41/25 - 13i/25?
#help-0
outer lark
sure
fast tiger
I got this notification
fast tiger
I got it, thanks
outer lark
no worries
prisma laurel
rigid island
well to start off
you need to find the equation of the bridge, then using solids of revoultion, rotate it around y axis to find its volume
then you need to find the normal force of the truck * the weight force of the truck
then multiply everything by 2
and you'll have your answer
lone heartBOT
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prisma laurel
.close
flat gyro
hey there, i don't understand this question. how are these A's the same? A^2 doesn't hold for the second part. are these just representations or what? if so, how do i solve it for sqrt(A^2)?
ancient saddle
hey there, i don't understand this question. how are these A's the same? A^2 doe...
Hello, those A's "are the same". I mean:
A² = A(A)
Also I think that info about the eigenvalues just holds for matrix A
vale wigeon
do you know the defn of the height of a tree?
right
to prove that the height of a tree is at most n we show that each node in said tree is in distance at most n from the root.
so let h be the height of (T, r) and let x ∈ V. try to show that dist(x,r') ≤ 2h.
no, just an arbitrary node.
placid zinc
Am I misunderstanding the question? Why couldn't we pick (T, r') to be a leaf or something with height 1?
Assuming the point we pick becomes the root of its own tree
lone heartBOT
@earnest carbon Has your question been resolved?
night hedge
Hello I am confused with the wording of this question. Can you explain to me the terminology? For question 23 I ended up trying to put it in vertex form. But its asking for general form.
night hedge
Question 27*
fathom mantle
lone heartBOT
@night hedge Has your question been resolved?
night hedge
oops sory
Was wokring on other problems
Yea so I guess I am confused
With how to build the general formula with h,k and x,y
long axle
y = a(x-h)^2 + k
Plug in h and k
Then plug in x and y to solve for a
Then multiply out everything and voila
night hedge
Ohhhhhhh I see I didnt have a 0
Or rather
Y
I was doing the formula with out an equal sign
lol
Thank you!
.close
ember dagger
Hey how do I do this?
lone heartBOT
Hey how do I do this?
vale wigeon
if there were no complex numbers involved here, would you be able to do this?
harsh shadow
Isn’t -3-i a complex number
i is an imaginary number
and imaginary numbers are complex numbers
ember dagger
Oh
For the x^2 part was right
Right
@harsh shadow
So it’s
X^2-3-i
Am I right
@harsh shadow
<@&286206848099549185>
lone heartBOT
@ember dagger Has your question been resolved?
agile mason
how do i go about solving this question ?
lone heartBOT
how do i go about solving this question ?
agile mason
me too homie
lone heartBOT
@agile mason Has your question been resolved?
agile mason
L(x)?
no?
long axle
Linearization
ocean sealBOT
Stephen
agile mason
now that i think about it, my teacher skipped this entire section but included it on the test review
so no i dont
long axle
Ur problem wants to find the approximation at x = 1, so for the formula, let a = 1
agile mason
and the tangent line is the derivative?
lone heartBOT
Available help channel!
silver wasp
How do I solve for question 5a?
lone heartBOT
How do I solve for question 5a?
silver wasp
lone heartBOT
@silver wasp Has your question been resolved?
tacit arch
,rotate
ocean sealBOT
tacit arch
How do I solve for question 5a?
divide the equation by 3 first
silver wasp
oh ok
tacit arch
silver wasp
how do I do that when like the x is x^3 x^6 like big numbers
silver wasp
oh ok
let me try it
how do I find a slate
wait is this one 5?
x=5
bec it doent have a slate
tacit arch
how do I find a slate
you mean slant?
silver wasp
yeah
tacit arch
that's correct, just horizontal and vertical
mortal mica
how exactly, is euler's formula applied here
lone heartBOT
how exactly, is euler's formula applied here
mortal mica
alpine sable
hellow
ocean sealBOT
ibn
hollow sparrow
keen plinth
engineers
ocean sealBOT
tough hamlet
Hi, for this:
lone heartBOT
Hi, for this:
tough hamlet
For the top part would I just go through all the numbers x has for the x(i) and y(i)?
