Im not quite sure that would work
#help-10
unique solstice
So say all you did
Was change the range that the sum goes across
So you start with
$\sum_{n=1}^7 4 \cdot 4^{n-1}$
warm shaleBOT
PapaBread
prime goblet
Ok
unique solstice
So then you can substitute m in for the n-1 in the exponent right
prime goblet
Yeah
unique solstice
So then you also have to change the bounds of the summation
You cant just leave it alone
You know that m=n-1 so any number relating to n in the bounds you would subtract 1 from
prime goblet
Ok
unique solstice
Because at the beginning n is 1
m=1-1 = 0
At the end n is 7
m=7-1 = 6
So therefore you can rewrite it as
$4 \cdot \sum_{m=0}^6 4^{m}$
prime goblet
Ok
warm shaleBOT
PapaBread
prime goblet
Kinda, so would that all be the sum?
unique solstice
Yeah thats about as simple as you can get it without using one of the special sum formulas
prime goblet
Okay
prime goblet
I don’t.
unique solstice
Hmm
Youve never heard of one and your teacher hasnt taught you anything like that?
tardy epoch
this is very similar to the name of the sum
prime goblet
No.
unique solstice
Oh wait is there a formula directly for that sum?
Well I guess you know most of how its derived now
prime goblet
Yeah
prime goblet
It looks familiar so probably.
prime goblet
Ok
unique solstice
Or at least I would assume so
prime goblet
Ok
obtuse pebbleBOT
@prime goblet Has your question been resolved?
indigo hedge
Why in nCr do u need to divide by r!
obtuse pebbleBOT
Why in nCr do u need to divide by r!
lusty goblet
Definition
indigo hedge
Definition
but like logically why does n! have all of the arrangments
i get that dividing by r! makes them unique
lusty goblet
It's given n items, pick r items without regard of order.
indigo hedge
Yeah but why does n! give u all the possible ways that n through 1 items can be arranged
lusty goblet
Well, for 1 item there are 1!=1 ways on how to reorder item.
Then given there are n! way to reorder n items, to calculate how many reorderings possible for n+1 items, do the following:
- Order n items, there are n! ways to do it.
- Place one more items either between items or before and after the whole item. There are n+1 slots available
indigo hedge
Is it like because there are N ways for the first part of order
N-1 option for second and so on
so u multiply out
lusty goblet
Yeah, like that.
indigo hedge
and then with combinations u divide by the (n-r)! so it will stop with how many items or numbers or letters u actually care about ordering
and then divide by r! to get rid of the nondistinct orders
lusty goblet
Yeah, like that.
obtuse pebbleBOT
@indigo hedge Has your question been resolved?
finite gazelle
3. Write down the possible number(s) of significant figures for each of the following
approximate values. (4 marks)
(a) 23 570
(b) 100 600
(c) 2000, correct to the nearest ten
(d) 0.093 60
i'm not sure what it's asking 😖
obtuse pebbleBOT
```
3. Write down the possible number(s) of significant figures for each of the ...
nocturne minnow
```
3. Write down the possible number(s) of significant figures for each of the ...
Why is it 4 marks?
finite gazelle
Why is it 4 marks?
it's an assigment
nocturne minnow
Like a test?
finite gazelle
not a test
nocturne minnow
But pretty sure it's asking for sig figs for each number
obtuse pebbleBOT
nocturne minnow
It's closing, give the bot a few minutes
finite gazelle
right
obtuse pebbleBOT
Available help channel!
timber moss
The mean number of TV sets is 2.24. The standard deviation is 1.1. A sample of 90 households is drawn. Calculate the The 10th percentile of the sample mean using an excel function
obtuse pebbleBOT
The mean number of TV sets is 2.24. The standard deviation is 1.1. A sample of 9...
@timber moss Has your question been resolved?
obtuse pebbleBOT
@timber moss Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
cerulean tartan
does the wronskian have a first order relation with any of its derivatives besides its first?
obtuse pebbleBOT
does the wronskian have a first order relation with any of its derivatives besid...
cerulean tartan
meaning, is $W + a(x)W^{(n)} = 0$ for any $n$ besides 1, where $W^{(n)}$ represents the $n$th derivative of the Wronskian?
warm shaleBOT
ykj3
slate zephyr
➡️ #❓how-to-get-help, please open a new help channel.
obtuse pebbleBOT
@cerulean tartan Has your question been resolved?
cerulean tartan
.close
strong moss
.close
obtuse pebbleBOT
Available help channel!
crisp dune
Shouldn’t m=0 be excluded as well?
obtuse pebbleBOT
Shouldn’t m=0 be excluded as well?
crisp dune
royal basin
so you think m=0 SHOULDN'T be part of the answer for part a? do i understand you correctly?
crisp dune
Yes
royal basin
why?
crisp dune
Because when we rearrange the equation
Or actually
Because it will make the function undefined
royal basin
look what happens when we set m to 0. here's the system of equations we get:
-2x = 1
3x - 2y = 0
this system is dead easy to solve
crisp dune
royal basin
are you sure that you aren't doing something like dividing both sides by m in doing your rearrangement?
that would cause complications for m=0 specifically.
crisp dune
Yeah so I make y the subject
royal basin
okay, see, if you're doing that, then you have to consider m=0 separately.
because the way you're going about it only works when m isn't 0
crisp dune
If the question was written in the form that made y the subject
Then I would consider m=0 being excluded?
royal basin
if the question were written as y = (2x+1)/m then that would be a different story
because in that case yes m=0 would be excluded a priori
obtuse pebbleBOT
@crisp dune Has your question been resolved?
radiant cobalt
hi guys does anyone know how to solve section d question 1
obtuse pebbleBOT
hi guys does anyone know how to solve section d question 1
radiant cobalt
implicit differentiation ?
