help-13

[vivid wadi]

by dividing everything by n

[plush wharf]

Ok thanks

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[analog jackal]

The teacher had never taught this before and the book does a poor explanation on how to do it, could someone explain what it's even asking me to do?

[rocky fern]

did they teach vectors?

direction and magnitude

[analog jackal]

We are supposed to be teached vektors but the teacher had rarely been to class this few weeks

[rocky fern]

I see

well they're pretty easy at this level!

Basically, you'd be taught the difference between a vector and a scalar - a scalar is a quantity, so it's only got magnitude - for example, 60 km/h, because we only have the value/magnitude, not direction. Vector's have both direction and magnitude, so 60km/h in the east direction is a vector.

What they want you to do here is draw an arrow that represents both of those things - direction and magnitude - to show a car going east at 60 km/h. The length of the arrow will represent the magnitude - 60 km/h - and the direction represents the direction in cardinal - East.

[analog jackal]

So I'm just supposed to draw an arrow with the length of 1cm for the 60 km/h?

To the east :P?

[rocky fern]

If that's how you'd like to define 60km/h, yup! It seems like they may want you to define your scaling

so 1cm/(60km/h)

[analog jackal]

It did say that the 1cm is representing a km/h and since the only thing the question said about km/h is 60 huh?

[analog jackal]

But for some reason my classmates is telling me it's 20km/h

?

[rocky fern]

Yeah, and the axes seem pretty small, so I'd say they're probs looking for 1cm/(60km/h)

[analog jackal]

I didn't get how they got 20km/h that's why I'm asking :P?

[rocky fern]

If you wanted to define the scaling as 1cm/(20km/h), it would be a 3cm arrow

so maybe that's it?

[analog jackal]

Wait what, so is it 60 km/h or 20? Bcz if it is 20 how did they get to 20?

[rocky fern]

Well, this all depends on how you want to scale your axes, really

The answer to the question is just a drawing, no? So the definition can be whatever, for example, yours as you defined it is 60km/h per centimenter - a 1cm arrow

But if your friend wants to define it as 20km/h per centimenter, they'd have to draw a 3cm arrow

[analog jackal]

Huh, so both answers are correct?

[rocky fern]

Depending on if they drew the right length arrow, yup

[analog jackal]

Ohh alr, ty ^^

[rocky fern]

np! if you plan to go into physics, engineering, or machine learning, vectors are super important, so good to learn them well

[analog jackal]

Sorry, extra question, It says to use a name for the vector, what name does it mean?

West east thing?

[rocky fern]

That is a bit tricky depending on what they want, but I'd say they want the starting point, which is (0,0)

And then the ending point, which is (0,1cm) - or (0,60km/h)

If they haven't defined anything else in relation to that, you'd start at the center - (0,0) - and then your arrow would end 1cm up - (0,1cm)

Depending on what they want, it could also just be (0,1cm)

[rocky fern]

but this seems more likely

[analog jackal]

Hmm alr

Ty ty (ˊᗜˋ)

[rocky fern]

[analog jackal]

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[still scarab]

this correct?

[worldly chasm]

I agree with 27/8

[still scarab]

cool

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[supple iron]

hi quick question why are the 5 triangles equal to 180 are there not 180 degrees in each triangle

[supple iron]

or i just heard thinfs ewrong

[remote trail]

All triangles should have 180 degrees interior angles

[supple iron]

yeah but like in a certain video i was watching it said all 5 triangles in the star ewual to 180

wait let me rewatcu it again

[slate lintel]

there are no triangles in that star

[vivid radish]

https://mindyourdecisions.com/blog/2018/12/03/what-is-the-sum-of-angles-in-a-star-challenge-from-india/

Are you referring to this?

[supple iron]

yyyyyesssss i think

nevermind i got it i hust needed a nap

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[sterile wedge]

I tried setting f(x) = 0 and showing using a negative example that the solution is not unique but have failed with that

Here is what it says in the answers but I couldn't really understand this

[cedar kiln]

@sterile wedge Has your question been resolved?

[sterile wedge]

<@&286206848099549185>

[cedar kiln]

@sterile wedge Has your question been resolved?

[sterile wedge]

Nope

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[potent fractal]

Hold on

[sterile wedge]

Oh hey

[potent fractal]

hey

[sterile wedge]

.reopen

[cedar kiln]

✅

[potent fractal]

Alright, so setting f(x) to 0 is correct

Because if u(x) and v(x) are both solutions of that ODE, then w(x) = u(x) - v(x) satisfy w'' + w' = 0

Amazingly, it's solvable

Do you know how to solve such ODE? w'' + w' = 0

[sterile wedge]

yeah using the r^2 + r = 0

[potent fractal]

yes

[sterile wedge]

so the homogenius solution is Ae^-x + B

[potent fractal]

correct

Now let's look at the boundary conditions

[sterile wedge]

alright

[potent fractal]

w'(0) = w(0) = 1/2 (w'(l) + w(l))

[mental trail]

what does w'(0) = w(0) tell you about A and B

[sterile wedge]

Not sure? It seems like useful for laplace transformation but nothing more

oh sorry

[mental trail]

not sure what you mean here

[potent fractal]

Substitute x=0 to w(x) and w'(x)

[mental trail]

no need for laplace

[sterile wedge]

it means A + B = -A

[potent fractal]

yep

[sterile wedge]

so -2A = B

[potent fractal]

We also have w(0) = 1/2 (w'(l) + w(l))

[sterile wedge]

that would mean A + B = 1/2 (-Ae^-l + Ae^-l + B)

which then gives

A + B = 1/2(B)

[potent fractal]

Yes, which automatically holds due to this

[sterile wedge]

So B = -2A

ahhh

[mental trail]

so to verify the boundary condition

you only need B = -2A

is there a unique solution?

