribution
if thats already satisfying then sure, thats already correct
it shows that it has
i) a set number of trials
ii) the probability of success
iii) since it's a million fish, probability of success doesnt change much when you catch a small amount of fish
true estuary
it shows that it has
i) a set number of trials
ii) the probability of success
ii...
cool makes sense
cheers for the help pal
worthy cedar
sure
safe radishBOT
@true estuary Has your question been resolved?
true estuary
sure
sry to bother u again, doing a probability question and need some assitance
dont want any answers or calcs yet
just want hints
cuz i still wanna do it myself
is the coin toss and him winning the games independent of each other?
thinking of using P(A intersect B)
.close
south sapphire
i'm so confused
if A = -2a
then y my teacher done -1/2 A ?
with b as well
-2a = -2*-18 = 36 right
lean otter
How do I figure out who to x with
safe radishBOT
How do I figure out who to x with
lean otter
2 anf -3 should be same so i can cut em
Common factor is 6 so
Wait
Halp
The LCM of 2 and 3 and 6. So you want to get the coefficients of x to be 6 (or -6) in both the equations. To do so, you multiply the first equation with 3 on both sides
So you get 6x + 9y = 12
Similarly what would you do to the second equation?
quasi bison
How do I figure out who to x with
wdym by "who to x with"?
lean otter
Similarly what would you do to the second equation?
X it with 2
Yup, correct
Hehe ty
quasi bison
don't use the letter x as a multiplication symbol
especially not when you have a variable named x
there's at least one person you've thrown for a loop with that
lean otter
It took me 2-3 re-readings to understand it as well
lean otter
lean otter
Every operation you do must preserve the equality of both the left and right side
If you had not multiplied the 2x term with 13 then the equality does not hold anymore
But I did multiply it with 3(14/13) on thr LHS
quasi bison
you are multiplying the entire lefthand side by 13
not just the second term
lean otter
why do I have to do with with every term oon LhS
You can't just magically prop numbers out of nowhere
quasi bison
$13 \cdot \paren{2x + 3 \cdot \frac{14}{13}} = 13 \cdot 4$
flat frigateBOT
Ann
quasi bison
this is what is actually happening
if you could multiply terms selectively you could prove that 2+2=5
lean otter
**Ann**
The idea behind this is that ultimately
\begin{gather*}
13 \cdot \qty(2x + 3 \cdot \f{14}{13}) = 13 \cdot 4 \
\underbrace{\f{13}{13}}_{= 1} \cdot \qty(2x + 3 \cdot \f{14}{13}) = 4
\end{gather*}
flat frigateBOT
♡A(lex)♡
lean otter
Can sm1 help me
You are effectively multiplying by 1, which does not affect the equality of the equation
lean otter
Can sm1 help me
Open your own channel
gentle shale
I don’t get it like math💀
There are a few channels above this one, under the category "Math help (Available)", Send your question in one of those to claim the channel
safe radishBOT
@lean otter Has your question been resolved?
frozen viper
safe radishBOT
frozen viper
-3/2 +3
how does that equal 3/2
this confuses me a bit
its like saying
-1.5 + 3
no?
frozen viper
what im asking i guess
is how do u manually do it
are u breaking it down into 1.5
or is there a way to calculate while keeping it -3/2
trim swan
No problem 👍
frozen viper
.close
safe radishBOT
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Available help channel!
lofty jetty
why derivative of x^x is not x*x^(x-1) = x^x and is instead (x^x)(lnx + 1)
peak estuary
spoiler you can't
lofty jetty
peak estuary
what's the derivative of e^x
lofty jetty
e^x
peak estuary
see, no power rule in sight
lofty jetty
that makes sense
peak estuary
power rule is only for x^n. base depends on x, exponent is fixed
warm tulip
how to find inflection point of y=e^-5x
safe radishBOT
how to find inflection point of y=e^-5x
drowsy moss
do you know how to find inflection points in general?
safe radishBOT
@warm tulip Has your question been resolved?
safe radishBOT
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Available help channel!
warm tulip
do you know how to find inflection points in general?
is it like finding second derivative and then finding the increase and decrease?
safe radishBOT
@warm tulip Has your question been resolved?
warm tulip
where it changes is an inflection point
idk how to do it when it's -5(e^-5x)=0 doe
like how do i find x when there's an e?
flat frigateBOT
drowsy moss
correct, it doesn't ever equal 0
so it's either always positive or always negative
same goes for your second derivative. it'll never be 0, so it will be either always positive or always negative.
warm tulip
🤔
warm tulip
same goes for your second derivative. it'll never be 0, so it will be either alw...
hmmmmmm so should i replace it was a +- ?
i'm seeing log on ur previous msg
?
i forgot how to do log tbh 😭
drowsy moss
you don't need to. It's never equal to 0, so it can't change from positive to negative (or vice versa) so it can't change concavity
since it can't change concavity, are there any inflection points?
junior smelt
i'm seeing log on ur previous msg
That's me, but I didn't read the line above it properly
warm tulip
since it can't change concavity, are there any inflection points?
naurrr
junior smelt
Just read the message in isolation (but of course, log(0) isn't defined)
warm tulip
so anytime there's an e is the answer just none
junior smelt
you don't need to. It's never equal to 0, so it can't change from positive to ne...