And similarly in the bottom?
tacit arch
yes. the summation over i is omitted because the author is lazy and thinks it's implied
lone heartBOT
lone heartBOT
Available help channel!
icy basin
help
lone heartBOT
@icy basin Has your question been resolved?
icy basin
<@&286206848099549185>
lone heartBOT
@icy basin Has your question been resolved?
amber nymph
V=4/3pir^3, differentiate with respect to t and equate it with 2 to get dr/dt, r=12ft. Next differentiate S and plug in the values you got from above
icy basin
thank you so much
atomic quarry
2 linear functions and 1 quadratic function such that the product of the 3 functions
build a quartic function with a double zero at -1 and a y-intercept at (0, -3). Write the equation
of the quartic function. Explain your reasoning
atomic quarry
2 quadratic functions such that the product of the 2 functions build a quartic
function with only 2 x-intercepts at (-2, 0) and (1, 0) and a y-intercept at (0, -8). Write the
equation of the quartic function. Explain your reasoning.
lone heartBOT
@atomic quarry Has your question been resolved?
twilit sleet
Can someone help me, in trying to figure how should i put this, The (TIME) the time was 6 years and 9 months how should i put it. Should juwt put it as 6.9. but im not sure if that's correct.
My only problem is the T i already know the rest.
Sorry I can't explain fluently since English is my second language.
atomic quarry
is this for me?
lone heartBOT
@atomic quarry Has your question been resolved?
tacit arch
is this for me?
No. they're new to the help channels system
lone heartBOT
@atomic quarry Has your question been resolved?
lone heartBOT
lone heartBOT
Available help channel!
silver furnace
Anyone know why this don’t work
lone heartBOT
Anyone know why this don’t work
silver furnace
Where
low quartz
silver furnace
I tried to do it 2 different ways
low quartz
see
now if you open the parentheses
the equation will become
6x-5x-2=1
x-2=1
x=3
@silver furnace do u get it!
silver furnace
<@749314753381531768> do u get it!
I think so (nice pic btw
Also the right side can’t be done like that???
Do I have to use substitution
low quartz
as your wish
there are three methods
to solve linear equation in two variables
1)graphical
2)substitution
3)elimination
you can use any of them
silver furnace
So the right side which was graph was it correct so far?
silver furnace
Ok thank you for your knowledge 🙏
silver furnace
Thanks! I usually have problems lol
low quartz
okk
gilded narwhal
Hi there can someone explain me how to answer a Age problem
lone heartBOT
Hi there can someone explain me how to answer a Age problem
umbral hatch
The problem being?
gilded narwhal
The sum of Patricks age ang mako's age is 58. Eight years ago, Patrick was twice as old as Mako then. How old is Mako?
gilded narwhal
Set up equations solve simultaneously
huh?
gilded narwhal
U know how to do that
I think I can't
umbral hatch
So say,
Can u solve X+y=2
And 4x-6y= 233
Don't actually solve it cuz it's a random thing
But do know how u would approach it
Using those 2 equations to find X and y
gilded narwhal
Sorry I can't understand
solid gust
Make a equation of
gilded narwhal
Make a equation of
p=patrick M=mako
P+M=58
solid gust
Make a equation of
gilded narwhal
Make a equation of
I don't know how create aequation from that
solid gust
Patrick
gilded narwhal
8-?
solid gust
So, how would you define Patrick 8 year ago?
gilded narwhal
8-(2p?
solid gust
Focus on the 8 year ago. Use P to define the age of Patrick 8 year ago.
gilded narwhal
8-P?
gilded narwhal
p-8?
solid gust
Since all the variables is on ages. So P-8 equals Patrick 8 years ago.
gilded narwhal
define what?
solid gust
Set up a equation
gilded narwhal
p-8*2?
solid gust
Define Marco 8 years ago
gilded narwhal
m-8?
solid gust
gilded narwhal
2(p-8) = m-8
solid gust
p=patrick M=mako
P+M=58
Solve with this
solid gust
You got 2 equations, use them to find the variables.
solid gust
2p-16 = m-8
Isolate m.
solid gust
Make that there's only m on a side. 2p-16=m-8
distant shard
gilded narwhal
Make that there's only m on a side. 2p-16=m-8
2p-16+8=m?
solid gust
p=patrick M=mako
P+M=58
Now just solve.
solid gust
2p-16+8=m?