[potent fractal]

Yep, and therefore we have a 1-parametric family of solutions, instead of 1

[mental trail]

yes given by A(e^(-x)-2)

[sterile wedge]

yeah great I just probably did a miscalculation

Cause I already tried it and I got taht A != A some gibbrish like that

[potent fractal]

happens all the time

[sterile wedge]

thanks!

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[potent fractal]

you're welcome

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[normal cipher]

uh do you have a particular question

<@&268886789983436800>

[radiant scaffold]

beat me to it lmao

[normal cipher]

idk if this is allowed

[cedar kiln]

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[final meteor]

difficult question man

[celest seal]

it is not.

[normal cipher]

ok 🙂

[celest seal]

for multiple reasons

we dont allow unsolicited ads and we dont allow opening help channels for non-help

[normal cipher]

ah okay

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[clever ore]

How do I find out how many three digit numbers there are with their digits arranged in descending order?

[stark bough]

It's wast no?

Just 3 digit do manually

[final meteor]

assuming repetitions dont count as descending, you can just divide the total number of 3 digit numbers without repetition by 3!

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@clever ore Has your question been resolved?

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[ripe oar]

Does this look right? im new to factorization. I know that x-2 is a factor of P(x).

[hot crag]

,rccw

[hot crag]

that's fine

but you can do it much much faster

[wraith dagger]

ren

[ripe oar]

ahhhh

yeah i see it now

thank you <3

[hot crag]

nw

!done

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[ripe oar]

https://tenor.com/view/monkeys-monkey-gorilla-ape-hug-gif-14004263079835426812

[hot crag]

aw

that's cute

[ripe oar]

ikr :D

[hot crag]

:D

[final meteor]

wholesome

[ripe oar]

have a great day/night

[hot crag]

you too man

[ripe oar]

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[full notch]

Prove that it has cycle with only 10 vertexs

Please help lol 😭😭

[crimson sedge]

!15min

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[full notch]

Sorry I forgot

[brazen mountain]

Who called me here?

[solid juniper]

what does this mean?

[full notch]

So the picture is obviously a graph

And every graph obviously has a cycle

[full notch]

I mean not every graph

But generally

And a cycle is that you can start moving from one vertex of the graph

And you are able to return to that exact vertex

[solid juniper]

but what does "with only 10 vertexs" mean

[full notch]

It is possible to return to each vertex with only moving through ten vertexes

Ten moves basically

[solid juniper]

there are 10 vertices on the graph

[full notch]

And ?

[solid juniper]

are you asking for something different than a cycle in the graph

[full notch]

Prove that there's a cycle in this graph that you can achieve it with ten moves

Do you understand it now ?

[solid juniper]

do you have the original question

[full notch]

That's the original question

[full notch]

It's ok bro I'll do it myself lmao

😂😂

[solid juniper]

i do not believe the question was verbatim:

Prove that it has cycle with only 10 vertexs

[full notch]

Does this make any sense?

[solid juniper]

sure

this is 3 "moves" right?
1 - 2 - 3 - 1

in other words you want a length 10 cycle

[full notch]

Yeah

[full notch]

Yep

[cedar kiln]

@full notch Has your question been resolved?

[solid juniper]

i don't think this has a length 10 cycle

[full notch]

Yep that's the point it doesn't have it lol

But we should prove that it doesn't have any

[solid juniper]

bruh why did you ask

Prove that it has cycle with only 10 vertexs
and then insist that was the original question

[full notch]

That's the question

You reach a point that you realise that it has none

[solid juniper]

.....

[full notch]

Then you gotta prove that it has none

[solid juniper]

you were asked to prove it has a length 10 cycle but really the writer's intention in asking that was for the students to realize that it doesn't have one and say the problem is erroneous and explain why rather than prove it has a length 10 cycle

[full notch]

Yeah lol

[full notch]

<@&286206848099549185>

[full notch]

Omg is there anybody here lol

[burnt vapor]

Yes

[full notch]

pls help lol

[full notch]

prove that in a petersen graph

[burnt vapor]

First, realise that if it has length ten, then it contains all vertices

[full notch]

we cant have a cycle with the lenght of 10

[burnt vapor]

It is also known as a Hamiltonian cycle

Second, realise that it must start and end at the same point, hence among the five edges that join the inner and outer cycle only an even number of them can be included in the cycle

So now we have two cases: either two of those edges are included, or four are

[full notch]

why tho

[burnt vapor]

Because if it's odd then you end in the other part

Each time you go through those edges you change from outside to inside

Or from inside to outside

[full notch]

oh daammmmm

i get it

[burnt vapor]

If you have four, you can assume wlog that the missing edge is the one at the top and then easily chase which edges must / must not be in the cycle until you reach a contradiction

[full notch]

wlog ?

