but i dont know whats the next step with the 2nd part
#help-13
timid sparrow
coral jewel
i asked first not
you left your channel to timeout, its only natural someone would claim it
open a new one
coral jewel
wheres the sqrt
ruby tree
umm you raised to the power of 2 kinda incorrectly i think. before doing so you should get the sqrt3/3 cos(x) to the other side together with the 1
timid sparrow
wheres the sqrt
shit i forgot about that
ruby tree
yeah you essentially turned this into a sqrt function
well not if you get it to the side thats what i am saying
you should leave the sqrt alone in one side
and it will just go
timid sparrow
you should leave the sqrt alone in one side
ok i will try that
coral jewel
you should leave the sqrt alone in one side
you are asking to square both side?
ruby tree
you are asking to square both side?
yeah
coral jewel
nuh uh, thats gonna introduce redundant roots
ruby tree
nuh uh, thats gonna introduce redundant roots
what?
coral jewel
which you have to retest it into the original equation again
ruby tree
oh well yes obv
timid sparrow
nuh uh, thats gonna introduce redundant roots
what is a redundant root
coral jewel
oh well yes obv
but with my approach you dont need to, in fact retesting root is less than ideal...
ruby tree
but with my approach you dont need to, in fact retesting root is less than ideal...
well idk if you get him to understand your way then sure
coral jewel
what is a redundant root
squaring both hand will introduce roots that is true on squared, but necessarily isnt for the original equation
like i said, this is less than ideal, and you are FAR better off trying my approach
timid sparrow
squaring both hand will introduce roots that is true on squared, but necessarily...
like when you have negative numbers?
timid sparrow
like i said, this is less than ideal, and you are FAR better off trying my appro...
could you explain in simpler terms
coral jewel
ok so can you resend the original equation
timid sparrow
wraith daggerBOT
فطر
timid sparrow
ye
timid sparrow
1 and square of 3 / 3
wraith daggerBOT
فطر
timid sparrow
ok
coral jewel
what is $\sqrt{a^2+b^2}$?
wraith daggerBOT
فطر
timid sparrow
pythagoras theorem?
timid sparrow
square root of (4/3)
coral jewel
so $\frac{2\sqrt3}3$
wraith daggerBOT
فطر
timid sparrow
ye
coral jewel
**فطر**
now, divide each hand of your original equation with this
it will work out, trust
timid sparrow
ok
coral jewel
tell me what you got
timid sparrow
this
timid sparrow
ye
coral jewel
send me what you got again
timid sparrow
coral jewel
ok anyway
so the final equation is
$\cos{\frac{\pi}6}\sin x+\sin{\frac{\pi}6}\cos x= \frac{\sqrt3}2$
now
timid sparrow
how?
coral jewel
can you tell me cos(?) = sqrt3/2?
timid sparrow
pi/6
coral jewel
and sin(?)=1/2?
timid sparrow
pi/6
wraith daggerBOT
فطر
coral jewel
can you apply the angle addition formula now?
timid sparrow
sin(pi/6 + x) = square root of 3 / 2
coral jewel
well, not -
coral jewel
its because i guided you literally step by step
this is quite literally the easiest way to tackle any question in this form
timid sparrow
i just didnt know that thing of dividing by square root of a squared plus b squared
coral jewel
now that you know
coral jewel
sin(pi/6 + x) = square root of 3 / 2
anyway, can you take it on from here now?
timid sparrow
ye i can
but my teacher is way too strict with the formulas we can use
so i have to see if he will allow me to use this one
cedar kilnBOT
If you are done with this channel, please mark your problem as solved by typing .close
cedar kilnBOT
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crimson sedge
can someone help me how to solve the quotient rule
cedar kilnBOT
can someone help me how to solve the quotient rule
onyx oyster
can someone help me how to solve the quotient rule
like prove it?
crimson sedge
here is the example
onyx oyster
so you want to know how to apply it?
