onyx viper
Thank you for the clue! My workings are a bit of a gobbled mess at the moment so I’m slightly embarrassed to send that here haha. I’ll try my best to continue working it out with what you said.
#help-0
dry bone
Prove that 5^{3^n} + 1 is divisible by 3^{n + 1} for all nonnegative integers n.
I've tried using induction and starting with n = 1 and setting variables accordingly but I can't seem to figure it out. I was wondering if I could get a hint in the right direction.....
lone heartBOT
Prove that 5^{3^n} + 1 is divisible by 3^{n + 1} for all nonnegative integers n....
@dry bone Has your question been resolved?
gray ingot
Prove that 5^{3^n} + 1 is divisible by 3^{n + 1} for all nonnegative integers n....
shouldn't you start with n=0
lone heartBOT
@dry bone Has your question been resolved?
dry bone
shouldn't you start with n=0
I'm not sure.....
lone heartBOT
@dry bone Has your question been resolved?
dry bone
shouldn't you start with n=0
Off the top of your head is there another way to do this? and is there a difference between 1 and 0?
noble sinew
Off the top of your head is there another way to do this? and is there a differe...
nonnegative integers
that is 0,1,2,...
alpine sable
Is there a formula needed to be followed for part b? In addition, would that mean no actual numbers are being used, simply 5x x and h
wide raven
Is there a formula needed to be followed for part b? In addition, would that mea...
no need of a formula
if you know that area of a rectangle = l*b
you're good
alpine sable
hmm
alpine sable
if you know that area of a rectangle = l*b
but wouldn’t it be l * w * h for surface area?
wide raven
wait no, not at all
wide raven
yes sir
wide raven
no no
seee
there are total 4 surfaces length 5x and width h
and one with 5x and x
so what do you think?
alpine sable
im slow sorry
honestly no clue.. if surface area is l * b im not sure what to multiply here
alpine sable
2(5w)(x)+2(x)(h)+(5x)(x)
wide raven
ohh yes exactly
alpine sable
omg really??
wide raven
it was my bad i said something wrong
wide raven
omg really??
yes sir
alpine sable
oh that’s fine!
wide raven
you did it
alpine sable
so i just multiply them out
wide raven
yes
wide raven
no worries
solemn island
Hello, i wanted to make a decode system. like 1234 is 3 5 7 5 because 1 + 2, 2 + 3, 3 + 4, 4 + 1. But now i dont know how to decode this system. Can somebody help me? thank you
solemn island
i also wrote a little bit code, maybe you can understand what i wanted to do:
num2 = input("Bitte gib deine Nummer ein: ")
j2 = [int(i) for i in str(num2)]
a2 = j2[0]
b2 = j2[1]
c2 = j2[2]
d2 = j2[3]
ezahl2 = a2 - b2
zzahl2 = b2 - c2
dzahl2 = c2 - d2
vzahl2 = d2 - a2
print("Hier ist deine decodierte Nummer:" + str(ezahl2), str(zzahl2), str(dzahl2), str(vzahl2))
tacit arch
How do you know it's even possible
tacit arch
What does 2143 give
solemn island
i dont understand, sry. what do you mean?
vale crag
if you encode 2143 in your way, what does it give as a result ?
vale crag
there's also the thing of, how do you handle inputs like 7777 ?
you'll be overflowing your digits everytime here
rapid kettle
at what speed a particle must be thrown from a tower of height 3.6m and at angle of 30degrees with horizontal so that it hits ground at 45degrees ?
its part maths part physics anyone ?
high rapids
draw the diagram?
lone heartBOT
@rapid kettle Has your question been resolved?
long panther
at what speed a particle must be thrown from a tower of height 3.6m and at angle...
alright solve for a few equations first
initial velocity be U
Ux=Uy * (sqrt(3))
(x and y components of initial velocity U)
and final velocity Vx=Ux as there is no change in velocity in x direction
(refers to velocity along x direction)
as the angle of landing is 45 degrees
Vy=Vx
therefor Uy * (sqrt(3))=Vy
now apply equations for an object in constant acceleration
you'll find Uy
and thereafter Ux
combining them U can be discerned
lone heartBOT
lone heartBOT
Available help channel!
alpine sable
How do you answer this?
lone heartBOT
How do you answer this?
