help-27

[fervent ledge]

i am platinum

[upper schooner]

I was wondering, I figured

[smoky hamlet]

look

im back

lol

[upper schooner]

Copycat

[smoky hamlet]

wdym

who else is platinum ;

[upper schooner]

As in you're both the same

[smoky hamlet]

lol you're funny

can i add you

[upper schooner]

But anyways hopefully that was all good

And sure, if you want

[smoky hamlet]

do you want

[upper schooner]

Why not

[smoky hamlet]

woah youre old

doing phd?

[upper schooner]

Nooo I'm not did a masters though

[smoky hamlet]

lol dont be sad cuz of your old age hah

be proud that you made it ere

[upper schooner]

I'm more than happy in my mobility scooter

[smoky hamlet]

are you pro-lgbt

[upper schooner]

Possibly, can't say

[smoky hamlet]

i mean you male/female

or what

i dont understand the any pronouns

[upper schooner]

Basically idc what you refer to me as

After all, who even says I'm a real person

[smoky hamlet]

man your emojis are weird

anyway, it's 4 in the morning i gotta sleep bye bye

cya

.close

[devout snow]

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[upper schooner]

See ya later

[devout snow]

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[timid badger]

why why

[timid badger]

Is 1/12 * ln(4) the same as

1/6 * ln(2)

[dense lynx]

my face when the log rule :cereal:

[timid badger]

:c don't make me afraid of math

ty

.close

[devout snow]

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[dense lynx]

noo it was chartbit’s reactions which i thought were funny

[timid badger]

oh

I don't have reactions

weird

[dense lynx]

fascinating

[timid badger]

I thought I got bulli

xd

[dense lynx]

🎉

[devout snow]

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[forest stirrup]

i rewrote as 25^(1/2) / 25^(log5(sqrt(2)).

dont know how to simplify the denominator

[heady plinth]

use the fact that $(a^b)^c=(a^c)^b$

[woven radish]

coak

[forest stirrup]

5^(log5(sqrt2)))^2

?

[heady plinth]

Yep

[forest stirrup]

ok that should be 2 then

[heady plinth]

2^2

Oh wait

Yes haha didn’t see the root

[forest stirrup]

so its 5/2 right

[heady plinth]

Right

[devout snow]

@forest stirrup Has your question been resolved?

[devout snow]

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[devout snow]

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[jaunty gazelle]

Could someone please help me with this problem?

[devout snow]

@jaunty gazelle Has your question been resolved?

[wispy solstice]

have you tried following the steps?

[devout snow]

@jaunty gazelle Has your question been resolved?

[jaunty gazelle]

Could I show you my work?

[devout snow]

@jaunty gazelle Has your question been resolved?

[devout snow]

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[bright juniper]

I got A and B teams in one city . A teams young people (under 25) the cheerleaders proportion is 2:3 and the rest (over25) cheerleaders proportion is 3:5 what is the proportion thro the wholesome city if the 25 year old cheerleaders full amount is 1/3

[rigid pewter]

if i understand correctly, $A = \frac 2 5, B = \frac 3 8$, so $\frac 1 3 A+\frac 2 3 B = \frac{23}{60}$?

[woven radish]

b

[bright juniper]

Well A and B are tight but then its wrong

You didn’t use the fcat that 1/3 is 25

A)61:99 B)4:5 C) 9:11 D)8:7 E)23:37

One if them is the answer

[rigid pewter]

i said 1/3 of the cheerleaders are in group A (and the rest are in group B)

i got E), because $23:37=\frac{23}{23+37}=\frac{23}{60}$

[woven radish]

b

[rigid pewter]

if that's not what they meant i'm not sure how else to interpret the question

[bright juniper]

How is 23/60 E)??

[rigid pewter]

do you know how to convert between a fraction and a ratio

like how the ratio 1:2 is the same as the fraction 1/3

[bright juniper]

Well yes but

Let me hear the explanation first how did you do it

[rigid pewter]

my answer was that out of 60 cheerleaders, 23 are in group A
which means there are 37 cheerleaders left over in group B
therefore the A:B ratio is 23:37

[bright juniper]

No i mean from the start every step

[rigid pewter]

ok well the question gives us:

• the A proportion is 2:3
  this is 2/5
• the B proportion is 3:5
  this is 3/8
• 1/3 cheerleaders are in A
  so the remaining 2/3 are in B
  then we just add together
  (1/3)A + (2/3)B
  = (1/3)(2/5) + (2/3)(3/8)
  = (2/15) + (6/24)
  = 138/360
  = 23/60

i'm assuming you can add and multiply fractions

[bright juniper]

Wait why are 1/3 cheerleaders in A?

[rigid pewter]

you said

if the 25 year old cheerleaders full amount is 1/3
i assumed this meant "if the amount of cheerleaders younger than 25 is 1/3"
because it's the only interpretation that made sense to me
but if you can take a picture of the question directly or something i'll double check

[bright juniper]

That’s right but why can’t 2/3 be in A and 1/3 in B or does it not matter?

[rigid pewter]

if you do the math for (2/3)A + (1/3)B, you ultimately get 47/120 or 47:73

[bright juniper]

So thats wrong?

[rigid pewter]

yeah you're saying the wrong amount of people are in each group here

[bright juniper]

How do we know 1/3 is in A tho the problem never says that

[rigid pewter]

oh it doesn't?

can you take a picture of the question

[bright juniper]

Its in a different language

But it says that 25yeas old people are 1/3 and that the full amount in A and B

Both teams

@rigid pewter

[rigid pewter]

without the question i'm not really sure what to tell you lol
this doesn't make much sense
i could try google translate i guess?

