#help-13
fallen solar
i have no idea
fallen solar
yes
cedar kilnBOT
@modest wing Has your question been resolved?
hidden canopy
a b and c are three variables.
a is proportional to b^2
a is also proportional to root of c
b = 4.5 when c = 2.25
Find b when c = 8
I am struggling to find the constant and I don't know how to do it, can someone elaborate please
hidden canopy
I mean I tried to simplify it into k x 20.25 = k x 1.5 but I'm not sure how to figure out k from there
stone hearth
you need to use different constants for the two proportionalities
hidden canopy
I thought it would be the same constant though because its 4.5 when c is 2.25
and they are equal to each other because they are linked by A
stone hearth
but a is proportional to b by a different constant
and to c by a another one
try that
hidden canopy
but how do i figure out the constant with A being unknown
or do i use 20.25 x k = k x 1.5 as the way to figure out the constant
stone hearth
$$ a = x\dot{}b^2 $$
$$ a = y\dot{} \sqrt{c}$$
$$ \implies x \dot{} b^2 = y \dot{} \sqrt{c}$$
wraith daggerBOT
Daw
hidden canopy
ok i think i see where u getting at but why are y and x different constants
stone hearth
because a is proportional to b by a different magnitude
and to c by a different one?
x and y are the constants of proportionality
stone hearth
I mean b^2 and \sqrt{c}
stone hearth
so could x be 1 and y be 13.5
I don't think you can find them, but you don't have to
just solve for x/y
by using values of b and c from scenario 1
and then solve scenario 2 with the newfound value of x/y
hidden canopy
ok
is the answer 10.4 then
is that what b is
it sounds right
@stone hearth (sorry for ping) could you confirm
stone hearth
I don't know, but I think that should be it if you did the calculations correctly 😓
check if they have answers on the back
hidden canopy
they dont
but ill tell u what i did
so in the first scenario
i made x 1 and y 13.5 so they became equal
i then substituted it into the 2nd scenario
actually it is 108
nvm
its 10.4
but 108 rooted
is 10.4 to 3 sig figs
so i substituted it into the 2nd scenario and i got 108 so i rooted it and i got 10.4
stone hearth
i made x 1 and y 13.5 so they became equal
wait what 
hidden canopy
well 😅 i thought u said use x and y from the first scenario into the 2nd
stone hearth
You could but you didn't have to put anything into x and y 🤔
You would get x/y from the first scenario
hidden canopy
yes thats what i did i got it from the 1st scenario
stone hearth
Oh okay
hidden canopy
and i used x and y frm 1st scenario into the 2nd
and i got 108
and then i rooted it
stone hearth
I can't calculate it rn but it should be good if you did everything right
steel ledge
Hi ! I'm trying to solve this equation.
cedar kilnBOT
Hi ! I'm trying to solve this equation.
steel ledge
When calculating z, I found z = 5 (cos (-3/5) + i* sin (4/5))
I'm not sure where to go from here.
crimson sedge
note that z^2 = (-z)^2 for any z in C
steel ledge
I think I can use (a+b)^2 ? But I'm wondering what should I do if i stumble on a teta that doesn't look like anything I know, (instead of 1/sqrt(2), we have 3/5 for example)
crimson sedge
When calculating z, I found z = 5 (cos (-3/5) + i* sin (4/5))
you found that this is a solution?
steel ledge
it's not the final solution, I calculated the module which turned out to be 5 and then put it in factor of the expression
I think
steel ledge
it isn't
crimson sedge
what is the meaning of it then?
steel ledge
I'm trying to find the solution, I don't know how to. In a previous exercise, in order to solve this type of equations with z^n, we were told to calculate the roots of z, so that's what I was trying to do here. But since I can't find the argument I am stuck
crimson sedge
well maybe the quickest thing is to use the quadratic formula
steel ledge
i'm going to try thank you
crimson sedge
polar coordinates should also work fine though
steel ledge
polar coordinates is that what I tried to do? Sorry I don't know the translation of everything
crimson sedge
yea
steel ledge
I'm not sure what to do when I find angles that look like 3/5 and -4/5 then? Like is there a way for me to place them on the trigonometric circle
crimson sedge
what's -3 + 4i in polar?
steel ledge
it's what i was trying to do find
cedar kilnBOT
@steel ledge Has your question been resolved?
fresh warren
to solve abs(1-x/2x+1) => 1
cedar kilnBOT
to solve abs(1-x/2x+1) => 1
fresh warren
can you convert it to
1-x/2x+1 => + or - 1?
or its simply not possible considering this is a inequality?