real gazelle
In general, lcm = product / gcd (try thinking about why this is)
alpine sable
In general, lcm = product / gcd (try thinking about why this is)
can you elaborate?
real gazelle
Yeah so for example if we have 6 and 8
6 = 2*3
8 = 2* 2*2
from there we get that the gcd = 2
and their product is 48
now how do we get the lcm? we just divide the product by the gcd to get 24
And we can check that it works, lcm = product / gcd
that should be enough info for you to solve the problem
real gazelle
no problem!
lone heartBOT
Available help channel!
paper holly
what would P(A) be equal to?
lone heartBOT
what would P(A) be equal to?
paper holly
the professor said that {a} would not be an element of P(A), but shouldn't it be, since its a subset of A?
tacit arch
{a} is an element of A, not a subset
paper holly
{a} is an element of A, not a subset
but wouldn't P(A) have a subset of A, which is only {a}?
ohh
you're saying {a} wouldn't be in P(A), but {{a}} would be?
because its supposed to be in a set
swift shore
you're saying {a} wouldn't be in P(A), but {{a}} would be?
Exactly, yes
paper holly
Exactly, yes
thanks!
swift shore
However, note that {a} will be in P(B)
tulip compass
hello grandmasters of mathematics, im new here, and im a software engineer, but sometimes my brain goes on standby mode and decides an easy solution but that wont be as performant for a simple problem. perhaps someone could help me.
So, lets say i decide a number for example 2. Which means something will happen every 2 times, but counting the first time as one. Lets take the following numbers list as an example
0,1,2,3,4,5,6,7,8,9 ..
since i decided the number 2. it will happen on 0 (because its the first, the first always counts), and then on 3 , 6 and 9. because theres a gap of 2 between them as i decided.
If i decided the number 3, it means it will happen every 3 times, so it wouild happen on: 0,4 and 8.
So the question is, what simple calculation can i do to determinate if the number is a "YES it happens" or a "NO it doesnt happen", for the example where i decided every 2 times, it would happen "YES" on 0, 3, 6 and 9.
Its quite simple i often have a hard time explaining my own problem.
Of course i could simply solve this situation but starting on 0, counting 2, if at least 2 passed, then "YES" otherwise "NO" ,but this would be the easier way and it would be much better if for example i could use some formula that if the rest is 0 then that means it is "YES" otherwise its "NO".
quite hard to explain but hope someone gets me
tacit arch
What in the heck
Can you just summarize your essay into a math question with only necessary details
swift shore
It’s fine
rough thicket
oh okay
swift shore
@tulip compass is the starting number always zero?
tulip compass
yes
swift shore
Does the sequence always move up by 1 each time?
tulip compass
yes
swift shore
Oh
So your question is, given any whole number and the gap size, decide whether it “happens” in the sequence 0,1,2,3,…
tulip compass
okay so:
a range of numbers [0,1,2,3,4,5,6,7,8,9,10...... untill N]
now i decide a gap, for example 2. Which means that it is true after every 2 numbers. So its true on 0 (because its the beggining) and also on 3,6,9 etc.. every 2 times.
I need a simple way to use the variable "gap" and calculate some number that if its 1 or something like that then it means it is "true" .
hope its simpler
yes
exactly
that
tulip compass
So your question is, given any whole number and the gap size, decide whether it ...
exactly this
swift shore
It’s quite easy
tulip compass
i want like some kind of divisian calculation that allows me to determinate if the result is for ex: 1, then it means it happens in this number
it should be, i am just complicating things probably
How would you do that?
swift shore
Notice that if the gap size is 2, then all the numbers that happen are 0,3,6,9,12,…, i.e. all the multiples of 3
swift shore
If the gap size is 3, it’s all the multiples of 4 (0,4,8,12,16,…)
tulip compass
holy shit i feel stupid, thank you very much
swift shore
Np, don’t sweat it lol
lone heartBOT
Available help channel!
sharp moth
I'm not sure why f(x) does not equal zero in pink
lone heartBOT
I'm not sure why f(x) does not equal zero in pink
sharp moth
I understand if you put x = 0 you'll evaluate something that's undefined
abstract fractal
If it's undefined at x=0, why do you think it should be defined?
sharp moth
But f(x) never evaluates to zero?