[bright juniper]

Wait ill put it in a better way

There are two football teams in the city, A and B. The fans of the youth part of the city's population (under 25) fans proportion is 2:3 and the rest (over 25) fans are 3:5 what is the proportion in the whole city if the Total fans under 25 years old full amount is 1/3

@rigid pewter

[rigid pewter]

ok i think it's pretty clear now

Total fans under 25 years old full amount is 1/3
out of all the fans (the full amount), 1/3 are under 25

[bright juniper]

under or 25 yes

they can also be 25

[rigid pewter]

i think this question pretends there aren't any people aged exactly 25

[bright juniper]

ok

so what do we do?

@rigid pewter

[rigid pewter]

"1/3 of people are young and 2/3 are old" is still the best interpretation i think

[bright juniper]

so the way you did it was correct?

[rigid pewter]

yeah

i mean, it did get me the correct answer

[bright juniper]

yup ok thanks

can you help me with another problem?

@rigid pewter smaller one

[rigid pewter]

ok

[bright juniper]

ok so i got a clock the big and the small arrow the big arrow is 8cm and the small is 4 how much is there traveled distance at 2:05 AM

[rigid pewter]

ok let's look at the big hand

it's moved 2/12ths of the way around right

[bright juniper]

why?

well yes

i see

the big one 1/12?

[rigid pewter]

wait 24 or 12 hour clock

[bright juniper]

like the round clock

12 h one

[rigid pewter]

that would be either 2/12 or 2/24
clocks are almost always 12 hours so 2/12

yeah

and that hand moves around in a circle obviously
one with radius = 8cm

[bright juniper]

ok

we are talking about the small arrow or the big one?

[rigid pewter]

big arrow

do you know what the circumfrence of a circle with r=8 is?

[bright juniper]

16pi?

[rigid pewter]

yes

and it's gone 2/12ths of that distance

[bright juniper]

ok

so?

[rigid pewter]

so we just do 2/12ths of 16pi

multiply (2/12)(16pi)

and that's your distance

[bright juniper]

for the big one now the small one

[rigid pewter]

think you can do it yourself?

you know the radius

[bright juniper]

1/12 * 8pi?

[rigid pewter]

that's it

then you just add together

[bright juniper]

why is the big one 2/12 and the small one 1/12

should it not be the other way around?

[rigid pewter]

if it's 2 AM, the hand has passed 2 of the 12 hours
if it's :05, the hand has reached 5 of the 60 minutes

[bright juniper]

So there proportions are 1:4 right?

[rigid pewter]

the proportion of what to what?

[bright juniper]

The traveld distance of the arrow

[rigid pewter]

traveled to total distance? it's 2:10 and 5:55 (= 1:11) for big and small respectively

[bright juniper]

Where what?

[rigid pewter]

?

[bright juniper]

Nvm thanks

[rigid pewter]

ok lol

[bright juniper]

.close

[devout snow]

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[devout snow]

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[idle bloom]

Need help with this question

[solar goblet]

what have you tried

[idle bloom]

im just stumped im so tired right now been doing homework all night

might just have a brain fart

[solar goblet]

ok so lets see f(x) first

what do you notice in f(x)?

[idle bloom]

its a constant ?

[solar goblet]

pardon?

[idle bloom]

sorry im just really confused

f(x) is a constant function because there is no x term.

[solar goblet]

okay heres a different question

what type of equations are these 4?

[idle bloom]

all exponential ?

[solar goblet]

correct!

do you know what does the monoticity of their graph depend on?

[idle bloom]

i think so increasing and decreasing?

[solar goblet]

yes, but when do they increase? when do they decrease?

[idle bloom]

if " x " is more than 1 it increases and if its in between 0-1 it decreases ?

[solar goblet]

not x

$f(x)=a^x$

[woven radish]

فطر

[solar goblet]

when do thy increase, when do they decrease?

[idle bloom]

if a is more than 1

it increases

and 0-1 decreases

[solar goblet]

correct!

[solar goblet]

now lets get back to f(x)

now, which graphs do you think could be f(x)?

[idle bloom]

iv

[solar goblet]

and you are indeed correct

what graph do you think fits g(x)?

[idle bloom]

ii

[solar goblet]

correct!

what about h(x)

[idle bloom]

iii

[solar goblet]

and its obvious for j(x)

[idle bloom]

and if i get this right i leaves i(x) to be i

[solar goblet]

and there you go

[idle bloom]

thank you so much

god bless

have a great rest of your day

[solar goblet]

!done

[devout snow]

If you are done with this channel, please mark your problem as solved by typing .close

[idle bloom]

.close

[devout snow]

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[devout snow]

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[oblique surge]

How can i find where this function is increasing or decreasing

And how i fins the peak

And the lowest point

[wicked turtle]

try completing the square

[oblique surge]

What do u mean

[cold raptor]

Do you know about derivatives?

[oblique surge]

If i take b^2-4ac it is negatively

<0

Yeah its <0

[cold raptor]

Do you know about first order derivative test and 2nd order derivative test?

That is how this question is to be done I believe

[oblique surge]

I don't understand what are you talking abour

[cold raptor]

Do you know about differentiation?