[burnt vapor]

Without loss of generality

[full notch]

oh lol

[full notch]

but whats the contradiction ?

[burnt vapor]

You have to "chase" which edges are in the cycle and which are not

That's a pretty standard procedure, have you never done anything similar?

[full notch]

like you mean brute force my way ?

[burnt vapor]

No

You color for example green the edges that must be in the cycle and red those which must not be

[full notch]

oh

[burnt vapor]

And then for example if a vertex has all edges red except for two, then those two must be green

[full notch]

nope ive never done smt like that

[burnt vapor]

You use arguments like that one and at some point you obtain a vertex with too many red edges

[burnt vapor]

Well, then you have to do it now for the first time

[full notch]

how do you make the edges green or red tho

like with what logic ?

[burnt vapor]

You begin with this

Now consider the edge at the top

The cycle must go through it, so it must have two green edges, one whe the cycle enters and another one where it leaves

Thus

[burnt vapor]

You get that

Iterate

[full notch]

oh thanks i get it

[burnt vapor]

And that's the case where we have four edges

Of the ones between the two cycles

If we have two, I think you can do pretty much the same, but there is another argument

Since there are only two edges, the 10-cycle must enter the outer cycle, go through all five vertices, and then leave, as it won't return there

Hence, the first and last vertices must be adjacent

Same with the inner cycle

But you can't choose the two edges such that both pairs of end vertices are adjacent

[cedar kiln]

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[vapid gyro]

guys how do I do the one above 6

[daring vault]

@vapid gyro do u have a clearer photo? i cant see the letters

[vapid gyro]

nvm I got the answer 😅

[daring vault]

kk

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[opal venture]

Find the extreme
values
of the function 𝑓(𝑥, 𝑦) = 4𝑥^2 + 10𝑦^2 subject to the
constraint
𝑥^2 + 𝑦^2
= 4.

[opal venture]

Can someone solve this and let me know the solution I wanna check if I did it correct or not.

Have I made error in the partial derivatives?

[lusty grotto]

Ur derivatives seem to be correct

[opal venture]

I found lambda
Then substituted in the other equation to get y and then substituted in g(X,y) to find x
But I feel like it's wrong

Could U solve it for me and send the solution so I see if I did anything wrong.

[lusty grotto]

x(4 - lambda) = 0
y(10 - lambda) = 0
are the equations u get by setting the partials equal to 0

So either x = 0, or lambda = 4
At the same time, either y = 0, and lambda = 10
What combination of these can happen at the same time

[opal venture]

x =0 and y=0

[lusty grotto]

Then that's ur answer

[opal venture]

So no extreme points

[opal venture]

Ok thanks a lot.

.close

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[mental trail]

you should already have the eigenvalues of A

and just like Trace(A) = sum of eigenvalues of A

you'll find that, since A^k has eigenvalues lambda^k, with lambda the eigenvalues of A

Trace(A^k) = sum of (eigenvalue)^k

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[upbeat pike]

I want to kms

[upbeat pike]

Is this cor4ect?

😭😭

[lusty grotto]

Oh dear

U cud probably try multiplying by the conjugate of the denominator first before differentiating

[final meteor]

yea man wth you should've simplified 😭

[upbeat pike]

How does it help

Still have to use quotient rule

And it makes it more complicated

If it was limit then sure but idk if rationalization will help

[lusty grotto]

What does rationalising give u?

[upbeat pike]

Numerator will be denominator whole square and denominator will be numerator whole square?

Ohh

(A-b)²/(a-b)²

No wtf am I on abou5

[lusty grotto]

(numerator)/(a + b) = [numerator*(a - b)]/(a² - b²)

The conjugate of a + b is a - b

I asked u to multiply the top and the bottom by that

[upbeat pike]

I've been doing long ass derivatives for the whole day I want to die

But u can't so that lmao

It's an angle

U can't simplify theta

It's taninverse ( theta)

Cant change it

Rught?

[lusty grotto]

U can simplify theta

Does multiplying theta by 1 change theta?

Theta = theta*1

1 = (a-b)/(a-b)

[cedar kiln]

@upbeat pike Has your question been resolved?

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[livid trellis]

how can I find the closest point in the line from (-3, 3)

[livid trellis]

I need to find (x, y)

[final meteor]

you have the equation of the line right

[livid trellis]

yep y=x+1

oh wait, somehow I got it

.close

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[smoky finch]

help

[empty kindle]

I think I see a triangle forming

[smoky finch]

i got it now

[empty kindle]

lol

I mean

if you think about it

they don't want you to use formulas

so intuitively

[smoky finch]

i don't know if it can be done that way

[empty kindle]

i was just kidding in reference to a message you sent in another channel

[smoky finch]

yea i understood that

[empty kindle]

if you take two points of a parallelogram and then take a third, the difference from that third to the closest is equal to the difference of the fourth to the second point

[smoky finch]

it said without calculating the distance

[empty kindle]

I mean

what distance formula exactly does it refer to

I just want to subtract pairs of points

and check it works out

[low cipher]

challenge: give me the $\frac{y_2-y_1}{x_2-x_1}$ for every pair of 2 points

[wraith dagger]

оωo

[empty kindle]

like subtract point 1 from 2 and that should be equal or sign flipped equal to point 3 from 4

and same with 1 and 3, 2 and 4

[smoky finch]

this formula has to be applied

[empty kindle]

its not distance, just vectors

[smoky finch]

.close

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[low cipher]

here: we can clearly see the 2 pairs of parallel lines

[cedar kiln]

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[torpid solstice]

Hi can someone help me with this

[honest rain]

2n x 6

=

4n-11

Put that together

[torpid solstice]

???

