well what dont u understand
#help-0
shell widget
tame moss
static basin
b = 3a + 15
lone heartBOT
b = 3a + 15
open folio
To make a the subject is the answer:
Ok so b = 3a - 15
open folio
You want to make a the only variable, so you need to get rid of the -15
How would you do that?
open folio
b + 15 = 3a
static basin
b = 3a + 15
static basin
Yes got that
static basin
Ahhhh decide the 3!
alpine sable
👍
static basin
Divide
alpine sable
yes
static basin
So it’s b - 15 = a
open folio
b/3 - 15/3 is fine
alpine sable
So it’s b - 15 = a
Yes but if you divide by 3 on one side of the equal you will also have to do it on the left side
open folio
its soupossed to be b - 15/3 = a
no
open folio
not b/3 - 15/3 = a
yes
open folio
$\frac{b-15}{3} = a$
ocean sealBOT
Breeziboi
alpine sable
**Breeziboi**
Yeah it should be that
static basin
So I got it right the first time?
open folio
You can break this into something else that can be further simplified
$\frac{b]{3} minus \frac{15}{3} = a$
ocean sealBOT
Breeziboi
$\frac{b]{3} minus \frac{15}{3} = a$
```Compilation error:```! File ended while scanning use of \frac .
<inserted text>
\par
<*> 521326998195273729.tex
I suspect you have forgotten a `}', causing me
to read past where you wanted me to stop.
I'll try to recover; but if the error is serious,
you'd better type `E' or `X' now and fix your file.```
open folio
$\frac{b}{3} - \frac{15}{3} = a$
ocean sealBOT
Breeziboi
open folio
There we go
@static basin
Not sure what I did wrong...
But here we go
You can break this apart
Do you see how to simplify this more?
static basin
No
open folio
What is 15/3?
static basin
5
ocean sealBOT
Breeziboi
open folio
@static basin Is there any further simplifying that can be done?
static basin
Yeah but why are you dividing b by 3
open folio
Yeah but why are you dividing b by 3
Go back to b = 3a + 15,
We did b - 15 = 3a
That 3 we divide on both sides to isolate a
static basin
Yes
ocean sealBOT
Breeziboi
static basin
Yes
open folio
You follow?
static basin
Yes
open folio
Yes but where dividing b -15/3
Correction: (b - 15)/3
static basin
Yes
open folio
You have to watch out for things like that
We are dividing the ENTIRE left side
Not just one part
open folio
Yes
Ok for example, lets use x and y
Alter x/5 + y/5
Since they are common denominators we can add them
static basin
So sorry x+y
ocean sealBOT
Breeziboi
alpine sable
Ok for example, lets use x and y
Alter x/5 + y/5
Undisctrubute the /5 since its in common with all of the terms
static basin
Thank you
open folio
Thank you
No problem
By the way, algebra is a pretty important and reoccouring skill, so make sure you practice :)
static basin
Wait, I thought you could only subtract powers with the same base number?
open folio
Wait, I thought you could only subtract powers with the same base number?
Powers and bases are completely different haha
Thats exponents
static basin
Unless you can do vectors? 😂😂
static basin
On?
open folio
But physics vectors? Perhaps
static basin
Yes
open folio
Show me
static basin
Is tomorrow ok?
static basin
Ok what time is it there now?
static basin
Ok, how about tomorrow at the same time?
open folio
Ok, how about tomorrow at the same time?
Sure
tight yacht
I understand the correct solution, but can anyone point out why this is wrong?
Integral(1/2x)
= integral(1/2 x 2/2x)
= 1/2 integral(2/2x)
using integral(f’(x)/f(x)) = ln(f(x)):
= 1/2 ln2x + C
Obviously this is wrong as:
integral(1/2x) = 1/2 integral(1/x)
= 1/2 lnx + C
What am i doing wrong in the first method? Lnx is obviously not equal to ln2x lol
tight yacht
i know all of A2 integration (edexcel) but this really simple problem has confused me lmao
last tendon
they are the same up to a constant of integration
tight yacht
omg
last tendon
Also don't use x for multiplication and the integration element. That is annoying on the best of days
tight yacht
discord formats *s
thats why i use x lol
Whoops at missing the log law
its kinda late and i just started overthinking
buoyant kayak
you can use latex or put a \ in front of * to get around italicizing
slender glacier
hi i need help with this series of questions involving complex number. everything kind of connects with each other so it might be easier to just start from the beginning :(( sorry its so long
lone heartBOT
@slender glacier Has your question been resolved?