2p-16+8 => ?
gilded narwhal
2p-16+8 => ?
huh?
gilded narwhal
-24?
gilded narwhal
-12?
solid gust
What is 16 - 8
gilded narwhal
8 oh wrong number HEHE
solid gust
2p-16+8 => ?
So...
gilded narwhal
M=4P?
solid gust
What is M in terms of P?
gilded narwhal
IDK
solid gust
You use the second equation in the first one.
P + (2P + 8) = 58
I think that will be.
solid gust
P + (2P + 8) = 58
You'll find Patrick's age by this. And use this in the second equation, so that you find Marco's age.
Gtg, good luck.
gilded narwhal
3P+8P=58?
gilded narwhal
Gtg, good luck.
ok thank you for teaching me.
lone heartBOT
@gilded narwhal Has your question been resolved?
frigid abyss
lone heartBOT
lone heartBOT
@frigid abyss Has your question been resolved?
lone heartBOT
@frigid abyss Has your question been resolved?
naive timber
answer is b
3 is number of sides figure A has right because x equals number of sides figure A has
and 6 is number of side figure B has
frigid abyss
@naive timber thank you so much
naive timber
no woz
empty plover
if a=bq+r , gcd (a,r)=gcd(a,b)
?
euclidean division
lone heartBOT
if a=bq+r , gcd (a,r)=gcd(a,b)
?
euclidean division
vale wigeon
yes, this is true
and can be proven directly from the defn of divisibility and some simple properties thereof
empty plover
turned out false, i think you might have misread it
a = 8, b = 3, alors r = 2
a ^ b = 1
a ^ r = 2
tho thanks a lot
.close
lone heartBOT
alpine sable
.thats not how the euclidean algorithm works tho
empty plover
.reopen
lone heartBOT
✅
empty plover
wdym
alpine sable
.q=2 means r=0
empty plover
a=3*2+2
alpine sable
r needs to be 0≤r<q
empty plover
q is 3
alpine sable
then b is 2
alpine sable
yea
empty plover
divide 8 by 3
empty plover
hold on
ok lets call q our quotient again
8=3*2+2
so 2 is q
3 is b
no i am not
i think you are
alpine sable
ok, then that should say gcd(a, r)=gcd(a,q)
empty plover
yeah the theorem is false as stated it turned out
empty plover
ok, then that should say gcd(a, r)=gcd(a,q)
but it seems youre giving me another one
that is true
alpine sable
I'm just going by common notation
empty plover
q is quotient by common notation
empty plover
you're saying gcd(a, quotient)= gcd (a,remainder)?
alpine sable
no
alpine sable
remainder and quotient
empty plover
ah and why is that true
alpine sable
and can be proven directly from the defn of divisibility and some simple propert...
^
empty plover
intutiively
alpine sable
factor out gcd
empty plover
idk what you mean
alpine sable
if d|a and d|q, then clearly d|r
runic ledge
hi !
runic ledge
is 1 or 2 exact?
empty plover
1
empty plover
its .close
rich panther
lone heartBOT
rich panther
How do I begin with to solve this equation?
delicate jacinth
If you do $k = \sqrt[3]{x^3+1+\sqrt[3]{x^3+1+\cdots}}$, you have $\sqrt[3]{x^3+1+k} = k$
ocean sealBOT
sopinha
ocean sealBOT
sopinha
delicate jacinth
$\sqrt[3]{x^3+1+2022} = 2022$
ocean sealBOT
sopinha
delicate jacinth
,w \sqrt[3]{x^3+1+2022} = 2022
ocean sealBOT
rich panther
**sopinha**
But the first one is square root not cube root
delicate jacinth
$2022 = \sqrt[2]{x^3+1+\sqrt[3]{x^3+1+\cdots}} \iff 2022^2 = x^3+1+\sqrt[3]{x^3+1+\sqrt[3]{x^3+1+\cdots}} \iff 2022^2-x^3-1 = \sqrt[3]{x^3+1+(2022^2-x^3-1)}$
ocean sealBOT
sopinha
alpine sable
solving a degree 6 9 polynomial 
alpine sable
ah yeah
alpine sable
oh damn, thats nice
delicate jacinth
yes
rich panther
but then when solving for x it doesn't give out a match answer to the multiple answers
these are the answers that given below the question
delicate jacinth
all of these?