Why

how

[honest rain]

Because the left side equals to the right sudd

What I would do is put them beside each other like I typed out

And try to single out n on one side

Because the bases equal the same as well sooo

[torpid solstice]

I got till this

😭

[drowsy mountain]

uhhh

are you on 7

or 8?

[torpid solstice]

7

[drowsy mountain]

i would expand the brackets

[torpid solstice]

How

[drowsy mountain]

laws of indices

uhhh idk how to use the bot to get it up

ill send you an image

https://www.google.com/url?sa=i&url=https%3A%2F%2Fthirdspacelearning.com%2Fgcse-maths%2Falgebra%2Flaws-of-indices%2F&psig=AOvVaw01AIOAEbl_yXiw9WhnO2oK&ust=1730922053936000&source=images&cd=vfe&opi=89978449&ved=0CBQQjRxqFwoTCKi8m6T5xYkDFQAAAAAdAAAAABAE

oh shoot hold up

so use the bottom left one

and then use logs

[honest rain]

12n=4n-11

thats what i have so far

[drowsy mountain]

how did you get 12n?

genq

[drowsy mountain]

$(3^7n)^3=3^21n$

$(3^7n)^3=3^(21n)$

damn wtf 😭

[honest rain]

im ngl taf im literally trying this with u LOL

we are doing similar questions

[drowsy mountain]

try and work with that ?

[honest rain]

16n-11

yes

[drowsy mountain]

and then

you

[honest rain]

yeah add the like termzies

[drowsy mountain]

shoot what do you do next 😭

you dont get to cancel out the 3 right?

do you subtract

YES

divide

so you do (3^21n)/

oh shoot you ant

cant

OH OH

TAKE LOGS OF BOTH SIDES

[honest rain]

LOGS IS CHEATING TAF

isnt it?

[drowsy mountain]

IS IT?

nope

youre allowed a calculator right?

[honest rain]

idk i dont use it cause it looks cheating

yes

[drowsy mountain]

then its not cheating :]

is it A level?

or geese

gcse

[honest rain]

i just took over this mans chat

[drowsy mountain]

aint no way 😭

oh shoot

[honest rain]

i was interested in the questions

[drowsy mountain]

yeah you can uhh

[honest rain]

DAMMIT

[drowsy mountain]

you can uhhhhhh

since the bases are the same

you can set the exponents equal

then just do

21n=16n-11

and then just solve for n

so 5n =-11

[drowsy mountain]

yeah i got it

[honest rain]

why is it 21 -16n

BRUH

[drowsy mountain]

cause

you have

[honest rain]

it should be divdes no

[drowsy mountain]

(3^7n)^3

nope

cause its (3^7n)^3

and so

you multiply

7n by 3

to get 21n

do you get it ?

[honest rain]

yeah i kind of get it

[drowsy mountain]

good :]

[honest rain]

i wish i knew the logs technique tho

[drowsy mountain]

you dont need logs haha

i was just overcomplicating it

[honest rain]

taf do u know how to rationalize the denominator

[drowsy mountain]

yes

[honest rain]

please help me

[drowsy mountain]

whats the question

[cedar kiln]

@torpid solstice Has your question been resolved?

[cedar kiln]

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[tough mist]

Hi could someone explain System of equations?

[vast pike]

you are supposed to learn it from book... perhaps we can help you here to understand some specific part that you couldn't figure out

[tough mist]

well yea i skipped 8th grade and messed up. now i need it and its hard. anyways the part im struggling with the most is after i understand what x stands for. Example

2x+3y=6

x-y=1

X=Y-1

i usually mess up after this part

[torpid stag]

you know x is y-1

so you replace x with y-1

in the first equation

and you obtain an equation where only y appears

[tough mist]

2(Y+1)+3y=6 ?

[cedar kiln]

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[hazy dawn]

the question is on samping distribution and chi square distribution

I'm struggling to understand the answer

so the probability of the chi squared being over 7.841 is 0.25, why is that not unusual?

[cedar kiln]

@hazy dawn Has your question been resolved?

[cedar kiln]

@hazy dawn Has your question been resolved?

[empty kindle]

I suppose it depends on interpretation, but that's 1 over 4 tests getting that result, if the company runs a lot of tests(and it probably does) that could just be bad luck. At least on my stats class we usually considered something unusual when its below 5%

yeah, I think the most common significance is 95%

I could be wrong though

[hazy dawn]

Thank you

I'm not sure how 0.25 relates to the stdev of 1

[empty kindle]

did you professor ever mention what's the "default" significance they will use?