slender glacier
what's the modulus and arg of z
so for a) i), i got z=a cis b
and I think I get a) ii) as well
lone heartBOT
@slender glacier Has your question been resolved?
slender glacier
<@&286206848099549185>
lone heartBOT
@slender glacier Has your question been resolved?
merry coral
Why did the US want to kill Castro? I can't find a straight foward answer anywhere.
grim delta
Why did the US want to kill Castro? I can't find a straight foward answer anywhe...
because democracy
anyway
merry coral
because democracy
but like Castro overthrew Bastia who was a freakin dictator backed by the US
simple turtle
Why did the US want to kill Castro? I can't find a straight foward answer anywhe...
Any math question?
naive valley
batista
i guess we could calculate the angle of missile launches to travel from cuba to florida or something?
simple turtle
i guess we could calculate the angle of missile launches to travel from cuba to ...
That will help
naive valley
optimize all the things
grim delta
i guess we could calculate the angle of missile launches to travel from cuba to ...
more of a physics question
we should take this to the physics discord
naive valley
yeah true, but physics is just applied math with some additional axioms
simple turtle
optimize all the things
Find the maximum impact
Find the probability of USA getting hit first
merry coral
find the optimal path to -113.78N, 45.68E
simple turtle
find the optimal path to -113.78N, 45.68E
That's tough one.
We should close for math?
naive valley
it's a trick question, latitude only goes to +/- 90 degrees
and north is positive not negative lol
damn australians
simple turtle
it's a trick question, latitude only goes to +/- 90 degrees
I love Australians. It's who's running the place.
naive valley
i have no quarrel with them except for their upside down view of the world 😆
simple turtle
i have no quarrel with them except for their upside down view of the world 😆
USA or other place isn't any better. Good and evil every race, place..
merry coral
yeah I got to where I harness when I walk around
naive valley
USA or other place isn't any better. Good and evil every race, place..
truth
tall wing
Why did the US want to kill Castro? I can't find a straight foward answer anywhe...
can you not use the help channels for this, thanks.
.close
lone heartBOT
lone heartBOT
Available help channel!
golden lava
I can't seem to figure out how to slove these
lone heartBOT
I can't seem to figure out how to slove these
tardy rapids
I can't seem to figure out how to slove these
Use Chord product property for the second one
golden lava
Use Chord product property for the second one
Thank you man
ancient sand
hello
lone heartBOT
@golden lava Has your question been resolved?
lone heartBOT
lone heartBOT
Available help channel!
alpine sable
anyone know how to solve this
lone heartBOT
anyone know how to solve this
blazing saffron
anyone know how to solve this
Do you know what those brackets represent
lone heartBOT
@tardy temple Has your question been resolved?
zenith compass
I want to ask part b of this question
lone heartBOT
I want to ask part b of this question
zenith compass
Those are my very messy workings
Seems I am on the wrong track
Can anyone give me some ideas how to do it in a better way?
lone heartBOT
@zenith compass Has your question been resolved?
stone scroll
lone heartBOT
stone scroll
My answer is 10 but I'm not really sure if I'm correct
I used the combination formula to multiply the given in each menu then I added them together
ripe rain
Sus looks like a test
tacit arch
Is it a test?
stone scroll
Yep a diagnostic test
lone heartBOT
@stone scroll Has your question been resolved?
stone scroll
Ah nvm I got it
zinc parrot
can some explain to me why is there two sin wave instead of 1
zinc parrot
i got all the values
but i dont get why it goes to the negative
i dont get what u mean by odd
is it just a rule or smth
ok
yes
woah
thats cool
i know
so one sine wave would be fine
right
alright
thanks
yeah okay
oh ok
cant u just use signs
like
-1/2
to show that it goes right
left
i mean
oh
ok
oh
ok
got u
okayy
let me fix the whole thing now
thanks
.close
idle cedar
I know (a) but not (b)
lone heartBOT
I know (a) but not (b)
vague coral
formula of the area of a triangle
idle cedar
formula of the area of a triangle
YEs but I dont have base and height
This chapter is about pyhtagoras' theorem
slender gull
I think they can't use the heron's formula here.
vague coral
YEs but I dont have base and height
just find it
slender gull
Yes, find the height, base you already have.