<@&286206848099549185>
yeah
wraith daggerBOT
azeem321
sand ether
can be - or + x
Right. So when $x>0$, $|x| = x$ and when $x<0$, $|x| = -x$
wraith daggerBOT
azeem321
sand ether
Now, whenever you have to solve inequalities. It's best that you make one side 0. It's much easier to show that $\big |\frac{1-x}{2x+1} \big | - 1 \geq 0$
wraith daggerBOT
azeem321
paper shale
Let A={0,1,2} {2,5,8} = {(0,2), (0,5), (0,8), (1,2), (1,5), ( 1,8), (2,2), (2,5), (2,8)}.
A relation R on A is defined by : (a,b) R (c,d) if and only if (a+b) is a divides (c+d).
(i). Draw a Hasse diagram for poset A
(ii). Determine the maximum, minimum, maximum, and minimum elements (if any) in poset A.
(iii). Determine LB (0.8) and GLB (0.8).
(LB = Lower Bound, GLB = Greates Lower Bound)
paper shale
guys help me how to draw a hasse diagram :/
cedar kilnBOT
@paper shale Has your question been resolved?
cedar kilnBOT
@paper shale Has your question been resolved?
cedar kilnBOT
@paper shale Has your question been resolved?
potent glen
How do I solve this integral? I tried integration by parts and things got weird really fast.
cedar kilnBOT
How do I solve this integral? I tried integration by parts and things got weird ...
@potent glen Has your question been resolved?
foggy merlin
How do I solve this integral? I tried integration by parts and things got weird ...
this integral diverges
cedar kilnBOT
@potent glen Has your question been resolved?
potent glen
this integral diverges
How would you go about finding that though? I know that you would integrate the interval then evaluate at (-inf, inf) using limits, but I don't know how to integrate the function
south juniper
@potent glen Use by parts
foggy merlin
How would you go about finding that though? I know that you would integrate the ...
integration by parts
cedar kilnBOT
@potent glen Has your question been resolved?
floral thistle
@potent glen u = 7x, dv = e^(x/6) dx
cedar kilnBOT
cedar kilnBOT
Available help channel!
crimson sedge
This is wrong right?
cedar kilnBOT
This is wrong right?
cedar kilnBOT
@crimson sedge Has your question been resolved?
crimson sedge
<@&286206848099549185>
severe acorn
This is wrong right?
the answer is right
but 10^-18 * 10^19 = 10^(-18+19)
so no real difference
of course, using (a^n)/(a^m) = a^(n-m) is better
cedar kilnBOT
@crimson sedge Has your question been resolved?
cedar kilnBOT
cedar kilnBOT
Available help channel!
slate rapids
Can someone please explain how did we end up with this?
cedar kilnBOT
Can someone please explain how did we end up with this?
leaden otter
Product rule applied in reverse
slate rapids
Product rule applied in reverse
Oh I see now thanks
prisma sluice
you have tan(θ − 10) = 0.51 how do i get theta?
cedar kilnBOT
you have tan(θ − 10) = 0.51 how do i get theta?
prisma sluice
i always forget
i cant just do arctan(0.51) cuz the -10
i know there is a formula that you can use but i dont have it
should i try to use Tan(A-B) formula for this ?
prisma sluice
rewrite tangent in terms of sines and cosines
yooo its you again
violet flume
but then you can use a more elementary formula
yea lol
i was wondering if youd rememer
prisma sluice
ofc
violet flume
yea rewrite in sines and cosines
then use normal difference formula
sicosico coco sisi type stuff
prisma sluice
what do you mean by rewrite in sines and cosines (i probably will know if i see it)
wraith daggerBOT
jan Niku
prisma sluice
yes yes
violet flume
so what does tan(theta - 10) equal
violet flume
**jan Niku**
this is true for any x
prisma sluice
ok
violet flume
theta - 10 fits that restriction
prisma sluice
ok
violet flume
hey i wonder $\mp$
wraith daggerBOT
jan Niku
violet flume
nice
prisma sluice
so the answer i want to say is probs wrong
hmmm
ill say it anyway
ohh sweet its just sin(theta -10)/ cos(theta - 10)
violet flume
yea
so you dont absolutely need to do this
but if you do
you only have to memorize those two formulas
we have a sin difference and a cos difference
have you memorized them yet?
prisma sluice
ohh yeah
violet flume
notice sine-sign-sicosico
cosine is coco sisi
opposite sign
notice cosine has an O in it
like opposite
and cosine difference means COsine COmes first
prisma sluice
ok wait
violet flume
idk these are mnemonics i liked
prisma sluice
i work from this
violet flume
yea
prisma sluice
this means we use sin(a-b) / cos(a-b)
violet flume
yup
prisma sluice
and basically use that formula
leaden otter
Isn’t writing in terms of sin and cos a bit overcomplicating? To calculate theta that is. Tan inverse does work
prisma sluice
ok once i found out A i need to find out all the solutions for it between 0 and 360 degrees which is a piece of cake
violet flume
Isn’t writing in terms of sin and cos a bit overcomplicating? To calculate theta...
