polar hemlock
and (a)
#help-26
topaz sinewBOT
@delicate pine Has your question been resolved?
delicate pine
violet topaz
How to write this: Question number 20
topaz sinewBOT
How to write this: Question number 20
violet topaz
I understand that we are adding +5 in previous result.
But how to write that in set-builder notation? 😀
neon iron
{X€Z | x+5}
iron frigate
5n+2
wintry venture
helo
neon iron
Count how many squares a is to the left and how many squares up
wintry venture
oh so thats how
neon iron
Sideways is x axis so the first number and up or down is y axis so second number
If point is to the left then first number will be negative
If point it down then second number will be negative
wintry venture
thank you bro, big help
minor creek
hi need help
topaz sinewBOT
hi need help
topaz sinewBOT
@minor creek Has your question been resolved?
misty sphinx
@minor creek If 9 cows haven't had calves, then 245-9 is the amount of cows that had calves, that's 236 cows.
None of them had more than 2 calves, that means some of the 236 cows had 1 calve and some had 2 calves
set x the number of cows that had 1 calve
set y the number of cows that had 2 calves
the total of cows that had calves is 236, so x+y=236, therefore y=236-x
the total of calves had by y cows is 2y because each of them had 2 calves
the total of calves had by x cows is 1x because each had 1 calve
therefore, the sum must be the total amount of calves, which is 357
2y+x=357
we found that y=236-x, so replacing:
2(236-x)+x=357
472-2x+x=357
472-x=357
x=115
minor creek
thanks byeu
dense tangle
i have tried everything
topaz sinewBOT
i have tried everything
dense tangle
i have absolutely no idea what to do here
topaz sinewBOT
@dense tangle Has your question been resolved?
dense tangle
<@&286206848099549185>
acoustic tangle
Try factoring the expression
acoustic tangle
Also, when you have 2 consecutive even numbers, one of them is definitely a multiple of 4
dense tangle
wait that makes a lot of sense
acoustic tangle
So therefore (n - 1)(n + 1) is multiple of 2*4
Now we only need to prove that n(n - 1)(n + 1) is divisible by 3
Because 24 = 8*3
dense tangle
yep
acoustic tangle
So, when you have 3 consecutive numbers
One of them is definitely a multiply of 3, right?
acoustic tangle
Yes
dull cloak
topaz sinewBOT
dull cloak
I have tried to find T1 but this gave me the wrong answer and idk where I made a mistake
topaz sinewBOT
@dull cloak Has your question been resolved?
dull cloak
<@&286206848099549185>
topaz sinewBOT
@dull cloak Has your question been resolved?
mortal thunder
I have tried to find T1 but this gave me the wrong answer and idk where I made a...
Your T_1 looks correct
Are you sure it's given wrong?
dull cloak
Yeah, I tried it a couple times and it still tells me it’s wrong… thanks for confirming my answers though! I think I’ll ask my teacher about it tomorrow.
.close
topaz sinewBOT
topaz sinewBOT
Available help channel!
thorn nova
topaz sinewBOT
thorn nova
Z is complex. Solve for Z
vital relic
didnt we get this?
vital relic
308 and 309?
thorn nova
yes
vital relic
Think geometrically
The modulus will be either 0 or 1
in both equations
Next, if z is a solution for one, clearly so must its conjugate
Because the cube of z is a real number.
thorn nova
The modulus will be either 0 or 1
how'd you decide this
vital relic
are you familiar with polar form
thorn nova
yes
thorn nova
my book never uses polar form to solve exercises tho lol
vital relic
you are solving r^3 = r
or r^3 = r^2
in either case r = 0 or 1
Then the roots must be the roots of unity, if not zero. Since they cube to make 1
thorn nova
How is the conjugate written on polar form tho?
it it like r*e^(-ix)
vital relic
yes
thorn nova
vital relic
but I am just thinking geometrically
conjugation is reflection in the real axis
multiplication is rotation.
thorn nova
isn't multiplication rotation and homothety
vital relic
the roots of unity come in conjugate pairs
thorn nova
vital relic
Just rotation if you're thinking just about the argument.
thorn nova
my books uses this term frequently
vital relic
besides, we established it is a root of unity so it has modulus 1
vital relic
just familiarise yourself with polar form...