vague coral
the height of the triangle CDE is the perpendicular line to DE that passes through C
and to find his length, Pythagore is your best friend
idle cedar
well i know the length
vague coral
of the height ?
idle cedar
wait
vague coral
Then do it if you have it
idle cedar
no
idle cedar
ok so i assume F is a point on ED which FC is the height
vague coral
yes
idle cedar
but how to find FC
slender gull
You will have to also use FE and FD.
idle cedar
but what is FE and FD
idle cedar
FE^2+FC^2=EC^2
slender gull
Right.
vague coral
yes but do you know the length of EC ?
idle cedar
FD^2+FC^2=DC^2
idle cedar
yes but do you know the length of EC ?
no
slender gull
Bruh.
vague coral
it was never said that CDE is a an isoscele triangle
idle cedar
it was never said that CDE is a an isoscele triangle
and?
vague coral
I don't know, your exercises didnt give much information
idle cedar
@vague coral or i can take CD as the base
vague coral
the height is not even in the triangle if you do that
idle cedar
well we can assume G is a point on BC and EG is perpendicular to GD
and EG will be the height
vague coral
and ? its worse than the first one
I mean, the height will be hard to find too
And I don't want to make assumptions we are doing maths
idle cedar
or we can try to get the area of triangle EBD and subtract triangle ECB
vague coral
still hard because the height will be painful to find
Maybe use Heron formula I dont know at this point
But still hard because we dont know EC
vague coral
idle cedar
but we dont have EC
vague coral
thats what I said
we need extra information for this problem, I would consider the exercise incomplete i guess
I can easily make an assumption that EC = CD, but we are doing maths here
idle cedar
actually we can try to prove it
idle cedar
bruh
lone heartBOT
@idle cedar Has your question been resolved?
lone heartBOT
@idle cedar Has your question been resolved?
lone heartBOT
lone heartBOT
Available help channel!
cunning trout
lone heartBOT
cunning trout
I’m not sure what to do in this question
gray ingot
can you find the radius?
gray isle
as usual, start with a diagram
cunning trout
can you find the radius?
That’s what I’m trying to do
But I’m confused with the diagram, it’s confusing to me
gray ingot
do you know what a sector is?
cunning trout
A part of the circle
gray isle
what attempts have you made to find the radius?
gray ingot
A part of the circle
any part?
cunning trout
So pi x r^2 =5 pi
gray ingot
yes
gray ingot
alright
gray ingot
So pi x r^2 =5 pi
so what is r?
cunning trout
Radius
gray ingot
no I mean its value
gray isle
no
cunning trout
?
gray ingot
its not 2.2
cunning trout
I did it on the calculator
gray isle
what are you putting into your calc
gray isle
perhaps it would be better to first isolate r in your equation
and avoid using a calculator until it's needed
cunning trout
r=square root of 5
gray ingot
ok, now do you know how the angle subtended by an arc is related to the radius and arc length?
cunning trout
No
gray ingot
gray ingot
keep in mind that theta is in radians
cunning trout
Yep
gray ingot
you'll need to convert to degrees for your answer
gray ingot
But we know r, what about L?
read the question
cunning trout
So 3cm
tight locust
unsolvable
cunning trout
Wait what?
tight locust
i mean if we're being really technical about it we can't solve this problem because there's no units for the area given
cunning trout
So is the length 3cm right?
tight locust
yeah
lone heartBOT
lone heartBOT
Available help channel!
sullen bramble
Are we able to use the remainder theorem here? Or do we use long division?
slender gull
Remainder theorem.
sullen bramble
So do we substitute 1/2 in the equation?
slender gull
Sure.
sullen bramble
Ok thanks. This question is asking me to find the remainder. So do I substitute -sqrt(2) in the eqution then?
slender gull
First of all.
slender gull
You can just use (-2) for x^2 everywhere.
However, long division works here just fine so do what seems easier.
alpine sable
Ok thanks. This question is asking me to find the remainder. So do I substitute ...