i guess
prisma sluice
i guess <:thonk:406575732563902485>
look u can use this
violet flume
sure\
if u wanna memorize another formula
you dont need any of them tho
u can use inverse tan
leaden otter
What’s the point of expanding tan(theta-10) even?
violet flume
or do it the cool way we were doing before
yea idk
i just took finals
im gonna blame that
what were doing is nonsense elp1
sorry
prisma sluice
np
prisma sluice
but there is a -10
leaden otter
Doesn’t matter. We are left with theta-10 on the left
digital solar
wait im new here but couldnt you just say x=theta-10, and evaluate tan(x)=0.51
leaden otter
Yep
prisma sluice
wait so how would that look
prisma sluice
ye how would the evaluation look
leaden otter
$\tan(x)=0.51\implies x=n\pi+\tan^{-1}(0.51)$
prisma sluice
there is no way i can just do arctan(0.51 -10)
wraith daggerBOT
Euclid31415
leaden otter
$x=\theta-10\implies \theta-10=n\pi+\tan^{-1}(0.51)\implies \theta=10+n\pi+\tan^{-1}(0.51)$
prisma sluice
$x=\theta-10\implies \theta-10=n\pi+\tan^{-1}(0.51)\implies \theta=10+n\pi+\tan^...
wait so are you just ignoring the -10?
wraith daggerBOT
Euclid31415
prisma sluice
so its just arctan(0.51) + 10
leaden otter
Yep
leaden otter
It wasn’t that hard
prisma sluice
and if it was tan(4x) = 0.4 would we do arctan(0.4) / 4
leaden otter
Yes
leaden otter
You should also consider the n*pi stuff though
prisma sluice
You should also consider the n*pi stuff though
is that to do with radians?
or the angle
leaden otter
It is to do with the fact that tan(x)=0.51 has infinite solutions differing in multiples of pi
prisma sluice
It is to do with the fact that tan(x)=0.51 has infinite solutions differing in m...
ok so what is the n in n*pi
leaden otter
ok so what is the n in n*pi
Any integer
leaden otter
like 912091231
$\tan(x)=\tan(n\pi+x)\forall n\in\mathbb{Z}$
wraith daggerBOT
Euclid31415
prisma sluice
**Euclid31415**
dude im seeing set theory stuff (im worried)
npi is the angle then right
?
leaden otter
Yes. n*pi is an angle
prisma sluice
ok good
leaden otter
dude im seeing set theory stuff (im worried)
It’s just tan(x)=tan(n*pi+x) for all integer n
crimson sedge
4pi divided by 3/4 --> is this 4pi/12 or 16pi/3
cedar kilnBOT
4pi divided by 3/4 --> is this 4pi/12 or 16pi/3
bold vine
$\frac{4\pi}{\frac{3}{4}} = 4\pi \cdot \frac{4}{3} = \frac{16\pi}{3}$
wraith daggerBOT
Shen
digital solar
ya that looks good
digital solar
4pi divided by 3/4 --> is this 4pi/12 or 16pi/3
if ur ever stuck on smthn like this, multiplying by recipricol is much easier
so 4pi *4/3
crimson sedge
Is it okay thay I convert all the denominators to be the same
For my scale and period
crimson sedge
It looked weird but I think that it was mainly due to the restrictions
crimson sedge
but scale might not be in pi
Wdym?
pearl marsh
need some help with imaginary numbers, I get that i^2 will be the opposite number but what if its like i^3 or i^6
dense wing
$i^3=i^2\cdot i$
wraith daggerBOT
Mosh
dense wing
also "the opposite number" is a very strange name for "-1"
pearl marsh
like the question i^2(5i-3i^3)-4i^6
dense wing
yeah... what about it?
pearl marsh
here i know that i^2 turns into -1
dense wing
yeah, so i^3=-i
pearl marsh
it's the same thing?
wraith daggerBOT
Mosh
pearl marsh
so if it's i^3, i change the -3i^3 to a +3i?
pearl marsh
ok so what if it's like 9i^3 it's -9i
pearl marsh
what about i^6
dense wing
$i^6=i^2$ by the four cycle symmtery
wraith daggerBOT
Mosh
pearl marsh
-1?
dense wing
or $i^6=(i^3)^2$
wraith daggerBOT
Mosh
dense wing
yes
dense wing
yep
pearl marsh
ok ok ok
dense wing
repeats cyclically for all integers
pearl marsh
i got it
dense wing
because multiplication by i is a 90 degree rotation
dense wing
yes..