crimson sedge
i get it a little bit but i still get confused when the given is long
onyx oyster
or how to prove it
digital cliff
you can prove it with the product rule relatively easily
sonic thistle
digital cliff
product rule is more derived from the limit definition of derivatives as far as im aware
crimson sedge
this my solving idk if its right i got confused mid way
digital cliff
,rccw
wraith daggerBOT
digital cliff
your derivatives are wrong for u and v, and i dont like the way youve written it either
saying u=u' and v=v' is incorrect process
crimson sedge
how is that wrong
digital cliff
tell me how you got 4 and 3x
crimson sedge
ok so i got the 4 by multiplying the 2 to its x^2 and i got the 3x by applying the power rule
digital cliff
youre not doing either thing right
crimson sedge
how so 😢
digital cliff
2x^2-4x+5 differentiated to 4x-4
by the power rule
x^3+10x^2 goes to 3x^2+20x
x^n -> nx^(n-1) remember
digital cliff
si
i think you should review power rule a bit more before looking at the quotient rule
crimson sedge
wait
can u answer that one for me
dw its just an example my reviewer
not a hw or smth
digital cliff
,w differentiate (2x^2-4x+5)/(x^3+10x^2)
wraith daggerBOT
digital cliff
the factoring on the bottom is they factored out x from inside the bracket
cedar kilnBOT
@crimson sedge Has your question been resolved?
brazen girder
Can someone knows how to create truth table about this? Thank you
orchid panther
Start by drawing two columns and 4 rows for the 4 possible truth values for p and q
p q
0 0
1 0
0 1
1 1
For example
Then the other columns would be the other different statements
For example youd have one column for p <-> q implies (not p or q), another for p implies (q and p) and so on
brazen girder
For example youd have one column for p <-> q implies (not p or q), another for p...
Yeah but how do you if its true or false ?
orchid panther
Wdym
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Available help channel!
buoyant jackal
Please help me with this one
cedar kilnBOT
Please help me with this one
buoyant jackal
I tried a lot but can't be even close to the answers
buoyant jackal
make a and b fulfill the remaining factors needed for 99
what?
buoyant jackal
99=3^2\*11
12=3\*2^2
we can write directly as 9 * 11 and 3 * 4??
digital cliff
im doing prime factors
12=2^2 * (3) and 99 is 3^2*11
so a and b need to have 3 and 11 as factors
not both, just either or
then again it wouldnt matter
if 12ab has the prime factorisation of 99 as a factor, then it is a multiple of 99
is what im getting at
digital cliff
with 12ab being a 4 digit number
ah
buoyant jackal
like it means 99 * something = 12ab
buoyant jackal
okkk
there is one more
i know like y will be odd
y = (763 - 2x)/3
by this
rigid lava
why is that odd
buoyant jackal
see
wait
sorry y = positive
oh, i got it
Can you plot root over root n on number line?
cedar kilnBOT
@buoyant jackal Has your question been resolved?
sweet badger
this question is from the topic differentiability....Can sm1 help me understand this question ..and help me solve this question.....
final crag
this is really not readable at all but you can find dy/dx by noting dy/dx = (dy/dt) / (dx/dt)
and then find d^2y/dx^2 by differentiating that again
sweet badger
final crag
this is really not readable at all but you can find dy/dx by noting dy/dx = (dy/...
yeah so use this
what have you tried?
you have $\frac{dx}{dt} = ap \cos pt$ for example
wraith daggerBOT
OssihLikesBlue
final crag
you can similarly find $\frac{dy}{dt}$ and then $\frac{dy}{dx} = \frac{\frac{dy}{dt}}{\frac{dx}{dt}}$ and then differentiate that with respect to $x$ to get $\frac{d^2y}{dx^2}$
wraith daggerBOT
OssihLikesBlue
final crag
@sweet badger
sweet badger
ohh ....Thank you
cedar kilnBOT
@sweet badger Has your question been resolved?