delicate jacinth
,w 2022^2-x^3-1=2022^(2/3)
ocean sealBOT
rich panther
delicate jacinth
**sopinha**
we got this before
rich panther
you're right
delicate jacinth
but still does not give any of the answers
rich panther
rich panther
but still does not give any of the answers
yeah
i think the question is wrong
it should be all square root
rich panther
rich panther
the answer is the same as ង (The last answer)
lone heartBOT
lone heartBOT
Available help channel!
alpine sable
Can I write my question here?
lone heartBOT
Can I write my question here?
alpine sable
Please don't mind the listening part
- Since the graph shows 30 m/h is equivalent to 25
The answer is 25?
- 5 fewer shirts means 95 shirts per week so it'll be 11 dollars. So $11×100(shirts)=
$1100?
- 17,14,11 so 17 years old? Bcz it says Jeremy was 41 *last year?
- Can u teach me the formula, I don't know how 😔
- 13/20 because number of the outcomes/total number of outcomes?
lone heartBOT
@alpine sable Has your question been resolved?
lone heartBOT
@alpine sable Has your question been resolved?
alpine sable
<@&286206848099549185>
shut pewter
1. Since the graph shows 30 m/h is equivalent to 25
The answer is 25?
You almost got it, but it's asking for 5 hours of travel
x represents the speed while the y axis represent the miles per gallon
We know that 30m/h = 25 m/g
And we needed to how many gallons of gas are needed for a 5 hour travel with a constant speed of 30 miles/ hour
so just do 25 times 5
shut pewter
- here, we know that a sphere has a radius right?
But the radius is inscribed in the cube
And so does the whole sphere
So basically, it's like a ball perfectly fitted in a box
We know that if we measure the diameter of the sphere, it is the same as the side of the cube
So 2radius = diameter = side of cube
Since it is a cube, all sides are the same
And by using Pythagorean theorem, we can find the diagonal line of the cube
How to find it? Simple! Just find first the hypotenuse of the square (you can use any of the faces of the cube, but use the bottom face of the square for easier understanding).
So we now have the hypotenuse of the square, then us it and one side of the cube to get the diagonal via pythagorean theorem again.
solid bay
does anyone know this, I’ve had other questions where I get the formula and get it right quickly, but this one I’m struggling (im not the smartest just getting back to school after awhile of being gone)
shut pewter
does anyone know this, I’ve had other questions where I get the formula and get ...
Pleases next time, learn on how to use the channels on to how to ask for help
shut pewter
does anyone know this, I’ve had other questions where I get the formula and get ...
This is basically just a sector of a circle
A circle has an angle of 360 degrees
alpine sable
Thanks @shut pewter I'll tell u the answer and the method so could u wait for me?
shut pewter
Thanks <@910156963181101086> I'll tell u the answer and the method so could u wa...
Sure y not?
So anyways @solid bay , a circle has an angle of 360 degrees.
Meaning, it's a full rotation
If you spin yourself
Then it's a rotation
That's just basically what angles are
A portion of a full rotation
And at that example, we can see that the circle has a portion of a rotation
So the given degrees / 360 (area of a circle)
shut pewter
Yes, and the other sides should also be tangential to the circle
Since it's a sphere touching the sides of a cube
If the sides of a cube is tangential to sphere, it means that it perfectly fits
Think of it as a square box that has a ball inside that perfectly fits it
alpine sable
Mhm
shut pewter
So the given degrees / 360 (area of a circle)
@solid bay this is your answer now read this https://discord.com/channels/268882317391429632/488120190538743810
shut pewter
The hypotenuse of the
Not exactly
A cube is 3d, that's a square
which is 2d
Think of it as a ball that is perfectly fitted inside a square box
alpine sable
alpine sable
4 isn't it?
shut pewter
If you look it at the front you will see something like this
shut pewter
If you look it at the front you will see something like this
You can see that the diameter is equal to the sides of the cube right?
alpine sable
Yes 👍
shut pewter
I think you have now the general idea on how to solve this
shut pewter
Look again at your picture
How do you think you will find the diagonal of the square?
alpine sable
By using the Pythagorean theorem
shut pewter
How do you think you will find the diagonal of the square?