dense wing
i^100 is?
pearl marsh
1
dense wing
yep
pearl marsh
thx
cedar kilnBOT
@pearl marsh Has your question been resolved?
cedar kilnBOT
cedar kilnBOT
Available help channel!
crimson sedge
cedar kilnBOT
crimson sedge
how does one convert this to lhopital?
glad kestrel
set the limit equal to some number L, take ln of both sides
glad kestrel
you're gonna use log laws to bring the exponent down
glad kestrel
$(1+\frac{1}{t})^{2t}=L$
wraith daggerBOT
a disappointing son
glad kestrel
where L is just whatever the limit is equal to
glad kestrel
ln(1) is not 1
glad kestrel
yep
glad kestrel
cannot
you can only use lhopital if you have infinity/infinity or 0/0
not infinity*zero
gotta rearrange some more
glad kestrel
yeah that's why i said gotta rearrange some more
crimson sedge
i see
glad kestrel
from 0*infinity you can't use lhopitals
glad kestrel
but yeah once you do this you can
kindred pike
can someone help me with the simplification here? i get really confused trying to simplify things like this. i understand that the endgoal is to cancel the h variable but im a bit lost.
short socket
can someone help me with the simplification here? i get really confused trying t...
$$\frac {\frac{1}{x+h+2} - \frac{1}{x+2}}{h} = \frac {\frac {x+2}{(x+h+2)(x+2)} - \frac {x+h+2}{(x+h+2)(x+2)}}{h}$$
wraith daggerBOT
HELLOBELLO
short socket
there now you can simplify it and calculate the limit
kindred pike
i am just confused on how to get to the second step there
like the simplifying itself is what im lost on
i need it broken down if thats okay
am i just trying to get common denominators?
radiant topaz
am i just trying to get common denominators?
Ye
cedar kilnBOT
@kindred pike Has your question been resolved?
cedar kilnBOT
cedar kilnBOT
Available help channel!
cedar kilnBOT
<#486841085210132490> help pls
cedar kilnBOT
cedar kilnBOT
Available help channel!
quartz sedge
verify sin4x = 8cos^3xsinx-4cosxsinx
cedar kilnBOT
verify sin4x = 8cos^3xsinx-4cosxsinx
quartz sedge
I managed to get to 8cos^3sinx-4cosxsin^3x
but idk how to get rid of sin^2x to get the answer
bright surge
@quartz sedge you're obviously wrong somewhere
tropic oxide
show work
bright surge
expand to sin2xcos2x+sin2xcos2x
then?
quartz sedge
2(2sinxcosx)(cos^2x-sin^2x)
bright surge
2(2sinxcosx)(cos^2x-sin^2x)
yeah?
quartz sedge
2(2sinxcos^3x-2sin^3xcosx)
bright surge
yep?
quartz sedge
now im stuck
quartz sedge
verify sin4x = 8cos^3xsinx-4cosxsinx
.
modest wing
oki
ill do it one sec
it was easy
as
hell
bro it was so easy
where are u getting stuck
tropic oxide
I managed to get to 8cos^3sinx-4cosxsin^3x
are you sure that eight wasn't a four?
glad kestrel
do not give answers
modest wing
fine
hint use 2cosxsinx = sin2x
and 2cos^2x -1 = cos 2x
use them and u will get them lel
quartz sedge
oh i was using the cos2x = cos^2x-sin^2x
glad kestrel
bro it was so easy
also this person is probably younger than you, don't be an asswipe
quartz sedge
im not gonna tell my age to someone random on the internet
quartz sedge
👍
quartz sedge
2(2sinxcosx)(2cos^x-1)
modest wing
2(2sinxcosx)(2cos^x-1)
perfect
quartz sedge
so simplify and ill get answer?
modest wing
yes sir
modest wing
lol
neon arch
i have this q and the answer its right?
cedar kilnBOT
i have this q and the answer its right?
glad kestrel
,rotate ccw
wraith daggerBOT
glad kestrel
looks right
past sequoia
Hello
past sequoia
I need some help to clear my confusion....