differentiate everything with respect to y?
obtuse pebbleBOT
@radiant cobalt Has your question been resolved?
radiant cobalt
<@&286206848099549185>
obtuse pebbleBOT
@radiant cobalt Has your question been resolved?
royal solar
differentiate everything with respect to y?
really doesn’t matter. you both dx/dy and dy/dx have to multiply to give you -1 so it’s upto you really
because one is the reciprocal of the other and -1 is it’s own reciprocal
sterile wyvern
What's the derivative of cos^2(x) ?
jagged cedar
is it -sin(2x)?
sterile wyvern
Yes! So, do you have any ideas now?
jagged cedar
absolutely no idea
sterile wyvern
You have sin(2x) at the numerator
jagged cedar
am i gonna substitute it?
sterile wyvern
Try the substitution u=cos^2(x)
sterile wyvern
du = -sin(2x)dx, so there is a mistake
jagged cedar
what if i substitute the sin(2x) into 2sin x cos x?
then du = 3/4 cos(x) sin(x)
nevermind
????
obtuse pebbleBOT
@radiant cobalt Has your question been resolved?
cursive zinc
glossy ibex
d/dx cos^2(x) = -sin(2x)
glossy ibex
u = 1 - 3/4cos^2(x), du = 3/4sin(2x)dx
glossy ibex
it says 3/4 there
jagged cedar
wait, what if u=cos^2x, du = -sin(x)dx
glossy ibex
-sin(2x)dx*
jagged cedar
d/dx cos^2(x) = -sin(2x)
just like this
jagged cedar
-sin(2x)dx*
yeah
glossy ibex
ok and then
glossy ibex
u = 1 - 3/4cos^2(x), du = 3/4sin(2x)dx
this is what ur suppose to do
jagged cedar
glossy ibex
you cant cancel from outside the integral
glossy ibex
if it cancels with du then you dont get du anymore
glossy ibex
sin(2x)du = sin(2x)*(-sin(2x)dx) ??
@jagged cedar if you solve the integral post your steps here
jagged cedar
guess i'm wrong
glossy ibex
prob
glossy ibex
u = 1 - 3/4cos^2(x), du = 3/4sin(2x)dx
use this
i got that because constant coefficients like -3/4 are easy to integrate since you can move them outside the integral
with this sub you end up with $\int 4/3du/u^8$
jagged cedar
warm shaleBOT
DETOX
jagged cedar
what's next?
jagged cedar
should i substitute it into v before i use the power rule?
glossy ibex
NO
its already substituted into a familiar form
can you integrate 1/x^8 ?
just use reverse power rule
||1/x^8 = x^-8||
obtuse pebbleBOT
livid lodge
hey guys, sorry if i posted in the wrong channel i’m new here, but the third line of working in this solution doesn’t make sense to me ? how do you assume it is greater than 4. thanks for help 🙂
obtuse pebbleBOT
hey guys, sorry if i posted in the wrong channel i’m new here, but the third lin...
drowsy girder
Well if sin²2theta is less than 1
And 1/2 becomes 1/4 after squaring
Worst scenario 1/4 * 1 is 1/4
And 1/1/4 is 4
weak elk
help
drowsy girder
Whats the question?
drowsy girder
Well do you know how to calculate area of a triangle?@weak elk
drowsy girder
So what area cant you find?
weak elk
the rectangles
drowsy girder
The 13*5 rectangle?
obtuse pebbleBOT
@weak elk Has your question been resolved?
weak elk
I see 1 rect and 1 triangle
yes
its a triangular prism
there is 3 rectangles and 2 triangles
.close
fossil dove
Can anyone help me? Why is this always true?
obtuse pebbleBOT
Can anyone help me? Why is this always true?
fossil dove
It was something like it's true because x is all that exists in the universe in the latter statement?
obtuse pebbleBOT
@fossil dove Has your question been resolved?
worthy comet
P(x,y) holds for all x and all y, so especially for the y with y=x
brittle swan
√(2x + 1) = √(5x - 32) is what they’re trying i guess
spiral maple
√(2x + 1) = √(5x - 32) is what they’re trying i guess
Yeah, but you shouldn't be guessing in the 1st place.
unique solstice
spiral maple
That's clear
How you typed it was the furthest from clear
square both sides
the operation of squaring something
do that to both sides..
You've never seen $a^2$?????
warm shaleBOT
Mosh
warm shaleBOT
PapaBread
broken maple
obtuse pebbleBOT
broken maple
is this even correct?
i think it should be dy dx not dx dy
we are required to change the order of integration and compute
sage geode
Ye it should be dy dx I think
Because x going from x to infinity doesn't make sense lol
naive fern
Hi, would any of you happen to know if there is a way to rescale a normal distribution from interval [a, b] a and b being the values at 3 stds from the mean to interval [a, c], where c is smaller than b in a way that preserves (approximately) the original gaussian's mean ? I was thinking of using a skewed norm, but it is unclear what I must set the parameters to in order to achieve my goal.
obtuse pebbleBOT
Hi, would any of you happen to know if there is a way to rescale a normal distri...
naive fern
To give more context, I'm trying to recreate a similar setting as one can create with a Bernouilli distribution, i.e. to rescale the parameters and the PDF in order to insure that no sample taken from the rescaled distribution can leave the bounds determined by the rescale factor.