lilac nest
In this case it doesn't because you can't divide by 0
sharp moth
I don't understand the inclusion of this:
abstract fractal
If you didn't include it, then you'd be saying the range of f is all R
But it's not
lone heartBOT
@sharp moth Has your question been resolved?
sharp moth
There is no case in which f(x) would equal zero
lilac nest
No, because f(x) is equal to zero only if the numerator is also equal to zero. So, in this case x² would have to be equal to zero, which means x=0, but zero is outside the domain of the function.
abstract fractal
There is no case in which f(x) would equal zero
That's exactly why 0 is restricted from the range. We only include the values that f equals
sharp moth
Is that the same for the domain as well?
abstract fractal
Yes
We only include values in the domain that x can be
But x can't be 0, so we exclude it
warm carbon
what does the line on the right with the epsilon = 0 mean?
lone heartBOT
what does the line on the right with the epsilon = 0 mean?
mortal trellis
$\frac{dS[y(t)+\epsilon z(t)]}{d \epsilon}$ evaluated at $\epsilon=0$
ocean sealBOT
Denascite
mortal trellis
similar to the notation $\int_a^b f(x) dx = F(x) \Big|_a^b = F(b)-F(a)$
ocean sealBOT
Denascite
mortal trellis
if you wanna think of it like that
hard remnant
Why sin is defined as opposite over hypotenuse?
lone heartBOT
Why sin is defined as opposite over hypotenuse?
hard remnant
the same thing about cos equal adjacent over hypotenuse?
that what i got in google : 'The sine is always the measure of the opposite side divided by the measure of the hypotenuse. Because the hypotenuse is always the longest side, the number on the bottom of the ratio will always be larger than that on the top.'
Idk who can accept this proof
wary stream
https://math.stackexchange.com/questions/3444210/understanding-of-sine-opposite-divide-by-hypotenuse
Maybe this will help
hard remnant
sorry but I'm not asking why the sin of an angle If side lengths of the triangle changed, but why sin is opposite over hypotenuse how they invent this rule?
anyway thanks for sharing some information
mortal trellis
well they probably noticed at some point historically that the ratio opposite/hypotenuse is interesting and only depends on the angle. so they studied it and gave it a name. tbh I don't really understand what you are asking?
wary stream
sorry but I'm not asking why the sin of an angle If side lengths of the triangle...
It's honestly how math defined it. It's been like that for years and every just goes with it
Like why did we decide to count 1, 2, 3..., and not 3, 1, 2... because we defined like that it's normal just to see it like that
hard remnant
well they probably noticed at some point historically that the ratio opposite/hy...
maybe you are true
Do you know guys how the calculator switch between cos to cos^-1
I mean the algorithm behind that
mortal trellis
they probably use the first few terms of the taylor series or something similiar
hard remnant
maybe you are true
I mean if what you were saying is true it's quite impressive how they found it interesting and nowdays we all know how cos and sin play a tremendous role in mathematics
mortal trellis
or the CORDIC algorithm
well all of the math that we know today was "found" at some point
we didn't find some old textbooks with these definitions
lone heartBOT
lone heartBOT
Available help channel!
tropic oasis
lone heartBOT
tropic oasis
how did my professor
in the 2nd to last step
go from x^2 inside the sqrt denominator
to a single x in the sqrt
did he do a mistake?
solemn grove
did he do a mistake?
no
and you can do chain rule to verify
it’s prolly way easier
you don’t need to physically sub in u = 1/x and do dy/du * du/dx
but do that in your head
you’ll get the same answer a lot quicker
tropic oasis
but how did he go from x^2 as the denominator
to x without canceling anything else out
solemn grove
but how did he go from x^2 as the denominator
under the square root
when it comes out
it’s just x
mate, trust me
you don’t need to remember anything, you can derive these on the spot
solemn grove
I remember doing that like ages ago back in hs
solemn grove
yeah
solemn grove
yeah
tropic oasis
dy/dx = 1/sin(y)*x^2
solemn grove
no
solemn grove
dy/dx = 1/sin(y)*x^2
minus cancels
solemn grove
the inverse cos from that
sin^2 + cos^2 =1
that’s where the next step is derived from
tropic oasis
how do i do that
solemn grove
rearrange for cos
tropic oasis
i dont remember much
for trig
could you show me a visual example?