Use polynomial division
lone heartBOT
Use polynomial division
solar adder
lone heartBOT
slender gull
What have you tried so far?
solar adder
lone heartBOT
solar adder
im unsure on how to do it
alpine sable
do you know the properties of exponents?
vivid citrus
you can rewrite $\sqrt{a}$ as $a^{\frac{1}{2}}$
ocean sealBOT
Itz_Aladdin
vivid citrus
and after that you can use the exponent properties as aimane said
solar adder
i still dont get it
gray isle
do you know your exponent laws?
specifically the ones related to multiplication and division?
solar adder
specifically the ones related to multiplication and division?
i think i only know those ones
vivid citrus
if it helps you can write everything as a multiplication too
solar adder
a^x times a^y = a^ (x+y) ?
gilded vessel
start by writing the bottom in exponent form and simplifying the top
can you do that?
neon bramble
Is there a way I can prove that m∠3 < m∠4?
lone heartBOT
Is there a way I can prove that m∠3 < m∠4?
hollow shale
@neon bramble Find the angle sum of triangle UST using both angles 3 and 4.
lone heartBOT
@neon bramble Has your question been resolved?
neon bramble
im not sure how to do that
hollow shale
What is the interior angle sum of a triangle?
neon bramble
180
hollow shale
Do you know what angles on a straight line must sum to?
neon bramble
180 i think
neon bramble
Yes
hollow shale
So ∠UTS = 180 - ∠4
Now we try finding the sum of the angles in the triangle UST.
Which we know is 180.
What 3 angles sum to 180 in that triangle?
neon bramble
∠3, ∠UST, and ∠UTS?
hollow shale
(All this to prove your inequality by the way)
hollow shale
∠3, ∠UST, and ∠UTS?
Yep.
So can you form an equation for the sum of those angles?
And then substitute in our value for UTS?
neon bramble
∠3 + ∠UST + ∠UTS = 180?
is that right?
hollow shale
Yes.
hollow shale
And then substitute in our value for UTS?
.
neon bramble
∠3 + ∠UST + (180 - ∠4) = 180?
hollow shale
Yes, now simplify this and see if you notice something.
Put the angles ∠3 and ∠4 on opposite sides of that equality.
hollow shale
You can simplify this more. Notice the two 180's on either side. Also we would ideally have the angles have a positive sign.
neon bramble
Oh
hollow shale
In the end, you should get:
∠3 + ∠UST = ∠4
See how this basically proves your inequality?
neon bramble
Ohhh
Wait so
∠3 + ∠UST + 180 - 180 = ∠4
∠3 + ∠UST = ∠4
Is that the right way to do it
hollow shale
Yep.
rotund pumice
I'm trying to check if $\sqrt{1-x^2}$ is injective. If $f(a) = f(b)$, then $a = b$.
At one point I reach that $a^2 = b^2$, so I square root both sides, and here's where I have problems.
Square root of $a$ and $b$ can be $\pm a$ and $\pm b$
So is it true that $a = b$ ?
ocean sealBOT
0MegaP0int
alpine sable
I'm trying to check if $\sqrt{1-x^2}$ is injective. If $f(a) = f(b)$, then $a = ...
This function isn't injective, as x= 1 and x=-1 both give 0
rotund pumice
So a = b but also a = -b?
I know it's not injective but I have problems understanding how the equality works on that minus-plus scenario
alpine sable
I know it's not injective but I have problems understanding how the equality wor...
a^2 = b^2 doesn't imply a=b. You can't make progress
sudden hinge
So `a = b` but also `a = -b`?
Kinda, yes. This implies that the only point where it is injective is basically a = b = 0. Everywhere else, it isn't.
alpine sable
I know it's not injective but I have problems understanding how the equality wor...
What are you trying to do?
rotund pumice
Hmmm
rotund pumice
What are you trying to do?
I'm trying to find out if $\sqrt{1-x^2}$ has an inverse, by checking if its bijective
ocean sealBOT
0MegaP0int
rotund pumice
If I restricted the domain to [-1, 0), the fact that a^2 = b^2 does not imply a = b still holds? And therefore, even if the domain is restricted, it is not injective?
sudden hinge
I'm trying to find out if $\sqrt{1-x^2}$ has an inverse, by checking if its bije...
You could also argue that this can't be bijective, because for a composition f(g(x)) to be invertible, you need inverses for both f and g to exist. But we know g(x) = 1 - x^2 isn't invertible (as any parabola)
alpine sable
If we restrict the domain, then yes, it is injective (bijective too I think). And it would be its own inverse.
solve for x in y=sqrt(1-x^2)
We can prove that it's bijective by proving that it's continuous AND strictly decreasing/increasing on a given domain
alpine sable
You could also argue that this can't be bijective, because for a composition f(g...
g isn't invertible in R but it is in [0;+inf[ and ]-inf;0] I think
Long story short it depends on the domain
sudden hinge
oh yes on some restricted intervals it is
alpine sable
Yeah that's what I was thinking about
rotund pumice
So if we know that the domain is [-1, 0), we can conclude that when we reach the fact that a² = b², it has to mean that -a = -b ?
and from there we can indeed conclude that a = b
alpine sable
So if we know that the domain is [-1, 0), we can conclude that when we reach the...