To give even more context, here's the paper that has me thinking: https://www.aaai.org/AAAI21Papers/AAAI-9199.MerlisN.pdf, specifically Algorithm 1, in the else statement. This effectively rescales the sample taken from the Beta distribution within the interval [0, 1 - epsilon] instead of [0, 1]
Actually, I think for my use case I could get away with a truncated normal. It would preserve the mean while making sure samples are taken in the desired interval. Thanks rubberduck mathematicians 😉
.close
fiery wraith
hey, if its not too much to ask, how would i get to this result?
obtuse pebbleBOT
hey, if its not too much to ask, how would i get to this result?
fiery wraith
stone coral
can anyone help me with this stat problem
A large state-university system is considering a proposal to change the academic calendar. A random sample of 320 faculty were asked their opinion about this proposal. From this sample, 120 faculty were in favor of the proposal to change the academic calendar; 176 faculty were opposed to the proposal to change the academic calendar; and the remainder were undecided. Based on this survey data, find the margin of error for a 96% confidence interval estimate of all faculty opposed to this proposal to change the academic calendar.
fiery wraith
dude, i claimed this channel already 
stone coral
sorry
timid silo
Substitute e^2x as u then use double angle formula
obtuse pebbleBOT
@fiery wraith Has your question been resolved?
fiery wraith
.close
obtuse pebbleBOT
fiery wraith
.reopen
obtuse pebbleBOT
✅
fiery wraith
still not a bit sure on how to follow up with the double angle formula lol
timid silo
Substitute u=1+e^2x n then use cos2x=2cos^2(x) -1
fiery wraith
ah, the whole 1+e^2x? i thought it was just the e part lol
timid silo
Yep
woven summit
obtuse pebbleBOT
woven summit
How to transform this to be able to use Vieta's formulas?
woven summit
assuming x_1 and x_2 represent the roots
Yes
high lily
then your two roots can be represented as
x_1 and (x_1)^2
woven summit
then your two roots can be represented as
x_1 and (x_1)^2
I don't see how this could help
high lily
is this part of a larger question?
woven summit
Yep
high lily
what's the whole question
woven summit
what's the whole question
high lily
i suppose you should first differntiate f(x)
high lily
you don't really need vieta's
x_1 and x_2 are roots of f'(x)
consider solving f'(x)=0
note that f'(x) can be factorised
woven summit
I get this ugly answer.
a should be 2 😅
obtuse pebbleBOT
@woven summit Has your question been resolved?
warm shaleBOT
Kepe
tardy epoch
nope
warm shaleBOT
Kepe
fallow rose
obtuse pebbleBOT
tardy epoch
obtuse pebbleBOT
Available help channel!
rotund ingot
Is $\emptyset \cup { a } = { \emptyset , { a } }$ or $\emptyset \cup { a } = \emptyset , { a }$?
obtuse pebbleBOT
Is $\emptyset \cup \{ a \} = \{ \emptyset , \{ a \} \}$ or $\emptyset \cup \{ a ...
warm shaleBOT
veganlatina
warm shaleBOT
Mosh
spiral maple
it's all elements in either {} or {a}
still wren
could i get some help? not sure where to start pls and thanks:)
also a step by step approach could help me the most
obtuse pebbleBOT
nocturne minnow
<@&286206848099549185>
You have to wait at least 15 minutes before pinging helpers
nocturne minnow
Nope
obtuse pebbleBOT
Available help channel!
acoustic vessel
Hi! I have a question about probability and poker. I will use "." for multiply because of italics.
INTRODUCTION
In poker (52 cards, 1 to 10 + J + Q + K, four suits), the frequency of:
- Four of a Kind is: 624 possible combinations = 13C1 . 4C4 . 12C1 . 4C1 which means:
(one number).(all suits of that number).(one number other than the one previously used).(one of the suits)
Alternatively, it can be calculated as 13C . 4C4 . (52-4)C1, this last part means one card other than the four previously used. - Three of a Kind is: 54912 = 13C1 . 4C3 . 12C2 . (4C1)^2 which means:
(one number).(three suits of that number).(two numbers other than the one previously used).(one of the suits for each of both cards)
This calculation already excludes the chance of a four of a kind. - Pair is: 123552 = 13C1 . 4C2 . 12C3 . (4C1)^3 which means:
(one number).(two suits of that number).(three numbers other than the one previously used).(one of the suits for each of the three cards)
This calculation already excludes the chance of a three or four of a kind.
QUESTION
How do I calculate the chance of a three of a kind or a pair, without excluding the chance of something better? I mean, I want to know the chance of having a pair, even including the few times I could be lucky and draw more than 2 cards of the same (like drawing 3 or 4).
obtuse pebbleBOT
Hi! I have a question about probability and poker. I will use "." for multiply b...
acoustic vessel
WHAT I TRIED
- Pair: 1528800 = 13C1 . 4C2 . (52-2)C3 which means:
(one number).(two suits of that number).(any three cards other than the two already used) but I'm not sure if that is right.
I tried to use the same line of thinking to calculate the chance of a poker pair but using the (52-x)C3 formula for the rest of the pair, but it gives me a different result: 1349088 = 13C1 . 4C2 . (52-4)C3 which means:
(one number).(two suits of that number).(three cards other than the two already used and the other two that are the same number)
Why this is different from 13C1 . 4C2 . 12C3 . (4C1)^3? - Three of a Kind: 61152 = 13C1 . 4C3 . (52-3C)2 which means
(one number).(three suits of that number).(two cards other than the three already used) but I'm not sure if that is right.
I tried to use the same line of thinking to calculate the chance of the poker three of a kind but using the (52-x)C2 formula for the rest of the three of a kind, but it gives me a different result: 58.656 = 13C1.4C3.(52-4)C2 which means:
(one number).(three suits of that number).(any two cards other than the three already used and the one that is the same number but hasn't been used)
obtuse pebbleBOT
@acoustic vessel Has your question been resolved?
acoustic vessel
Would you mind looking at my formulas? <@&286206848099549185>
tardy epoch
why the spoilers?
check if your answers match up here:
https://www.math.mcgill.ca/dstephens/323/knitr/knit-01-Combinatorics.pdf
acoustic vessel
why the spoilers?