As here you know that e^{"something"} is always strictly greater than zero
warm tulip
oke
junior smelt
so anytime there's an e is the answer just none
Eh, in this case in particular you know there aren't any points of inflection
There may be cases where you have an e in it but it does have a point of inflection, but I'd have to check that for you
warm tulip
Eh, *in this case in particular* you know there aren't any points of inflection
so leik none when it's asking inflection or max and mins?
oh ok
junior smelt
,w plot x^3 e^x, {y from -3 to 3}
flat frigateBOT
junior smelt
so leik none when it's asking inflection or max and mins?
Yeah for your original question, no maximum or minimum points
[though you have y=0 as an asymptote]
warm tulip
wut ok
also i took my retake today for the test we were working on 😳😳
and........ i tink i knew how to do everything besides the e one and inflection basically
but it also asked me this weird one i'll see if i can get the test and look at it
junior smelt
and........ i tink i knew how to do everything besides the e one and inflection ...
Awww fair enough, that's nice! Do you feel happy with how it went overall?
warm tulip
it was something like f(-1)=4 and f(2)=7 in open interval (-1, 2)
and it was like
i. f(x)=4 anywhere on -1<x<2
ii. f'(x)=3/4 anywhere on -1<x<2
iii. there r max and min on dis interval
i wus so confuse
warm tulip
Awww fair enough, that's nice! Do you feel happy with how it went overall?
i feel i know how to do more now but i'm nervous because the test didn't show how many points each question was...........
let's just pray i at most only got inflection wrong
junior smelt
i wus so confuse
Ah yeah that's a trip, did they say that f was continuous on the closed interval [-1,2], or differentiable on the open one?
warm tulip
😭😭
warm tulip
Ah yeah that's a trip, did they say that f was continuous on the closed interval...
ummmmmmm i think it said continuous and differentials but i don't think it had closed interval
junior smelt
<:monkagiga:651816911964995584> i feel i know how to do more now but i'm nervous...
Ahhh yeah that can be really nerve inducing as you don't know which ones you should focus on!
junior smelt
let's just pray i at most only got inflection wrong
Yep we shall be praying for you 📿
warm tulip
yaaaaa
junior smelt
ummmmmmm i think it said continuous and differentials but i don't think it had c...
Hmmm yea, then I can see i being false if they're not continuous on the closed version, as the intermediate value theorem won't apply there
warm tulip
and semester almost ending, so i rly need the grades up
🤔 hmmm okee
phew i didn't pick that
is it just knowing the theorems for that quế tôn
oops
question
junior smelt
and semester almost ending, so i rly need the grades up
Yep yep, of course, hopefully you manage it! 
junior smelt
is it just knowing the theorems for that quế tôn
It's theorems and also counterexamples, making sure you know the theorems well enough to know where they don't apply
junior smelt
Like if they say you don't have to be continuous on $[-1,2]$ but are on $(-1, 2)$, you could define:
$$
f(x) =
\begin{cases}
4 & x = -1 \
7 & x = 2 \
x^2 + 69 & -1 < x < 2
\end{cases}
$$
flat frigateBOT
chartbit
warm tulip
wow piece wise
junior smelt
wow piece wise
Yep haha
junior smelt
Because you can choose any function you like that's continuous/differentiable for the middle bit
It's a random choice, but note that x^2 + 69 is never equal to 4 anywhere in between -1 and 2 exclusive
[or anywhere else for that matter]
junior smelt
In fact, even if it were closed, that wouldn't be enough, just create a line between the points (-1,4) and (2,7)
warm tulip
what even is diff between closed and open
is it like the domain stuff
like how infinity's always parenthesis
junior smelt
Closed interval is $[a,b]$ (you include the endpoints), open interval is $(a,b)$ (you exclude them)
flat frigateBOT
chartbit
junior smelt
Yep yep for now that's all I think you need to know now about the difference between open intervals and closed intervals
If you do analysis or topology at some point in more detail you'll deal with "open sets" and "closed sets", but that's for the future haha
junior smelt
Hmmm I don't think it would be(!) though I'm not familiar with how that's set up to say of course, maybe if you deal with sequences you might come across it?
rough lance
drogados
warm tulip
Hmmm I don't think it would be(!) though I'm not familiar with how that's set up...
aw naaaaa 😨
okeee
anyways
i am hunger i will eat now
junior smelt
i am hunger i will eat now
Yep fair fair! I'm actually eating now 🥘
safe radishBOT
@warm tulip Has your question been resolved?