it is used much more often than cartesian form
thorn nova
Any place to look that at? My book just shows the equation in polar form, but never really shows actual samples of exercises solved with that feature
Most of the times i try to solve using standard form of the complex numbers, so a + i*b
vital relic
idk honestly
thorn nova
Thanks anyway, I just didn't think much of geometry to solve this stuff
i thought it'd all be just algebra
The definition i studied tho for complex multiplication is this:
GEOMETRIC INTERPRETATION OF MULTIPLICATION BETWEEN COMPLEX NUMBERS
Multiplying a complex number z1 by a complex number z2 having modulus r and argument theta is equivalent to applying to the point representing z1 a rotation around the origin of rotation angle theta and a homothety of ratio r```
Is it ok?.close
lime stratus
$$-(1/5)x+(1/5)y-z+1=0$$
i would like some assistance in finding the equation of the normal line to this surface in parametric form
thorny flameBOT
Calculusstruggler
lime stratus
i know it involves the coefficients but im not too sure about how to incorporate the points
its at (4,4,1)
do i plug the points in to the x,y,z values?
sweet shard
this might be helpful
https://users.math.msu.edu/users/gnagy/teaching/11-fall/mth234/l06-234.pdf
topaz sinewBOT
@lime stratus Has your question been resolved?
sharp dew
topaz sinewBOT
sharp dew
The value of n looks weird, it should be greater than 1
Can someone check the process out for me? Is there anything illegal
Start from the blue arrow, ends at the blue underlined
mighty bane
topaz sinewBOT
chrome glen
What are you having trouble with?
mighty bane
no.1
chrome glen
Are you familiar with the concept that "per" in something like $20 per hour is like division?
With units
Like how miles per hour is just
$\frac{miles}{hour}$
thorny flameBOT
PapaBread
mighty bane
Are you familiar with the concept that "per" in something like $20 per hour is l...
no 
chrome glen
Hmm
Well like if you made 80 dollars in 4 hours
How many [dollas] did you make "per" hour
mighty bane
20
chrome glen
Ye
So "dollars per hour" is kinda like dollars divided by hours right?
Since 80 dollars/4 hours = 20 dollars per hour
mighty bane
So "dollars per hour" is kinda like dollars divided by hours right?
yes
chrome glen
And you should find with these kinds of units
That they behave a lot like regular numbers
Like for example
Unrelated to your question but still related in concept
If you multiply 30 miles per hour by 5 hours
You get 150 miles
Because when you multiply miles/hour by hour
The hours cancel out and youre left with just miles
$\frac{miles}{\cancel{hours}} \cdot \cancel{hours}$
thorny flameBOT
PapaBread
chrome glen
Your problem is no different
Except in the name of the unit
20 dollars per hour
And you wanna find out how many hours it takes to get 60 dollars
I would personally use a formula
It helps me think through problems
Especially when they get really convoluted and annoying
So similar to the earlier example
Where 30 miles per hour * 5 hours = 150 miles
Your equation would be something like
$20 \ dollars \ per \ hour \cdot H \ hours = 60 \ dollars$
static void
NICE CANCEL
thorny flameBOT
PapaBread
static void
I love that
chrome glen
Yes the cancel latex operator is very epic
static void
I will definetly be using this 🤝
chrome glen
junior widget
$2^{x-6} + 2^{x} = a * 2^{x}$
topaz sinewBOT
$2^{x-6} + 2^{x} = a * 2^{x}$
thorny flameBOT
Breeziboi
junior widget
I have tried simplifying 2^(x-6) into 2^x * 2^-6 but I still dont see how that helps... because the + 2x is still there
neon iron
$2^{x} + 2^{x} = 2*2^{x} = ?$
chrome glen
No
junior widget
...Am I missing something here
chrome glen
Im not sure
neon iron
@junior widget just factorize $2^{x}$ out
thorny flameBOT
qabrein
junior widget
How tf do I do that lol
neon iron
You should get $2^{x} * (2^{-6} +1)$
thorny flameBOT
qabrein
junior widget
$2^{x} * 2^{-6} + 2^{x}$
thorny flameBOT
Breeziboi
neon iron
Happens
thorny flameBOT
Breeziboi
junior widget
...
neon iron
Yea should be
junior widget
.close
slender fjord
topaz sinewBOT
static void
The function is continuous right
topaz sinewBOT
@slender fjord Has your question been resolved?
slender fjord
.close
inner yoke
how do i simplify 1/cos^2x / 1/sin^2x
topaz sinewBOT
how do i simplify 1/cos^2x / 1/sin^2x
leaden tusk
dividing by a fraction is the same as multiplying by it's reciprocal
inner yoke
dividing by a fraction is the same as multiplying by it's reciprocal
so would it be cos^2x/sin^2x
full sun
leaden tusk
so would it be cos^2x/sin^2x
not quite
your question is
$$\frac{\frac{1}{\cos^2(x)}}{\frac{1}{\sin^2(x)}}$$
thorny flameBOT
a disappointing son
leaden tusk
?
