help-0

[alpine sable]

oh

so that is correct?

[drifting hull]

yes

[alpine sable]

ty

.close

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[grizzled field]

I'm getting 20 meters for this question, but the answer the book says 80 meters.
I'm assuming that when you solve the system that want you take your answer and subtract it by 100. My question is why?
Question: The equation: y+4x=100 represents your distance (in meters) from the finish line x seconds after you begin your leg of a relay race. The equation y+3.8x=96 represents your opponent’s distance from the finish line. How far do you need to run until you catch up to your opponent?
Solve using a system

[magic root]

is this just simply 2^5?

[grizzled field]

I believe it is 6 ways 2G x 3R

[drifting hull]

No: it would be 2^5, if you can distinguish between all balloons

it is 5 choose 2, if you know binomial coefficients

[magic root]

this thing?

is that a binomial coeeficient?

[drifting hull]

yes

[magic root]

Ohh, i didn't learn these yet, i saw my friend doing them.. imma learn them..

[grizzled field]

so it's not 2x3?

[drifting hull]

it helps for this problem

[magic root]

thats what i was thinking

[drifting hull]

No it is 5 * 4 /(2 * 1)=10

[grizzled field]

what where did 4 come from?

[drifting hull]

You have 5 choices to place the first green balloon, then 4 choices for the second one (as one is already occupied). Now you counted each situation twice, as you decided which balloon you placed first, so you have to divide by 2

[magic root]

Ohh

the question said that the the only topic covered in the question was number sense 😂

but its easier ur way

Tysm!

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[grizzled field]

.open

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[grizzled field]

I'm getting 20 meters for this question, but the answer the book says 80 meters.
I'm assuming that when you solve the system that want you take your answer and subtract it by 100. My question is why?
Question: The equation: y+4x=100 represents your distance (in meters) from the finish line x seconds after you begin your leg of a relay race. The equation y+3.8x=96 represents your opponent’s distance from the finish line. How far do you need to run until you catch up to your opponent?
Solve using a system

[wary stream]

20 is the value for x, which is measured in seconds. You need to plug in 20 sec, into the equation y + 4x = 100, since that is the equation for you, and you're solving for y, the distance

[lone heart]

@grizzled field Has your question been resolved?

[solemn grove]

question ?

oh sorry i just saw it

so is y the distance

[wary stream]

I explained it already

[solemn grove]

no, x is the distance

[wary stream]

x is time

[solemn grove]

oh

[wary stream]

Measured in seconds

[solemn grove]

sorry, i’m reading everything now

[wary stream]

Maybe you should have read everything first before trying to answer the question that someone else replied to

[solemn grove]

apologies

[lone heart]

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[dim elm]

Can someone help me with this?

The product of Kevin's age (in years) two years ago and his age four years from now is one more than twice his present age. What's his present age?

[alpine sable]

Hey, before I help you can you let me know which grade is this question from?

[dim elm]

It's for 10th grade

[alpine sable]

uhm alright

fine

First of all I'd suggest to define some variables

Like, Kevin's Age $= x$

[ocean seal]

SKJJ

[proven rune]

let x be kevins age
acc to the q , (x-2)(x+4) = 2x+1
solve the eqns to get

x

@dim elm

[alpine sable]

you shouldnt post full solutions tho

[dim elm]

Oop, alr

Thx

[proven rune]

@wary stream hi bro how r u

[wary stream]

They just gave the equation, that's not the full solution

The full solution is solving for x

[proven rune]

@alpine sable .

[alpine sable]

there's no reasoning as to how they arrived there, solving the equations isnt hard

@dim elm if your problem is solved, you may .close the channel

[dim elm]

Oke thx y'all

[proven rune]

np gl

[dim elm]

.close

[lone heart]

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[wary stream]

Words in math makes it significantly difficult, to determine the proper equations

[lone heart]

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[alpine sable]

.open

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[grizzled field]

if I was to plug in 20 for x; that would give me y+4(20) = 100

y+80=100

y=-20

[lone heart]

@grizzled field Has your question been resolved?

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[polar swan]

can someone help me simplify this

[alpine sable]

@polar swan do you know the formula for $^nC_r$?

[ocean seal]

!!!