balmy yoke
need help with e)
cedar kilnBOT
need help with e)
balmy yoke
my answer is -16/21
but in my answer key its -16/63
but I double checked and all my steps look correct
mental trail
show your work
balmy yoke
ok
digital cliff
what did you get for tan x and tan y
wraith daggerBOT
digital cliff
how were you cancelling in an addition?
mental trail
'simplifying 3 with -12' is something you do with multiplication, not addition
for addition, you put everything on the same denominator
cedar kilnBOT
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Available help channel!
crimson sedge
How can i show this limit
cedar kilnBOT
How can i show this limit
crimson sedge
Maybe using lhopitals?
cedar kilnBOT
@crimson sedge Has your question been resolved?
crimson sedge
<@&286206848099549185>
ruby tree
Maybe using lhopitals?
maybe idk try make the fractions like fractions and then lhopitals
but idk where that would lead
crimson sedge
The denominator stays 0
cedar kilnBOT
@crimson sedge Has your question been resolved?
amber oriole
Hi can sm1 explain the approach to this problem?
cedar kilnBOT
Hi can sm1 explain the approach to this problem?
amber oriole
like let's say I pick a chairperson from the committee
well then there would be n choices
and then out of the (n-1) ppl, i make a comittee of any size
why would it be 2^(n-1)?
on the left hand side, if I pick k ppl to form a committe from an n large group, then the number of ways to pick those k ppl would be nCk
and then from those k ppl I chose a chairperson, there would be k choices to pick a chairperson
but then why is there a summation sign on the left?
<@&286206848099549185>
<@&286206848099549185>
fathom night
like let's say I pick a chairperson from the committee
well then there would be ...
For the remaining (n-1) people there's 2 choices of whether they're included or not so 2^(n-1)
fathom night
For the summation the committee size can range from 1 to n
So you account for committees of all possible sizes
From k=1 to n
amber oriole
OHHHH
cuz u want to dtermine the total possible
number of ways
but k can go from 1 to n
so u need to sum over to get the total possible
ok ok
aight thank u
fathom night
👍
amber oriole
.close
cedar kilnBOT
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Available help channel!
opaque bane
cedar kilnBOT
opaque bane
Please help
modern compass
Please help
what do you have for a definition of prism?
opaque bane
what do you have for a definition of prism?
Opposite sides are equal and cross section is constant
C d e was my first thought
modern compass
so which objects meet that definition, or which can you exclude because they fail?
modern compass
are the cross sections of C constant?
opaque bane
are the cross sections of C constant?
If it was rotated yes but in this form no
But for my answer I put d and e but it said I was wrong
modern compass
If it was rotated yes but in this form no
apply that reasoning to A
modern compass
Also, because one face of C is larger than the back face, if you cut it perpendicularly (which you should be doing) the cross sections won't be constant
C is the bottom part of a very tall, narrow square pyramid.
so it is not a prism.
opaque bane
So it’s a, d, e
Would this be the final answer?
modern compass
yes
opaque bane
Same
cedar kilnBOT
@opaque bane Has your question been resolved?
cedar kilnBOT
@opaque bane Has your question been resolved?
crimson sedge
cedar kilnBOT
crimson sedge
????
modern compass
do you know about Riemann sums?
cedar kilnBOT
@crimson sedge Has your question been resolved?
crimson sedge
do you know about Riemann sums?
Yes
orchid valley
how would i go about solving this? i dont know where I went wrong because i followed the accompanying video
crimson sedge
how would i go about solving this? i dont know where I went wrong because i foll...
Use the power series formula
f^n(a)(x-a)^n/n!