inner yoke
yes
leaden tusk
what would the reciprocal of the denominator be?
inner yoke
sin^2x
inner yoke
do i also multiply the denominator by cos^2x?
leaden tusk
no
you're just rearranging the problem
dividing by fraction = multiplying by reciprocal
reciprocal of denominator = sin^2(x)
so you're multiplying 1/cos^2(x) by sin^2(x)
inner yoke
the denominator goes away right?
leaden tusk
in a sense, sure
leaden tusk
mhm
inner yoke
i have absolutely no clue how to simplify from here
leaden tusk
pythagorean identity
thorny flameBOT
a disappointing son
leaden tusk
do you know how to multiply fractions..?
native arch
Im trying to review these practice questions given to us but I dont know how to solve em, I need to find the solution of the equation in the interval 0 degrees < x < 360 degrees, Idek what it means or what to do first, can someone explain the steps to me?
These are a few of the practice questions
topaz sinewBOT
Im trying to review these practice questions given to us but I dont know how to ...
static void
@native arch Lets do the first one together
So first, lets try to get x to one side
The first step should be(?):
native arch
<@!930803347865358336> Lets do the first one together
Alright
native arch
The first step should be(?):
Should we move it to one side and combine both cos x ?
Sorry if its wrong
native arch
Ah alright also i like your ganyu pfp
native arch
Like terms merge together
Would it be 2cosx then or cos^2x ?
native arch
Yeah since two variables put together should just be squared right?
mortal thunder
nope
native arch
Oh wait isnt x basically an invisible 1? So then 2y?
mortal thunder
two numbers put together are added. Variables are representatives for the numbers
static void
Think of these cos(x)'s as like terms
native arch
Alright
thorny flameBOT
sills
native arch
So after we combine the like terms it would be 2cos(x) = sqrt3
static void
So after we combine the like terms it would be 2cos(x) = sqrt3
Yup
cos(x) is still not by itsself
One last thing we gotta do
native arch
Would it be dividing both sides or one side by 2?
static void
Would it be dividing both sides or one side by 2?
Both sides
You can't modify one side
So divide both sides and you'll get ...
topaz sinewBOT
@native arch Has your question been resolved?
static void
Would it be cos(x) = sqrt3/2 or 0.86 ?
Yup
This is on the unit circle!!!
So you might have 2 answers? 👀
static void
pi/6 or 11pi/6 ?
Perfect
Sorry the problem took so long to solve
But thats basically how you do it
native arch
Ah
static void
Most often than not you will get something equal to a unit circle value
Then you'll want to solve with either degress or radians
Seems like in this problem it wants degrees since it said 0 < x < 360
native arch
Sorry the problem took so long to solve
Its alright I get it, I help sometimes in biology and chemistry so its hard to help everyone at once
static void
Im trying to review these practice questions given to us but I dont know how to ...
I need to find the solution of the equation in the interval 0 degrees < x < 360 degrees
So you want a degrees answer
static void
Would that be the final answer then or is there something we do after that?
x = 30 deg x = 330 deg
degrees circle
native arch
Lemme write this down one second
I iust asked my teacher and she said writing both of those as the answer is fine 
static void
Yay nice
native arch
So for the second question i can see tan, would i transform that into
sin(x)/cos(x)?
static void
Have you done your trig identities yet?
native arch
Yeah
native arch
i have a sheet here
so then the equation would be sin^2x - sinx/cosx cosx = 0?
I dont know how to use the bot sorry
thorny flameBOT
sills
native arch
why is multiplied ?
static void
Why is what multiplied
static void
What's next?
native arch
Sorry back but i cant really think of anything except isolating the terms or smthing like my notes say
static void
$\sin^2(x) - \frac{\sin(x)}{\cancel{\cos(x)}} \cdot \cancel{\cos(x)} = 0$
thorny flameBOT
sills
static void
@native arch
ill give u next step cus i dont want to sleep on u not finishing your math problem
native arch
Ahh i did that but i thought it wasnt allowed since one was a fraction and one wasnt
static void
$sin(x)(sin(x) - 1) = 0$
thorny flameBOT
sills
static void
Ahh i did that but i thought it wasnt allowed since one was a fraction and one w...