[hazy dawn]

0.05

[empty kindle]

oh that's just because to calculate P(X > k) if X is not the normal distribution with average 1 and stdev 1 then you have to do some scaling to get there

[hazy dawn]

I see

[empty kindle]

you use $P(Z > \frac{k - \mu} \sigma)$

[wraith dagger]

Sires

[empty kindle]

here sigma is 1 so you just look up the difference to the average

[empty kindle]

isn't that the error? or am I confounding the terms

oh yeah I'm mixing it up

but yeah, if he said 0.05 and its 0.25 then its way above the threshold of unusual

[hazy dawn]

I see that makes sense

Thank you

[empty kindle]

np

[hazy dawn]

.close

[cedar kiln]

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[open peak]

i have a question

[open peak]

😭

can u get a different channel

[oblique prawn]

oh wtf u sent it before me

i thought i was the first one

[open peak]

i made this plot of the gamma function using matplotlib, is it mormal that the phase abruptly goes from -π to π in some places?

[cedar kiln]

@open peak Has your question been resolved?

[cedar kiln]

@open peak Has your question been resolved?

[austere hull]

can you show the code? might try it on matlab or py

[cedar kiln]

@open peak Has your question been resolved?

[worldly chasm]

No

It's not normal to have discontinuities in a continuous function.

[cedar kiln]

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[pallid atlas]

How do I do these

[cedar kiln]

@pallid atlas Has your question been resolved?

[pallid atlas]

<@&286206848099549185>

[merry solstice]

what have you tried

[humble comet]

Rationalize the denominatior

[merry solstice]

and what questions

[pallid atlas]

I don’t know how to do it

[merry solstice]

ok

so

in mathmatics, people don't like having a square root denominator

so

[pallid atlas]

I was out the day she taught it 😭😭😭

[merry solstice]

how would you simplify 1/sqrt 2

[pallid atlas]

What

[merry solstice]

ok

so if I told you to simplify 1/sqrt 2, how would you di t?

*do it?

[pallid atlas]

My problem doesn’t have a square root of two…

I’m working on 17-

[merry solstice]

no it's just an example

[humble comet]

It's an example

[pallid atlas]

Oh

[pallid atlas]

2 ^-1?

[merry solstice]

no

you would multiply both sides by sqrt 2

so

[pallid atlas]

Oh

[merry solstice]

1/sqrt 2 *(sqrt2/sqrt2)= (sqrt 2)/ 2

[humble comet]

You see the 1/√2 and √2/2 are the same

[pallid atlas]

I guess-

[merry solstice]

basically

you rationalize

[humble comet]

Check it

[merry solstice]

or mutliply the denomiator by a square root value that makes it a whole number

@humble comet

do you want to explain it or should I

[humble comet]

You do bro

[merry solstice]

alr

[merry solstice]

now

[humble comet]

I'm not good at teaching

[merry solstice]

lets take your problem

[pallid atlas]

Walk me through this step by step as blatantly as you can

[merry solstice]

6/(-6-5sqrt6)

[pallid atlas]

I’m autistic and it’s most likely the only way I will understand what you’re explaining

[merry solstice]

we know that

[pallid atlas]

🧍🏻 how-

[merry solstice]

we need to make the denominator a numerator

you get that right

[pallid atlas]

Yes

[merry solstice]

so, how do you think we should do this

[pallid atlas]

Well my teacher said multiply by the inverse

[merry solstice]

yes

[pallid atlas]

Idk what that is tho

[merry solstice]

do you know the difference of squares

[pallid atlas]

I think..?

[merry solstice]

ok

so write the formula

if you don't know, it's a^2-b^2=(a+b)(a-b)

[pallid atlas]

Uh..I don’t think that’s how she did it-

[merry solstice]

this is perfect for eliminating both sides because it makes both squares

[merry solstice]

let me finish first

[pallid atlas]

I have an example of hers if you’d like-?

[merry solstice]

so

[pallid atlas]

Ok-

[merry solstice]

we have -6-5sqrt6

[pallid atlas]

Yeah

[merry solstice]

to apply this

we can have -6-5sqrt6 be the (a-b) part right?

so

[pallid atlas]

Sure-

[merry solstice]

that means that the (a+b) part is -6 + 5sqrt6

because it is +b

but it also means we have to multiply the numerator by -6+5sqrt6 for the expression to be equal.

6/(-6-5sqrt6) * (-6+5sqrt6)/(-6+5sqrt6)

is

equal to the original expression

[pallid atlas]

Ok..

[merry solstice]

multiplying it ut

6(-6+5sqrt6)/(-6+5sqrt6)(-6-5sqrt6)

now apply difference of squares to the denominator

[pallid atlas]

Ok..

[merry solstice]

what do you get

or do you want me to do the calculation with you

[pallid atlas]

Please

[merry solstice]

which one

[pallid atlas]

Do it with me

[merry solstice]

ok

so we know that (a+b)(a-b) = a^2-b^2

we have a as -6 and b as 5sqrt6 from above

so

that expression is equivalent to

(-6)^2-(5sqrt6)^2

that is equal to

36- 150

or -124

[pallid atlas]

Ok- now do you want me to show you how she did it or..?