Then find the pattern with that
Then the interval of convergence is found by taking lim n—> inf a(n+1)/a(n)
cerulean sail
(what may help more is if you can relate the original function to something that's "close enough" to something you know the power series for, then use that...)
orchid valley
Use the power series formula
this the formula?
crimson sedge
(what may help more is if you can relate the original function to something that...
is that even practical for this function?
which fuynction
crimson sedge
this the formula?
no this is the formula
opal schooner
$\sum_{n=0}^{\infty} ax^n = \frac{a}{1-x}$
wraith daggerBOT
Triaxyz
opal schooner
-1<x<1
crimson sedge
i mean if he doesnt know the formula for power series
why would he use the fast way
to use substitution and such
u havew to understand the mechanismns
to an extent
for substitution
cerulean sail
this the formula?
(also if you know this, you know the power series for related functions, such as 1/(1 + x) and ln(1 + x) 
)
opal schooner
because taylor series expansion is unnecessarily complicated for a function like this
orchid valley
yea i havent learned taylor series yet
crimson sedge
i think for someone who doesnt know the formula
the fast way
is dumb
yes then learn the formula
haha
dont do substituion stuff yet
crimson sedge
do it 3 times then just find the pattern and eventually learn
the subsitution
stuff
@orchid valley
orchid valley
you usually learn geometric series before taylor
yeah taylor series is literally the last thing in my class lol
crimson sedge
you already did polar/parametric?
opal schooner
then dw about doing taylors if you havent covered it
you know geometric series yes?
orchid valley
yes
opal schooner
zhats literally all you need then
opal schooner
**Triaxyz**
try turning your function into the right hand side of this format
orchid valley
i got
opal schooner
,w x / (15x^2 + 1) = (x/15)*(1 / (1-(- x ^2 / 15)))
wraith daggerBOT
opal schooner
1sec
opal schooner
i got
they are not the same
when you distirbute this, you get $\frac{x}{15+x^2}$ which is not f(x)
wraith daggerBOT
Triaxyz
orchid valley
ah thats true
cedar kilnBOT
Available help channel!
formal pasture
how do i find irc of this
cedar kilnBOT
how do i find irc of this
formal pasture
instantaneus rate of change
low holly
You can use the quotient rule to find the derivative here
low holly
instantaneous rate of change is just the derivative of the function i believe
low holly
Yeah that works too
low holly
But you're missing a minus sign in between
formal pasture
oh yesyes
formal pasture
like what do i do with this
low holly
( f(v+h) - f(v) )/ h
formal pasture
yea
low holly
f(v+h) is adding h to v, not adding h to f(v)
low holly
suppose it was easier and f(v) = 1/v
formal pasture
what do i change
low holly
what would f(v+h) be?
low holly
That would be f(v)+h
formal pasture
so where do i add h
low holly
to v
low holly
Well yes, f(v+h) is evaluating the function f at the number (v+h), which is a different number than (v)
low holly
For example, if $f(x) = \frac1x$, then $f(x+h)=\frac{1}{x+h}$
wraith daggerBOT
π=√g
low holly
Almost, why is there v^2 + h in the bottom?
wraith daggerBOT
formal pasture
like rhis?
low holly
You're adding h to v, not v^2 remember
(and you have to put parentheses for the numerator)
wraith daggerBOT
formal pasture
like this?
low holly
$$\frac{1600 (v+h)}{(v+h)^2 + 6400}$$
wraith daggerBOT
π=√g
low holly
Yeah, add to v
formal pasture
why r we squaring h
low holly
Basically replace all the v with v+h
wraith daggerBOT
formal pasture
so like this
low holly
Yeah but good luck working with that
formal pasture
eevbecrvr
low holly
Are you sure you need to use limits to prove this?
formal pasture
yes
low holly
Ok well, expand the square, then put both fractions on the same denominator, add the terms in the numerator, and simplify
formal pasture
Ok well, expand the square, then put both fractions on the same denominator, add...
then
cedar kilnBOT
@formal pasture Has your question been resolved?
lilac knot
mental eagle
Hello! I'm trying to figure out how to isolate y" in this diffeq. I've used the langmuir-blodgett relation for the e^x but im quite stuck on the rest. I can't use numerical methods, and must do it algebraically
mental eagle
I would be happy to clarify the problem if the handwriting is unclear
cedar kilnBOT
@mental eagle Has your question been resolved?