Because there was too much text for the eye
tardy epoch
you don't want us to read it?
acoustic vessel
It is intended to be read, I just put the spoiler because I though it make the text easier to not lose the line. I will remove it
timid silo
How can I find the tsa and if I have enough paint?
tardy epoch
How can I find the tsa and if I have enough paint?
This channel's occupied. See #❓how-to-get-help
acoustic vessel
check if your answers match up here:
https://www.math.mcgill.ca/dstephens/323/kn...
The answer isn't there.
In normal poker, the chance of for example a pair is calculated as the chance of having two cards of the same number (that math is already shown at wikipedia and at my Introduction part).
What I want to know for a pair, is the chance of having at least two cards of the same number. That means, that if any of the three remaining cards is the same number that the first two, I want it to be included in a pair chance, and not being removed like in normal poker (because in normal poker you would never want to use a pair if you have a three or four of a kind).
I'm not sure if the math I used in my attempts its correct, because when I try to recreate the normal poker math using the other method (52-x)Cy instead of 12C1 . 4Cy I get a different result.
acoustic vessel
In normal poker, if you have AAA23 it automatically stop counting as a pair, because three of a kind is better. That means that if you search in internet what is the chance of having a pair, the math will exclude this example, because three of a kind is better than a pair. However, three of a kind contains a pair (if you have three Ace, it means that you at least have two Ace) and so I want to include it in the chance of having a pair
tardy epoch
Just add the probabilities of pair and three of a kind then
They're disjoint events
Or use inclusion exclusion formula if you want to derive it yourself
acoustic vessel
I did some formulas, but I'm not sure if they are right. For having the number of combinations of a pair or better (so a three or four of a kind would be included) I tried with 13C1 . 4C2 . (52-2)C3 = 1.528.800
However, if I sum the poker chance of a pair, of two pairs (they already include one), of a three of a kind (if you have three, you have at least two), of a full house (if you have a three of a kind and a pair, you at least have a pair), four of a kind (if you have four, you at least have 2) that gives me 1.281.072, so I'm sure I'm missing something.
Additionally, I tried to re-create the formula of a pair 13C1 . 4C2 . 12C3 . (4C1)^3 but written in a different way 13C1 . 4C2 . (52-4)C3 that I think should be the same, but gives me a different result and I don't understand why.
The part that is different 12C3 . (4C1)^3 vs (52-4)C3 I don't understand why it gives a different result.
I mean 12C3 * (4C1)^3 would be explained as the combinations of taking 3 cards out of the twelve numbers that remains (because one number is already taken by the pair) and then multiply it by the combinations of the four different suits that exist, once per card (that is why ^3). Instead (52-4)C3 would be explained (if I'm correctly) as the combinations of taking 3 cards out of the 48 cards that are remaining on the deck (because two cards were already used by the pair, and two other cards would convert the pair into a three or four of a kind), but they give different results.
Comparizon:
- In four of a kind: 12C1 . 4C1 and (52-4)C1 are equivalent.
- In three of a kind: 12C2 . (4C1)^2 and (52-4)C2 aren't equivalent.
- In a pair: 12C3 . (4C1)^3 and (52-4)C3 aren't equivalent.
What I don't understand is why they aren't equivalent
obtuse pebbleBOT
@acoustic vessel Has your question been resolved?
obtuse pebbleBOT
@acoustic vessel Has your question been resolved?
last cypress
hi
nocturne minnow
https://media.discordapp.net/attachments/763586648209883176/943298470486364240/u...
What are you stuck on?
Just create the equation based on the given info
ember crag
Hey, so im very stuck here
nocturne minnow
Hey, so im very stuck here
finite atlas
need help with substitution
obtuse pebbleBOT
need help with substitution
finite atlas
so far i know that i can replace it and make it x/sqrt(u)
tardy epoch
so far i know that i can replace it and make it x/sqrt(u)
don't write an integral in terms of mixed variables
finite atlas
wdym
tardy epoch
Your $u = x^2 + 1$, right?. you have to express $x\ dx$ in $u$ and $du$ variables.
warm shaleBOT
riemann
finite atlas
so i would make it u/sqrt(u^2+1) du?
tardy epoch
how'd you get that?
tardy epoch
so far i know that i can replace it and make it x/sqrt(u)
you made a substitution here
tardy epoch
so i would make it u/sqrt(u^2+1) du?
and undid it here
finite atlas
you said substitute the x and u
tardy epoch
no i didn't
tardy epoch
Your $u = x^2 + 1$, right?. you have to express $x\ dx$ in $u$ and $du$ variable...
read this again
finite atlas
how should i do it?
tardy epoch
tardy epoch
great. do example 1d
finite atlas
this one?
the problem looks similar ill try
im still lost
i tried it
i dont get it
tardy epoch
what part don't you get
finite atlas
substituting the u
tardy epoch
which line
tardy epoch
did you follow these calculations?
finite atlas
yea im using the du
tardy epoch
when it becomes u
what about it?
tardy epoch
did you follow these calculations?
did you write the original integral down
finite atlas
yes
tardy epoch
do you see $xdx$?
warm shaleBOT
riemann
finite atlas
yes
tardy epoch
what is that equal to
finite atlas
-1/8du
tardy epoch
how does that become -1/8
there's your answer
finite atlas
how does it become -1/8du
tardy epoch
how does what become -1/8 du?
finite atlas
the -8x
tardy epoch
did you follow these calculations?
you said you followed these calculations
finite atlas
i did but i dont know how it they got the answer
tardy epoch
did you follow these calculations?