It is part of calculus

To find where the given function is increasing or decreasing and it's maxima minima, youll need to differentiate it

then use the first order derivative test or 2nd order derivative test

[oblique surge]

No i dont know differentiation

What this

And how it is done

[cold raptor]

where did you get the question from

[cold raptor]

it will be difficult for me to explain from scratch, you can search it up on youtube though

[oblique surge]

Its gives me this function

And i need to find the highest and lowest point

And when it goes up and down

Thats the question

[limpid dove]

this is just a quadratic

it will always be decreasing, then at a point 0, then increasing again

[oblique surge]

Can you explain it pls

[limpid dove]

you can use the formula $(\frac{-b}{2a}, \frac{-D}{4a})$ to find the minima, and there is no maxima

[woven radish]

math X meth ✓

[limpid dove]

youve done quadratic equations?

[oblique surge]

Yeah i have done that

But if you calculate D its <0

[limpid dove]

that doesnt matter, we arent solving for the zeros in the equation

D<0 means the roots dont exist

[oblique surge]

Yeah

[limpid dove]

graphically, it means that the function never goes below the x - axis

its minima is above the x - axis

yk how a quadratic graph looks like?

[oblique surge]

Yes

[limpid dove]

k

so here, the graph 'opens' upward

[oblique surge]

Yea

[limpid dove]

k

[oblique surge]

But where is the lowest point

[limpid dove]

then, the vertex is at $(x, y) = (\frac{-b}{2a}, \frac{-D}{4a}) $

,tex $(x, y) = (\frac{-b}{2a}, \frac{-D}{4a}) $

[woven radish]

math X meth ✓

[limpid dove]

this is the lowest point of the graph

[oblique surge]

How is this proven

I havent learnt anything like this

[limpid dove]

this usually isnt proven in class, since its a bit hard to derive from the normal quadratic

if you know differentiation, then its quite easy to derive

but keep this in mind

[oblique surge]

But the problem is i dont know differentiation

I dont know how to use it

[limpid dove]

yeah its fine, to prove this you can use differentiation, but to use the formula, none is needed

[devout snow]

@oblique surge Has your question been resolved?

[oblique surge]

Not yet

I still don't know how to do it

I don't know differentiation

And there is no other solution

[icy barn]

imagine if u have have a function thats decreasing, going down u might say, then at a point it start to increase, going up, then logically this point where the function changes behaviour has to be the lowest point

[oblique surge]

Yes i understand that

But how i find this lowest point

Without differentiation

[icy barn]

do u really need to prove it, i mean didnt u learn about this role?

[icy barn]

also u dont need differentiation, if u know the roots of the quadratic equation

then the middle point between the two roots has to be that point where the lowest in graph

[devout snow]

@oblique surge Has your question been resolved?

[oblique surge]

Yes

[devout snow]

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[sly jacinth]

Probability question, not quite sure how to answer Part C

also curious of why two of my approaches gave me different answers

First I tried $P(|X - \mu| < 1\sigma) = P(Z < 1) + P(Z > -1) = P(Z < 1) + (1 - P(Z \le 1)) = \Phi(1) + (1 - \Phi(-1)) = \Phi(1) + (1 - (1 - \Phi(1))) = 2\Phi(1)$

[woven radish]

Conquest

[sly jacinth]

then out of curiousity, I tried to do the same thing but in a different way

$P(76 - 9 < X < 76 + 9) = P(67 < 9Z + 76 < 85) = P(-1 < Z < 1) = \Phi(1) - \Phi(-1) = \Phi(1) - (1 - \Phi(1)) = 2\Phi(1) - 1$

[woven radish]

Conquest

[sly jacinth]

So curious how to answer the answer correctly, also why those two gave different answers

<@&286206848099549185>

[somber harbor]

sup

is it just the last one u dont get

remember that 1 sd from the mean is an absolute value

2*.8413-1 is gonna be 2P(z<1)-1

the area you are looking for is the bright area

1 standard deviation from the mean both sides

WAIT LOL

nvm i think ur right bro

just didnt multiply ur answer by 100

🤣

@sly jacinth

[sly jacinth]

wait what

hmm

oh so that's what they meant

hmm

[somber harbor]

wut no bro

[sly jacinth]

Still not sure why the first method doesn't work

[somber harbor]

its a percent

u answered with a decimal

u didnt multiply by 100

🤣

[sly jacinth]

yeah I get that part

[somber harbor]

oh ok then u got it right boss

your method makes complete sense and is completely correct

[sly jacinth]

yeah for the second method, the first method I used for a previous question and I'm not sure why it doesn't work here. Basically need to know why it doesnt work so I dont use it on a test or something

[somber harbor]

wdym your method works

[sly jacinth]

I showed two ways I did it. Solving $P(|X - \mu| < \sigma)$ was the first one

[woven radish]

Conquest

[sly jacinth]

oh wait a minute, it could be because

sigma is literally 9 here. I needed to add 76 to it or something

wait no

yeah im lost

[somber harbor]

im confused now, the first method should work

[somber harbor]

this is wrong

[sly jacinth]

oh I see. the algebra was wrong

[somber harbor]

yeah

the first equality is not true

i mean second

$P(67 < 9Z + 76 < 85) = P(-1 < Z < 1) is not true$

[woven radish]

sake

[sly jacinth]

lol. when I said the algebra was wrong, I was referring to the $P(|X - \mu| < \sigma) = P(Z < 1) + P(Z > -1)$

that part I'm pretty sure is correct. you're looking at the second method I tried still. the correct one that gave 2\Phi(1) - 1

[woven radish]

Conquest

[sly jacinth]

but thanks. I think I got it from here.