[polar swan]

Yes

Here’s what I have so far

[median moth]

uuuh correct me if I'm wrong but shouldn't the formula be:

[polar swan]

i see that now

😅

[median moth]

no worries <3

[polar swan]

.close

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[proper dragon]

Hi, I have a question, the Cartesian product of a set with itself it's equal to?

[pale kestrel]

ordered pairs of the original set

AxA = {(a, b) : a, b in A}

[proper dragon]

Ooh okay okay, and then how Can I calculate the power set of AxA?

[echo socket]

I guess {S: S⊆AxA}

[twilit dune]

written as $A^{2}$,

[ocean seal]

alshfik

[proper dragon]

but then how can I calculate the power set of A^2?

[vale wigeon]

just as you would calculate the power set of anything else

[twilit dune]

i think he wants an algorithm?

[vale wigeon]

are you asked to write it out explicitly or just its cardinality?

[proper dragon]

cardinality I have to compare with other cardinality

[vale wigeon]

okay so you are not asked to write out the entire set

[proper dragon]

the cardinality of this

[vale wigeon]

do you know how to find the cardinality of P(S) when |S| is known?

[twilit dune]

X is finite?

[proper dragon]

vs the cardinality of this

[proper dragon]

Yes

[proper dragon]

2^|S|?

[vale wigeon]

yes

and do you know how to find the cardinality of a product set when the cardinalities of both factors are known?

[proper dragon]

no

[vale wigeon]

so if someone said "Let A be a set with 420 elements and let B be a set with 69 elements. Find |A × B|" you would be unable to answer. do i understand you correctly?

@proper dragon

[proper dragon]

eehh, I have to answer which of both have more elements, so that is cardinality, no?

[vale wigeon]

this does not answer my question...

i'm trying to figure out if you really don't know how to find |A×B| knowing |A| and |B|, or if you do know but think you don't.

[proper dragon]

mm can I understand it like a multiplication, or is wrong? because I get confuse Cartesian product are tuples

[vale wigeon]

this again does not answer my question...

please do not dodge my questions

[proper dragon]

no, no sorry my mother language is not english, so I'm trying to translate to spanish that is my language, I don't understand how to calculate the cardinality of AxB

[vale wigeon]

I don't understand how to calculate the cardinality of AxB
see this is what i wanted to hear

and now i can tell you

$|A \times B| = |A| \cdot |B|$

[ocean seal]

Ann

[proper dragon]

:000

But, If A = B, then...? is for example |A| = x, so that will be x^2?

[vale wigeon]

yes

[proper dragon]

and then this is equal to 4

[vale wigeon]

multiplying a number by itself is the same as squaring it

no, that is not equal to 4.

[proper dragon]

4 elements

{∅, {{∅}}, {{X}}, {∅, {X}}}

[vale wigeon]

no, P(P(X)) does not necessarily have exactly 4 elements.

you're thinking of P(P({X})), which is not the same as P(P(X)).

[proper dragon]

P(X) = {∅, {X}}, is wrong?

[vale wigeon]

yes...

that is wrong

very wrong

again, you're confusing X with {X}

those are not the same thing

besides, you said before that |P(X)| = 2^|X|, and now you're claiming that P(X) consists of only 2 and not 2^|X| elements?

[proper dragon]

aaaa, and I don't know what is |X|, the number

sooo, P(X) = 2^|X|, then P(P(X)) will be P(2^|X|) anddd

[twilit dune]

|P(X)| = 2^|X|

[proper dragon]

2^(2^|X|)??

[twilit dune]

also P(2^|X|) is the powerset of a cardinality, not of a set

[vale wigeon]

it's not great that you're conflating a set with its cardinality

[proper dragon]

so I can't use the definition of 2^|X|

[twilit dune]

?

[proper dragon]

I can't use the defintion of 2^|X| here, right? because both say it, is the power of cardinality not the power set of a set

[proper dragon]

this is wrong

[twilit dune]

what exactly do you mean defintion of 2^|X|

it is 2 multipled by itself |X| times

[proper dragon]

sorry sorry, I get confuse, 2^|X| is the cardinality of power set

then I'm trying to know the cardinality of P(2^|X|), so...

[proper dragon]

I don't know, is wrong?

P(P(X)) = 2^P(X)?