crimson sedge
pls help with how to start this related rates
cedar kilnBOT
pls help with how to start this related rates
acoustic quartz
Do you know the formula for volume of a cube
crimson sedge
pls help with how to start this related rates
Relate the sides to volume by using side lengths
A = side * length
Volume*
ok
So if volume = side * length
And the equation for a side is x^2
Then try to get surface area
In that equation
Ok
sorry I am still a bit lost
V=x^3
Surface area = 6x^2
Solve for x^2
Plug into volume
Perhaps that will help
but I need to take the derviative
when do I do that
When you relate the two
acoustic quartz
U can derive volume of cube formula
then plug in what u know
dv / dt = 3s^2 ds/dt
sides are 10, dv is 20
crimson sedge
Find ds/dt by deriving S = 6x^2
acoustic quartz
Find ds/dt by deriving S = 6x^2
Would u also be able to find it deriving volume?
crimson sedge
Ahh ok so ds/dt = 12x
We need to be careful here
Dv/dt = side length ^2 dsidelength/dt
And Dsyrface area/dt = 12x dx/dt
if you call both s you will confuse urself
Make the lengths a variable
And make the surface area a different variable
acoustic quartz
if you call both s you will confuse urself
Wait whatd u get as an answer
cause when i did it i got 8
acoustic quartz
Let me attempt
lmk what u get
crimson sedge
lmk what u get
i got 8
acoustic quartz
dV/dt = x/4 dS/dt
Whats happening here?
crimson sedge
Whats happening here?
All the substitution
acoustic quartz
i see
crimson sedge
i did it like this. v=x^3. dv/dt = 3x^2(dx/dt) I solve for dx/dt. then I differintate surface area = 6x^2/ so we get ds/dt = 12x(dx/dt) I subsisute the value of dx/dt and the value of x = 10
Related rates is all about finding equations that relate the two
Things
That are changing
With respect to eachother
@crimson sedge @acoustic quartz thank you for the help
now I got it
crimson sedge
<@456226577798135808> <@711469140736475146> thank you for the help
No worries
final hornet
cedar kilnBOT
final hornet
!status
cedar kilnBOT
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
sly abyss
System of equations
sly abyss
Or quite frankly
The easiest way to do this problem with a calc
Is exponential regression
inland stirrup
Do two points define a unique exponential?
final hornet
can we get of b^-2 by multiple b^-1 on both side
sly abyss
?
inland stirrup
Wat about y = ab^cx?
final hornet
Okay
inland stirrup
Why not?
final hornet
...
inland stirrup
U can also do y = ab^cx +d?
sly abyss
Bro
Why tho
Why not just make it in the form of a x b^x
It’s whole numbers
If you do that way
a and b are both whole numbers
inland stirrup
Because idk if two points will uniquely define an exponential function
sly abyss
Find a formula
The questions says
Keep it simple.
@final hornet
What have you tried?
final hornet
Sorry I got a bit distracted with the dicussion
sly abyss
No worries
inland stirrup
We still need to figure out the uniqueness
sly abyss
All due respect the problem isn’t asking anything about that
tender beacon
inland stirrup
All due respect the problem isn’t asking anything about that
Oh so any random exponential function that satisfy both points will work?
inland stirrup
If you add plus c youll get all of the possible equations
Cuz youll have theree variable and two equations right?
sly abyss
Man just find the simplest equation
inland stirrup
It also says "open response"
inland stirrup
They want the student to talk about all the possible functions
sly abyss
Bro 😭
final hornet
So could we remove b^-2 with * b^2?