I was computing the distance between two points in a cartesian plane
Actually nvm i'm freaking dumb
.close
sharp orbit
cedar kilnBOT
sharp orbit
help, should i do the 2x-5 first?
i think the answer for that is -10 but that doesn't really make sense
wait no is it -2.5
deft mirage
Convert 8 and 4 to powers of 2 and try it
tropic oxide
what do you mean by "do the 2x-5 first"
cedar kilnBOT
@sharp orbit Has your question been resolved?
wraith daggerBOT
mrbrown
Hint $$ \log_{a}(b^c) = c \log_{a}(b)$$ I forgot how to prove this equation though. 😅
sharp orbit
wait so you should solve the logs for each side?
crisp jackal
no, wait. I was meaning to say that we can take the x in the exponent and put it infront of the log. This should make it easier to solve for x.
like
$$ \iff x \log_{4}(8) = 2x-5 $$
wraith daggerBOT
mrbrown
crisp jackal
🙂
cedar kilnBOT
@sharp orbit Has your question been resolved?
crimson sedge
@sharp orbit Yellow is a girl, right?
crimson sedge
**mrbrown**
```latex
Hint $$ \log_{a}(b^c) = c \log_{a}(b)$$ I forgot how to pro...
@crisp jackal Just assume
log(b^c) = log(bbbbbbb...) = log b + log b + log b + ...
= c log b
It's a lame way, I know but quite good for beginners explanation.
crisp jackal
ohhhhhhhhhhhhhhhhhhhhhhhh, that is pretty good! 🙂 thank you!
crimson sedge
That assumption will quite break for negatives and fractional powers.
I guess we have to dive in the realm of binomial distribution or e^x then.
Yellow left me :(
crisp jackal
I can see it working with negatives like log(b^(-c)) = log((1/b)^c) = log (1/b * 1/b * 1/b ....) = log(1/b) + log(1/b) + .... = c log (1/b). Fractional powers could be a problem indeed.
crimson sedge
I can see it working with negatives like log(b^(-c)) = log((1/b)^c) = log (1/b *...
Oh yeah, just realized 1/b can be rewritten in the form of log 1 - log b and log 1 is 0.
Thank you this time xD.
crimson sedge
cedar kilnBOT
crimson sedge
I've found minus 0.0289 but probably incorrect
I mean, what is x here? And can we calculate this integral directly by ordinary integral rules after parametrizing it?
$\int_{\gamma} x \abs{dz}$
wraith daggerBOT
Cüneyt
lilac totem
Just wanted to say, I have no idea what you are talking about and I'm just learning calculus
I don't even understand a fricking linear function
untold torrent
@lilac totem What?
floral thistle
that isn’t a thing
crimson sedge
Wdym
stupid question but are the people that is good at mathematics good in playing poker? 
floral thistle
absolute value bars around dz
lilac totem
stupid question but are the people that is good at mathematics good in playing p...
Poker is illegal in my country
:(((
crimson sedge
Poker is illegal in my country
Turkey?
untold torrent
Maybe talk about this somewhere else...?
crimson sedge
absolute value bars around dz
Teacher wrote it himself
floral thistle
exactly redstone
crimson sedge
am i in a turkey server?
floral thistle
please go to a non help channel
lilac totem
please go to a non help channel
You asked me UwU
crimson sedge
Okay, is anyone here able to solve the question?
crimson sedge
India (I think betting on poker is not allowed)
ohhh
floral thistle
in that case, the bars probably don’t mean absolute value
although i’ve never seen this notation
crimson sedge
in that case, the bars probably don’t mean absolute value
I don't know, this is what teacher wrote
And he calculates that absolute values as if it's complex number
Like
floral thistle
bruh is this a contour integral
crimson sedge
Okay thanks anyways
cedar kilnBOT
@crimson sedge Has your question been resolved?
cedar kilnBOT
@crimson sedge Has your question been resolved?
cedar kilnBOT
@crimson sedge Has your question been resolved?
normal wraith
And he calculates that absolute values as if it's complex number
isn't that just the usual "ds" that's used in line integrals then?
crimson sedge
I don't know and I don't think so
floral thistle
@crimson sedge since this is a contour integral, you can ask in #real-complex-analysis
crimson sedge
okay
cedar kilnBOT
@crimson sedge Has your question been resolved?
grand juniper
I'm stuck on how to start this question. I know I'm supposed to get 2 matrices and perform row reduction on both sides, but not really sure how to arrive at these 2 matrices to begin with since these are different sizes
feral oyster
I'm stuck on how to start this question. I know I'm supposed to get 2 matrices a...
There might be a diff way with row reduction but the way I was taught is first you plug in the first basis into T. Then you represent that output as linear combinations of the second basis.lmk if u need clarification
grand juniper
T(x) = (4,4,0)
T(y) = (-1,3,5) , (-1,3,5)
T(z) = (2,-5,1) , (-2,5,-1)
Is this right?
feral oyster
No
feral oyster
T(x) = (4,4,0)
T(y) = (-1,3,5) , (-1,3,5)
T(z) = (2,-5,1) , (-2,5,-1)
Is this ri...