Division is opposite of multiplication
So the operation cancels out
static void
**sills**
Use zero product property
And solve
Ok bye goodnight have fun doing math
topaz sinewBOT
topaz sinewBOT
Available help channel!
untold solstice
What is the answer to this?
topaz sinewBOT
What is the answer to this?
untold solstice
cause if you have x = 0
then everything in the numerator is 0
in the denominator you have 0 - 0
nimble elm
Have you tried L'hopital
untold solstice
we haven't talk about it in class but I saw it in the syllabus
is it this thing?
vital relic
no.
vital relic
no
untold solstice
I just have no idea how the answer is 3
according to wolfram alpha
Idk if I'm supposed to be able to do this since they just gave me a "mock final exam" to prepare for my midterms
vital relic
I can't see how to do this without lhopital atm
wary oak
try splitting the fraction into two factors, then divide the left one by x (numerator and denominator)
vital relic
try splitting the fraction into two factors, then divide the left one by x (nume...
1/0 - 1/0 ?
wary oak
no
vital relic
taylor is the same as lhopital
mortal thunder
-,-
vital relic
Anyways, you do it ansh smh
mortal thunder
I'm sure they've been told: $\sin x = x - \frac{x^3}{3!} + \ldots$
thorny flameBOT
Ansh
mortal thunder
at least...
vital relic
thats literally using lhopital
mortal thunder
👀 realllyy?
vital relic
yes
chrome glen
The hospital rule
vital relic
lhopital is just applying taylor
mortal thunder
I feel otherwise UwU
untold solstice
Considering we technically havent even gotten to derivatives yet, ig I'll just skip this one
mortal thunder
frozen perch
nuuuuuuuuuuuuuuu
mortal thunder
hmpf @vital relic
vital relic
what?
mortal thunder
also, I don't really think discouraging people from learning few must learn expansions during their limit lessons is a good thing 👀 :ppp
vital relic
i said lhopital follows from taylor
if you use taylor, theres nothing stopping you from using lhopital
mortal thunder
I mean... sin x, tan x and cos x, ln(1 + x) are a must, (1 + x)^{n}
solemn wigeon
What is the answer to this?
If you assume the limit isn’t 0, you can find the limit of 1/(itself) and then at the end flip it again
So find $\lim_{x \to 0} \frac{1}{the function}$
thorny flameBOT
M.E.G. Yottachad
solemn wigeon
But if u get 0 for this then idk
mortal thunder
if you use taylor, theres nothing stopping you from using lhopital
except... 1) you need to be checking the form at each step
2) you need to differentiate more than just twice or several times on multiple occasions
3) L'hopital literally requires you to differentiate stuff when you've just started with your Limit lessons
so
screw L'hopital
period.
solemn wigeon
,w limit as x goes to 0 x(1-cos(x))/(x-sin(x))
thorny flameBOT
solemn wigeon
Yeah it’s good
Okay so do what I said
Flip it and use those formulae
,w limit as x goes to 0 x/(1-cos(x))
thorny flameBOT
mortal thunder
$\frac{x \cdot x^2 \qty(\frac{1-\cos x}{x^2})}{x^3\qty(\frac{x-\sin x}{x^3})}$
solemn wigeon
Oh
thorny flameBOT
Ansh
mortal thunder
that's how you'd normally do it
vital relic
except... 1) you need to be checking the form at each step
2) you need to diffe...
???
solemn wigeon
1-cos / x^2 goes to infinity
mortal thunder
huh?
vital relic
It's literally a consequence of taylor
mortal thunder
it goes to 1/2
vital relic
if you're using lhopital you are using taylor, just a shortened form
solemn wigeon
My b
mortal thunder
Shuri.. did you read?
vital relic
Why do you need to check the form at each step?
You differentiate once, and most of the time, that's it.
mortal thunder
cmon Shuri
mortal thunder
except... 1) you need to be checking the form at each step
2) you need to diffe...
what about 3) ?
vital relic
derivatives here.
mortal thunder
so? how'd you explain the √(1+x) approximations to hs precalc physics students?
by teaching them L'hopital?
or by giving them an expansion they can use for a while till they're good enough to prove it
or establish it at least
no right!?
untold solstice
<@!221421641438068746> use this
sorry what do I do with this?
vital relic
In my eyes, one is a consequence of the other, so idk.
mortal thunder
that's exactly what I'm tryna say here.. Taylor is an established series.. and I'm only advising sin x, cos x and tan x at the best
untold solstice
I can see they're equivalent but how do I manipulate it to make it work
vital relic
solemn wigeon
He can’t use it
mortal thunder
@untold solstice are you familiar with these:
vital relic
They haven't done differentiation
mortal thunder
!? if not.. it'd be nice to know them
Shuri
I'm just giving them some useful stuff to remember..
solemn wigeon
no lhopital no Taylor series
mortal thunder
!?