.close

[devout snow]

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[somber harbor]

BRUH YEAH IT IS I CLICKED THE WRONG ONE

mb

[somber harbor]

yeah this one is right

[devout snow]

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[smoky gyro]

for 2b) how come the answer is AB? when i drew out the vectors and stuff i got BA

[smoky gyro]

Oh wait

It’s supposed to go from vector AD to DB right

So it faces the other way ok

lol

.close

[devout snow]

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[fervent ledge]

@smoky gyro isnt it AB

[smoky gyro]

thats what i said

the answer is AB

[fervent ledge]

ok

[devout snow]

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[mystic mountain]

Trick question (1/10)^75

[heady lantern]

?

@mystic mountain

[mystic mountain]

I just told u the answer, it's a trick question

[heady lantern]

is 1/10 as a fraction?

[mystic mountain]

Yes, you can also use 0.1

[heady lantern]

ok

also

cann u check my work?

[mystic mountain]

Is it the same question twice ?

Seems ok 5^17)^3

[heady lantern]

Noi accidentally sent it twice lol

[mystic mountain]

=5^51

[heady lantern]

if u couldnt see my answer

englarged

@mystic mountain

[mystic mountain]

It seems ok

[heady lantern]

what about this

@mystic mountain

@fervent swallow

<@&286206848099549185>

[royal carbon]

yes

[heady lantern]

is this right?

[opal cloak]

i think they want 0.75 as a fraction

[royal carbon]

Yeah it's 75/100

[opal cloak]

?

3/4

[heady lantern]

look at the exponent

[opal cloak]

yeah

convert 0.75 to a fraction then solve it

[heady lantern]

can u solve it

I dont hhave a calcualor

im on phone

@opal cloak

<@&286206848099549185>

[devout snow]

@heady lantern Has your question been resolved?

[devout snow]

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[dense obsidian]

Why is does this practice problem say the same equation gives two different answers?

[dense obsidian]

wait 1 is negative

mb

i stared at this problem for too long without seeing it

[restive river]

its not the same since one's lower bound is pi/2 and the other is -pi/2

[dense obsidian]

yeah T_T

[devout snow]

@dense obsidian Has your question been resolved?

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[halcyon kernel]

How do I find the y value of the centroid for the thick blue curve?

[halcyon kernel]

I know the length of the curve which is

x bar was just this

52.786/10.9238

How do I go about solving for the y bar?

[devout snow]

@halcyon kernel Has your question been resolved?

[devout snow]

@halcyon kernel Has your question been resolved?

[icy barn]

y bar would be also y

[devout snow]

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[pearl pulsar]

I don't understand why the integral from 2 to 0 is positive but the integral from 0 to 2 is negative?

[red turret]

what?

[woven radish]

Dyssrupt

[pearl pulsar]

So basically they want us to interpret each integral based on area on this photo\

[pearl pulsar]

yeah ik that rule but why does it give a positive answer?

[red turret]

area is positive

also they should have the bounds as 0 to 2

[versed juniper]

do you know what ftoc is

[red turret]

2 to 0 is well..

[pearl pulsar]

Yeah ik but im doing the hw based on the previous chapter

[pearl pulsar]

yes so 2 to 0 should be negative, no?

[red turret]

to calculate the area, you take the absolute value of the integral.

because area is positive

[pearl pulsar]

Oh but then why is 0 to 2 negative that's what im having trouble understanding?

[red turret]

what the flip

[pearl pulsar]

Ye 😂

[red turret]

they are telling me that the area is -4

💀

[pearl pulsar]

yeah im confused isn't that just one rectangle and 1 triangle

below the curve

also

we have absolute value problems seperately on the same problem

it's just from 0 to 2 i don't see anything below the x-axis so i don't see how it could possibly be negative

[versed juniper]

bugged 🗣️

[pearl pulsar]

probably

Okay so this is a mistake with the book then not me right 😂

[wooden veldt]

yes this is definitely a mistake of the question, bring it up w/ your teacher

[red turret]

yeah, even if you calculate the integral (not area) from 0 to 2, its 4 and from 2 to 0 is -4

[pearl pulsar]

Thank you so much guys! glad we could clear this up

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[red quartz]

just so confused on getting the derivative

i brought it down

[eager nova]

What have you tried?

[red quartz]

1/x ln (x)

-1/x^2 * 1/x

or product rule

-1/x^2 *ln(x) + 1/x * 1/x

[eager nova]

U trying to do derivative of x^(1/x)?

[red quartz]

yse

yes

[eager nova]

Potential exponential rule

[red quartz]

ln(x) * x * -1/x^2?

[eager nova]

x^(1/x) * d/dx (lnx * 1/x)

[red quartz]

is that not what i had before

just with the x^ (1/x) from log differentiation?

[granite laurel]

!status

[devout snow]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[red quartz]

1

yes

[woven radish]

Dyssrupt

[red turret]

try differentiating both sides

[red quartz]

and when you get derivative

f'x/fx = 1/x^2

[granite laurel]

Do you know how to find the derivative?

[red turret]

did you use quotient rule?

[red quartz]

-1/x^2

wait

is it just

-ln(x) / x^2?

[red turret]

not quite

[devout snow]

Show your work, and if possible, explain where you are stuck.

[woven radish]

Dyssrupt

[red quartz]

oh ok

so 1/x^2

[red turret]

right

[red quartz]

do i just plug now?

[red turret]

also x^(1/x) is just f(x)

so bring it back to LHS

since we need f'(x)/f(x)

[red quartz]

it back even tho it's log differentiation

i did ln(y)

y' / y no?

[red turret]

yeah

but well, you took it to RHS in your calculation

not that it matters, but..

[red quartz]

ok

so i put it back

then plug

what's ln(e^-1)?