Yes, this is true. Since a=-b can't possibly be true if a and b are in [-1;0)
rotund pumice
.close
lone heartBOT
lone heartBOT
Available help channel!
alpine sable
They need to finish the work in 96 hours
They work for 8 hours everyday
Therefore they need to work overtime of
96-8(4) = 64 hours
Overtime rate = 1.5 * 7.5
Therefore, total payment for 4 men should be
4(64 * 11.25 + 32 * 7.5)
Guys can you see if I have done it correctly or I have messed up in understanding the question
lone heartBOT
sudden hinge
@alpine sable 4 days = 96 hours
every man works 8 normal hours per day => 8 * 4 = 32 normal hours per man
so in total the men work 32 * 4 = 128 normal hours in these 4 days.
the project however requires 224 hrs, so 224 - 128 = 96 hrs are still left which will be overtime work.
alpine sable
But in 9ii it says if the project is to be completed in 4 days so isn't 4 days the maximum limit
@sudden hinge
vital ocean
it isnt the maximum limit, but the question is asking if it was completed in 4 days how much did they work
sudden hinge
But in 9ii it says if the project is to be completed in 4 days so isn't 4 days t...
it still is
alpine sable
im confused on how 2 do this problem (；^ o ^)
lone heartBOT
im confused on how 2 do this problem (；^ o ^)
alpine sable
im confused on how 2 do this problem (；^ o ^)
also this is abt solving problems involving permutation :D
lone heartBOT
@alpine sable Has your question been resolved?
sudden hinge
So you have 7 distinct letters
first look at how you might place the L
basically we have to fill in these places _ _ _ _ _ _ _
where could L possibly be here?
all work except for the first one right? because if the L is at the first place, the I cannot be left to it
alpine sable
OHHH :O
rotund plank
Can’t we just ||take the number of combinations and divide by 2? Since for every I…L we have an L…I?||
Permutations* but you get the idea
alpine sable
how many combinations are there ?-?
rotund plank
Are you familiar with this sort of notion
If we have 5 distinct numbers we can rearrange them in 5 x 4 x 3 x 2 x 1 ways
We can place the first object in 5 ways, leaving 4 remaining places where we can place the next, and so on
It follows from the exact same logic
alpine sable
kind of T-T im still a bit new 2 it bcos we jus learned it yesterday 🏃♀️
rotund plank
What state of your education are you in?
alpine sable
What state of your education are you in?
in asia, im in 10th grade :D
rotund plank
Alright so like 15/16 sort of thing?
alpine sable
yes ^o^
alpine sable
mhm
alpine sable
take ur time sir :'D
rotund plank
_ _ _ _ _ _ _
Right
So consider the first place there
And also consider each of the letters we can use
So H, O, L, I, D, A, Y
How many different letters could we place in the first slot?
lone heartBOT
rotund plank
.reopen
lone heartBOT
✅
alpine sable
How many different letters could we place in the first slot?
I THINK 6 ? bcos if u put L in first slot u cant put 1 to the left ??? i dunno ToT
rotund plank
Let’s imagine we didn’t have any restrictions like that
So we can use any letter we want
alpine sable
then 7 ? :o
rotund plank
Yeah
So now, after we’ve placed one there, how many could we then place in the next slot?
alpine sable
another one ? T-T
rotund plank
How many different letters
alpine sable
5 ! :o
rotund plank
Yeah and then we can just continue in the same way
Basically, since we can place 7 different letters in the first slot, and once one is place we have 6 in the next, and so on
We can count the numbers of total permutations
We multiply the amount of possibilities in each place
And so we have $7! = 7\cdot 6\cdot 5\cdot 4\cdot 3\cdot 2\cdot 1 = 5040$ TOTAL combinations
ocean sealBOT
dk.dkn
rotund plank
Does that make sense so far?
alpine sable
ohhhh i see :o
alpine sable
Does that make sense so far?