of how i would do that in this case?
after getting dy/dx=1/sin(y)*x^2
solemn grove
sin^2 + cos^2 =1
^^ do you know this formula
solemn grove
$sin^2(\theta) + cos^2(\theta) = 1$
ocean sealBOT
Rylo
tropic oasis
yep
tropic oasis
ohh okay
tropic oasis
like that?
solemn grove
just use $ to enclose what you type to use tex
and now sqrt both sides
to get sin
tropic oasis
$sin^2(theta) = 1-cos^2(theta)$
ocean sealBOT
manuel
tropic oasis
$sqrt(sin^2(\theta)) = sqrt(1-cos^2(\theta))$
ocean sealBOT
manuel
solemn grove
$\theta \phi \pm \leq$
ocean sealBOT
Rylo
tropic oasis
$sin(\theta) = sqrt(1-cos^2(\theta))$
ocean sealBOT
manuel
solemn grove
$sin(\theta)= \sqrt{(1-cos^2(\theta)}$
ocean sealBOT
Rylo
solemn grove
yeah, just backslash before the the sqrt and curly brackets for everything under the sqrt
anyways
solemn grove
$sin(\theta)= \sqrt{(1-cos^2(\theta)}$
substitute that for sin x in our equation
tropic oasis
dy/dx = 1/sin(y)*x^2
solemn grove
dy/dx = 1/sin(y)*x^2
^^
tropic oasis
$dy/dx = 1/x^2\sqrt{(1-cos^2(\theta)}$
ocean sealBOT
manuel
tropic oasis
ohhh
solemn grove
and cos theta =
solemn grove
what?
tropic oasis
tropic oasis
OH
tropic oasis
yesyes
tropic oasis
but the one i have
is cos(theta)
and the one im plugging it into
is cos^2(theta)
tropic oasis
y=1/x?
solemn grove
$cos^2(\theta) = (cos(\theta))^2$
ocean sealBOT
Rylo
ocean sealBOT
manuel
solemn grove
after getting dy/dx=1/sin(y)*x^2
We have sin y
don’t we
$dy/dx = 1/x^2\sqrt{(1-cos^2(y)}$
ocean sealBOT
Rylo
solemn grove
so far so good?
solemn grove
yeah
tropic oasis
cos(y)=1/x
tropic oasis
mhm
solemn grove
sub that in for this
tropic oasis
i'm confused on this part exactly
solemn grove
$\frac{dy}{dx} = \frac{1}{x^2\sqrt{1-cos^2(y)}}$
ocean sealBOT
Rylo
solemn grove
yeah?
solemn grove
$cos(y) = 1/x$
ocean sealBOT
Rylo
solemn grove
$cos^2(y) = 1/x^2$
ocean sealBOT
Rylo
solemn grove
$\frac{dy}{dx} = \frac{1}{x^2\sqrt{1-\frac{1}{x^2}}}$
ocean sealBOT
Rylo
solemn grove
yeah, dw
and baso just use \frac for fractions
with same curly brackets
but does it all make sense now?
ocean sealBOT
manuel
solemn grove
mb that it took me a while
No it’s cool
tropic oasis
rearrange the formula
solemn grove
you’re learning
tropic oasis
cos^2+sin^2=1
solemn grove
and that’s cool
tropic oasis
and substitute
solemn grove
yep
tropic oasis
i just dont get how
solemn grove
which part
tropic oasis
cos^2(theta) is 1/x^2
solemn grove
line 1
tropic oasis
i know 1/x^2 is the quotient rule
solemn grove
What’s line 1
tropic oasis
on my professor's work?
tropic oasis
cos^2(y) = (1/x)^2
solemn grove
there you go
solemn grove
Yeah no, trust me. you’ll be fine
Everything you did today either has to do with sin2 + cos2 = 1 or rearranging equations
tropic oasis
yeah i'm going to piece everything together and retry number 1
thank u so much for the help!
rlly apprecaite it
solemn grove
no worries mate
feel free to dm if you need anything more
I’ll check in the morning
@tropic oasis
don’t forget close
- to close
tropic oasis
.close
alpine sable
lone heartBOT
wary stream
Use the given lengths to find the forces in each member
lone heartBOT
@alpine sable Has your question been resolved?
stable night
lone heartBOT
stable night
can someone tell me how to solve this? i have no clue
clear stump
whats origin
stable night
0,0,0
clear stump
ight im off
real gazelle
What have you tried so far?