junior smelt
Welcome back 
warm tulip
yay thank u
junior smelt
Anyways, where were we.. 
junior smelt
we could just do my review packet
Cool cool, we can! Show me what we working with!
warm tulip
ooook lemme jus roll out of bed
warm tulip
Cool cool, we can! Show me what we working with!
for 3b
why did we use sim?
sin
?
i don't understand bc isnt horizon the one adjacent to theta
junior smelt
So you know how $\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$, right?
flat frigateBOT
chartbit
warm tulip
yas
junior smelt
We have the "opposite" as 4m, and we know that the fish is pulling the line at the rate of 0.5 m/s
So with that we can find out the rate of change of the angle, as we're given that we want to find that when we're z is 5m
junior smelt
i don't understand bc isnt horizon the one adjacent to theta
Remember $\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$ btw
flat frigateBOT
chartbit
junior smelt
hmm ok
Does that help to answer your question?
Basically take a look at the triangle we're working with!
warm tulip
but isnt horizon like a horizontal line
?
ohh yea it is but it asking when its changing, so the horizon either goes up or down?
junior smelt
but isnt horizon like a horizontal line
It is, you want the angle between the one marked x and the one marked z in your triangle picture!
junior smelt
ohh yea it is but it asking when its changing, so the horizon either goes up or ...
The horizon doesn't change, but the angle does!
junior smelt
then cant u use cos and still get same answer? or
Well if you use cos, your life would be much harder for you
Look at this here
You aren't given x explicitly, but you are given that blue where the guy's standing
warm tulip
Well if you use cos, your life would be *much* harder for you <:sadcat:547124024...
so use given
should u always use given then
?
well i gues u should
junior smelt
Use whatever will make your life the easiest, in this case we have a fixed value there so we should use that one as it's less pain
junior smelt
Cool cool! So are you happy with that one now?
warm tulip
ummm i gues 😭
junior smelt
ummm i gues 😭
Guess? how can we make you know?
junior smelt
idk so u just use sin cus given?
Basically, use sin because we're given the opposite as a fixed value and want the hypotenuse
warm tulip
oooooooooooooooooooooook
junior smelt
Right let's go on this one!
warm tulip
yes yes!!!
junior smelt
I see you've drawn in the rectangle for me at least 
junior smelt
Right, so give me a second to make a drawing for you
Just define x to be as it looks like in the picture
Wait shit I'm stupid
Give me one second
Silly mistake I made there
junior smelt
wut is da r-x
Because the bottom bits form radii of the circle as well, so those bits must add up to r
Actually hmmmm I don't think this is the way to do it 
not that it won't work, but it's longer than I think it should be
I'm thinking today we should cheat 
what you think @warm tulip? If I see the solution then I can try and work backwards from it
warm tulip
Actually hmmmm I don't think this is the way to do it <:thinkies:827642567775748...
oops sory i go tdistracted
oke oke
as long as i understand hopefully
junior smelt
Oh so they kinda did it like me in the end then, fair enough I guess
Probably I messed something up in my working out I think
warm tulip
wuh
junior smelt
I didn't differentiate mine right, silly mistake
junior smelt
u just sleepy
Well you might have a point there but I'm gonna push through so me and you can do this one 💪
junior smelt
Silly mistake I made there
Right let's go back to this picture, are you happy with it?
junior smelt
Cool cool, now we're gonna pretend that solution didn't exist 
We're gonna work with this one
So what's the area of that rectangle?
Or to break it down, what's its width and what's its height?
junior smelt
it width is 2x and height is o
Correct for the width, the height though...
I've labelled it on the picture for you!
junior smelt
Oh that's my poor writing!
warm tulip
what the how u get that
ohh curly fry 🤤🤤🤤🤤
o ok
wait wat but that is rectangle
?
oh u use radios
warm tulip
o okkk
junior smelt
Yep, so happy?
warm tulip
junior smelt
Let's go then, now, what's the area of that rectangle?
warm tulip
A=xy
junior smelt
it width is 2x and height is o
Hmmm not quite, I mean by using the fact that the width is what you said here
junior smelt
It was meant to be that this was the height
and the height is this!
warm tulip
o okk
safe radishBOT
@warm tulip Has your question been resolved?
safe radishBOT
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Available help channel!
severe moss
Hello, this is a question from the igcse textbook on similar shapes and i have no idea where to start
safe radishBOT
Hello, this is a question from the igcse textbook on similar shapes and i have n...
wintry condor
you need to use the ratio of similitude
what would the ratio of similarity of A:B be?