You need to plug in (1,1,0) into (4x+y+z, y-z) then do that for the other 2 basis vectors
grand juniper
4(1,1,0) + (-1,3,5) + (2,-5,1), (-1,3,5) - (2,-5,1)
(4,4,0) + (-1,3,5) + (2,-5,1), (-1,3,5) - (2,-5,1)
(5,2,6), (-3,8,4)
feral oyster
No no no
You should obtain 3 different vectors
So one for (1,1,0)
Another for (-1,3,5)
And the last one
feral oyster
Ye
cedar kilnBOT
cedar kilnBOT
Available help channel!
red mural
noah is painting boxes that are all the same size he used 2 ounce of paint to cover 1 2/3 how many ounces are needed for 1 box
crimson sedge
sin2pi ... is 0?
cedar kilnBOT
sin2pi ... is 0?
violet rapids
@crimson sedge Which math class are you in?
violet rapids
Ugly ass formatting is confusing you
violet rapids
Sorry, I wasn't talking about your math.
The way the math is formatted on the paper is confusing
$y=2\sin\left(2\pi\cdot\frac{t-1}{3}\right)+6$
wraith daggerBOT
sills
cedar kilnBOT
@crimson sedge Has your question been resolved?
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deft saddle
a merchant bought an article for $x, he put in his shop for sale at marked price 70% higher than its cost. the article was then sold to a customer at a discount at 5%. what was the percent gain for the merchant by selling the article
cedar kilnBOT
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violet rapids
You wrote all the variables you need to know
deft saddle
how do I know the percent gain of the merchant by selling the article
deft saddle
uh
cedar kilnBOT
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crimson sedge
lim r=0 (sin(x^2)/x^2) equal 1 right??
cedar kilnBOT
lim r=0 (sin(x^2)/x^2) equal 1 right??
crimson sedge
lim r=0 (sin(x^2)/x^2) equal 1 right??
what's r?
but you change the variable r to x so fix the r=0 part
and yes when lim sin (anything) / (anything) when anything ---> 0 is equal to 1
ohh
IDK about multivariable's limit though from what I was taught that's not how you prove it but maybe I'm not knowledge enough
just to be clear I'm talking about x^2+y^2 = r^2
ok but why here we took lim in c1 and c2 to check if its exist or not but in the first one we just checked one time
I don't think I'm qualified to answer that, sorry
ok no problem, thanks for helping me tho
I can tell you about the second one but I don't know about the first one
yeah go ahead
so for 1 variable we have left and right limit if
left limit = right limit
then the limit exists
What are left and right limits ?
The neighbors of what our variable is approaching ( most examples x is approaching some [x----> some number] value so the neighbors are values bigger and smaller than x )
so far good?
so the neighbors are on a single axis
now i get it
What about 2 variable ?
there are on 2D surface ( 2 axis )
3 variable ? 3D space ( 3 axis )
4 variable ? we can't imagine it but if we could 4D space
what essentially we are doing is finding paths around that lead to that point
if all of the paths have the same limit then the limit exists
how many paths are there ? infinity
granite harness
Umm I think the limit for sin(r^2) is not right. Basically it’s gets super big at r goes to 0. It doesn’t. Converge because you can find sequences that go to -1 and that go to 1
This is also called the topologist’s sine curve. Weird discontinuity.
Oh nevermind it’s fine because you’re dividing by r. But if you weren’t. Trouble.
crimson sedge
What's the limit at x=0 ?
https://www.desmos.com/calculator/sl66gpj6qd
sorry yes its discontinues at 0 but we are not talking about discontuinty
granite harness
Ahhh I know what I’m thinking of sin(1/r)
crimson sedge
A random shape I drew of one of the neighbors and it's paths
granite harness
No I know we’re talking about limits. Sorry totally different function. And it’s probably be mean to have in regular calculus
crimson sedge
No I know we’re talking about limits. Sorry totally different function. And it’s...
Yes
so ok?
Now I understand thank you so much
I know this far IDK about what you did
crimson sedge
Now I understand thank you so much
yw
I'll say it again cause it's important you can't prove that a limit exists using paths just that it doesn't exist ( cause there are infinity paths you need to try)
crimson sedge
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cedar kilnBOT
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opaque frigate
What nominal rate of interest, compounded monthly, corresponds to an effective rate of 11%?