But how are you going to use it?
shut pewter
The hypotenuse of the
Look at the other picture that you draw earlier
shut pewter
The hypotenuse of the
This is the what you will see if you look at it at the bottom
alpine sable
Right triangle?
shut pewter
Right triangle?
Yes
shut pewter
The hypotenuse of the
This is what you will see at the bottom if you put a diagonal stick inside the box
alpine sable
So, all sides are 4 cm
shut pewter
So, all sides are 4 cm
Yes
alpine sable
4✓2?
solid bay
<@829935067828191312> this is your answer now read this https://discord.com/chan...
Thank you, and next time if I ask for help I’ll use the correct channel, my apologies.
shut pewter
But we are trying to find the 3d diagonal
shut pewter
Thank you, and next time if I ask for help I’ll use the correct channel, my apol...
np
alpine sable
Ohhh ..
shut pewter
4✓2?
in the Pythagorean formula, this would be a
And b would be the side of the cube
which happens to be 4
use a^2 +b^2 here
alpine sable
Yep
shut pewter
So what is your answer?
alpine sable
4✓2???
shut pewter
<@456226577798135808>
Here is a better representation
The one labelled as shorter diagonal or the bottom one is 4 square root of 2
4✓2
alpine sable
4
alpine sable
Ohhhhhhhhhhhhhhhhhhhhhhh
alpine sable
Ohk
shut pewter
Or just use this
If you used again the pythagorean formula, you will get the same answer here
So ✓((4✓2)^2+(4)^2) = 4✓3
shut pewter
Sure
alpine sable
So for number 2 ,
Do we use the system of equation?
Uh, could u help me for the probability question
shut pewter
About number 2 @alpine sable , what grade level are you now?
alpine sable
I'm at 9 rn but, this is a central/ enrollment exam sample for my junior high school and I have the exam tom.
shut pewter
I'm at 9 rn but, this is a central/ enrollment exam sample for my junior high sc...
Aaaah
Because the only thing I can think of solving this is by differentiation
And you're still at grade 9, so that would be a problem
alpine sable
Ohhhhh
shut pewter
Have you done parabola?
alpine sable
Is it grade 9 ?
shut pewter
Dunno about your educational system
How about discriminant of roots
I remember of learning that during grade 9, did they teach you discriminants also?
alpine sable
Is that like quadratic function?
shut pewter
Is that like quadratic function?
Yeah
alpine sable
Yeah I've learn it
shut pewter
So let's do this step by step
alpine sable
Okes
shut pewter
Let's start with the increase in price first
For every dollar of increase in price, there is a decrease in sales by 5 tshirts
alpine sable
Yes mhm
shut pewter
Back then, they were selling 100 t shirts, right?
alpine sable
Yess
shut pewter
So what equation would we use to determine the number of new sales after the increase in price?
For example, I increased the price by $5, how many tshirts are now sold weekly?
alpine sable
(10+5)100
shut pewter
(10+5)100
Nah
that would be 15 times 100
the product would be 1500
Are you saying that the sales increase because I increased the price by 5 dollars?
That seems counterintuitive and contradicting to our problem
alpine sable
Yes no one would buy it
alpine sable
There's something wrong with it
shut pewter
(10+5)100
You're saying this is the equation for the number of tshirts sold weakly after the increase
Try to find another equation that suits the problem
Try to substitute it by 1 first
Then 2
Then 3
Try increasing the price by 1, 2, then 3
See the relationship
alpine sable
100-(10-n)
shut pewter
100-(10-n)
You already got the idea of 100 - something
Find that something
Reread the problem, there's a "5 decrease" in the sale of t shirts for every "$1 of increase"
alpine sable
100(10-n)
shut pewter
100(10-n)
try to multiply 100 inside the parenthesis
It says 1000 - 100n
Then substitute 1
1000-100 = 900
You're saying that there are 900 tshirts that are sold after increasing the price by a dollar
shut pewter
100-(10-n)
You almost got it in here
For every a dollar of increase, there's a 5 decrease in sales of t shirts
alpine sable
100-(100-n)
shut pewter
100-(100-n)
Almost
shut pewter
100-(100-n)
But still wrong at the right part
shut pewter
For every a dollar of increase, there's a 5 decrease in sales of t shirts
Think of this
How would you calculate for the decrease in the sales of t shirts?