@severe moss
severe moss
how would i find that with this shape?
wintry condor
A and B both have a flat line
you can find the length of those lines and find the ratio of similarity
severe moss
1 to the square root of 5?
wintry condor
not 1
wintry condor
yes
severe moss
ohhh
wintry condor
now you know the length ratio you can find the area ratio
severe moss
2:5?
wintry condor
yup
severe moss
thank you so much
wintry condor
np
safe radishBOT
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Available help channel!
regal hatch
hello very Urgent help required
safe radishBOT
hello very Urgent help required
regal hatch
i want to integrate this function
stray socket
What's with the urgency
lean otter
They're on the cusp of inventing a new theorem obviously
frosty estuary
Just fyi, the help here is not to solve your homework for you last Minute, but to help you to understand it.
regal hatch
What's with the urgency
sorry , i am on physics server , solving a question so i am keeping a person waiting that is helping me
dθ/sqrt (Cos θ - Cos(K))
θ varies from -K to 0 , given K is a constant angle
so nobody is gonna help now ? thats sad 😪
merry sleet
you just want an answer or you want help in maths?
if you just want an answer ask wolfram
sand minnow
,w int_{-k}^0 dx/sqrt(cos(x)-cos(k))
flat frigateBOT
sand minnow
wolfram no likey
no idea what this is but thats what integral calculator says
F is "incomplete elliptic integral of the first kind"
whatever that means
sand minnow
bottom thing is an approximation, the others are equivalent statements. does not look like there is supposed to be a pi anywhere here as far as i can tell. seems a mistake was made somewhere else if this is not what you are expecting
woeful plume
F is "incomplete elliptic integral of the first kind"
It means don't try to go any further
regal hatch
.close
sly wyvern
Can someone explain 3 a for me?
safe radishBOT
Can someone explain 3 a for me?
lean otter
Spam trig ratios a few times
But consider the upper left triangle first
Try to find the adjacent side's length
woven swan
how did u get that x = 12 sqrt(2)?
i don’t think that is the correct answer
sorry
nvm
that is correct actually
at least for x
safe radishBOT
@sly wyvern Has your question been resolved?
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Available help channel!
stoic moss
Solve/simplify integral
safe radishBOT
Solve/simplify integral
plucky elk
pretty straightforward power rule and trig integral with chain rule
stoic moss
I have a picture of my attempt, but I end up getting - (pi*R^4)/32
So originally it is called sin^2 but I change that to 1/2 - 1/2 * cos(2 theta)
plucky elk
you lost a factor of 1/2 somewhere in this step
stoic moss
I move the - 1/2 infront of the integral
plucky elk
and the - sign became a + for some reason
stoic moss
So 1/4 * R^4 becomes - 1/8 R^4
plucky elk
So 1/4 * R^4 becomes - 1/8 R^4
then your integrand needs to factor out the -1/2
stoic moss
Can you explain that please?
plucky elk
you have (1/2 - 1/2 c) as your integrand. how do you factor out -1/2?
stoic moss
Ohh, its 1/2 * (1 - c)
plucky elk
Ohh, its 1/2 * (1 - c)
be consistent with your minus signs
plucky elk
I move the - 1/2 infront of the integral
minus here
stoic moss
Ohh so the 1/2 in the integral becomes - 1/2?
In the first term
Nvm I got it, thanks for the help
lean otter
In the triangle ∆ABC, let G be the centroid, and let I be the center of the inscribed circle.
Let α and β be the angles at the vertices A and B, respectively. Suppose that the segment
IG is parallel to AB and that β = 2 tan−1
(1/3). Find α.
safe radishBOT
In the triangle ∆ABC, let G be the centroid, and let I be the center of the insc...
quasi bison
@lean otter have you made any progress thus far?
safe radishBOT
@lean otter Has your question been resolved?
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Available help channel!
versed minnow
- We take a loan of 50000
- Task b: How many monthly payments does it need if the monthly interest rate is 0.1% to pay back the entire loan?
Am I crazy or is it impossible to solve this without knowing the size of the monthly payments? I know the necessary formula, but we lack both a (size of the monthly payments) and n (amount of payments). In the solutions a is = 500, but how am I supposed to know this from the task alone?
safe radishBOT
- We take a loan of 50000
- Task b: How many monthly payments does it need if th...
versed minnow
(simply posting the picture if there are any german speaking users here, but I translated everything necessary into the text above)
ember sphinx
- We take a loan of 50000
- Task b: How many monthly payments does it need if th...
i think
ember sphinx
- We take a loan of 50000
- Task b: How many monthly payments does it need if th...
what does that von 1% mit mean
coz 1% of 50,000 is 500
versed minnow
0.1% is the monthly interest rate
but 0.001* 50000 would be 50 and not 500
also that would be the amount of interest, but a is the amount of the monthly payment (including interest, but also payback)
ember sphinx
Well when i google translated it
(1 point) If you want to pay off the loan at an annual interest rate of 1% with a one-off payment after 5 years, how large should the paid-in amount be?
(2 points) With a monthly interest rate of 0.1%, how many monthly installments does it take to repay the entire loan?