r= ?%
opaque frigate
<@&286206848099549185> pls help me
sly iris
Yeah
opaque frigate
I have too many formula
sly iris
This is the formula for converting nominal to effective
opaque frigate
This is the formula for converting nominal to effective
rn I am trying to solve it
opaque frigate
This is the formula for converting nominal to effective
can u help me again
Id wanna make
mistake
sly iris
Just plug the numbers in
opaque frigate
Just plug the numbers in
can u look
sly iris
((i+1)^(1/n) - 1)*m
opaque frigate
((i+1)^(1/n) - 1)*m
I did Ig
opaque frigate
((i+1)^(1/n) - 1)*m
what is your answer
opaque frigate
Same as yours
yeh
opaque frigate
Post the exact text of the question
I will cry
we were right
A zero-coupon bond is a bond that is sold for less than its face value (that is, it is discounted) and has no periodic interest payments. Instead, the bond is redeemed for its face value at maturity. Thus, in this sense, interest is paid at maturity. Suppose that a zero-coupon bond sells for 9,150$ and can be redeemed in 20-years for its face value of 35,000$. What is the annual compound rate of return?
Annual compound rate = x% (Round to two decimal places as needed.)
opaque frigate
A zero-coupon bond is a bond that is sold for less than its face value (that i...
can u help me
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opaque frigate
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lusty zephyr
Can someone help me understand where to begin here? I don't really understand what arg(z+1) means
lusty zephyr
is it literally just adding 1 to cos
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lusty zephyr
<@&286206848099549185> need help with proving 2Arg(z +1) = Arg(z)
Nvm, it's just double angle formula
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cedar kilnBOT
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shy dock
hi
shy dock
im doing long division and i was wondering
why does the lecturer in this video put zeros in the division?
couldnt he just have
x-3 ✔️ 6x^4 + -9x^2 + 18?
floral thistle
some people do that so they can have all powers of x in there
i don’t do it though
livid hound
it makes it clearer, makes more room and you will be less likely to make mistakes
ideally you'd want terms with the same power aligned
shy dock
ideally you'd want terms with the same power aligned
i understand
livid hound
you don't have to explicitly write the 0 if you don't want to. you could leave a gap and be aware of what's happening
shy dock
x-3 ✔️ 6x^4 + -9x^2 + 18?
would it be alright if i did it in this form? 🤔
shy dock
i understand, thank you :)
wraith daggerBOT
ℝamonov
livid hound
$x-3)\overline{6x^4 + \ \ \ \ -9x^2 \ \ \ \ +18}$
wraith daggerBOT
ℝamonov
floral thistle
that’s exactly what i do lol
livid hound
would be more appropriate
nimble dirge
Hey there, I'm stuck in this Ruffini exercise, I've already solved the bottom part, giving me (x-2)(x+4)(x-3)(x+3) but I can't seem to get 0 in the top part no matter what numbers I try. Thanks in advance
nimble dirge
I've tried ±1, ±2, ±3, ±4, and ±6 to no avail
cedar kilnBOT
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nimble dirge
Maybe there's another method to factorize it?
cedar kilnBOT
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nimble dirge
<@&286206848099549185>
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compact verge
I think you can’t factorise the numerator nicely
You’re not going mad lol it just can’t be done
nimble dirge
I see, well it's nice knowing I'm not missing something lol
Could it be a way to modify it so It can be factorised?
Like, idk. Changing x^4 to x^5 to have that extra 0?
nimble dirge
I think i got it, would
frac (x-3)(x-2)(x+3)(x+4)(x+1)
(x-2)(x+4)(x-3)(x+3)
be the correct answer if the exercise is changed to this?
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eager mist
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eager mist
so for d i got the limit as x--->infinity to be 1/7.
i am confused on how to apply that to part (e)
also there is a typo, it is meant to say "use answer to part (d)"
cedar kilnBOT
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quartz frost
If d is correct then i would assume 1/7 to be the asymptote
echo briar
with piecewise functions, say you have f(x)=x{x>3:1,x<2:2}, is there a way so that the x getting multiplied by two if x<2 “connects” with x(1)?
echo briar
the slope is one at x>2, I need the part of the line at x<2 to touch with the part that is x>2
I’ll pull an equation from desmos
I do not want that gap. I need to find a way so that the x>2 line moves to meet the other line
upper abyss
Oh, that's very weird
Non-standard notation
Well, what are we allowed to do to these lines?
The simplest way to connect them is to forget they're piecewise and make it f(x) = x
echo briar
if I remove the piecewise portion then the line with a slope other than one is removed as well
I don’t see a way to make it so that the lines will connect no-matter what happens to the second line’s slope since every time I change it, it moved in y value
upper abyss
Okay so you want that left line moved, but with the same slope
echo briar
yes
either one can move as long as their slope stays the same
I’m wondering if there’s some magic equation used to automatically make ends meet
upper abyss
f(x) = {x > 2:x, x < 2:2x - 2}
I'm not skilled with desmos, hopefully it accepts that notation
smoky stump
cedar kilnBOT
smoky stump
this is for (p)
what i want to know is whether taking the +- of a root as seen above
would change the inequality
so if you have a -root(x^2 -2) would this be y >= to it?
upper abyss
I would avoid the notion of a square root, here
smoky stump
why?
wouldn't it be easier to solve if we take square roots?