Did you find equations for OR and AB
Also do you know what a basis is
lone heartBOT
✅
stable night
Did you find equations for OR and AB
sorry this is possible?
i dont have any points/directions thou
stable night
Also do you know what a basis is
is it the origin?
real gazelle
No forget about that idea then
find equations for the lines in terms of a and b
it actually doesn't matter the number of dimensions you're working in as long as it's ≥ 2
stable night
find equations for the lines in terms of a and b
for this ill need
- direction vectors
- a point on both a and b (0,0,0)
idk how to get the direction vector thou
last ether
You don't need direction
$$\cos{(45)} = \frac{A\cdot B}{||A||\cdot||B||}$$
Did it break so bad it didn't even load 💀
Oh it loaded
But it broke
ocean sealBOT
Umbraleviathan
stable night
OH
last ether
You know that b is a unit vector
last ether
Tbh I never learned lambda notation in school
stable night
oh lol
lemme try writing that down
okay
so
wait so this is like the "equation" representing a and b
then cos(45) is sqreroot(2)/2
last ether
Yeah
It says that for vector B, the b part is a unit vector
Meaning that a = 1
So $||B|| = 1$
stable night
Meaning that a = 1
wait why is this a
tight locust
this might be helpful
ocean sealBOT
Umbraleviathan
stable night
this might be helpful
hmm yea it def helps visualising
stable night
**Umbraleviathan**
ye
so now i have root(2)/2 = (a . b)/|a|
sorry idk how to write in latex lol
tight locust
hmm yea it def helps visualising
you can think of it as a 'tilted' coordinate grid
tight locust
i wouldn't say you should always do that
but it's helpful to develop that intuition
tight locust
which part?
stable night
wait no actually i still dont know how to solve the first part
like i can visualize and see it now but idk how to derive it
stable night
erm one sec can we tackle part i first xD
stable night
so OR would be at the end of the longer green arrow
tight locust
yeah
lone heartBOT
@stable night Has your question been resolved?
tight locust
OR starts at 0a+0b and goes to 3a+5b, we represent the line OR = t<3,5>
AB starts at 1a + 0b and goes to 0a + 1b, we represent the line AB = <1,0> + s<-1,1>
This yields the system:
3t = 1 - 1s
5t = s
can you solve?
stable night
One moment
tight locust
we use <x,y> here to represent xa + yb
stable night
Okay so i can solve for t and s then find OR
tight locust
what do you get for s and t?
tight locust
do you know the vector form of lines?
tight locust
position vector + (free variable)(direction vector)
and that free variable is what allows it to be a line, which is a 1D object that varies with 1 variable
stable night
Oh thats 1D?
Now i know what 1d actually is lol
I thought 1D is just a point
Eh wait it is
tight locust
a line is a one dimensional object because it varies with one variable
stable night
Also for the z axis for this question itll judt be 0 right
stable night
a line is a one dimensional object because it varies with one variable
Oh right
tight locust
we're working in 2D space so there is no z axis
stable night
Then 2D is on a x y plane?
tight locust
anything that varies with 2 variables is 2 dimensional, it doesn't have to be a plane. we can parameterize the surface of a sphere with only 2 variables
but let's not get too off track here
solve the system
tight locust
don't even think about x and y lol. we're not using the standard basis
tight locust
yep
stable night
Err slightly
tight locust
like if i wrote <3,5> that means 3a + 5b
tight locust
yes
stable night
Rhen s = 5/8
tight locust
a and b are not variables to solve for
stable night
OH
tight locust
they are our "units" if you will
tight locust
no, because x and y are not used as vectors typically
think of them as i and j
if you've ever worked with that notation before
tight locust
so what's the point of intersection?
stable night
1/8(3a,5b)
tight locust
not just that
even if you wrote <3a,5b> that wouldn't be correct. that would mean:
(3a)a + (5b)b
stable night
oh i see
okay i get
erm the length of projection is someething like this right
but in this case for part ii, OR is far beyond OB tho
or does it mean line ob
tight locust
let me show you
tight locust
stable night
Oh so the length of projection would work even if <3,5> is far beyond <0,1>
tight locust
yeah
tight locust
"How much of OR goes in the direction of OB?"