Write your answer as a formula, possibly including ln(*); you don't have to calculate them.
that is the same 'paid in amount' for part b i think
otherwise yea it would be impossibler
versed minnow
but wait a second
in a we calculate the size of the payment if we pay the whole loan off after 5 years
in b we want to calculate how long it takes us if we make small payments every month
but how can we find out how long it takes if we dont know the size of the small payments?
ember sphinx
what did u get as ur answer for part a
versed minnow
well that would be 50 000 * (1.001)^5 which results in 52550.50
ember sphinx
well that would be 50 000 * (1.001)^5 which results in 52550.50
erm
seems right
yea idk than
sorryt
empty gyro
What is the formula for interest rate?
safe radishBOT
@versed minnow Has your question been resolved?
versed minnow
What is the formula for interest rate?
Hmm what do you mean with that?
empty gyro
I don't study economics, and how you pay back a loan can be varied in structure, so I just want to be certain what method you are learning here.
versed minnow
second
empty gyro
Like, what is a monthly installment?
versed minnow
well we basically use a formula that defines PresentValueOfLoan = PresentValueOfAllFuturePayments
empty gyro
I wish I knew German right now
versed minnow
so normally Id use the left formula with 50000 = Formula for Present Value of all payments
but to use that formula we need to know 3 out of 4 variables, which are
- Loan size
- Size of regular payments
- interest
- amount of regular payments
in the task above both the size of the regular payments and the amount of regular payments are unknown, thats why I am so confused
safe radishBOT
@versed minnow Has your question been resolved?
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@versed minnow Has your question been resolved?
versed minnow
<@&286206848099549185>
lean otter
Ayo alter, brauchst du hilfe?
safe radishBOT
@versed minnow Has your question been resolved?
thin path
Any one can please help me with this sum
safe radishBOT
safe radishBOT
Available help channel!
glossy mulch
Using the class intervals given below, so that the frequencies are roughly equal
0 ≤ x ≤ 25, 26 ≤ x ≤ 29, 30 ≤ x ≤ 34, 35 ≤ x ≤ 38, 39 ≤ x 43, 44 ≤ x ≤ 50, 51 ≤ x ≤ 100
construct a grouped frequency table using the class intervals and calculate the estimate for the mean and a 5-point summary plot
Draw the two (Q2, Q3) 5-data summary plots on the same scale and axis
safe radishBOT
Using the class intervals given below, so that the frequencies are roughly equal...
glossy mulch
I just need help understanding this question and where to start since to construct a grouped frequency table you need f. and the questions doesnt provide the frequencies
<@&286206848099549185> sorry for the ping
.close
safe radishBOT
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Available help channel!
static vale
Is $\int{{(-1)}^x}$ dx not possible?
safe radishBOT
Is $\int{{(-1)}^x}$ dx not possible?
static vale
Oh shi
flat frigateBOT
lean otter
well (-1)^x isn't defined almost everywhere
static vale
Oh
lean otter
so if you are using riemann integration, then its not possible
lean otter
np
static vale
.close
slow fern
A person bought two articles A and B at a total cost 8000 rupee. He sold article A at 20% profit and article B at 12% loss. In the whole deal, he made no gain and no loss. Find A and B.
safe radishBOT
A person bought two articles A and B at a total cost 8000 rupee. He sold article...
slow fern
(This is a bigger part of a problem I came across)
Let price of article A be x rupee.
Then, price of article B is (8000-x) rupee
Selling price of article A and B would be 120x/100 and 88x/100 respectively
compact ferry
not 88x/100 but you had the right idea
quasi bison
Selling price of article A and B would be 120x/100 and 88x/100 respectively
nope
compact ferry
because price of B = 8000-x
lucid grotto
safe radishBOT
lucid grotto
How do I solve this question?
I dont have the idea of where to start
quasi bison
make a diagram of the fence
denote one of the two dimensions of the fenced-in region with a variable like x
lucid grotto
quasi bison
,rccw
flat frigateBOT
quasi bison
those are the prices per foot of fencing.
that's important.
anyway, okay, so yes, that's what the enclosed region looks like.
lucid grotto
quasi bison
... where did the letters x and y come from?
quasi bison
okay, so you went ahead and made letters for both dimensions?
you have to write down on your paper which letter stands for what.
lucid grotto
okay got it
quasi bison
@swift fjord what do you mean? this is an optimization problem.
swift fjord
900000 = 15x + 9y
lucid grotto
Just write a system ong
yeah but for optimization i dont know how it works with cost
quasi bison
@swift fjord don't just blurt out answers
swift fjord
<@692912115823935570> what do you mean? this is an optimization problem.