sly abyss
nah I wouldn’t do that
Easiest way
Divide the top of an bottom
So you have 128/.125= a/a x b^5
1024
b^5
b=4
128= a x 4^3
128=64a
a =2 , b=4
Sorry I have to go soon
So I just told you the answer but
f(x)=2(4)^x
sly abyss
Have fun and go solve that yourself
inland stirrup
Bruhh, its the proper solution
sly abyss
Not the proper solution
It says find a formula
Standard form of an exponential
Is y= a(b)^x
inland stirrup
U are forgetting about the other solutions
sly abyss
Ok go and find these other solutions and report back to me
I’m going to find the easiest solution
Because the problem asks for one solution
sly abyss
Bro you are getting on my nerve 😭
inland stirrup
Just for education try to find the general solution
sly abyss
Read
sly abyss
Ye have fun with that
final hornet
So you have 128/.125= a/a x b^5
@sly abyss Ty I try your method
inland stirrup
Ye have fun with that
There no way u a mathematician
final hornet
@sly abyss Should I leave this open or close?
sly abyss
You can close
inland stirrup
U should at least tell that its not unique
final hornet
.close
cedar kilnBOT
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Available help channel!
pale creek
cedar kilnBOT
feral isle
Ok so
Try factorizing the numerator in the first parenthesis
And the denominator in the second parenthesis
Result should be -4 I think
bleak flame
how do you factor (x^2-4)?
(x+2)(x-2) difference of two squares
bleak flame
also 3x-6?
3(x-2)
prisma gull
(x+2)(x-2) difference of two squares
great thanks
cedar kilnBOT
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pale creek
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civic meteor
Hi, I have a question about vector functions.
Why is derivative of speed d|v(t)|/dt not equal to magnitude of acceleration |a(t)|?
civic meteor
just like speed is distance/time shouldn't magnitude of acceleration be speed/time?
e.g when solving for min/max speeds setting d|v(t)|/dt = 0 would solve for t value where min/max occurs but why cant you just set |a(t)| = 0 to solve for t
when i tried doing this, i got difference answers
hollow trail
you can have a nonzero acceleration when the speed isn't changing, because acceleration can change direction as well as speed
e.g. if an object is moving in a circle at constant speed it has a constant nonzero magnitude of acceleration (to change direction), but its speed is constant, so the derivative of speed is 0
cedar kilnBOT
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sweet ridge
hello
sweet ridge
merp
need help
a family have 5 childrens. the oldest age 2 times the youngest, while 3 others age less 3 years from the oldest, 4 more years then the youngest, and less 5 years from the oldest. If the average of their age is 16 years, so the quadrat of difference between 2nd child and 3rd child is:
sorry if bad translate
so my answer is:
please ping!
fallen moat
i just realize somethig
what happened?
sweet ridge
uhhhh
sweet ridge
one more e in the 3rd box should fix the rest
fallen moat
2e+2e-3+e-4+2e-5+e
like that?
sweet ridge
yeah the answer allow .5...
cedar kilnBOT
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Available help channel!
covert raptor
cedar kilnBOT
covert raptor
for the third paragraph
what does it mean for the notations?
like what is g(x) refers to?
what is the "x"?
TIA
cedar kilnBOT
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covert raptor
.close
magic solar
Hi guys, for b)ii), im struggling to algebraically manipulate it into the form.
pastel vault
Hi guys, for b)ii), im struggling to algebraically manipulate it into the form.
Comparing coefficients, -(1 + i) = -1 - i is z0
And indeed the conjugate of z0 is -1 + i = -(1 - i)
And also you can see what r^2 is from this: be careful of the minus sign
magic solar
hmm
r^2 is one
wait
r^2=-1 so r=i?
ah I see, I wasn't really using part a) which made it 10x more difficult than it needed to be
wait what am i saying
r is real smh
pastel vault
r^2=-1 so r=i?
Yep
magic solar
oh what
but isn't this saying that the modulus of a point shifted is r, so r must be real?
pastel vault
We're in the complex plane so the radius can actually be an imaginary number
pastel vault
but isn't this saying that the modulus of a point shifted is r, so r must be rea...