yes :D
rotund plank
Alright
That’s a very important concept to know for these sorts of questions
Now for this question specifically, we can rearrange the word however we want, the only restriction is that I must come before L
Since the letters come one after the other, for any arrangement with L and I in one place, we could just swap them around. In exactly one of those our condition is satisfied
So how many permutations do you think we’ll have for that question?
alpine sable
hold o n sir my brain is dying 〒▽〒
rotund plank
Let’s just forget about the letters other than L and I for now
So consider _ _ L _ _ I _ for example
alpine sable
mhm :'D
rotund plank
Now obviously _ _ I _ _ L _ is also valid right? We can just swap the letters around
Just imagine random letters placed in the other slots
alpine sable
ohhh :o
rotund plank
For example A D L H O I Y
We can also have A D I H O L Y
So you can see that for any permutation, there is a complement to that with the letters switched over
And for just one of those is I to the left of L
alpine sable
ohh i see :O but how do i calculate on how many ways that they can be rearranged though bc wouldnt that take a while if i manually do it ? ToT
rotund plank
Not if you think about the trick to it
So we have 5040 total ways of arranging that group right?
From before
alpine sable
yes, i remember ! :D
rotund plank
7 x 6 x 5 x 4 x 3 x 2 x 1
Alright
In each of those, we do have the letters I and L, right?
alpine sable
yes :O
rotund plank
And in each case, either I comes before L, or L comes before I
Because they can’t be in the same place
alpine sable
mhm
rotund plank
Can you work out in how many of our 5040 original arrangements I is before L?
rotund plank
Okay let’s think about this
If we have some arrangement with I before L
We can swap the letters and get another valid arrangement
And the other letters remain the same
So we could group our arrangements into pairs right? Pairs of arrangements where they are the same word, but with I and L swapped over?
alpine sable
Can you work out in how many of our 5040 original arrangements I is before L?
then does that mean it just stays the same then bc only I and L was swapped or am i wrong T___T
rotund plank
5040 is the amount of every single arrangement
But we could split those arrangements up into pairs, so in half of the arrangements I comes before L, and vice versa
Can you work out how many now?
rotund plank
Yeah, all the question requires is a small trick
If you want to learn more about this topic (combinatorics) you should look into the nCr function, it’ll make lots of these questions very easy
alpine sable
ohhh i see thank u ! i hope i wasnt much of a bother (￣ o ￣*)ゞ
alpine sable
can i ask more questions if that's alright ?-?
rotund plank
Go for it
outer stump
outer stump
Hey so
My question is, how exactly did they evaluate the limit for the first integral
After they apply the limit, the exponential in the first integral just disappears
How ?
barren bolt
im pretty sure that since the integral varies from 0- to 0+ they just assume that the exponential is 1
which it will be since that type of integral is really a limit
its just engineering things tbh
barren bolt
e^0=1
and since the integral goes from 0- to 0+ they just use that fact
the integral is a limit anyways so they just take the limit preemptively im pretty sure
barren bolt
i mean tbh an integral from 0- to 0+ seems slightly sus
its like an integral over a delta function
outer stump
In what sense
barren bolt
well it's only non-zero if the function is discontinuous at 0
so for most functions it doesnt even mean much
but the discontinuity of f doesnt matter to exp since it is definitely cont.
thus you can just take that limit on the exponential
outer stump
So ok
Because the bounds are situated near 0
Unless the function is discontinuous, it evaluates to 0?
barren bolt
yeah since if the function were continuous then the limit of 0- and 0+ are the same
since that is one way to define continuity
if both sides of a limit are equal
outer stump
Ok and why is it possible to evaluate the exponential and not function f?
barren bolt
well we dont know whether f is continuous
but we do know exp is
so it will be 1 for sure
i think it would be more clear if they did that simplification afterwards
but it doesnt make a difference really
whether they take the limit before or after evaluating the integral
if you want, try to work it out but keep the exp term in until the end
the lim as s goes to infinity will stay a little longer that way
but it'll still work in the end
outer stump
Hmmm
I think i get the logic behind it
So for f to stay we have to assume it's discontinuous
At 0
barren bolt
yeah otherwise the integral is zero
robust tangle
Hi Im currently trying to do induction homework and I'm a bit confused by it I think. The problem is that basically I have to prove that 1/(3n-1)(3n+2)= n/6n+4 and I don't think I'm doing it properly because the step I'm currently on I can't see how its correct
vale sapphire
Do you mean (3n-1)/(3n+2) or something
Because there is no way that's correct as it stands
The former tends towards 0 as n → +∞ and the latter tends towards 1/6
gray isle
do you have the question exactly as stated?