solemn wigeon
Mclaurin to be specific
mortal thunder
Yeah (@_@;)
well, aren't they called Taylor-McLaurin?
well whatever
It's nice to have them till you can establish them during .. idk calc 2!?
topaz sinewBOT
mortal thunder
there is one more thing you could try
untold solstice
the TA who sent me the mock exam griefed me
mortal thunder
substitution
topaz sinewBOT
Available help channel!
mortal thunder
claim!
mortal thunder
$\lim_{x\to 0} \frac{x - \sin x}{x^3}$
thorny flameBOT
Ansh
thorny flameBOT
Ansh
acoustic tangle
Why sub tho
vital relic
without anything, we only have sinx/x -> 1, (1-cos)/x^2 -> 1/2. Is it really possible to reduce to either?
mortal thunder
$= \lim_{3y\to 0} \frac{3y - 3\sin y + 4\sin^3 y}{27y^3}$
thorny flameBOT
Ansh
mortal thunder
$= \lim_{3y\to 0} \frac{3y - 3\sin y}{27y^3} + \lim_{3y\to 0} \frac{4\sin^3 y}{27y^3}$
thorny flameBOT
Ansh
mortal thunder
$L=\frac{L}{9} + \lim_{y\to 0} \frac{4\sin^3 y}{27y^3}$
thorny flameBOT
Ansh
mortal thunder
$\frac{8L}{9} = \lim_{y\to 0} \frac{4\sin^3 y}{27y^3}$
thorny flameBOT
Ansh
vital relic
u did it 🤔
mortal thunder
$L =\frac{1}{6}$
thorny flameBOT
Ansh
mortal thunder
I guess that settles it
@vital relic 👀 we would've unintentionally helped with a mock exam-
🙊
idekkk
untold solstice
well I mean isn't a mock exam basically homework
vital relic
wait u used triple angle formula lmao
untold solstice
that doesnt count for marks
vital relic
you've certainly opened my eyes for limits without series
mortal thunder
Also, it's a common practice to remember some useful results before deriving it
Like F = ma = m(v2 - v1)/(t2 - t1) in mid school lol
Having peeps remember taylor series to some commonly used functions is much better a practice than encouraging them to use L'hopital tbh
is still only my opinion tho 
@untold solstice if you got your answer from the above discussion, should I close?
.close
kind dock
Can someone help?
.close
.reopen
.close
24joithu3grwbejfawknghuan
p90UT4WJGIwhouibrjks nDFMcxsjkDIOgwru8yhnsbkldrojiwh4y8roisnjfkblbrwhuyi4rasjbnzkf
topaz sinewBOT
Available help channel!
icy pilot
@gleaming thunder @vital relic
topaz sinewBOT
<@!484702191156985877> <@!321445119171756033>
icy pilot
leaden tusk
what is your question...?
icy pilot
what is your question...?
On
I was asking what happens when there is a number other than 1 in the numerator
would it look like the 2 1/3? (different numbers than example)
leaden tusk
no, as they said that's mixed fraction notation (which is rarely used)
something like $3\frac12$ means $3+\frac12$
thorny flameBOT
a disappointing son
icy pilot
yeah but with parenthesis
leaden tusk
i guess it could be somewhat the same concept then, i guess...?
though you just need to use exponent rules
$\frac{2}{5^{-2}}=2\cdot 5^2$
thorny flameBOT
a disappointing son
leaden tusk
reverse the sign of the exponent by bringing it to the other side of the fraction
thorny flameBOT
geoxcaliber
icy pilot
or does the number on the numerator
just automatically go to the left (multiplied)
and since for the example it's a one and doesn't make a difference, it's not shown?
leaden tusk
i'm not sure what that's supposed to be
$\frac{2}{5^{-2}}=2\cdot\frac{1}{5^{-2}}=2\cdot 5^2$
thorny flameBOT
a disappointing son
leaden tusk
you could split it like that if you'd like
leaden tusk
just automatically go to the left (multiplied)
i understand what you're going for here though, and yes, the number on the numerator will just be multiplied out front, and they didn't write it in your example because it's a 1
icy pilot
Yeah I meant the -2 on the five
icy pilot
i understand what you're going for here though, and yes, the number on the numer...
in that case isn't $2\cdot\frac{1}{5^{-2}}$
thorny flameBOT
geoxcaliber
icy pilot
different from $2\cdot 5^2$ because of the 1 on top?
leaden tusk
no, the 1 doesn't change anything
thorny flameBOT
geoxcaliber
thorny flameBOT
a disappointing son
ember galleon
ember galleon
im still lost haha
sweet shard
im still lost haha
did you try sills' suggestion?