It's saying the radius is in a dimension perpendicular to the xy-plane
Like the circle will be vertical
magic solar
the answers say the radius is 1, im guessing its the same thing?
pastel vault
pastel vault
the answers say the radius is 1, im guessing its the same thing?
Yeah so of course you have to take the modulus of i so 1
magic solar
ah
pastel vault
This is the graph of f(z) = z^2 + 1 for when z is a complex number
We're using the 3rd dimension to represent what happens when z has an imaginary part
And y is still the output of the function
So that explains the vertical circle part
pastel vault
We're in the complex plane so the radius can actually be an imaginary number
I should say the radius vector here
magic solar
although
this would make the equality in a) not entirely true would it?
it would have to be |r|^2 ?
pastel vault
it would have to be |r|^2 ?
Nah so there -r^2 = 0
So r = 0
Yeah so it would just be a single point
A degenerate circle
magic solar
dang circles can be degens too
pastel vault
Yep
So it comes naturally from the definition
You just have to ask the right questions to see what maths tells you about those weird situations
pastel vault
True
cedar kilnBOT
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foggy estuary
Henlo, I'm kinda stuck on this question
cedar kilnBOT
Henlo, I'm kinda stuck on this question
foggy estuary
They ask to simplify
candid mason
So what are key theorems for exponents/indices?
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peak minnow
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peak minnow
By rotation of axis, eliminate xy term. Identify the conic and its elements
Supposed to be a hyperbola, but i can't seem to remove X and Y terms to get that
Would like help in here
delicate elm
are you trying to solve the equation at the very top
peak minnow
are you trying to solve the equation at the very top
Idk bro
This is the question
And the one I'm trying to solve is a part of this
<@&286206848099549185>
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slow fiber
when would you go from rectangular to spherical coordinates
cedar kilnBOT
when would you go from rectangular to spherical coordinates
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slow fiber
.close
river silo
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swift terrace
think of the transformations being made
first of all you have -x
which does what?
river silo
-x makes a reflection along the y axis
river silo
four units to the left
river silo
which moves it 3 units up
swift terrace
and that's all you need 😉
river silo
🙂
swift terrace
first flip, then move 4 then add 3
river silo
what would it look like if i reflected it along the y axis
river silo
yes
swift terrace
river silo
swift terrace
gladly
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stone tulip
5n^2 +12n+6=0
cedar kilnBOT
5n^2 +12n+6=0
crimson sedge
@stone tulip
hot crag
@stone tulip ?
split pike
5n^2 +12n+6=0
Try using Quadratic formula, rational root theorem, factorization by middle term splitting or by completing the square to find the values of n
hot crag
Try using Quadratic formula, rational root theorem, factorization by middle term...
a. RRT isn't necessary
b. factorization is just unnessary
c. CTS is tedious with this and jjust is
stone tulip
Forgot to dm you..
hot crag
sure
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.reopen
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✅
wraith daggerBOT
ren
stone tulip
@hot crag ? :))
hot crag
?
hot crag
<@1158357921290260500> ? :))
ye?
stone tulip
You told me to come back here so you could help
stone tulip
U do -6 to start out?
wraith daggerBOT
ren
hot crag
uh
one sec
alr
simplify
also
one thing's wrong
you wrote -(12)^2 outside the sqrt
it's -b not -b^2
cedar kilnBOT
hot crag
alr
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paper sentinel
I’m so confused on how to do this, I know log2x is x=2^y but I do not know how to multiply the -2 or add the 4. I keep getting the wrong graph.
jolly jay
I’m so confused on how to do this, I know log2x is x=2^y but I do not know how t...