[twilit dune]

P(2^|X|) is not meaningful, you are taking the power set of a cardinality, the power set function is supposed to act upon a set

[proper dragon]

so, how can I answer which of both have more elements than the other? P(x^2) x P(x^2) and P(P(X)) = P(2^|X|)

[lone heart]

@proper dragon Has your question been resolved?

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[alpine sable]

How do i do this

[alpine sable]

someone plz help

<@&286206848099549185>

[wary stream]

You have to wait at least 15 minutes before pinging helpers

[alpine sable]

oh my bad

[lone heart]

@alpine sable Has your question been resolved?

[lone heart]

@alpine sable Has your question been resolved?

[noble sinew]

Expand the terms?

[alpine sable]

im doing uh

wait let me see what kind of thing this is

wait nvm i alr did it

u can close this if u want

[noble sinew]

You type .close

[alpine sable]

.close

[lone heart]

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[old wolf]

<@&286206848099549185> Question, how do you usually do this? I will appreciate if equation is provided. thanks in advance!
This is not an homework or assignment, I just wanted to solve such problem because I might encounter this thing in the future.

[old wolf]

I actually started it by dividing the difference of old RED % and new RED % from 5k and got 2.5M, now I'm stuck if I'm right or incorrect.

Thanks in advance!

5,000 / (New Red% - Old Red%)

[wanton junco]

what do the percentages represent exactly?

[old wolf]

% of the total sales (RED & BLUE combined)

so the first row was the % distribution before RED acquiring 5k sales, then 2nd row is the new % distribution.

[lone heart]

@old wolf Has your question been resolved?

[lone heart]

@old wolf Has your question been resolved?

[old wolf]

<@&286206848099549185>

[wanton junco]

you could use a linear system of equations no?

do you happen to have answers for this @old wolf

[old wolf]

Yeah, but I'm not quite sure if I'm right, 2.5 M?

But the first row will not be the same with what's given...

@wanton junco Can you guide me every step please?

[wanton junco]

notice that in both rows

the total of sales is 2.5M still

[wanton junco]

I'd like to but im not sure if im getting the right numbers so I would hate to mislead you

[old wolf]

So you mean, this equation is enough?

[wanton junco]

the equation accounts for the difference in sales if the total amount of sales didn't change

i.e. if the 5k sales red gained came directly from blue

however, if the total amount of sales increases along with red
then the 39.1% of sales comes from a new number of sales

[old wolf]

Do you mind putting things in variables or equation?

Wait I guess I did confused you with the value of blue at first row...

It should be like this...

If 2.5M is the answer how comes the first row distribution is not equal with what's given??

[wanton junco]

im not sure it's the answer infact

im trying to see if I can get a decent solution

[old wolf]

But you're getting my point right?

This is bugging me. hahaha

[wanton junco]

do you have more details about this?

[old wolf]

Actually that's all

You said use linear equation.

Can you show me your steps ?

[wanton junco]

essentially my method would consist like this

call z the total amount of sales

[old wolf]

ok

[wanton junco]

thus we know that 38.9/100z=x

now we're told taht after 5000 sales the total amount of sales has increased for both z and x thus we have that

x+5000=39.1/100(z+5000)

however the general results I get from this are not too compliant...

and I feel like im missing something here

[old wolf]

How old are you by the way?

[wanton junco]

me? 21

[old wolf]

Sigh, good. I thought you were too young. hahaha

[wanton junco]

what exactly is too young lol?

[old wolf]

I mean it's a shame if someone like 8 years could do such math than me. haha, because I'm already 27 years old.

I mean I love algebra before but now I'm thinking that this is just a petty problem but can't be sure with my answer. hahahaha

[wintry lotus]

Ok children, solve your maths

[wanton junco]

help us Buxy

[old wolf]

haha, yow! What's up?

[wanton junco]

I swear im missing something

I mean...
honestly? this? I would hardly call it math
it's just a bit of logic and computations

[wintry lotus]

Large numbers and such are, imo, somewhat concerning so having a 2nd pair of eyes check is comforting

[old wolf]

let me resend it.

[wintry lotus]

Thought it was solved, let me read real quick

[old wolf]

We need a wizard to confirm if we're doing it right... xD

[wanton junco]

our savior has gone

perhaps it is time to summon the angels @old wolf

[wintry lotus]

Should be something like... 1,500,000 as the total at the start

[wanton junco]

1,500,000 exactly?