gray isle
yes, to ensure you aren't misrepresenting the problem
robust tangle
okay
gray isle
and/or omitting important details
robust tangle
The one I was looking for help on was number 1
but if its just a case of doesn't apply i was hoping to get help for one of the others instead
gray isle
you pretty much omitted the entire series....
gray isle
have you done any induction before?
robust tangle
I have but I'm still a bit confused by it
the first thing I tried to do was set n=k
gray isle
can you show what you've done so far?
gray isle
this is structured poorly, those stray k+1 hovering around don't help either
robust tangle
oh sorry
I'm still trying to remember and unsderstand the format so I would just put it there to remember what that value was
gray isle
you should also have text to separate each section and give brief descriptions of what you're doing
it's be a good idea to look up a few examples
robust tangle
i have list of them on my other monitor actually 😅
mine doesn't quite look like theirs so I'm looking for where I went wrong and to either start new or see what I did wrong
gray isle
start again
robust tangle
I have but I got lost again but I've done all the steps similar to the examples ive been looking at
would you like me to show what ive done over?
gray isle
you cant just ignore the whole series
robust tangle
I'm a bit lost by what you mean im sorry
gray isle
you can't just set
final term = sum of all the terms
robust tangle
but how would I use all the terms to find my answer then?
gray isle
first, write the equations properly
gray isle
yes
robust tangle
okay
do I go back to doing what I was doing before with checking for n=1 and setting n=k after?
gray isle
show me what you currently have now
robust tangle
currently its just the equation exactly as is copied down. I'm not sure where im messing up so i'm a bit scared to continue from here
gray isle
show me exactly what you have
robust tangle
gray isle
now what will the equation be when n=k
robust tangle
gray isle
what will the equation be for n=k+1
robust tangle
gray isle
now the goal is to show that's true using the equation from n=k
it'd also be helpful to have included the term with 1/((3k-1)(3k+2))
to prove that if true for $n=k$:
$$\red{\frac{1}{2 \cdot5} +\dots + \frac{1}{(3k-1)(3k+2)}} = \frac{k}{6k+4}$$
then it is also true for $n=k+1$
$$\red{\frac{1}{2 \cdot5} +\dots + \frac{1}{(3k-1)(3k+2)}} + \frac{1}{(3(k+1)-1)(3(k+1)+2)}$$
$$ = \frac{k+1}{6(k+1)+4}$$
ocean sealBOT
ℝamonov
robust tangle
oh
so I add the n=k and the k+1 together to get the k+1
I think I get it a bit
hold on
wouldn't the first thing I want to do is simplify the 2nd equation?
like distribute the 3 in the denomionator
gray isle
you can if you want
gray isle
no
combining the last two terms in the summation doest help you
and you aren't using the result from n=k either
(which if don't use, you aren't doing induction)
note what I highlighted in red in the image above
robust tangle
so it should look like = k/6k+4?
wait no
summnation is what comes after the equal sign right?
im a little lost sorry by what you mean exactly sorry
gray isle
summation is the sum of terms
the stuff on the right of the equal sign is the alleged simplified result
note that the red part in the equation for n=k,
is present in what you're trying to prove/show
robust tangle
okay so I dont want to add them is what I'm getting but I'm not sure what else I would want to do otherwise
would i want to get the result of k+1 on its own?
robust tangle
yeah the red one
gray isle
note that the red stuff is also present in the equation for n=k+1
gray isle
yes
robust tangle
and I want to add the result from K+1 to it
gray isle
wdym by add the result?
gray isle
try not to overthink this
robust tangle
on the left side
gray isle
what does the
red stuff =
robust tangle
n=k
gray isle
no
robust tangle
but its the same?
gray isle
red stuff does NOT equal the equation n=k
robust tangle
but its what happened when we set the last term as n=k from before?