Yea u just get A in terms of one variable and derive
quasi bison
you're not helping at all
swift fjord
yeah but for optimization i dont know how it works with cost
You’re still just optimizing area
Cost is set to be 900000
flat frigateBOT
Ann
quasi bison
the per-foot costs for fencing are 9 and 15 dollars per foot, not 9 and 15 cents per foot.
quasi bison
your equation is wrong anyway. you should take a more careful look at the diagram OP gave.
swift fjord
9000 = 15x + 18y
quasi bison
yes, that's better... (except was there really any need to blurt that out instead of letting OP arrive at it themselves?)
swift fjord
your equation is wrong anyway. you should take a more careful look at the diagra...
I don’t use diagrams I just didn’t read the question
swift fjord
XDDD
quasi bison
@lucid grotto do you at least understand where the equation 18x + 15y = 9000 comes from?
lucid grotto
yes
quasi bison
and do you also understand that the quantity to be maximized is xy?
lucid grotto
perimeter would be 2x + y and then when referring to cost it would just multiply with the respective costs resulting in 9000 = 15x + 18y
lucid grotto
lucid grotto
🥲
lucid grotto
shit
lucid grotto
yes
quasi bison
that makes it a little bit easier to optimize it
just clean it up and find the vertex
swift fjord
lucid grotto
just clean it up and find the vertex
okau
quasi bison
https://tenor.com/view/gigachad-chad-gif-20773266
using the quotient rule when the denom is a constant is nowhere near a chad move.
swift fjord
U don’t need to derive with quadratics
lucid grotto
what?
swift fjord
the vertex comes from -b/2a
lucid grotto
you always take the derivative in optimaztion questions ryt?
swift fjord
which is the maximum/minimum x value
lucid grotto
the vertex comes from -b/2a
can you please explain this
quasi bison
the extremum of a quadratic function can be found without calculus
for a very special case
lucid grotto
coz we have to take derivatives according to the prof
swift fjord
I think you need to check up on your quotient rule too…
You did it very incorrectly
If you want to derive
Split up the fraction
Into 2 terms
And power rule
lucid grotto
just clean it up and find the vertex
i don’t think i was able to do that
quasi bison
missed a zero here
safe radishBOT
safe radishBOT
Available help channel!
pastel briar
How does P_D(D) work
safe radishBOT
How does P_D(D) work
pastel briar
(D-\lambda_1) for example, what is that? Matrix minus a scalar? How does that work
hasty wagon
I think it's talking about this
https://en.m.wikipedia.org/wiki/Matrix_polynomial
pastel briar
I mean, it is kinda talking about that but the fact that $(D-\lambda_1)(D-\lambda_2).....(D-\lambda_n)$ contains a matrix minus a scalar doesn't help me
flat frigateBOT
Yeetus
pastel briar
Or perhaps expanding it gets rid of the issue. Didn't think about that possibility
That is probably it lol
.close
ivory barn
Yes, I am disgustingly bad at math in my 2nd year of college. Could someone please breakdown the steps in solving this problem? I'm takin notes.
safe radishBOT
Yes, I am disgustingly bad at math in my 2nd year of college. Could someone plea...
worthy hemlock
You've never seen the square root symbol?
sly field
yeah
ivory barn
bro the last time i did math was... a while ago...
sly field
and 9/9 is?
worthy hemlock
Then what's (-1/9)(9)?
ivory barn
9/9 is 1
lean otter
Yes, I am disgustingly bad at math in my 2nd year of college. Could someone plea...
[(-\f19) \s{81} = -\f{\s{81}}{9}]
[= -\f{\s{9^2}}{9} ]
flat frigateBOT
♡A(lex)♡
ivory barn
Then what's (-1/9)(9)?
when ur multiplying fractions
sly field
1 time(-1 ) is
worthy hemlock
dont u just multiply horizontally
Yes
worthy hemlock
so it'd be -1 * 9, 9 * 9
Where's this 9 * 9 from?
worthy hemlock
You have $\frac{-1}{9}(9)$
ivory barn
?
flat frigateBOT
dldh06
ivory barn
so its -1 * 9, 9 * 1
worthy hemlock
so its -1 * 9, 9 * 1
If that 9 * 1 is supposed to represent the denominator, then yes
safe radishBOT
Please read #❓how-to-get-help
ivory barn
which is 9/1
ivory barn
-9/9
worthy hemlock
Which is?
worthy hemlock
Yes
ivory barn
just to clarify, its -1/1
and not (-)1/1
like the negative remains above the bottom fraction
worthy hemlock
$\frac{-a}{b} = \frac{a}{-b}$
flat frigateBOT
dldh06
worthy hemlock
Doesn't matter if the negative is in the numerator or denominator
ivory barn
i see
so any negative in either the numerator or denominator
means the result will be negative
but what if both are
worthy hemlock
What's a negative divided by a negative?
ivory barn
positive
gotcha
can i continue wuth another question or
do i need to open a new thing
to clarify, im using problems on this site https://afoqtpracticetest.com/math-knowledge/
safe radishBOT
@ivory barn Has your question been resolved?
versed minnow
Ayo alter, brauchst du hilfe?