sweet shard
it's not that different. do whichever is easier for you
ember galleon
i attempted to do that with this one but i get lost at this part:
sweet shard
or better: do both and see that they give the same answer
ember galleon
step 3 i dont get
i dont understand where the 1/3 is coming from
or the 2/3 and 2/9
ember galleon
not really im kinda just brushing by in this class
sweet shard
can you take the derivative of $u e^u$ ?
thorny flameBOT
riemann
ember galleon
i dont know
sweet shard
integration by parts is gonna be hard if you don't know the product rule
this is a good refresher for derivative rules which you'll need to do integrals
ember galleon
.close
topaz sinewBOT
topaz sinewBOT
Available help channel!
summer crow
Hey, could anyone help me solve this one?
topaz sinewBOT
Hey, could anyone help me solve this one?
junior widget
Where are you stuck?
summer crow
at the very beginning of it, the 1/2 and the 1/3 confuse me
how do i multiply the 1/2 with (x-5)
so
1*(x-5)/2?
junior widget
1/2 times x = x/2 and 1/2 times -5 = -5/2
junior widget
Yes
summer crow
alright, thank you
i will try to solve it and i will tell you my final answer
I got X=9
junior widget
Yes thats right
summer crow
.close
zinc coral
I am struggling on qs 4
topaz sinewBOT
I am struggling on qs 4
velvet roost
could someone show me the steps to get the right answer? I tried two times and I got two different answers
topaz sinewBOT
could someone show me the steps to get the right answer? I tried two times and I...
velvet roost
.close
fair brook
topaz sinewBOT
fair brook
Can anyone slove c
thin goblet
Can anyone slove c
fair brook
Can you write it as a sentence
thin goblet
Clara is more likely to win as the chance that she wins (22/36) is greater than the chance that monty wins (14/36)
is that ok?
thin goblet
no problem :)
topaz sinewBOT
@fair brook Has your question been resolved?
fair brook
Yep
gusty meadow
Just doing this for fun but
topaz sinewBOT
Just doing this for fun but
gusty meadow
$7
7\sqrt(6)
42
42\sqrt(6)$
thorny flameBOT
Anthropomorphic Megaman Jowooooo
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
gusty meadow
$a_n = 7 \times \sqrt(6)^{n - 1}$
thorny flameBOT
Anthropomorphic Megaman Jowooooo
gusty meadow
**Anthropomorphic Megaman Jowooooo**
Compile Error! Click the <:errors:504266556...
I'm trying to find the n sequence for this and after a lot of trial and error I got this
mortal thunder
That has a name to it. Consider google-ing "sequences generated with common ratio"
It's called a Geometric Progression btw.
topaz sinewBOT
@gusty meadow Has your question been resolved?
gusty meadow
That has a name to it. Consider google-ing "sequences generated with common rati...
tysm! found it here https://www.purplemath.com/modules/series3.htm#:~:text=The number multiplied (or%20divided,always%20get%20this%20common%20value.
but still confused on how they did it
- Ok so I find out it's a geometric sequence
- Common ratio = $\sqrt(6)$
thorny flameBOT
Anthropomorphic Megaman Jowooooo
thorny flameBOT
Anthropomorphic Megaman Jowooooo
gusty meadow
- Plug in values, a is the first term so a = 7, r is the ratio so r = $\sqrt(6)$
thorny flameBOT
Anthropomorphic Megaman Jowooooo
gusty meadow
$a_n = 7*\sqrt(6)^{n - 1}$
thorny flameBOT
Anthropomorphic Megaman Jowooooo
gusty meadow
OH I GOT IT
@mortal thunder this looks right to you?
My steps
i followed the purple math thing
mortal thunder
decent
fair brook
no problem :)
Just To say Monty wims
topaz sinewBOT
@gusty meadow Has your question been resolved?
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gusty meadow
.reopen
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gusty meadow
.close
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.close
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cosmic tide
how
cosmic tide
ping please
empty sail
ping please
Create a proportion between the two objects
cosmic tide
the ratio is 1/2
empty sail
The ratio of the heights and the ratios of the areas
You have two heights and an area, create a proportion to find the unknown
empty sail
Yes
cosmic tide
can i do
since 5.2 is the area of 1.6
devide 5.2 by 1.6
then multiply that by 3.2 ?
empty sail
Yes
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stone adder
topaz sinewBOT
stone adder
can any1 help me with this?
topaz sinewBOT
@stone adder Has your question been resolved?
stuck wagon
do you still need help, I can show you how it's solved
granite cypress
Hello! Could somebody check if my answer is correct? Thanks!
topaz sinewBOT
Hello! Could somebody check if my answer is correct? Thanks!