[merry solstice]

sure

[merry solstice]

so 6*(6+5sqrt6)/-124

[merry solstice]

ueaj

yeah

that's what I did

I just put it in detail

[pallid atlas]

Ok

Reading math is a tad difficult for me to grasp

[merry solstice]

or 5+sqrt6/-24

Oh wait the whole thing is negative

so final answer -5-5sqrt6/24

[merry solstice]

yes that's understandable

do you understand now?

[pallid atlas]

Ok hold on let me put this on paper

[merry solstice]

alr ping me when ur done

[pallid atlas]

Right so like that

Then I multiply..something on the bottom

The notes are unclear

And multiply everything on top

[merry solstice]

yeah

you multiply the top and the bottom

[pallid atlas]

Top and bottom..?

[merry solstice]

-6(-6+5sqrt6)/(6-5sqrt6)(6+5sqrt6)

[pallid atlas]

Huh..

[merry solstice]

yeah

because it is equivalent to 1

[pallid atlas]

Ok…

So…which top and which bottom-

[merry solstice]

...

you multiply the original thing by 6-5sqrt6/6-5sqrt6

[pallid atlas]

So both of the bottoms-

[merry solstice]

no the numerator and denominator

[pallid atlas]

But they’re both the same?

[merry solstice]

yes

but we need them to rationalize the denominator

[pallid atlas]

Ok-

[merry solstice]

@humble comet

can you explain this to milo

[pallid atlas]

Sorry

[humble comet]

What should I teach?

Haven't you taught?

[merry solstice]

can you explain why we should multiply by the reciprocal thingy to itself

to make the denominator rational

[humble comet]

Yeah you dont want irrational numbers to be in the denominator

[merry solstice]

it's fine I was like this at one poin

[merry solstice]

milo doesn't quite understand why though

just explain the little bit about why

[humble comet]

Actually we do rationalize to make the equation look simple

[humble comet]

Mhmm

[pallid atlas]

Do I just treat the square root like a variable-

[humble comet]

@pallid atlas what you don't understand?

[pallid atlas]

What am I multiplying

[humble comet]

Actually you're not solving the problem, you just simplify it

[humble comet]

Well

[pallid atlas]

And do I treat the square root like a variable

[humble comet]

Wym?

[pallid atlas]

My example doesn’t have 3 numbers so I’m a lil confused on what to do with 3 numbers

[humble comet]

Send the problem

[humble comet]

17?

[pallid atlas]

He’s

Yes**

[humble comet]

You're approach is right go ahead bro

[pallid atlas]

What am I multiplying 😭😭😭

[humble comet]

(-6+5√6)/(-6+5√6)

[pallid atlas]

Do I have to foil it?

Is there a shortcut?

[humble comet]

Well

Use this formula

For denominator

(A+b) (a-b) =a^2-b^2

[humble comet]

Well you see it's clearly in this form

[pallid atlas]

Uh..sure

[humble comet]

Well in the numerator you should have to multiply

[pallid atlas]

Just 6 • -6 -5 square root 6

[humble comet]

Yeah for the numerator

[pallid atlas]

Does the square root act like a variable or no?

[humble comet]

Wym give an example bro

[pallid atlas]

Like does it stay the same but the 5 gets multiplied

[humble comet]

Yeah yeah

[pallid atlas]

Ok

So -36+30 square root 6

[humble comet]

No

+36-30√6

[pallid atlas]

Oh I didn’t catch the negative

Woops

Now on the bottom-?

[humble comet]

Yeah

[humble comet]

Use this formula

[pallid atlas]

I think my teacher said there was a sort of shortcut but idk if it applies with 3 terms

She said just…multiply like that-

[humble comet]

That's what the shortcut I'm talking about

[pallid atlas]

Oh 🧍🏻

So just…

-6 • 6, -5• 5 and sqrt 6 • sqrt 6?

[humble comet]

(6*6) -(5.5.6)

[pallid atlas]

What is the second one-?

[humble comet]

Second one?

[pallid atlas]

The second parentheses

[humble comet]

You can see it clearly in the formula (a+b). (A-b) =a^2-b2

So

B=5√6

What would it become if you square it

(5√6) ^2

[pallid atlas]

Ohhh ok that makes more sense

So -36 and -25sqrt6?

[humble comet]

No

36 and 25*6

[pallid atlas]

Wait

No

Just 6

[humble comet]

It's a typo

It's 36 and 25.6

You didn't apply the square for √6

I'll be back in 10 minutes

[pallid atlas]

Ok

[humble comet]

Well

Did you get the answer

[pallid atlas]

Not yet

I was using the bathroom 🧍🏻

So 36 25sqrt6

That can’t be the answer tho right..?

[empty spear]

how did ug et that

[empty spear]

ur multiplying by the conjugate

nvm in looking at the wrong problem

[pallid atlas]

???

[empty spear]

u didnt square this properly

[pallid atlas]

That’s what I thought..