write this out on paper
then you didn't follow it
do you get $du = -8x dx$ ?
warm shaleBOT
riemann
finite atlas
yea from the u=1-4x^2 it becomes -8x
tardy epoch
solve for $x dx$
warm shaleBOT
riemann
tardy epoch
it's better to write this as
$\int (1-4x^2)^{-1/2} x dx$
warm shaleBOT
riemann
tardy epoch
$du = -8 x dx$ implies $-8 du = x dx$ ?
warm shaleBOT
riemann
tardy epoch
you multiplied -8 to both sides and got $(-8)^2=1$ ?
warm shaleBOT
riemann
finite atlas
yea
tardy epoch
,calc (-8)^2
warm shaleBOT
Result:
64
start here and try again
finite atlas
wait no divide from both
oh ok
divide -8 from both sides
xdx becomes - 1/8
since theres imaginary 1
on du
tardy epoch
there are no imaginary numbers here
finite atlas
i get it
tardy epoch
did you follow these calculations?
do you really follow these calculations yet
finite atlas
x^2 becomes 2x
tardy epoch
you're rushing your algebra
finite atlas
1/2x du
tardy epoch
**riemann**
don't make this mistake
finite atlas
would it be 1/2sqrt(u)?
because du = 2xdx
and then dx would be 1/2x du
it would be 1/2sqrt(u) du
got it
.close
mystic saffron
obtuse pebbleBOT
sinful kraken
plug cos^-1(3/4) or arccos(3/4) in your calculator
mystic saffron
hmmmmmmmm
is there any rule that says like if you move cosx over to another side it becomes cos^-1
?
anyways thanks
.close
pastel karma
hello i have a simple question
obtuse pebbleBOT
hello i have a simple question
pastel karma
i am rewatching a lecture video from my professor (calc 2) and in the video we are reviewing some rate of change stuff since we just started up the semester again. The function given was f(x)=x^2+3x
i was solving ahead and keep getting -10 whenever i plug -2 into the function but professor gets -7
my calculator also agrees with me and i cant seem to figure out why
im sure it is a stupid mistake onmy end
simple dove
Your professor probably did f’(2) vs f(-2) ie evaluated the derivative
acoustic vessel
.reopen
compact kiln
i know i was just in a channel but i need help with another one and thats it umm this one looks intimidating because of the <0
obtuse pebbleBOT
i know i was just in a channel but i need help with another one and thats it umm...
lean wigeon
I believe that it expects you to use the value it gives you for tan and the sign of cos to determine what quadrant theta is in, and then compute the values from there. That should help a bit.
compact kiln
I believe that it expects you to use the value it gives you for tan and the sign...
the value 0?
lean wigeon
Not quite, it says that it is less than zero, so you know it must be negative. So you should identify in which quadrant both cos and tan are negative, and base your answers around that.
compact kiln
so i have to draw a triange out
lean wigeon
A unit circle would also help, but either would work.
compact kiln
wait one question does theta haave to have a hypotnuese as one of its sides
lean wigeon
Yes, because if it didnt then it would be in the place of the right angle, which you would not want.
compact kiln
ok
so
i have this
a triangle with both opssite (-4) and adjacent (-3)
that mmake up the -4/-3
and when i use a pythagorean tryple
wait it doesnt matter what order i plug these in in the pythagoeran triple cus none of them are hypotnuse right?
lean wigeon
that mmake up the -4/-3
Well, it says the tangent should be -4/3, but with those sides the tangent would be 4/3, since the two negatives cancel out.
compact kiln
Well, it says the tangent should be -4/3, but with those sides the tangent would...
r both of them negativeon the triangle?
lean wigeon
I would recommend having something like this on hand, so you can see where the angle should be and see which of the sides should be positive or negative.
compact kiln
what is that
lean wigeon
It is a chart that shows the signs of the trig functions in the different quadrants. When you have problems that have negatives in them, it is useful to have a chart like this in your notes. Do you have a unit circle?
compact kiln
i lost mine
do i need it i wanna know how to di it with simply the triange
oh wait i need to figure out the quadrent
ill just search it up
got it so what now
lean wigeon
So which quadrant is it in?
lean wigeon
Figure what out?
compact kiln
where it sits in the unit circle
arent i suppsed to do that with the 4/3
also was i supposed to plug anything in the pythagorean triple
lean wigeon
I would recommend having something like this on hand, so you can see where the a...
Its probably more useful to use a chart like this to identify it. Based on what you know from the question, which of the four quadrants would the angle be in?
lean wigeon
also was i supposed to plug anything in the pythagorean triple
Not yet
compact kiln
Its probably more useful to use a chart like this to identify it. Based on what ...
negative are?
so like
let me try the chart
the bottom part of the chart i assume?
5 area
lean wigeon
You would want to look at which of the functions are negative in each quadrant and use that to identify which quadrant it would be in from there.
compact kiln
function?
lean wigeon
sin, cos, tan, the trig functions
compact kiln
but
i cant really figure that out apart from quadrent 4 where -4/3 sits
or quadrent 2
lean wigeon
It would be in quadrant 2, since it is the only one where both cos and tan are negative
compact kiln
would it be easier i fiugred out all of the sides firt
csc and cot arent negative?
wait is that given in the question
wait the -4/-3 canceled out and became postive right
i think i have an answer
lean wigeon
Well, you are supposed to figure out whether or not they are negative from either making a triangle or from using a unit circle/sign chart. Then make sure that the trig functions have the right value and that would be your answer
compact kiln
cos 5/4 & cot 3/4
lean wigeon
wait the -4/-3 canceled out and became postive right
No, there is only one negative, not two
lean wigeon
No, it is the same as $\frac{-4}{3}$ or $\frac{4}{-3}$
warm shaleBOT
opfromthestart
hybrid gull
$-\frac{a}{b} = \frac{-a}{b} = \frac{a}{-b}$
warm shaleBOT
Shen
hybrid gull
The negative sign can go:
- On top
- In the middle
- On the bottom
It doesn't actually matter
compact kiln
oh ok so either side could be negative?