tight locust
why would we do that
stable night
Err am i mistaken cus i thought the questions asking us to do that
stable night
Err if u dont mind can u highlight the length of projection of OR on OB
tight locust
yep
tight locust
yep
tight locust
let's just use the projection formula
our 'a' here is OR
our 'b' here is OB
or actually let's make this even simpler
solve for |b|
stable night
cos 45 = |b| / |a|
tight locust
solve for |b|
stable night
|b| = |a| cos45
tight locust
i got it
alright it's getting late
a_x = |a|cos45
the projection is 3a_x + 5|b|
|b| is 1
so we have:
3|a|cos(45) + 5
@stable night
lone heartBOT
@stable night Has your question been resolved?
lone heartBOT
lone heartBOT
Available help channel!
alpine sable
whats the integral of ln(x+2)
lone heartBOT
whats the integral of ln(x+2)
alpine sable
\begin{align*}
\int (x+2) \cdot \ln(x+2) \ \mathrm{dx} &= (x + 2) \cdot (x \ln{x} - x) - \int{(x \ln{x} - x)} \ \mathrm{dx}\
&= (x + 2) \cdot (x \ln{x} - x) - \int{x \ln{x}} \ \mathrm{dx} - \int x \ \mathrm{dx}\
&= \boxed{(x + 2) \cdot (x \ln{x} - x) - \left(\dfrac{x^2}{2} \cdot \ln{x} - \left(\dfrac{x^2}{2} \cdot \dfrac{1}{x}\right)\right) - \dfrac{x^2}{2} + c}
\end{align*}
ocean sealBOT
devil
alpine sable
im not sure where $x\ln x-x$ comes from
ocean sealBOT
devil
alpine sable
nvm got it
\begin{align*}
\int \ln x \ \mathrm{dx} &= \int 1 \cdot \ln x \ \mathrm{dx}\
&= x \cdot \ln x - \int \frac1x \cdot x\
&= x \cdot \ln x - \int 1\
&= x \cdot \ln x - x
\end{align*}
.close
lone heartBOT
ocean sealBOT
devil
lone heartBOT
Available help channel!
silk hollow
lone heartBOT
tacit arch
What are you stuck on
silk hollow
when i look it up the answer is always x = 9 (im trying to solve for x) but i dont know how to get there
I always do (x-6) to the power of 2 = x and dont know how to solve from there
tacit arch
I always do (x-6) to the power of 2 = x and dont know how to solve from there
Use the quadratic formula
vale wigeon
you are in 8th grade, doing stuff with logarithms, and yet you have never worked with quadratic equations before?
vale wigeon
equations of the form ax^2 + bx + c = 0
long iris
Equations with squared x
silk hollow
equations of the form ax^2 + bx + c = 0
never ever heard of that
vale wigeon
then you have no business doing shit with logarithms lmao
why did your teacher give you a problem you aren't equipped to solve?
silk hollow
this is the question before on the sheet and its ez to solve, but I have no clue about that one
long iris
Is this your schools leson thing
silk hollow
Is this your schools leson thing
wym
silk hollow
why did your teacher give you a problem you aren't equipped to solve?
idk mann lmao I just dont want to fail it
vale wigeon
your teacher gave you a problem that, by your own admission, you do not have the tools to solve.
long iris
Do you choose to study logarithyms or school just says you
silk hollow
Do you choose to study logarithyms or school just says you
this is what I was assigned by my teacher as homework
vale wigeon
go and tell your teacher "This equation reduces to (x-6)^2 = x, which is a quadratic equation, but I have never worked with these before and cannot be expected to solve it."
silk hollow
go and tell your teacher "This equation reduces to (x-6)^2 = x, which is a quadr...
alr ty, bc what I was doing was getting x^2 + 36 = x
vale wigeon
(x-6)^2 is not equal to x^2 + 36.
vale wigeon
ignorant, not dumb.
you admitted to never having heard of quadratic equations before. that is called ignorance, not stupidity.