How would you calculate the number of t-shirts that wouldn't be solve after increasing the price for a dollar?
@alpine sable
What if you increase the price by 1?
What would be the decrease in the sales of t shirts?
alpine sable
Uhmm
shut pewter
Reread the problem, there's a "5 decrease" in the sale of t shirts for every "$1...
hint
shut pewter
100-(10+n)
Nooooh
That would be 90 + n, you're saying again that the number of t shirts increases for every increase in price
Try to think small first @alpine sable
What would be the total number of t shirts that would be sold if you increase the price by $1?
alpine sable
95
shut pewter
100-(10+n)
Do you think you're going to get 95 here if you substitute 1?
alpine sable
No
alpine sable
No
shut pewter
What would be the total number of t shirts that would be sold if you increase th...
No what I mean is do this again
But this time, the increase is $2
alpine sable
Ohh, 90
alpine sable
85
alpine sable
Decreasing by 5?
shut pewter
Decreasing by 5?
YES THAT'S WHY I ASKED YOU TO REREAD THE PROBLEM
So (Original number of t shirts) - (decrease in t shirts)
100 - something
What is the equation of something
alpine sable
100-(5×n)
shut pewter
100-(5×n)
THAT'S IT
So the total tshirts sold is 100 - 5n
Let's leave it aside and go back to the problem
We are going to use this later on
alpine sable
Ok
shut pewter
So according to the problem, what would be the total sales for a week?
What would be the total profit?
alpine sable
$1000
alpine sable
100 t-shirts multiplied by $10
shut pewter
100 t-shirts multiplied by $10
So number of t-shirts multiplied by price
alpine sable
Yes
shut pewter
We already have the solution for the t-shirts
so (100 - 5n) x (???)
The ???, what do you think would it be?
hint : (??? is the price, create a relationship for the price based on the problem)
alpine sable
$1000 and $1100 if it's 95 t shirts
shut pewter
$1000 and $1100 if it's 95 t shirts
You got this wrong also
shut pewter
$1000 and $1100 if it's 95 t shirts
What method did you use here?
shut pewter
Is it $1095
Wrong
Almost you got the tens place wrong
@alpine sable , start thinking small again
shut pewter
Reread the problem out loud and see if you notice something
alpine sable
(10+1)
shut pewter
So (10 + increase in price right)?
alpine sable
Yes
alpine sable
Increase in price
shut pewter
Increase in price
So the equation for the new price is?
alpine sable
(10+n)
shut pewter
so (100 - 5n) x (???)
Refer to this again
So number of t-shirts multiplied by price
What would be the equation now, @alpine sable ?
alpine sable
(100-5n) x (10+n)
shut pewter
(100-5n) x (10+n)
If you try to expand this, this is a quadratic equation
@alpine sable You have seen a quadratic equation, right?
alpine sable
Yes I have
alpine sable
(100-5n)^2 + (10+n) + n
shut pewter
(100-5n)^2 + (10+n) + n
No
alpine sable
Wait rq pls I need to 💤
I'll be back soon sorry and thanks for helping me I appreciate it, although we couldn't reach to the end I had the encouragement to learn. Thanks again😭😢😊
lone heartBOT
@alpine sable Has your question been resolved?
ancient pecan
lone heartBOT
ancient pecan
what values of x are possible for this function
been absent for a month so i missed a lot of things
shouldn't it be
x*x - 4 =/ 0
and the answeres are x=/2 and x=/ -2 ?
or what
pliant cedar
the ln function is real-valued for positive real numbers
echo socket
Logarithm can't be defined for nonpositive numbers, so you need to solve (2x - 5)/(x^2 - 4) > 0
alpine sable
you also have to account for the log
echo socket
And, yes, x^2 - 4 can't be 0
pliant cedar
so u want x such that (2x-5)/(x^2 - 4) > 0
ancient pecan
so u want x such that (2x-5)/(x^2 - 4) > 0
oh...
molten root
Hi, I'm learning and I don't know how to do this example. Can anyone do this and give me a step by step guide on how to do it.
lone heartBOT
Hi, I'm learning and I don't know how to do this example. Can anyone do this and...