Gerne ja
safe radishBOT
@versed minnow Has your question been resolved?
coral sierra
Hi, i have some problems with these both equations. Its 7 Years ago i did stuff like this, could someone maybe help me please to get a calculation way?
The Answers are:
11) 316.73
12) 2155.14
safe radishBOT
Hi, i have some problems with these both equations. Its 7 Years ago i did stuff ...
wind agate
can you use a calculator?
safe radishBOT
@coral sierra Has your question been resolved?
willow inlet
The first one you multiply by 2√n
And then you get √n=2•1.96•4.54
You square that
And get the answer
Second one you are supposed to move 1.96 to the other side
0.02/1.96=√A (A represents the fraction inside a square root)
0.01=√A
Square that and you solve the equation a bit more
deep depot
safe radishBOT
deep depot
In this circle O is the centre proof that x=y+z
But I got that x=(y+z)/4
And if x = y+z then
x/x=1/4
flat frigateBOT
deep depot
So here 15.147 is the figure
deep depot
In this circle O is the centre proof that x=y+z
And the question is ditto same
deep depot
If there's any misunderstanding with my handwriting then you could ask me
deep depot
$2x=3
\newline 2x=4
\newline 5=180-2x
\newline 6=180-2x
\newline 360=180-2x+180-2x+y+z
\newline 0=-4x+y+z
\newline 4x=y+z
\newline x=\frac{y+z}{4}$
flat frigateBOT
Arnab
safe radishBOT
@deep depot Has your question been resolved?
deep depot
<@&286206848099549185> 🥲
safe radishBOT
@deep depot Has your question been resolved?
hasty wagon
oh
hasty wagon
$2x=3
\newline 2x=4
\newline 5=180-2x
\newline 6=180-2x
\newline 360=180-2x+180-...
its the other way round
x = 2 times angle 3
x = 2 times angle 4
hope that helps!
@deep depot
fickle trail
safe radishBOT
fickle trail
For my first try I attempted to use diamond method but it doesn’t work with those numbers, add to 3, multiply to -6
Could it still be solved using the diamond method or best to scrap that and start over?
obtuse jackal
should be x+3 on the 3rd line
fickle trail
Could I have used quadratic formula instead of diamond method to solve?
tall bough
Is diamond method only for tertics?
obtuse jackal
tertics ?
fickle trail
should be x+3 on the 3rd line
Ty
tall bough
Third degree
fickle trail
Diamond method is used to find factors of ax^2 + bx + c
deep depot
Grouping
obtuse jackal
which would be useless here because the 18 is outside
fickle trail
which would be useless here because the 18 is outside
No I can still use it on the brackets I believe
deep depot
that's what he did on line 3
Oh yeah I didn't saw it 🥲
obtuse jackal
but a product - 18 isn't going to be easy to factor
fickle trail
fickle trail
should be x+3 on the 3rd line
Thanks for spotting that
I’m not allowed to treat this with quadratic formula?
It’s a factor, in brackets
obtuse jackal
you can
fickle trail
Or is it the -18 that is not allowing this?
obtuse jackal
but I challenge you do find a simple way of using it to factor the whole thing
fickle trail
To my understanding quadratic formula has to be equal to zero
I can treat this 3 term polynomial factor as equal to zero?
obtuse jackal
it's irrelevant
fickle trail
Or it needs to be the entire left hand side equal to 0?
Well, diamond method was not working for me here.. normally quadratic formula is like using a chainsaw to break twigs, far too overkill
fickle trail
But any flaw in logic with using QF for this factor? It can be done. But should it be done…
Just wanna make sure this factor is fair game
obtuse jackal
but when they give you one then usually it's either that one term is missing (basically always the constant one, then it's just x(quadratic)) or that it's easy to factor by grouping
fickle trail
Alright
obtuse jackal
you can factor that quadratic. All I'm saying is it's hardly helpful to factor the cubic
fickle trail
So I think I can treat anything in brackets with the quadratic formula if I want to
obtuse jackal
you could, but you need to wonder what for
fickle trail
Yeah
obtuse jackal
try to give a purpose to your ideas
a lot of math exercises go "if I did this, I'd like such property to hold" and are about verifying that property as the main challenge
fickle trail
So my method of factor by grouping is pretty much the only way to solve this?
obtuse jackal
at least the only simple one
fickle trail
OK
Can you think of another way? If you couldn’t use factor by grouping?
Diamond method didn’t work sooo..