What is it tho? @empty spear

[empty spear]

the deominator?

denominator?

u multiply (-6-5sqrt6) by its conjugate (-6+5sqrt6)

which gets u -144

36-(25*6)

[pallid atlas]

RHATS WHAT I FHOUGHT

[empty spear]

but

u gotta multiply the conjugate to the top and bottom

[pallid atlas]

I already did the top

[empty spear]

okay nice

[pallid atlas]

36 + 30sqrt6/-144

[empty spear]

pretty sure the + is a -

[pallid atlas]

?

[empty spear]

36 - 30

[pallid atlas]

Ohhhhh

[empty spear]

cuz -6(5sqrt6)

[pallid atlas]

Yeah

Ok so…

Do I simplify from there 🧍🏻

[empty spear]

yeah

all divisible by 6

[pallid atlas]

Ok thanks

So 6-5sqrt6 /24

?

[empty spear]

looks right

idk if the signs are all right but imma assume theyh are

[pallid atlas]

Thank you

.close

[cedar kiln]

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[cedar kiln]

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[crude sable]

4. b) 3.84X103 N [up]

I have the answer i just need help getting to it

[clear umbra]

free body diagram then analyse the forces

[cedar kiln]

@crude sable Has your question been resolved?

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[lone lagoon]

Why.

Why does this happen.

The angle is 90, yes.

But m1*m2 is not equal -1!

[humble karma]

The angle doesn't seem to be 90

[lone lagoon]

ah, then I am right

[lusty grotto]

U can use the angle tool in geogebra to actually measure the angle if u want

[cedar kiln]

@lone lagoon Has your question been resolved?

[cedar kiln]

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[cedar kiln]

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[misty gazelle]

hello! does anyone know the overall parent functions I need to know to solve exponential and logarithmic functions? this one is apparently exponential decay but it would really help me out if someone could provide the parent functions to remember. i have a test tmrrow and im trying to cram

[misty gazelle]

update; the HA is now y=2

i’m trying to solve for the y intercept as that will get me extra credit now

[lean lotus]

y intercept is when x=0

[misty gazelle]

yeah but the exponential rules is screwing me up

so 1/4^-1??

i’m not sure how to solve that

[narrow scarab]

when u have a negative exponent just find the inverse

so u could do 1/(1/4) which is just 4

then plus 2

[misty gazelle]

ohhh crap i really have to remember the properties

by any chance do you know the overall parent functions i have to know?

i know 2^x is one

[lean lotus]

just know how an exponential function would look like

and generally how logs look like

[misty gazelle]

but this one is supposedly exponential decay, do i have to remember that one too?

[lean lotus]

its just an exponential function but decreases

[narrow scarab]

well u can know its decay since it’s a fraction to the exponent

no matter what u do, it’s gonna get smaller

u can plug in values of x to see if it’s decreasing or increasing and check ur work that way

[misty gazelle]

thank you gang, also, for the y intercept, i got (0,6)?

would that be accurate?

[narrow scarab]

i believe so

[misty gazelle]

domain for exponentials is mostly always all real numbers right?

[narrow scarab]

yes

be careful for logs and natural logs cuz they have vertical asymptotes

[misty gazelle]

i see, thank you so much

[narrow scarab]

https://mathbitsnotebook.com/Algebra2/Exponential/loginverse.jpg

here’s a good picture for reference

[misty gazelle]

perfect, i appreciate it lots

the origin would move to (1,3) right?

i tried graphing it and this is what it looks like for me, is that correct?

and the range is from (2, positive infinity) ?

[lean lotus]

graph looks right

[misty gazelle]

thank u

i’m confused on how to get from step three to step 4

i understand why we keep the same base

but what happened to the 4x

and where did the 3x come from

and why does the 9 now have no x

😅

oh gosh i think i may have written it wrong

[narrow scarab]

i can’t tell if that’s a 4 or a u or a 9 or the letter a

i’m slow h

[misty gazelle]

there’s no a’s in there so it’s probably a 9

hold on imma rewrite it

[narrow scarab]

check step 2 out. i think u wrote something wrong in an exponent

or else i’m dumb

[misty gazelle]

okay i tried fixing it, now im confused on why the exponent for 3 is a -2

on step 4

[crimson sedge]

oh I see

[misty gazelle]

like how did i get from (1/3)^2 to (3)^-2

[crimson sedge]

4x + 9 - 3x

this is wrong

[narrow scarab]

they are the same thing

[crimson sedge]

you didn't distribute 3(3-x)

step 3 is wrong

[misty gazelle]

how is it supposed to look like then?

9-3x?

[crimson sedge]

yes

[misty gazelle]

ohhhh

that makes sense

so then step for step number 4, it would be 3^ 9+x instead?

[crimson sedge]

yes

[misty gazelle]

thank you :( you guys are seriously being life savers rn, it takes me a tad bit longer to learn stuff because i constantly need to ask questions

i appreciate it

[crimson sedge]

nw

[misty gazelle]

is this correct? it’s the same exercise i just want to make sure i didn’t mess it up

[narrow scarab]

check the signs in ur exponent when u combine them in ur fourth step

[lean lotus]

step 4 is wrong

[misty gazelle]

got it! just fixed that

thank u

also i haven’t gotten to question 8 or 9 yet but when do i know when i have to check for the answer?

[lean lotus]

when ur answer feels wrong?