(x-6)^2 expands to x^2 - 12x + 36, anyway.
silk hollow
(x-6)^2 expands to x^2 **- 12x** + 36, anyway.
yeah that makes no sense to me, ima just sort it out with my teacher, ty for ur help
long iris
alr ty, bc what I was doing was getting x^2 + 36 = x
In the start ot of homework did your teacher told you number must be like 4.0000 and not 4.274525 i dont what that means
median oar
i would imagine you were not expected to solve it algebraically but guess and check by the situation you described
long iris
i would imagine you were not expected to solve it algebraically but guess and ch...
Yeah thats what i thought
silk hollow
yeah idrk what u guys are even saying lol so ima just assume I havent learned this yet and take it up with him
mb for wasting time
median oar
im saying since u haven't learned how to do this properly
maybe you were just supposed to guess
silk hollow
maybe you were just supposed to guess
ooohhh
median oar
because i know sometimes teachers will just let you have a go and see what u can come up with
silk hollow
yh ik wym now
vale wigeon
i think such problems ought to have a disclaimer on them tbh
silk hollow
so should i just assume I cant do the rest of these questions?
or do those ones not require quadratics or whatever that is
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tropic oasis
lone heartBOT
tropic oasis
how would i go about solving this?
median oar
do you know about calculus?
tropic oasis
yes
i know f'(x) = 5x^4 - 3
and i know g(x) inverse is 1/f'(x)
g(x) = 1/5x^4 - 3
median oar
can you find g(x)
tropic oasis
yes
median oar
what's g(x)
tropic oasis
g(x) = 1/5x^4 - 3 this right
tropic oasis
o
median oar
ok so do you know how to find g'(x)
median oar
um
tropic oasis
i dont understand that very well
from my understanding we basically need to find derivative of g(x) as that would be the slope?
for g?
with the provided x,y values?
median oar
$f'(f^{-1}(a)) = \frac{p}{q}\
(f^{-1})'(a) = \frac{q}{p}$
ocean sealBOT
Frosst
tropic oasis
so its basically a reciprocal?
median oar
well kinda but you need the other value as your parameter
cos inverses are flipped along x=y
so when you're looking at the inverse function
you need to look at the y at the x value
that's why it says (a) for the inverse
and the inverse in inside the f'
tropic oasis
i see
median oar
so you know on g -2,1 is that point flipped on the x=y line for f(x)
so if u find this point thats flipped, then calculate the gradient of f(x) at this point, then you can inverse it for the gradient on g(x)
median oar
that's the first step yeah
tropic oasis
and i can accomplish that by plugging in 1 into f(x)?
tropic oasis
(0,1)?
median oar
ok
tropic oasis
(1,-2)?
tropic oasis
i see
median oar
so now you know the corresponding point
you swap the numbers because it's reflected on the x=y axis
x turns into y
and y turns into x
tropic oasis
got it
median oar
so now you find f'(x) for the point 1, -2
lone heartBOT
@tropic oasis Has your question been resolved?
alpine sable
Fifteen people are to be divided up into three distinct committees, called Committee A, Committee B, and Committee C, each with 5 people.
lone heartBOT
Fifteen people are to be divided up into three distinct committees, called Commi...
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alpine sable
- (10 points) Fifteen people are to be divided up into three distinct committees, called Committee A, Committee B, and Committee C, each with 5 people.
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alpine sable
- (10 points) Fifteen people are to be divided up into three distinct committees, called Committee A, Committee B, and Committee C, each with 5 people.
i got two different answers, not sure which one is right or which one is wrong, can someone check for me
lone heartBOT
@alpine sable Has your question been resolved?
prime badge
i.m getting 0.659
you did 9c4 for some reason, instead of 8c4
(in the second solution)
alpine sable
i see, my b, thank you a lot
prime badge
oh np
alpine sable
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outer siren
lone heartBOT
outer siren
Is this answer right?
lone heartBOT
@outer siren Has your question been resolved?
lone heartBOT
@outer siren Has your question been resolved?
lost coral
how can i solve this?
AB is a line segment. A has the coodinates (a,b) and B has the coordinates (8,20). P is 1/3 of AB line segment and it has the coordinates of (2a,2b). Solve for A coordinates
minor needle
how can i solve this?