@granite cypress Has your question been resolved?
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@granite cypress Has your question been resolved?
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humble nova
why is the second choice wrong and can someone please help me understand what the numbers to the left of | means?
topaz sinewBOT
why is the second choice wrong and can someone please help me understand what th...
humble nova
past kayak
In set notation, {x ∈ A | some rule} means the set of all numbers in the set A such that the rule is followed. The second choice is false because {n ∈ ℝ | 2<n<9} describes all n in the real numbers such that n is between 2 and 9. Looking at the image, you can see we aren't looking at all the real numbers between 2 and 9
humble nova
In set notation, {x ∈ A | some rule} means the set of all numbers in the set A s...
so then do I know what the diffrent symbols mean? like A and Z?
orchid void
Z is integer
humble nova
Sot he lets stated are just integers
or is R the only one
that ssays that is is a real number
orchid void
integer does not include decimal or fraction while real numbers does
past kayak
There are multiple symbols for different sets.
ℕ is the set of natural numbers, which are numbers like 0, 1, 2, 3, etc.
ℤ is the set of integers, which is the same as the naturals except it includes negative numbers, like -3, -2, -1, 0, 1, 2, etc.
ℚ is the set of rational numbers, which includes the integers but also fractions like 1/2 or 3/4
ℝ is the set of real numbers, which includes the rationals but also irrational numbers like e or π
ℂ is the set of complex numbers, which includes the reals but also numbers like 2 + 3i
humble nova
In set notation, {x ∈ A | some rule} means the set of all numbers in the set A s...
also just confirming EVERY real value would look like a parabolas right?
past kayak
Wdym a parabola?
humble nova
if we were given limits
something like this
if we were given limits too
I just want to do a practice question so I can confirm I know
past kayak
Well, the domain is all real numbers, since you can input any real number and get an answer. The range is not though; no value outputs -2, for example
Also, that graph does not correspond to that equation
humble nova
what would be a good practice question for beginners
past kayak
Idk, what are you trying to learn?
past kayak
The internet has plenty of practice problems for domain and range, I'm sure. Khan academy generally has good examples and problems
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ebon trench
I don't understand, how do I do this? No answers please, just wanna know how to do this
topaz sinewBOT
I don't understand, how do I do this? No answers please, just wanna know how to ...
wary ingot
a,b,c are some edges
ab=96x
bc=2xy
ac=y/3
ab x bc x ac=a^2 b^2 c^2 = (abc)^2 =(96x)(2xy)(y/3)
wooden matrix
a,b,c are some edges
ab=96x
bc=2xy
ac=y/3
ab x bc x ac=a^2 b^2 c^2 = (abc)^2 =(9...
Read what they wrote...
wary ingot
Read what they wrote...
what do u mean?
wooden matrix
what do u mean?
They explicitly said "no answers"
wary ingot
They explicitly said "no answers"
o sorry
wooden matrix
well yeah, it's basically the entire soln
ebon trench
oh, can you please just explain how to solve this?
wary ingot
yeah, basically u just set the edges to a, b, c
ebon trench
but thank you
wary ingot
and you can represent the surfaces in form of a, b and c
and you are done there
the rest is very easy
topaz sinewBOT
wooden matrix
$\pi=4\int_0^1\frac{1}{1+x^2}\dd{x}$ then approximate the integral w/ trapezoidal rule
thorny flameBOT
Mosh
topaz sinewBOT
@remote grotto Has your question been resolved?
real nacelle
topaz sinewBOT
mild oasis
Cant you just substitute it in equation?
So 25/4 + 11/4 = 9
36/4 = 9
9 = 9?
Oh lol read the question wrong
y - y1 = m(x - x1)
real nacelle
Yes I did that but I still got it wrong.
mild oasis
Did you calculate the slope?
real nacelle
Change in y/ change in x right?
mild oasis
Umm i guess in linear equations yes
But this isnt a linear equation
$y^2 = 9 - x^2$
thorny flameBOT
Pluton
real nacelle
y=3-x
thorny flameBOT
Pluton
$y = $sqrt 9 - x^2$$
```Compilation error:```! Missing $ inserted.