lean wigeon
Yes, but you should use the information given to figure out which side it is.
compact kiln
so it is better if i adjust my answer as 5/4 csc & - 3/4 cot
cus thats whats on eht answer choices
lean wigeon
Yes
compact kiln
its c?
lean wigeon
Yes
winged abyss
how do you do this? im stuck on it and have no clue where to start
obtuse pebbleBOT
how do you do this? im stuck on it and have no clue where to start
@winged abyss Has your question been resolved?
obtuse pebbleBOT
@winged abyss Has your question been resolved?
winged abyss
.close
lyric yoke
obtuse pebbleBOT
lyric yoke
I am supposed to find the maximum revenue (accidentally wrote P as u can see) and I put it into a factored quadratic then expanded it and completed the square
I got +4 as my x value which would be 40 extra people
wait
I just noticed what I did wrong
.close
obtuse pebbleBOT
timid silo
where does the 2/3 and 3/2 come from ?
lethal bone
idle thunder
Circuit worksheets 😭
obtuse pebbleBOT
@timid silo Has your question been resolved?
brave bramble
Huh?
Do you know what F2 is?
Have you attempted to solve these with what you know? What issues are standing in your way?
obtuse pebbleBOT
@timid silo Has your question been resolved?
obtuse pebbleBOT
@timid silo Has your question been resolved?
obtuse pebbleBOT
@timid silo Has your question been resolved?
rigid kestrel
@timid silo search it in the theory part of book about what is F2. Because it is not clear.
mental solstice
If $I$ is a set, $\sigma$ is a measure on $I$, and $X$ is a Banach space, what does it mean for an operator $E:I\to X$ to be in $L^2(I, \sigma; X)$?
obtuse pebbleBOT
If $I$ is a set, $\sigma$ is a measure on $I$, and $X$ is a Banach space, what d...
warm shaleBOT
Camilleone
mental solstice
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
versed trail
Hi, i'm trying to fully understand and practice the doomsday rule, so far I used the method gaved my the youtube channel numberphile based on what John Conway did, and at the moment i'm getting good at it but sometimes i'm stuck
For exemple when I find my doomsday of the year and that the date I need to find is in the past compared to the doomsday I don't know how to proceed
Because if my doomsday for exemple is Monday (1) 14 march and the date I need to find is 19 march 2022 i just calculate the difference which here is 5, then I add my doomsday which is monday so 1, 5 + 1 = 6 I know the day is Saturday
But what if the date is in the past like i need to get the 03 march 2022 ? Because here the difference is 11 which i'm supposed to add my doomsday so 1 which is 12, 12-7 = 5 so the day is supposed to be Friday but in fact it's Thursday
I don't really know if i'm clear, and if you're familiar with this rule but I'm a bit stuck here
obtuse pebbleBOT
Hi, i'm trying to fully understand and practice the doomsday rule, so far I used...
@versed trail Has your question been resolved?
versed trail
.close
earnest verge
I cant understand fraction
obtuse pebbleBOT
I cant understand fraction
daring rock
If you have a question, just post it.
earnest verge
Tell me abt fraction pls
obtuse pebbleBOT
@earnest verge Has your question been resolved?
mystic saffron
what do you m ean by fraction
timid silo
tired ravine
Express -125/216 in power notation
timid silo
Express -125/216 in power notation
(5/6)^3
obtuse pebbleBOT
@timid silo Has your question been resolved?
obtuse pebbleBOT
@timid silo Has your question been resolved?
mild ocean
obtuse pebbleBOT
@timid silo Has your question been resolved?
obtuse pebbleBOT
@timid silo Has your question been resolved?
astral ivy
holy
@timid silo lemme rewrite this in latex, is this correct?
Let $v = f(r)$ and $r^2 = x^2 + y^2.$ Prove that $$\frac{\partial^2 v}{\partial x^2} + \frac{\partial^2 v}{\partial y^2} = f''(r) + \frac 1v \cdot f'(r).$$
abs_0
timid silo
```tex
Let $v = f(r)$ and $r^2 = x^2 + y^2.$ Prove that $$\frac{\partial^2 v}{\p...
Yes
timid silo
and likewise for dv/dy
Yeah that is where it is getting complicated
tardy epoch
.close
warm shaleBOT
Mathgeek007
finite saffron
obtuse pebbleBOT
lavish gate
say that C is total cost and t is time in hours
finite saffron
how would that look
lavish gate
well its like y=mx+c but in this context C=mt+c
$25 would be the constant because you need to rent the skis before skiing
and every 2 hours the total cost should go up by $15
finite saffron
Thank you
how would the y axis and x axis look on a graph?
nvm
@lavish gate can u help with another question
stray ridge
Does anyone know how to do this
obtuse pebbleBOT
Does anyone know how to do this
spiral maple
equate them and compare coefficients
spiral maple
Expand would be quicker
balmy mortar
How have you been at this for almost 2 weeks???
Do you know what equate coefficients means
Because that's what we keep telling you, but you don't seem to understand
balmy mortar
what???