AB is a line segment. A has the coodinates (a,b) and B has...
u know section formula?
lost coral
nope
minor needle
vectors?
lost coral
um nope
lost coral
well how do i calculate it without the coordinates
minor needle
now u can observe that to move from point A to P you need to add "a" in x direction and add "b" in y direction
and it's 1/3
to move into 2/3 u need to add them again
and the last time to move to the point B
lost coral
ok how about if i werent allowed to draw?
minor needle
ok how about if i werent allowed to draw?
how?
you can draw it on the paper
I've used GeoGebra cuz I'm lazy, but nvm
lost coral
but what if i had no space to draw during the exams
and they specifically said no drawing
minor needle
I don't see other solution that using section formula/vectors. U can also use analytic geometry, but solution would be so long
they don't require drawings
minor needle
this is what I was talking about
lost coral
cause this image dont show coordinates
lost coral
this is what I was talking about
huh u were?
minor needle
yes, P is 1/3 and P = (2a,2b)
2/3 is (3a,3b)
and 3/3 (point B) is (4a,4b) then
that's basically it
lost coral
wait so my answer is right?
minor needle
yes
lost coral
ow
i barely know anything about this topic
i just use inverse methods
i didnt even knew that there was a name for this
so this is called vector formula?
minor needle
no, you haven't used vectors
lost coral
section?
minor needle
I don't know if this has a specific name, I'd say just logical thinking
tribal oxide
lone heartBOT
tribal oxide
mortal trellis
what exactly is your question?
lone heartBOT
@tribal oxide Has your question been resolved?
tribal oxide
what exactly is your question?
Find fof
mortal trellis
I mean why did you post here
tribal oxide
I want to know if what i did is wrong or not
mortal trellis
it's not wrong. but I fail to see where you make a proper argument that f(x) >= 0 always. except the graph
try to write more words instead of just symbols
tribal oxide
it's not wrong. but I fail to see where you make a proper argument that f(x) >= ...
There is a case method also taught but its lengthy
mortal trellis
it's impossible to know what you are thinking just from what you wrote down
the case analysis doesn't take that long
and it's good to practice it for other problems where you can't just draw the graph and point at it
not that you even do that
tribal oxide
and it's good to practice it for other problems where you can't just draw the gr...
I know, i was thinking its been while i did the graph method💀
Thank you for your help
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lone heartBOT
lone heartBOT
Available help channel!
rustic hazel
lone heartBOT
oblique pier
Did you learn the formula for this?
rustic hazel
nvm you know similar triangle?
not really
oblique pier
not really
in your word, what do you think are similar triangle
rustic hazel
in your word, what do you think are similar triangle
triangles that have proportional lengths?
oblique pier
triangles that have proportional lengths?
and they have all of their angle are equal to the other triangle that is similar to them
yeah?
rustic hazel
and they have all of their angle are equal to the other triangle that is similar...
ye
rustic hazel
ok
oblique pier
Now
oblique pier
i want you to look at triangle GIH and triangle FIG
rustic hazel
i want you to look at triangle GIH and triangle FIG
bet have it open
guessing their similar
oblique pier
guessing their similar
We don't do guess here
oblique pier
Guess is dull and a waste of time
rustic hazel
nvm
oblique pier
bet have it open
Do you think
we can prove that those triangle are similar to each other?
rustic hazel
we can prove that those triangle are similar to each other?
we should try
but yes
i thnk
oblique pier
we look at the angles
hmm
alright imma tell you 3 of the way we can prove similar triangle
first is a-a (angle-angle)
which mean
if you can find 2 pairs of angle which each pair has 2 angle that are equal to each other
you can prove that they're similar triangle
since they have 3 of their angle equal to each other but NOT the length of the sides
rustic hazel
is there an aaa
oblique pier
is there an aaa
a-a is aaa
rustic hazel
a-a is aaa
oh ok
oblique pier
since you just need 2
oblique pier
well we know they both have right triangles
alright nice 1 angle
we need to find 1 more
rustic hazel
alright nice 1 angle
g and f?
oblique pier
good.
rustic hazel
deg
rustic hazel
i want you to look at FGI and HGI
yes
rustic hazel
what's special about them
tjeres an altitude
rustic hazel
forget the alitude
they look similar
oblique pier
they plus each other to give you 90 degree correct shub?
oblique pier
Now
rustic hazel
ok
oblique pier
Look at IFG and FGI