0?

oh wait they cancel

2e^2

mmmm

correct

thank you

.close

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[gloomy valve]

Could somehow explain the intuition behind using the MVT on a multivariable funciton

I am more than happy to walk through the problem, as it will also help me understand as well

<@&286206848099549185>

[devout snow]

@gloomy valve Has your question been resolved?

[onyx lion]

MVT guarantees that for a function of multiple variables, there exists a point where the instantaneous rate of change in any direction = the average rate of change over a path between 2 points. applying this to the lipscitz continuity proofs involves using the MVT to relate the difference in function values at two points to the difference between their coordinates, providing a formal connection between the concept of lipscitz continuity and the behaviour of the function across its domain

[devout snow]

@gloomy valve Has your question been resolved?

[devout snow]

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[hollow walrus]

Can I get help to find the equation of a vector passing through the points (1,1,0) and (0,0,1)?

[mystic mountain]

Equation ? Do you mean parametric curve?

[true sable]

To find the vector equation of a line between any two points, you can start at either point and travel a multiple in the direction between the two points

The direction between these two points is (1,1,0)-(0,0,1)=(1,1,-1)

So the vector equation is r = (1,1,0)+λ(1,1,-1)

[hollow walrus]

Oh thank you

[true sable]

Does it make sense intuitively?

[hollow walrus]

Yes

[true sable]

When it comes to vector problems try thinking of where do I start and where do I need to go

[hollow walrus]

Okay. Thank you a lot

[true sable]

Np 🙂

[hollow walrus]

how do u close?

[true sable]

.close

[hollow walrus]

.close

[devout snow]

Channel closed

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[hollow walrus]

.reopen

[devout snow]

✅

[hollow walrus]

I was just wondering...if I have a plane and a vector line how would I find the point of intersection?

I have an equation for the plane; (2/5)x+(3/10)y+(31/15)z= -7/10

and r = (1,1,0)+λ(1,1,-1) is the vector line equation. How would I find the coordinate where they intersect?

[true sable]

You can turn the Cartesian equation of a plane into the vector equation for a plane

[hollow walrus]

So basically convert (2/5)x+(3/10)y+(31/15)z= -7/10 into a vector form and then set both vectors equal to one another?

[true sable]

Yeah

[hollow walrus]

so basically that would be (2/5)x+(3/10)y+(31/15)z +7/10= (1,1,0)+λ(1,1,-1)?

how would u simplify that?

[true sable]

You can't do that comparison directly, since the LHS is in xyz and the RHS is in ijk

[hollow walrus]

oh...

Technically I could replace x,y,z as i,j,k couldn't I?

[true sable]

You have to find some equation where π = (,,,) + k(,,,) + μ(,,,)

[sullen island]

it's better to look at the problem the other way tbf

take a point on the line

[true sable]

π is the plane

[sullen island]

how do you check if it's on the plane?

[true sable]

Unfortunately not

[hollow walrus]

Would you not set it up equal to one another because that won't work?

[true sable]

The way to convert a plane from Cartesian to vector can be quite tedious so I want to understand platypus's method because I don't see where he's coming from

[hollow walrus]

Sure thing 👍

[sullen island]

well the points on line r have coordinates of the form (x, y, z) = (1+L, 1+L, -L) [lazy to type the lambdas]

[true sable]

So we choose an arbitrary L (set L = x) and see if it lies on the plane?

[sullen island]

checking if a given point is on a plane is not hard, you just plug it in

[true sable]

Nvm haha, yeah it's simpler

[hollow walrus]

so we basically just use guess and check?

[true sable]

I wish I'd thought of that for my exams 😭😭

[true sable]

No, you can just sub in 1+L for x, 1+L for y and -L for z, solve for L

Then you can get xyz

So I guess you kinda are just replacing xyz and ijk

[hollow walrus]

ok so (2/5)(1+L)+(3/10)(1+L)+(31/15)(-L) +7/10=0

and simplify that?

[true sable]

But not really actually

[sullen island]

=0

and find the L that works

[hollow walrus]

oh ok

let me try

[true sable]

May I ask where this question comes from?

Because turning a plane from Cartesian to vector may still be useful knowledge

[hollow walrus]

My cousin gave me this problem. He wanted to test me and I think he did.

I haven't really dug too far into vectors where I mastered it and I forgot a few important ideas which I am trying to remember. This question makes me want to master vectors now lol.

I was wondering what books you guys might use to learn vectors?

[true sable]

I learnt it in school from a textbook that the school had bought so it's not one that I could recommend to you unless you want to pay :/

[sullen island]

same for me

[hollow walrus]

I am fine with paying

[sullen island]

(& not in english)

[true sable]

Also yt videos tend to work really well

[hollow walrus]

oh ok

[hollow walrus]

which channel? I tend to watch JG organic chemistry tutor

[sullen island]

like I could give you recs for uni stuff, but you're prolly not interested in that atm

[hollow walrus]

I am in highschool rn lol

[true sable]

There are many, none that I can say off the top of my head but what you've mentioned is good

[hollow walrus]

ok thank you guys

[true sable]

What country are you in?

[hollow walrus]

United States

[true sable]

Ah ok, the textbook I was going to recommend probably isn't a good choice for you then (it is in English lol, just covers content you may or may not see)

[hollow walrus]

I am much ahead of the united states school curriculum. I am preparing for the JEE India because I am Indian and wanted to try it out.