By equating coefficients, you should have 3 equations (one of which is redundant)
Write them down and show us
stray ridge
I thought it was just comparing the coefficients
brittle swan
I thought it was just comparing the coefficients
it is
after comparing you obtain a system of equations
balmy mortar
Do you know what **`equate coefficients means`**
Look up a tutorial on this
I think you need it
You are equating the coefficients of x in each equation
in order to make the 2 polynomials the same
stray ridge
Is this sort of correct
balmy mortar
That is indeed equating coefficients
but you have only done it for the coefficient of x
balmy mortar
See this is why I think you should look up a tutorial
stray ridge
8 = 3a
warm shaleBOT
Shuri2060
balmy mortar
The 2 quadratics are the same if and only if
a=p
b=q
c=r
A similar statement holds in general for polynomials
stray ridge
So is this wrong
balmy mortar
Yes.
Look up a tutorial on equating the coefficients since you don't seem to understand
stray ridge
What makes it different to the first one I did
balmy mortar
**Shuri2060**
And / or read what I said carefully
stray ridge
Ok I have read it. What should I do if there is not an equal amount of terms on either side
balmy mortar
There are precisely 3 terms in a quadratc.
What you have above is a quadratic in x on both sides of the equation.
Identify the 3 terms.
balmy mortar
$$3x^2+2bx+8a$$
warm shaleBOT
Shuri2060
balmy mortar
What are the 3 terms of this quadratic expression
stray ridge
X bx and a?
balmy mortar
??????????????????
balmy mortar
**Shuri2060**
how the hell do you get that
stray ridge
What is a term
stray ridge
how the hell do you get that
You don’t need to sound condescending, just ask how I got to it
balmy mortar
How do I put this
How are you at this stage without having the basics of what a quadratic is
$$ax^2+bx+c$$
warm shaleBOT
Shuri2060
stray ridge
Ok
balmy mortar
So you identify the 3 terms here in exactly the same way
But the problem is not the left, but the right
stray ridge
3x^2 2bx and 8a
balmy mortar
$$3x^2+6ax+3a^2+b+2$$
warm shaleBOT
Shuri2060
balmy mortar
What are the 3 terms of this quadratic expression in x
stray ridge
3X squared 6AX 3a squared
stray ridge
And those
stray ridge
Yes but you want 3, and I gave you three
warm shaleBOT
Shuri2060
stray ridge
Yes, but didn’t you want 3 terms
balmy mortar
Of course, because there are ONLY 3 terms for any quadratic
stray ridge
So what should I do with the B and the two
balmy mortar
**Shuri2060**
All quadratic expressions in x can be written in this form
Agree or disagree?
stray ridge
Which form? The one you just did
balmy mortar
stray ridge
I agree
balmy mortar
$$f(x) = ax^2+bx^1+cx^0$$
stray ridge
Agree
warm shaleBOT
Shuri2060
stray ridge
So the bx^0 and 2x^0
balmy mortar
**Shuri2060**
Hint: write some brackets to find this form
stray ridge
So what are you asking me to do now
balmy mortar
Is this a quadratic expression in x?
stray ridge
Just add X to the power of zero for the last three terms
balmy mortar
$$f(x) = Ax^2+Bx^1+Cx^0$$
warm shaleBOT
Shuri2060
balmy mortar
So you can find me what A and B and C must be?
There are only 3 terms to any quadratic in x
3x^2
6ax
(3a^2+b+2)
=========
These are the 3 terms
There are only 3 terms
Each term without the power of x is known as the coefficient
Does this explain now what the process of equating coefficients is about?
stray ridge
Why did you get rid of the first two terms
balmy mortar
A polynomial in one variable (let's say x) consists of terms.
Each term consists of a single power of x multiplied by a constant
The constant is known as the coefficient
===
I mean honestly - I shouldn't be re-explaining all this to you which you should have gotten from classes/textbook.
Revise what polynomials or quadratics are...
stray ridge
Can you explain it in terms of the question
balmy mortar
stray ridge
That’s not what I don’t understand
balmy mortar
$$3x^2$$
$$6ax$$
$$(3a^2+b+2)$$
If you understand the definition, you should be able to apply it
stray ridge
I want to know why you have not included the first two terms
warm shaleBOT
Shuri2060
balmy mortar
What do you mean 'not include'
I have not missed anything out
The sum of all the terms is the original polynomial
stray ridge
Like how do you know to use those three and not the first three
balmy mortar
???????????/
===================================
A polynomial in one variable (let's say x) consists of terms that are summed together.
Each term consists of a single power of x multiplied by a constant. Different terms consist of different powers of x.
The constant is known as the coefficient
===================================
Understand the definition first before asking.
stray ridge
Ok
balmy mortar
If you still don't understand then I suggest looking up a video/page explaining the same thing to you
you could search up 'what is a polynomial'
balmy mortar
===================================
A polynomial in one variable (let's say x) c...
Like I am just rephrasing what I know
A book will be better
And more precise
stray ridge
My friend did this. Is it correct
stray ridge
Can You check to see if he made a mistake
balmy mortar
no.
mint phoenix
Can someone explain what I'm missing in this problem?
$$\int \frac{\sqrt{1-x^2}}{x}$$
my thought process is to make a trig sub for $$x = \sin(t)$$, then you get $$\int \frac{\sqrt{1-\sin(t)^2}{\sin(t)} = \int \frac{\sqrt{\cos(t)^2}{\sin(t)} = \int \frac{\cos(t)}{\sin(t)} = \ln(\sin(t)) +C = \ln(\sqrt(x))+C
I looked it up on wolfram and it says I should get $$\sqrt{1-x^{2}}-\left(\operatorname{arctanh}(\sqrt{1-x^{2}})\right)$$, which isn't equivalent, but looks very close.