@upper abyss so why do you think it is bad to take square roots?
this is similar coincidence in (q)
upper abyss
You've ended up with a confused statement. The ± doesn't make sense here
smoky stump
why?
if you root it, it would produce a +-?
and then is it correct if you do a + - you must reverse the inequality
upper abyss
And we're back to why roots aren't really the right way to discuss it
,w y^2 < x^2 - 2
upper abyss
Y'know what? I take it all back. Good solution!
smoky stump
how about for (q)
i will show you my working
So for this one, i don't know where to put the inequalities
so if i have y >= 1/x
where would i shade for the bottom left ?
wouldn't when y >= 1/x be when it is greater than the curve at the bottom left?
@upper abyss
cedar kilnBOT
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smoky stump
<@&286206848099549185>
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crisp herald
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crisp herald
I don’t know what number to use
violet rapids
So the sum of the shelves is 224
crisp herald
Yea
violet rapids
$s=\frac{1}{2}m\m=\frac{1}{2}l$
wraith daggerBOT
sills
crisp herald
I checked the back they got 128, 64 and 32 but I don’t know how they got it
violet rapids
Don't look at that
Not a really good explanation in my opinion
Use the equations I gave you
dusty plaza
small
crisp herald
Oh ok
violet rapids
The small shelf
dusty plaza
can i sit here and watch u teach as well 🙏 i should learn the quality way
violet rapids
Sure
dusty plaza
yayayay!!
crisp herald
So what do i put in as the variable?
violet rapids
The variable for what
crisp herald
Because they all have to equal 224
wraith daggerBOT
sills
violet rapids
Right?
crisp herald
Yes
crisp herald
mhm
violet rapids
s = 1/2 m
and m is 1/2 l
therefore
s = 1/2 ( 1/2 L)
$\frac{1}{4}l+\frac{1}{2}l+l=224$
wraith daggerBOT
sills
dusty plaza
OH so my variables were supposed to be l not x
violet rapids
Yes
crisp herald
So i just solve that?
violet rapids
You could have used x, y, z
It doesn't matter
Just make sure the right variables are in correct terms of eachother
violet rapids
So i just solve that?
Yup
Now you can solve for l
Then you can solve for s and m because you have those variables in terms of l
crisp herald
Lemme just try that real quick
dusty plaza
Lemme just try that real quick
how it go, fren?
crisp herald
Almost done
dusty plaza
Almost done
good!!
dusty plaza
you should get rid of the denominator with the LCM
crisp herald
Do i have to multiply 224 by 4 for that?
dusty plaza
Do i put the 224 over the 4?
yes and divide, i suppose
crisp herald
K
dusty plaza
Do i have to multiply 224 by 4 for that?
no sorry u were right
crisp herald
Im kinda confused
dusty plaza
so ur starting point is 1/4 l + 1/2 l + l = 224
crisp herald
Yes
dusty plaza
no i was right, what i got confused
crisp herald
So what do i do?
crisp herald
I tried that and thats where i got confused as well
dusty plaza
actually i multiplied by 8 instead
crisp herald
The smallest is 32
I checked back of the book
Its 32, 64 and 128
But idk how they got it
dusty plaza
yesyes and i'm so sorry for my lousy teaching
dusty plaza
better then any of my friends
LMAO tysm ily; good luck on ur studies
dusty plaza
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modern mulch
Anyone know how to finish these? really stuck and my exam is due tomorrow
cedar kilnBOT
Anyone know how to finish these? really stuck and my exam is due tomorrow
@modern mulch Has your question been resolved?
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proud oar
is this provable?
cedar kilnBOT
is this provable?
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cedar fern
Question about notation. In probability, the probability of two events happening at once is written $P(A\cap B)$. Does that mean that the probability of A happening twice (say, two heads in a row) is $P(A\cap A)$?
wraith daggerBOT
rcatalang
tropic oxide
no
there's no such thing as "A happening twice"
if your experiment consists of flipping a coin twice then you have an event for "first roll is heads" and a separate event for "second roll is heads" and their intersection is "both rolls are heads"
but $A \cap A$ is the same as $A$
wraith daggerBOT
Kanga Gang Annihilator Ann
cedar fern
so how would you write it in notation?
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bright surge
so how would you write it in notation?
you would show it as 2 separate events
bright surge
Question about notation. In probability, the probability of two events happening...
for this, we can have event 1 = heads the first time and event 2 = heads the second time
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