[true sable]

https://www.googleadservices.com/pagead/aclk?sa=L&ai=DChcSEwiNpozsgs2FAxUTl1AGHbG-BvkYABAJGgJkZw&ase=2&gclid=Cj0KCQjwiYOxBhC5ARIsAIvdH52FgwX3--3c4tjtF2c9m_H34Bm4eFXPwAFMW07BfayDo5aouwbRy8MaAlhKEALw_wcB&sph=&ohost=www.google.com&cid=CAESVuD2VJyyA2v_YpbpBoZYeAGYDmUUhVqVk0lXN0IKgErL9qygZmUTUPKItRfggBKgC_p_GZn7a59DAmD4ILuDgdHewhdGZScWN2NDXhR9YnlXS5vcI83N&sig=AOD64_1Wun-8KVbfXAThtda4PrlvGdd5jw&ctype=5&q=&nis=4&ved=2ahUKEwiOqIXsgs2FAxUcUkEAHQndDk8Qwg8oAHoECAUQDA&adurl= this is the textbook I used

Long link lol

[hollow walrus]

Pearson is an amazing author. Thank you

[true sable]

Their textbooks for the further maths a level are absolutely incredible

[hollow walrus]

I agree that the book are great

[true sable]

I think there are like 1 or 2 questions with wrong answers though lol

[hollow walrus]

Typically large textbooks like these have a couple of incorrect answers but it is fine.

[true sable]

But yeah, I absolutely loved vectors as a topic and I'm glad I could help

Have a good day

[hollow walrus]

You too thank you

.close

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[hollow walrus]

.reopen

[devout snow]

✅

[hollow walrus]

I am so sorry but when you find L do you plug that in back to the equation?

[true sable]

You know that xyz are 1+L etc

[sullen island]

yeah, and that gives you your point of intersection

[hollow walrus]

Ok thank you

.close

[devout snow]

Channel closed

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[true sable]

Also no need to apologise

[hollow walrus]

ok

wait

is L=42/41?

[true sable]

Idk I haven't done it 😅

[hollow walrus]

No problem

Is it fine if I show you a problem I found?

[true sable]

Yeah I got 42/41

[hollow walrus]

Yes!

[true sable]

What's up?

[hollow walrus]

ok

Oh the question got cut off

Did I say I was in high school? I meant I was in middle school sorry.

[true sable]

I don't know the education system in the us but that sounds like you're younger than you said 🤣😭, I'm impressed 😁

[hollow walrus]

thanks

Anyways in this problem above, C' is an unknown point how could you find it?

[true sable]

I can already see the answer being 1/3 just by looking at the numbers but we obviously have to show it lol, lemme think

*intuitively I mean

It's not like I already know for sure 😅

[hollow walrus]

the answer is not 1/3 just to say

[true sable]

Aww, so it's not some reciprocal of Pythagoras lol

I think I have a way to get to the answer

[hollow walrus]

I think we could basically create and use 3 dimensional geometry and take point for P, A, B, C, D, and then find the coordinates of B' and D' and create vectors to those points. Then we could create a plane? and when we find that plane couldn't we just find where the intersection of PC and the plain is and find that coordinate. The z value would be C'

Wait we were just discussing this 😅

[true sable]

We can draw two vectors, one from a to b' and a to d'. We know those lie on the plane and therefore we can add multiples of them to get to c', knowing the distances from the question we can figure out the ratio

[hollow walrus]

Ok let's do that

Should we take a coordinate value for A?

[true sable]

Just saying I don't have paper on me 😅

[hollow walrus]

Oh ok

[true sable]

I don't think we actually need any specific coordinates if you know what I mean, we can simply draw the vectors and get relations from those

[hollow walrus]

That will be quiet hard

[devout snow]

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[hollow walrus]

I see

[true sable]

Like if you had a 2d problem asking you how to get from one point to another

[hollow walrus]

ok

how would we find the vector from A to B'

the height would be 1/4

[true sable]

We can get angle abp, we know length ab and bb', so we can use cosine rule etc to get any lengths and angle we need for abb'

[hollow walrus]

interesting

[true sable]

Then the same for ad' etc

And maybe we can add ab' and a multiple of ad' to get pc'

[hollow walrus]

lets try

[true sable]

Ok, I'm sorry but I have to go now. I'll just leave you with my advice of 'try solving it with vectors and geometry trying not to get coordinates involved ' but if that doesn't work or you or someone finds a better way, try that instead

It's been great talking with you and good luck

[hollow walrus]

Thank you

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[viral rapids]

.close

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[limber wraith]

The terminal voltage of the 25.5V battery in the circuit shown is 20V. Determine the batteries internal resistance and the circuits resistors resitance

[limber wraith]

I got the internal resistance ( 1.1 ohms)

But got no idea on how to get the resistance of the resistor

Oops i sent it twic

[dense jay]

I=e/(r+R) (e for emf)

ie 25.5=Ir+IR , 25.5=5.5+5R

(though you can just remember terminal V is the V across R, just use R=V/I)

[limber wraith]

Can you explain?

Sorry i couldnr understand

@dense jay

[dense jay]

the first one or the second one

the first one is just V=IR for the whole circuit

the second is just V=IR purely for the load (ie resistor R)

[devout snow]

@limber wraith Has your question been resolved?

[devout snow]

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[rain berry]

I proved that the series converges but when I found the first term it was nowhere near pi which is what I am supposed to be comparing it to

[rain berry]

.close

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[noble mountain]

hi i need help with limits

[noble mountain]

gonna translate to english

only a minute

Using the digits 0 to 9 at most once each, find the values ​​of a, b and c, numbers
integers from zero to nine, to make the equality below true

i dont even know how to start lol i tried limit properties but i dont find an exit

[graceful cosmos]

The denominator will approach 0.

So if there's any hope for the limit to exist, the numerator must approach 0 as well

[devout snow]

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[stable isle]

How would I do this?