gray isle
in case it wasn't clear, by red stuff, I'm referring only to the stuff being highlighted in red
robust tangle
yeah
gray isle
wdym set the last term
robust tangle
its what we got at the end of the left side from when you told me n=k
so in the problem theres the addition of all the fractions
gray isle
it's the entire equation
robust tangle
and the red part is the last fraction in that side
gray isle
every single n is replaced with k
and the red part is the last fraction in that side
no
where are you getting that idea
robust tangle
is that not what it is
gray isle
no
gray isle
the red part is the summation up to the kth term
robust tangle
thats the part im not sure of I don't get how I can do that
like im not sure of the steps to take
gray isle
try not to overthink this
robust tangle
to do that
gray isle
basic substitution
gray isle
yes
robust tangle
instead of what it is currently
wait so is that what you've been trying to tell me this whole time?
wait but not 1 on the right
on the right 1 is k+1 i just went too fastr
gray isle
erase those 3 dots around the bottom left
robust tangle
oh sorry
gray isle
and the rest is more or less algebra
robust tangle
and my end goal is to make the right and left be the same number right
right and left of the equal sign
gray isle
yes
robust tangle
okay
so what I want to do now is factor the denominator for k so it becomes 2(3k+2)
which is a step in the right direction right?
and then from there make the denoinators between the 2 terms on the left the same so they can be added together
lone heartBOT
@robust tangle Has your question been resolved?
robust tangle
so i tried it that way and it definitely doesn't look right
but i'm not seeing how I can make them equal the same
rare basin
where is my mistake? C_2 should be -(4/3) not -(5/3)
lone heartBOT
where is my mistake? C_2 should be -(4/3) not -(5/3)
@rare basin Has your question been resolved?
lone heartBOT
@rare basin Has your question been resolved?
tacit arch
where is my mistake? C_2 should be -(4/3) not -(5/3)
can you show the original question
i can't really read your handwriting that well
rare basin
can you show the original question
mit is the german word for "with"
i think i have everything right untill the integral calculus
tacit arch
,w differentiate ((x+1)^3)/3 - 5/3
ocean sealBOT
tacit arch
,w differentiate (x+1)^2
ocean sealBOT
tacit arch
,calc ((1+1)^3)/3 - 5/3
ocean sealBOT
Result:
1
,calc (1+1)^2
ocean sealBOT
Result:
4
yea this looks right to me
lone heartBOT
@rare basin Has your question been resolved?
storm grotto
@tropic warren how far have you gotten?
tropic warren
Not far, are you a mod?
storm grotto
mod?
tropic warren
Yes
storm grotto
what's a mod?
tropic warren
Nvm
lone heartBOT
Available help channel!
peak gorge
Are you given a picture of rectangle N?
tropic warren
Are you given a picture of rectangle N?
No, just P
peak gorge
The answer is
Since rectangle N contains 5 square units, and Rectangle P contains 45 square units, divide 45 by 5 to get your answer
The answers 9
tropic warren
Thanks
peak gorge
Np
tropic trout
boobz
peak gorge
.close
lone heartBOT
tropic trout
l
lone heartBOT
Available help channel!
cyan marsh
lone heartBOT
@cyan marsh Has your question been resolved?
plain zodiac
lone heartBOT
plain zodiac
how do you get the LCM
wary stream
how do you get the LCM
If you have 1/3 + 1/23, how would you find the LCM?
plain zodiac
If you have 1/3 + 1/23, how would you find the LCM?
multiply 23 by 3
wary stream
And why would you do that?
wary stream
That's the same process for the question you had
You're multiplying all the denominators to get the LCM
Another way to think of it is clearing fractions
Fractions are harder to work with so if you multiply all the terms by the LCM, it makes all the terms not fractions
plain zodiac
You're multiplying all the denominators to get the LCM
how
wary stream
By multiplying all the denominators together
Here, 1/3 + 1/23, you did 23 * 3, to get the LCM
Same idea with 1/a + 1/b = 1/c
You multiply all the denominators and that's the LCM
wary stream
As I mentioned, the concept that is being demonstrated is, what I call, clearing fractions
It doesn't matter if there's an equal sign or not, the process is still the same, you multiply all the denominators together and that's the LCM
wary stream
That is what all means, it means every denominator
wary stream
its bc/abc + ac/abc = ab/abc?
This does not make it bc +ac =ab
plain zodiac
oh
wary stream
To find the LCM, you multiply all the denominators together, in your problem, the LCM is abc
Then you multiply all the fractions by that LCM
wary stream
You don't multiply by abc/abc
wary stream
Yes
plain zodiac
thank you
earnest bay
lone heartBOT
earnest bay
Not sure how to deal with the the angle x and 2x
timid oracle