<inserted text>
$
l.55 $y = $sqrt 9 - x^
2$$
I've inserted a begin-math/end-math symbol since I think
you left one out. Proceed, with fingers crossed.```
real nacelle
square root x^2=x no?
mild oasis
Yes this
real nacelle
Huh?
loud dawn
@real nacelle it says $$\sqrt{a+b} \neq \sqrt a + \sqrt b}$$
thorny flameBOT
abs_0
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)
loud dawn
Think about it: sqrt(16 + 9) = 5 ≠ sqrt(16) + sqrt(9)
mild oasis
Basically
(A + B)^x is not A^x + B^x
real nacelle
Ok.
mild oasis
And sqrt is just raised to 1/2
loud dawn
Anyway
loud dawn
Just surround math expressions with $’s
thorny flameBOT
Pluton
loud dawn
Well you could also have $$y = -\sqrt{9 - x^2}$$
mild oasis
Oh well now basically
thorny flameBOT
abs_0
mild oasis
$$f(x) = \sqrt{9 - x^2}$$
thorny flameBOT
Pluton
loud dawn
Wait what about the negative tho
mild oasis
Wait what about the negative tho
Meh same function just with a - to x
loud dawn
Not the same, it’s important to know why we wouldn’t use “-“ here
mild oasis
Because we are looking for a slope
loud dawn
Yeah we are
mild oasis
And 1 point x has 2 slopes here
1st slope = - 2nd slope
loud dawn
True but
If the point given had a negative y value
You’d have to use the -sqrt equation
Yeah
mild oasis
$$\d/dx{\sqrt{9 - x^2}}$$
thorny flameBOT
Pluton
loud dawn
@real nacelle can you use calculus
mild oasis
I think he must use calculus
real nacelle
Actually guys I got the answer
mild oasis
How did you get it?
real nacelle
It is change in y over change in x
loud dawn
How’d you get the change in y lol
mild oasis
It shouldnt be?
mild oasis
How’d you get the change in y lol
Also that
real nacelle
After you do this and simplify you get
loud dawn
The radius is perpendicular to the tangent line
loud dawn
The slope from origin to that point is the negative reciprocal of the tangent slope
mild oasis
The slope should be
$$-x/\sqrt{9-x^2}$$
thorny flameBOT
Pluton
mild oasis
@real nacelle did you get the b tho?
I mean you already got the slope so getting the b shoulent be big of a problem
frail gyro
What’s the diffrence of $/litre and litre/$
topaz sinewBOT
What’s the diffrence of $/litre and litre/$
thorny flameBOT
InLoveWithLearning
chrome glen
Wdym
brittle zodiac
liter and litre?
topaz sinewBOT
@frail gyro Has your question been resolved?
frail gyro
Do you mean in terms of units?
Yes
Like remember when you were teaching me
And you successfully did so
But
I forgot how to diffrentiate the diffrence of them
Like $/litre vs litre/$
chrome glen
Oh you mean money
frail gyro
Yea
chrome glen
I thought you were trying to do something with the tex bot
frail gyro
Oh no lol
chrome glen
dollars/liter would be like the price of a liquid per liter
mild oasis
Ohhhhh
chrome glen
liters/dollar would be like the amount of liters you can buy with a dollar
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desert bolt
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desert bolt
When I need to find the tangent line for this equation can’t I just use the power rule ?
desert bolt
Why when I use the actual formula I get something different
alpine dirge
wdym
desert bolt
Like the instanous rate of change formula
leaden tusk
the limit definition?
desert bolt
Yea should the equation of the tangent line be y=6x-11
leaden tusk
no
desert bolt
The derative is -6x plus 1 right
leaden tusk
yeah
desert bolt
So don’t I just plug in the -1 to find the slope of the tangent line
leaden tusk
mhm
alpine dirge
So don’t I just plug in the -1 to find the slope of the tangent line
i think you computed the slope wrongly lol
leaden tusk
wrongly
desert bolt
How
leaden tusk
how is -6(-1)+1 = 6
desert bolt
Oh I need to account for the one aswell
Sorry I did not realize that
So the slope is 7
alpine dirge
yea
alpine dirge
y - 4 = 7 (x + 1) yea
desert bolt
Huh
desert bolt
What is that
leaden tusk
desert bolt
Can’t we just do -4 is equal to 7x plus 1
desert bolt
Ok idk how to be we do it
leaden tusk
huh
desert bolt
So slope of the equation is 7
leaden tusk
mhm
desert bolt
How do we do that
leaden tusk
you might want to invest in learning point slope form
static void
$y - y_1 = m(x - x_1)$
thorny flameBOT
sills
alpine dirge
this comes much before derivatives
leaden tusk
it comes before calculus lol
static void
where x1 and y1 is the point where the line is tangent to the curve and m is the slope at x1, y1
topaz sinewBOT
@desert bolt Has your question been resolved?
polar oasis
how does a network model works ?
topaz sinewBOT
how does a network model works ?
polar oasis
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