I have to find z

so would z just be 90?

[winter patrol]

exact same principle as the previous question

no

[stable isle]

ok let me look at what I did last one

what number was i in for the last one if you remember?

[winter patrol]

wdym

[stable isle]

oh found it

so would I do 90=4z-10?

ok. thanks for the help again lol. Thank you :)

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[potent valley]

Help

[solar goblet]

tf is this

[solar goblet]

what do you need help with

[stable isle]

so basically for your problem it has to deal with slope and stuff

[solar goblet]

huh?

[stable isle]

idk havnt done slope in awhile lol

ima leave this to someone else

[solar goblet]

my brother in christ

[stable isle]

tf is ur discord doing 😭

[solar goblet]

oh my god

[upper schooner]

It's the way the image has been uploaded, with no background and dark text

[solar goblet]

my man

[potent valley]

WHOO[S

[potent valley]

Whats anser

[solar goblet]

for people using dark mode

[stable isle]

ahh light mode my eyes 😭

[solar goblet]

alright so

do you know what is the condition for 2 line equations to be parallel

[potent valley]

Whats answer

[solar goblet]

!noans

[devout snow]

The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.

[solar goblet]

answer this

[potent valley]

no

[potent valley]

Everyone calls me dumb

[solar goblet]

and are you gonna cry about iy

[solar goblet]

are you saying you dont know or are you refusing to answer

[potent valley]

I dont know

[ocean silo]

you know you can like be an actually respectable human person instead of yelling at people for trying to help you

[potent valley]

and I'm dumb

[solar goblet]

no you are not, but you look indeed dumb

thats why im telling you to stop saying "im dumb"

[solar goblet]

have you even put effort into thinking?

[potent valley]

for hours.

[solar goblet]

my ass

please, put in effort

[potent valley]

I did

My brain is dumb, everyone calls be dylexica alexica

which is true

Everyone here is smart

And I'm dumb

because my brain is different

I'm failing all classes

[solar goblet]

this is not your place to vent

[potent valley]

Just F's

All you do is ask me question, when you know I wont understand it

Becuase I was born dumb

everyone else here was born to be smart

[heavy current]

can you please not?

let's stop beating ourselves up

and return to the question

[potent valley]

no its true

Go ahead and ask me a shape questions, I wint understand it

[heavy current]

this isn't helping you solve the problem though

[potent valley]

so give me the answer

[heavy current]

no, we can't do that.

[potent valley]

Nothing helps me

[ocean silo]

you won't understand shit with the answer but without an explanation

[potent valley]

NOTHING HELPS ME

[weak cove]

Then close the channel

And move on

[fossil rampart]

It has to be satire

[ocean silo]

100%

[potent valley]

?

[weak cove]

Pending postgraduate

[heavy current]

you're not stupid, but if you're not willing to engage with us, why should we engage with you?

[solar goblet]

this may sound harsh, but no one honestly cares

we are here to help you, we are not your therapists

if you need to talk, do it with professionals or your parents

[weak cove]

Ok

[solar goblet]

my condolences

[heavy current]

sorry to hear that

[weak cove]

Bruh

[heavy current]

huh

[weak cove]

They just got spawned in

[potent valley]

so what now

[heavy current]

...do you want help with your question still?

it's not too late to still get it, you know

[potent valley]

Lets be honest, I'm a failure at everything

1. Making friends

2. School

[heavy current]

...

[solar goblet]

ill repeat, we are here to help you in your question, not your life

[ocean silo]

bro what is this

[weak cove]

<@&268886789983436800>

[solar goblet]

if you persist, ill call mods

oh nvm

[potent valley]

fine ill stop

[fossil rampart]

Is this a social experience

[potent valley]

go ahead and help me

[heavy current]

reposting

okay, have you tried anything?

[potent valley]

i stared that the screen

the numbers looks like there moving

[fossil rampart]

Do you know what is the form of an equation of a line ?

[potent valley]

no

I know nothing

[fossil rampart]

Where does this exercice come from ?

[potent valley]

I do workout

huh?

[weak cove]

They’re obviously trolling

[fossil rampart]

Yes the image comes from internet

So clearly trolling

[potent valley]

I dont understand

[solar goblet]

mods can we get this dude out please

[heavy current]

is it really a troll?

they've used help channels before it seems

[fossil rampart]

I searched the image

And it comes from sites

[potent valley]

oh

[devout snow]

@potent valley Has your question been resolved?

[devout snow]

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Remember:
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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[tepid sluice]

Can someone who is free teach me what is dot product in vectors🙏

[west carbon]

https://mathinsight.org/dot_product_examples#:~:text=three-dimensional vectors.-,Example 1,right angle%2C or obtuse angle%3F&text=we calculate the dot product,−10%2B18%3D12.

[tepid sluice]

What does it mean by projection of one vector onto another? <@&286206848099549185>

Also I didn't understand the unit vector part

[west carbon]

unit vector is a vector of magnitude 1

[tepid sluice]

Why did we take it tho

How was the magnitude affecting the dot product if only direction is involved?

[west carbon]

where

[tepid sluice]

https://mathinsight.org/dot_product

[devout snow]

@tepid sluice Has your question been resolved?

[tepid sluice]

No

Cmon bruh someone 😭🙏

@west carbon

[west carbon]

@tepid sluice give me 2 vectors and I’ll do the dot product if that is your question

[tepid sluice]

My question is why and how does it work

The geometry

And also the above questions

[west carbon]

Oh idk the geometry, only the computation

(X1,y1)dot(x2,y2) = x1x2+y1y2

Ez

[tepid sluice]

I mean yeah

That is ez but like dawg

Shi don't make sense 😔

[west carbon]

What part

[tepid sluice]

The geometry

Also the projection what do that represent

<@&286206848099549185>

[west carbon]

Dot product represents a measure of how close 2 vectors point in the same direction

[tepid sluice]

why is it cos theta tho

[devout snow]

@tepid sluice Has your question been resolved?