[crimson sedge]

you shuold always check your work

in math

[misty gazelle]

oh i just remembered my professor saying that there was a specific thing that we would have to check obligatory, and others not rlly nvm

on this exercise, i’m confused to why it’s vertical shift up by 2

[lean lotus]

u can write it as -ln(x+4) + 2

[misty gazelle]

and what would a horizontal reflection look like instead in a logarithmic function?

[misty gazelle]

oh okay so he just wrote it in a confusing way for no reason 🥲 ty

[lean lotus]

reflect along x axis

[misty gazelle]

hey i’m stuck after step 3

i’m not sure how to distribute that

[crimson sedge]

separate and put to e^

[misty gazelle]

like this?

[lean lotus]

no

let ln go to left side

and then apply log rules

[misty gazelle]

okay the problem might be that i’m quite unfamiliar with log rules, it’s been a while since i’ve seen them in hs 🥲 imma try it out

[lean lotus]

$a^{\log_a (k)}=k$

[wraith dagger]

pppoopoo

[lean lotus]

instead of a u use e

[misty gazelle]

would this be correct?

[lean lotus]

no

i meant + ln(x+4) to left side lol

-2 also works its just that i don't like to see negative numbers lol

so its personal preference i guess

[misty gazelle]

me neither i think i get what u mean

[sacred cypress]

Hello Everyone ✋
Any experienced Mathematician here ?

[lean lotus]

hi, plz go open ur own channel, this channel is occupied

#❓how-to-get-help

[misty gazelle]

but i’m trying to isolate for x right?

[lean lotus]

yes

[lean lotus]

but it has to be e^(x+4)

[misty gazelle]

idk if i did that right

[lean lotus]

yes

wait a second

how did u get 2/e = e^2

[misty gazelle]

good question, i thought it reminded me of the exponential property

[lean lotus]

i mean e^2 - 4 = x is the answer, but what u did was wrong

[misty gazelle]

how can i get to e^2 then?

[lean lotus]

so it was ln(x+4) = 2

you can rewrite it into e^ln(x+4) = e^2

and use log rules to get rid of the ln

so it would just be x+4 = e^2

[misty gazelle]

ohhhh i think i get it

thank you tor your help, i’m gonna try to get 3 hours of sleep and then go back to the grind i appreciate it

[cedar kiln]

@misty gazelle Has your question been resolved?

[cedar kiln]

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[quiet storm]

this is what i have so far, im pretty sure i’m supposed to use lagrange multipliers but tbh i’m not sure on how to solve the system of equations or if this is the right technique to even use

[cedar kiln]

@quiet storm Has your question been resolved?

[quiet storm]

<@&286206848099549185> help a brotha out with calc 3 hw

[cedar kiln]

@quiet storm Has your question been resolved?

[lusty grotto]

i think ur system looks correct

[quiet storm]

i’m not quite sure how to solve it though

[lusty grotto]

well $2x-3\lambda x^2y^2z=x(2-3\lambda xy^2z)=0$

[wraith dagger]

SilverSoldier

[lusty grotto]

x = 0, or the other thing is 0

do the same thing with the other equations

see which combination of results works together

u also need x^3 * y^2 * z = 1 to hold

so for example u can immediately reject x = 0 as a solution

[quiet storm]

i see, i will try in a moment

[quiet storm]

sorry, a little all over the place,
but instead of setting them equal to 0, i set them equal to lambda and tried my best to solve y and z in terms of x to put in the constraint equation

ended up getting 4 points and the numbers r hideous

[cedar kiln]

@quiet storm Has your question been resolved?

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[manic nova]

hey

[manic nova]

how do i find b

median and interquartile range

[cedar kiln]

@manic nova Has your question been resolved?

[manic nova]

.close

[cedar kiln]

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[cedar kiln]

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[midnight bramble]

Could someone talk me through the steps for this question please?

[midnight bramble]

Its been a long time since i last did histograms and am unsure how i would go about this question

[narrow scarab]

so in a histogram, the bars touch

each bar will just be labeled as the sales revenue for each range

and their heights will be the frequency

[midnight bramble]

Oh... i was putting the heights as the frequency density

Something like that, just without fd on y axis?

[narrow scarab]

yes perfect

[midnight bramble]

thanks eve

[midnight bramble]

How would one go about finding the fd from the histogram?

[narrow scarab]

theoretically it should look the same when u change it to frequency density since it’s the same thing

[midnight bramble]

oh ok

[narrow scarab]

lowkey idk

i believe it’s the frequency divided by the “width” aka the range for each bar

[midnight bramble]

to make it look neater, might i put on the x axis "Class width $1000's"

[narrow scarab]

so for the first one, it’s 4/5

[midnight bramble]

Oh, yeah that makes sense

[narrow scarab]

name the axis as given to u

“sales revenue (in $1000s)”

[midnight bramble]

Okie, tysm!

i been having a mini heart attack everytime i get a different looking histogram

[narrow scarab]

ur lucky to be able to do it digitally

cuz on paper my bars always end up crooked and ugly 😭😭

[midnight bramble]

teacher doesnt like having to read our handwriting, made us do it using word and excel 😢

[midnight bramble]

it is much faster than digital though