I can only think of QF
obtuse jackal
but when they give you one then usually it's either that one term is missing (ba...
otherwise it wouldn't be given unless it's some olympic/undergrad math I guess
fickle trail
Lmao OK
obtuse jackal
and then well... The cubic formula isn't that bad
fickle trail
It sounds like we try to get rid of cubics wherever possible
At least with Calc 1
Try to get it squared by factoring
obtuse jackal
mainly exercises are meant to be doable and not too painful
obtuse jackal
an exercise that's like 'factor the random quartic x^4 + 3x^3 - 2x² + x - 3" is either a miracle waiting to happen or a trip to WA
obtuse jackal
that's why you don't see such exos
fickle trail
Good to know.. I won’t be seeing crap like this
obtuse jackal
solving polynomials is something computers can do very well. That's enough
fickle trail
an exercise that's like 'factor the random quartic x^4 + 3x^3 - 2x² + x - 3" is ...
Actually with this one I would just factor x^2 from it
And leave the + x - 3 at the end of the factored form
Let’s see if I can do it haha
obtuse jackal
then it isn't factored
fickle trail
Wait lemme see haha now I’m curious…
obtuse jackal
,w factor x^4 + 3x^3 - 2x² + x - 3 over the complex numbers
random polynomials don't factor well
flat frigateBOT
obtuse jackal
pretty random roots
except for 1. And if you have 2 of these on a random quartic it's that a miracle happened
fickle trail
@obtuse jackal this is an approximation .. just curious.. does is it seem to be correct? Or I messed something up
Haha it doesn’t really solve for x. It’s just a mess. But wondering if the approximate idea holds up.
obtuse jackal
what idea ?
fickle trail
That I can do this
obtuse jackal
you can factor the quadratic inside, but it doesn't achieve anything
fickle trail
,w roots of x² +3x - 2
Using integers?
flat frigateBOT
fickle trail
Weird, the only thing that matches mine is root 17
obtuse jackal
you got the 3 wrong. It's -b so -3
fickle trail
Damn.. of course!
Interesting how they take that /2 for the entire denominator and change it to 1/2 *
I gotta remember that
I’m pretty sure that I can remove all denominators by doing that
No matter what they are..
obtuse jackal
you can pretend you did yes
fickle trail
Math can be beautiful when you finally start to make connections 🤩
obtuse jackal
there's cases where it's useful of course, but like... That's just writing a/b = 1/b * a ...
fickle trail
Yeah
Or taking 2x/3 and changing it to (2/3)x
Sometimes I see variable outside of the fraction but it’s the exact same thing as variable in numerator
Because everything is /1
Im gonna just make a wild guess here and say that 1 and 0 are the most powerful numbers in all of math.
Controversial to some mathematicians too.. from what I have been reading
Sometimes I wonder if it’s coincidence or just fate that computers use these numbers at the machine code level
Coincidence maybe.. on = 1, off = 0
obtuse jackal
0 and 1 are kind of random
like it's just binary
you could write it with a and b
you could even represent it with lmao and lol it'd still be binary
fickle trail
0 and 1 are kind of random
Random in the q-bit sense?
obtuse jackal
just so happens that 0 and 1 are nice to work with
fickle trail
Oh I see, it could be anything
fickle trail
you could even represent it with lmao and lol it'd still be binary
That would be a waste of memory tho haha
obtuse jackal
in base 16 we use the start of the alphabet to make 11...15
fickle trail
But it would 01 would still be more efficient than lmaolol
obtuse jackal
the advantage of using numbers is the simplicity of interpretation
of course
math is very rarely coincidences
obtuse jackal
At least with Calc 1
for instance, did you study integrals yet ?
fickle trail
Not yet
This semester
Differential and Integral are words I keep hearing
They are the inverse to each other?
fickle trail
“Inverse” is just another word for “opposite” right?
We can use those words interchangeably, but for math you hear “inverse” more?
Inverse operations, + - is the same thing as opposite operations, + -
I will be taking Calc 2 next semester
obtuse jackal
opposite -> + -
inverse/reciprocal -> f f^-1 and x 1/x
Inverse and reciprocal are technically different but nowadays no one cares nor bats an eye about a detail like that
fickle trail
yeah, I do see f^-1 as inverse (not called "opposite")
and it has to be a one-to-one function to be an inverse function. pass the horizontal line test.
actually it needs to pass the vertical line test too I think? to even be a function to begin with
reciprocal makes sense and I see that as different from "inverse" and "opposite" with no relation really
but maybe I am missing the details on that!
obtuse jackal
though technically the reciprocal function is very rare imo
fickle trail
oh a reciprocal function? i don't know if I have heard of that before
only inverse function
obtuse jackal
and when you get to the level where you ask whether 1/x is the inverse or the reciprocal, you're at the level where you don't explain that step so you stop naming it lol
obtuse jackal
oh a reciprocal function? i don't know if I have heard of that before
that's what I'm saying
everyone says inverse
but technically I think reciprocal is correct
fickle trail
interesting...
maybe that's why they use f^-1 for "inverse function"
I have always wondered why
obtuse jackal
what notation would you use ?
fickle trail
i have heard that some mathematicians don't like this syntax