[west carbon]

Because of trig

When you derive the angles

You can find videos of dot product derivations

[devout snow]

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Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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[tulip latch]

hello! this is perhaps a simple question

on the top, I'm unable to identify what the letters is in front of (a+h) and (a) are

due to bad handwriting

[solar goblet]

f

$\frac{f(a+h)-f(a)}h$

[woven radish]

فطر

[tulip latch]

oh yeah

f makes sense given the context of prime(derivative)

thank you so much!

.close

[devout snow]

Channel closed

Closed by @tulip latch

Use .reopen if this was a mistake.

[devout snow]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[lost creek]

Hi, can anyone guide me for this?

It’s a calculus based questions and we’re required to use convergence, divergence or even calculus concept

[rigid pewter]

which part?

[lost creek]

The one I submitted using the concept of statistics are not accepted

I’ll send my answer here

For a,b,c, I can’t see how to use calculus concept to explain for b and c. Okay, I just know for a when we integrate from negative infinity to infinity then we get 1, but then I use coding to find the answer

[lost creek]

Here, actually I shown like this

But my lecturer marked me half of the marks, and when I ask for solutions, she said it’s confidential, I just wonder how to get using calculus concept

[rigid pewter]

hmm that should be valid

in your second image, the shaded area is 15.87% of the total curve

[lost creek]

May I know how to clarify using the calculus concept?

[lost creek]

The answer is correct, just the method I use is coding and manually calculation also by statistics probability concept, my lecturer just marked me half. And didn’t tell us how to solve with calculus method

[rigid pewter]

well $\int_{185}^\infty f(x) dx$ represents the area under the curve starting at 185 and ending at infinity right

[woven radish]

b

[lost creek]

Yes, and i do this integration?

[rigid pewter]

yeah, the integral equals 0.1586...

[lost creek]

I know it’s improper integration, but the integration solvable by human?

Because from coding I can get the answer

[rigid pewter]

you're not expected to solve this

the question says use a calculator

so you can basically just type it in and get your answer

[lost creek]

Also, I wonder does this uses the convergence and divergences concept, because almost the half semester of this course, we’re focusing in divergence

[lost creek]

Oh, then for (a), basically I just use code to find the integration from negative infinity to infinity? (b) from 185 till infinity?

Then how about (c), how can I explain that? I know how to explain integration from 178 till 185 (the typo in question), but how I explain 0.5?

[rigid pewter]

i'm not sure what the typo is but they aren't equal as is

[lost creek]

Okay, I tried to integrate from negative infinity to infinity, I got 1.1789

[lost creek]

Yea, that’s a typo, should be integrate from 178 till 185

[rigid pewter]

oh okay

[lost creek]

May I know for (a), because I got greater than 1😅

[rigid pewter]

do you see how the orange area + the blue area is 0.5

[lost creek]

Yea, I actually plotted this as well

[rigid pewter]

and that the orange area is $\int_{178}^{185} f(x)dx$

[woven radish]

b

[lost creek]

Yea, I can understand this, basically is what I submitted but my lecturer said I didn’t fulfill the requirement

[rigid pewter]

$\int_{178}^{185}f(x)dx + \int_{185}^\infty f(x) dx = \int_{178}^\infty f(x) dx = \frac 1 2$

[woven radish]

b

[rigid pewter]

i guess the missing piece is actually explaining it using integrals?

[lost creek]

Hmm, half of the marks out of 15 because I didn’t explain this 😢

[lost creek]

But how to explain a?

Okay, for wolfram I got 1😅

[rigid pewter]

i used desmos

[lost creek]

Oh yea, I wanna ask how to plot this, because I don’t know how to use Desmos only I use Python, but my Python just show the range 140 till 240

[rigid pewter]

$f(x) = ...$ gives us the dark blue line and $0 < y < f(x)$ fills in the y values greater than 0 but less than $f(x)$

[woven radish]

b

[rigid pewter]

you can take a look at it actually https://www.desmos.com/calculator/l6987y1xj8

[lost creek]

May I know why I plotted this but it gives me nothing?

[rigid pewter]

it's just too short to see lol
zoom in around x=178
or change your x and y axis manually

[lost creek]

Oh I see

Is it just something for this for (a) till (c) since I showed the value here, just one question, how I produce the graph which I produce using python in (b) and (c)

[rigid pewter]

you can constrain your inequality - type in
$0<y<f\left(x\right)\left{178<x<185\right}$

[woven radish]

b

[lost creek]

Let me try

[lost creek]

Is it something just like this for a,b,c and overall?

For, the symmetry line for mean, is it just typing manually?

[rigid pewter]

do you mean $x = 178 {0 < x < f(178)}$?

[lost creek]

No, I mean the vertical line at x=178, because I plug in manually from 0 till 0.05699

[woven radish]

b

[rigid pewter]

sorry typo

this is that line though

[lost creek]

Should be y for the range

Anyway, thanks

But for question c, actually I don’t really know how to show

Should I also draw the area for 0.5?

Or directly show the area for 0.5 minus the integrand from 178 till 185?

[rigid pewter]

you could show both the area and the calculation result i guess

[lost creek]

Meaning like this for calculation?

Which is shown here by Desmos

[rigid pewter]

yeah that's good