Any idea what I'm missing in this problem?
obtuse pebbleBOT
Can someone explain what I'm missing in this problem?
$$\int \frac{\sqrt{1-x^2}...
warm shaleBOT
Carl
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
mint phoenix
$$\int \frac{\sqrt{1-x^2}}{x}$$
$$x = \sin(t)$$
$$\int \frac{\sqrt{1-\sin(t)^2}{\sin(t)} = \int \frac{\sqrt{\cos(t)^2}{\sin(t)} = \int \frac{\cos(t)}{\sin(t)} = \ln(\sin(t)) +C = \ln(\sqrt(x))+C$$
$$\sqrt{1-x^{2}}-\left(\operatorname{arctanh}(\sqrt{1-x^{2}})\right)$$
warm shaleBOT
Carl
$$\int \frac{\sqrt{1-x^2}}{x}$$
$$x = \sin(t)$$
$$\int \frac{\sqrt{1-\sin(t)^2}{\sin(t)} = \int \frac{\sqrt{\cos(t)^2}{\sin(t)} = \int \frac{\cos(t)}{\sin(t)} = \ln(\sin(t)) +C = \ln(\sqrt(x))+C$$
$$\sqrt{1-x^{2}}-\left(\operatorname{arctanh}(\sqrt{1-x^{2}})\right)$$
```Compilation error:```! File ended while scanning use of \frac .
<inserted text>
\par
<*> 412086528508952576.tex
I suspect you have forgotten a `}', causing me
to read past where you wanted me to stop.
I'll try to recover; but if the error is serious,
you'd better type `E' or `X' now and fix your file.```
mint phoenix
$$\int \frac{\sqrt{1-x^2}}{x}$$
$$x = \sin(t)$$
$$\int \frac{\sqrt{1-\sin(t)^2}}{\sin(t)} = \int \frac{\sqrt{\cos(t)^2}}{\sin(t)} = \int \frac{\cos(t)}{\sin(t)} = \ln(\sin(t)) +C = \ln(\sqrt{x})+C$$
$$\sqrt{1-x^{2}}-\left(\operatorname{arctanh}(\sqrt{1-x^{2}})\right)$$
warm shaleBOT
Carl
mint phoenix
Well, I guess one error I'm seeing already is that it should be ln(x) not ln(sqrt(x))
brittle swan
$\int \frac{\sqrt{1 -x^2}}{x} \dd x$ is your problem?
warm shaleBOT
Chromium
mint phoenix
Yeah
brittle swan
so you used trig sub?
mint phoenix
Yeah
mint phoenix
Yeah, forced to do trig sub. Full disclosure I'm a TA for a calc class I'm working on an example for trig subs. Trying to work through one myself and checking that my results are correct
brittle swan
oh so this is a problem you came up with lol
mint phoenix
More or less. I'm taking ideas from their homework
brittle swan
might wanna use $\int \frac{1}{\sqrt{1 - x^2}} \dd x$ instead
warm shaleBOT
Chromium
brittle swan
i don't think there's a way out except for trig sub
(so that you can show its ✨ superiority✨ )
balmy mortar
More or less. I'm taking ideas from their homework
?
Almost all integrals are not doable by hand
If I wrote random numbers/functions it would almost always be impossible
mint phoenix
Sure, but I would expect this one to be possible.
balmy mortar
All integration questions you see are handcrafted so they are possible.
By no means is that guaranteed
brittle swan
$\int_0^{\infty} \frac{\sin x}{x} \dd x$ 
warm shaleBOT
Chromium
balmy mortar
You should check in wolfram to see if it is even possible first.
mint phoenix
That's exactly what I did
Sorry, i think my first messgae got buried after I tried to fix my TeX
brittle swan
integral-calculator.com does a more specific job imo
mint phoenix
My problem is that wolfram disagrees with the answer I'd expect to get, and I'm not sure where I'm going wrong
brittle swan
free steps
mint phoenix
Already did
brittle swan
sometimes the problem lies in the + C
mint phoenix
brittle swan
they're referring to differenti constants altogether
balmy mortar
You can plot each step of your working as well
timid silo
How do I find a multiplicity of a zero in this
obtuse pebbleBOT
How do I find a multiplicity of a zero in this
timid silo
each unit is 1
and i understand that -4, 2, 6 are zeros
but idk how to find the multiplicity of it
i know how to understand if it’s a odd multiplicity or even
but idk how to find if it’s 1, 2, or 3
(the multiplicity)
raven spire
Figured it out. I forgot to substitute my 'dx' when I sub'd the 'x'
wow, yeah you forgot the dx = cos t dt
timid silo
<@&286206848099549185>
lean wigeon
Basically, you want to look at just the area around the zero, and see if it looks like x, x^2, x^3,etc.
take x=2 first, what does the area around x=2 look like?
raven spire
and i understand that -4, 2, 6 are zeros
say: f(x) = (x - a)^n q(x)
then, f'(x) = n(x - a)^{n-1} q(x) + (x - a)^n q'(x) = (x - a)^{n - 1} [ nq(x) + q'(x) ]
raven spire
Basically, you want to look at just the area around the zero, and see if it look...
for example at x = 2, the curve is increasing as it cuts x - axis, => f'(x) > 0 but f(x) = 0
so, multiplicity of x = 2, is 1
balmy mortar
but idk how to find if it’s 1, 2, or 3
You realise that this is surely impossible
You can only ever tell if it is odd or even from a rough sketch
If they tell you the degree of the polynomial or something, that might help things
tardy epoch
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
timid silo
someone help please
obtuse pebbleBOT
someone help please
sterile wyvern
You already have m and need b
sterile wyvern
,w d/dx(3.1 x^2-4.6 x) at x=7
warm shaleBOT
timid silo
ohh
sterile wyvern
,w solve 3.17^2-4.67 = 38.8 * 7 +b
timid silo
mb i used the wrong m
warm shaleBOT
obtuse pebbleBOT
timid silo
.reopen