@molten root Has your question been resolved?
plush stump
Hi, I'm learning and I don't know how to do this example. Can anyone do this and...
Its a GP with common ratio 1/e after taking x^2 common from every term?
molten root
I think so. I can't solve it
plush stump
I think so. I can't solve it
go learn about infinite GP's
molten root
Ok thanks, I will read it but I don't know if I can do it anyway.
idle raven
i cannt get this question
lone heartBOT
i cannt get this question
tacit arch
,calc e^(-1)
ocean sealBOT
Result:
0.36787944117144
oke second
tacit arch
fix that and you should be right
full briar
lone heartBOT
full briar
Can someone help me evaluate this sum? Help is very much appreciated
limpid turret
well what is cos(pi)?
full briar
-1
carmine beacon
correct... how about cos(2pi)?
carmine beacon
yes, so -1+1 = 0, so if k is odd, it will be -1, otherwise it's 1.
carmine beacon
you're welcome... so there will be a lot of cancelation
The answer is not zero, btw @full briar
full briar
Alright thanks
@carmine beacon Could you actually help me out with one more question?
carmine beacon
go for it
carmine beacon
Answer choice A? No that would not be equal to 1.
full briar
naw as in the lower bound of the integral
hoary heath
omg its elon tusk
full briar
omg its maya!
tacit arch
naw as in the lower bound of the integral
to find the correct bounds, evaluate your summand at the endpoints: i=1 and i=n and make sure your function matches them
full briar
to find the correct bounds, evaluate your summand at the endpoints: i=1 and i=n ...
Ye I get a = 1
and b = 2
if you do 1/n = (b-a)/n
carmine beacon
@full briar Probably the first thing I would check is your properties of logarithms. ln(ab) = ln(a) + ln(b).... ln(a+b) = ln(a*(1+b/a))
Once you know this, then you can compare what's different in your series to the integrals in the answer choices
lone heartBOT
@full briar Has your question been resolved?
vagrant gust
lone heartBOT
hallow citrus
lone heartBOT
@vagrant gust Has your question been resolved?
lone heartBOT
@vagrant gust Has your question been resolved?
mint gazelle
lone heartBOT
mint gazelle
i dont get where the bottom equation comes from
tribal haven
by the definition of inverse matrices
the two matrices on the left multiplied becomes the identity matrix
mint gazelle
by the definition of inverse matrices
the two matrices on the left multiplied b...
oh thats makes a lot of sense thanks
.close
steel beacon
Johnny’s candy factory produces 1200 kg of candies in 12 days using 9 machines. How many more machines will be needed to produce 1800 kg of candies in 6 days?
strange meadow
1200kg, 12 days, 9 machines
1800kg, 12 days, 13.5 machines
1800 kg, 6 days, 27 machines
27-9=18 more machines
@steel beacon
steel beacon
oh thanks!
steel beacon
.close
lone heartBOT
lone heartBOT
✅
steel beacon
i forgot i got 1 last question
The distance traveled by a car is directly proportional to the amount of gasoline it consumes. If the car consumes 21 liters of gasoline to cover a distance of 140 km, how many liters of gasoline is needed to travel 150 km?
strange meadow
this is a similar question
21liters, 140km
1.5 liters, 10km
22.5liters, 150km
you need 22.5 liters
strange meadow
lone heartBOT
strange meadow
really my question is does this definition for a group have to have e operation a = a or can it be the other way around
like a operation e = a
wikipedia says something else
it requires both to be true?
oh wait it doesn't matter the operation isn't associative
....
either way my question stands
strange meadow
is this the definition? or is it the wikipedia one
lone heartBOT
@strange meadow Has your question been resolved?
strange meadow
<@&286206848099549185>
pseudo ice
Could you send the other definitions from last time please?
pseudo ice
Wondering whether it would follow from one of those 🤔
strange meadow
im just asking about what the actual definition is
because the textbook and wikipedia are different
either way it isn't a group
pseudo ice
Hmm, what I’m wondering is whether the definitions are equivalent, tho I haven’t tried it yet
strange meadow
Hmm, what I’m wondering is whether the definitions are equivalent, tho I haven’t...