it would be easier to come up with some points to plot and connect the dots
paper sentinel
How though
jolly jay
plug in x values into the function
so let's take x=2 for example
what would -2 log_2(x) + 4 be
paper sentinel
That’s what I been trying to do but I keep getting it wrong I did -2(2^1)+4 and it gave me the wrong answer
jolly jay
so log_2(x) = 1
the log_2 asks "what number do I raise 2 by to get this number"
so if u wanna do log_2(2), you're asking "what number do I raise 2 by to get 2"
the answer is 1 right
so log_2(2) = 1
(not 2^1)
jolly jay
yeah, you're finding the right answer but you're plugging in 2^y instead of y
jolly jay
don't worry about the entire function for now
what is log_2(4)
paper sentinel
2^4? Idk
jolly jay
the log_2 asks "what number do I raise 2 by to get this number"
so if u wanna do log_2(4), you're asking "what number do I raise 2 by to get 4"
what is log_2(4)
paper sentinel
2
jolly jay
yeah
now we have that function y = -2 log_2(x) + 4
what do you get if you plug in x=4
paper sentinel
Ok I think I get it
paper sentinel
Thank you that was very helpful
jolly jay
yeah np
paper sentinel
I have another problem but it’s kind of different can I send it
weak otter
Yes
paper sentinel
paper sentinel
Idk how to do that
weak otter
Can you guess what the first step would be
paper sentinel
I think that’s the number the graph almost touches
hollow totem
I think that’s the number the graph almost touches
Yeah
Since for log(x); x must > 0
so x -1 must always > 0; thus x > 1
also
log base 2 also gives us a clue
as log_2(2) = 1
We can probably guess the shape of the graph to look like this
paper sentinel
Log_2(1) is 0?
hollow totem
Log_2(1) is 0?
Thats too
For graphing problem, the question tends to want u to find special point/feature of the function
For this region, we can argue since the growth of the log function is extremely small, and the different of x is small too
We could just assume, the graph looks like a line
So it will look like this
paper sentinel
Ok got it thanks 👍
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pulsar schooner
guys i need urgent help with stereometry. Im preparing for a test and started revising just fine until i run into the same problem again and again and again. The problem is about finding the distance between a point and a plain. Im struggling to understand how do i find where the intersection is, or when it is given - what to do with it. Here is one of the problems ive been stuck on.
- In a cube ABCDA1B1C1D1 point M is the center of the edge A1D1=1 and point N is from edge D1C1 such that D1N = 2C1N. Find the distance between point B1 and the plain (MBN)
pulsar schooner
I know that i need to build a triangle with the perpendicular but where and how I have no clue
heres a very messy image of what ive drawn so far (sorry its rotated)
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pulsar schooner
i just solved a problem not too different from this but again i assumed. I needd a specific method that tells me how and why i do what i do. I will write this new problem down here and then my solve. If you can please tell me why it worked out because i have no idea what i did
2)the base of a pyramid ABCDM is the rhombus ABCDS. The outer edge (idk the english term) BM is perpendicular to the base plain. The side and the diagonal BD of the rhombus are equal to 4 and the distance from point B to the outer plain CDM is equal to the square root of 3. Find the volume of the pyramid
solution) so starting off i found the altitude of the rhombus to be equal to 2sqrt of 3. Than i built a triangle BHM with point B1 laying on HM being the point which connects the plain CDM with point B at a 90 degree angle ( a perpendicular) and H such that BH is the altitude of the rhombus. From there using pythogor's theorem i found HB1 to be equal to 3 and using equalatheral triangles (BHB1 and BHM) i found BM to be 2. Than i jsut plugged everythign in the formula for the volume.
My main concern is why did buildign triangle BHM work
what says that the altitude of the rhombus lies on the same plain as the distance between B and CDM. For me it was just intuition but i need a certain proof that i can understand and use without overthinking it
and what do i do in the case of the first question where i have no idea where to build the triangle
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@pulsar schooner Has your question been resolved?
coral fulcrum
cedar kilnBOT
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crimson sedge
crimson sedge
Hello sorry I lost the channel I previously was on
royal loom
crimson sedge
Many apologies
shut pier
hey