how could they be
one is it's statement A and B the other is only statement A is necessary
pseudo ice
That’s what I’m trying out atm, trying to see whether I can derive the other conditions they state from that, but it might or might not work
strange meadow
i see
pseudo ice
Hmm, pretty much all definitions I have are like the Wiki one, and I can’t seem to show why they would be equivalent to your one (possibly because they’re not?) 😭
I’m not e.g. able to show that the inverse of an inverse is the original immediately
Hmmm I personally feel like having one of the conditions state both ways is essential (as then with one of them, I can prove the other)
pseudo ice
I was wondering whether these would be equivalent to the “usual” definition of a group - you know like when you also state that a(+)e=a and a(+)ahat = e
I’m at the point where if you assume just one of those others, the other one follows if you get me, but otherwise I can’t prove if they’d be equivalent, nor think of a counterexample
keen plinth
what
identity and inverse are separate group axioms
i wouldnt think we'd have to specify both if one were equivalent to the other
pseudo ice
What I mean is are these ones
pseudo ice
Equivalent to these?
pseudo ice
Closure I think is already implied, but see how here they have the purple bits
They don’t in the other one, if you get me?
keen plinth
oh you mean like
pseudo ice
(What I said was that if you had one of those purple bits, you’d get the other one)
keen plinth
commutativity?
pseudo ice
No not commutativaty
keen plinth
so i guess we need to show that the inverse of the inverse is the original element
ocean sealBOT
keen plinth
the inverse thing doesnt work
but if you assume that inverses works on both sides then you have that the identity works on both sides
ocean sealBOT
pseudo ice
Ahh I see, I came to the same conclusion
keen plinth
i have a shitty counterexample for the inverse one tho
ocean sealBOT
pseudo ice
Ohhhh shift operators
keen plinth
classic
pseudo ice
i have a shitty counterexample for the inverse one tho
Nah that’s actually goated 🐐
You’re an absolute legend man, honestly 🤩
pseudo ice
There we have it, those aren’t sufficient examples
pseudo ice
theres definitely a simpler example
Any counterexample would do for me tbh
Been ages since I’ve done operator theory 😂
keen plinth
pseudo ice
Thank you so much for that, big love 💜
We got’eem
Was thinking there would be one, but I would have never have thought of anything, me no creative 
pseudo ice
Closure I think is already implied, but see how here they have the purple bits
Tl;dr you need at least one of those purple bits, but if you don’t have both you fail
keen plinth
i have a feeling the inverses need to be both sided
regardless of how the identity is specified
pseudo ice
I get that if you’re both sided, that if you have an $a$, you get that there is a $a^{-1}$ such that $a^{-1} a=e$, and for that $a^{-1}$, there’s an $(a^{-1})^{-1}$ such that $(a^{-1})^{-1} a^{-1} = e$
Then $(a^{-1})^{-1} = (a^{-1})^{-1} e = (a^{-1})^{-1} (a^{-1} a) = ( (a^{-1})^{-1} a^{-1} ) a = ea = a$
ocean sealBOT
chartbit
pseudo ice
So then $(a^{-1})^{-1} = a$ and $a a^{-1} = e$
ocean sealBOT
chartbit
pseudo ice
Might be missing something tho?
ocean sealBOT
keen plinth
are you trying to show that a one sided inverse is both sided?
keen plinth
because the identity commutes with both of these
pseudo ice
because the identity commutes with both of these
Ahhh I see, yea fair point!
keen plinth
pseudo ice
**chartbit**
I really want to say this is right, but I've been burned plenty of times before by making hidden assumptions 🥵
keen plinth
well it looks fine
but actually
i think
the fact that L doesnt have an inverse is a problem
because
ocean sealBOT
keen plinth
from which you can conclude that all inverses are both-sided
keen plinth
and then you just repeat this proof
pseudo ice
Yea, think I'm reasonably confident that we get inverses both sided, assuming the identity is both sided
keen plinth
pseudo ice
Can you imagine I thought this would be a quick problem before getting to sleep 