[wintry lotus]

It works, but since the numbers are so large... a more precise number is 1,522,500

Basically Red = .389 of Population at the start, Then Red + 5000 = .391 (Population + 5000)

[wanton junco]

that is exactly the number I got

but it failed to produce the same sales number for blue in both scenarios

[old wolf]

how did you do that?

[wanton junco]

@old wolf can you check it in the table?

[old wolf]

Voila

[wanton junco]

oh

maybe I am the one who failed to type the correct number in the calculator

[wanton junco]

. this is what he did essentially

[wintry lotus]

1522500 is before adding in 5000

[old wolf]

wait but we

we are already getting the correct figures...

[wintry lotus]

R = .389x
R + 5000 = .391(x+5000)
=> .389x + 5000 = .391(x+5000)
=> 5000 - .391(5000) = .391x - .389x
=> 3045 = .002x
=> x = 1,522,500

(guess and check figures haha)

Not to brag, but I am 31 so I know a few more years of math

[old wolf]

Yeah thanks! appreciate it Sir! xD

[wanton junco]

so you are bragging

[old wolf]

.close

[lone heart]

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[wanton junco]

interesting...

.close

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[ruby crescent]

how do i solve for y

i did

180 = x + x + 5

combined like terms etc

and got 2x=175

x =87.5

is that correct or did i do it wrong

[pine kettle]

Is that an equilateral triangle

[ruby crescent]

yea

[pine kettle]

So every angle is 60 degrees

And every side is the same length

[ruby crescent]

o

[pine kettle]

Therefore y =...

[ruby crescent]

so its just 5

[pine kettle]

Yup

[ruby crescent]

ok ty

.close

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[delicate orbit]

https://gyazo.com/01aff73ee8281d75902c9d62f9a8a8e9

[delicate orbit]

i need to find the inverse of this function, so i chnaged the x to y and y to x

i then got $$x (2y+5) = 9y - 10$$

[ocean seal]

surv3y

[delicate orbit]

but now am confused as what i should be doing next for some reason

[buoyant kayak]

try distributing that x

[delicate orbit]

i then get

$$2xy + 5x + 10 = 9y$$

[ocean seal]

surv3y

[buoyant kayak]

now get all y terms on one side and other terms on the other side

[delicate orbit]

sorry i am so confused

wouldnt i divide by the y in 2xy

but that would take the y out of 9y

[buoyant kayak]

that would also make $\frac{5x}{y}$ and $\frac{10}{y}$

[ocean seal]

a disappointing son

[pale kestrel]

you're just making y the subject.

[buoyant kayak]

refer to this

[delicate orbit]

so would dividing the 9 be the best thing to do

[buoyant kayak]

no

[buoyant kayak]

this

[delicate orbit]

ya bout how do you want me to get the y in 2xy to the other side

if i want all my x to the left and y to the right

[buoyant kayak]

adding and subtracting terms?

[wary stream]

Move that entire term over

Because don't forget, you can factor

[pale kestrel]

2a + b + 1 = 5a. Make a the subject.

You don't just divide everything by a.

[delicate orbit]

ok so i then got $$5x + 10 = 9y - 2yx$$

[ocean seal]

surv3y

[delicate orbit]

where i can factor the y out

[buoyant kayak]

yep

[delicate orbit]

and get $$ y(9 - 2x)

then just divided both sides by 9-2x

[wary stream]

Yes

[buoyant kayak]

👍

[lone heart]

@delicate orbit Has your question been resolved?

[lone heart]

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[restive tendon]

how does that equal that

that makes no sense

[pale kestrel]

makes sense to me.

whats the issue.

[restive tendon]

i just dont understand the process

on the top

how does

sqrt(x) * (-sinx) = -2x * sinx

[pale kestrel]

what?

Ok, firstly

If I gave you 2 fractions summed together

Would you know how to combine them?

[restive tendon]

yes

lol

OHHH

ITS FRACTION COMBINATION

LOLLLL

i missed that

thank you

appreciate it

[lone heart]

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[alpine sable]

Can someone explain what this is asking me exactly?

[buoyant kayak]

to simplify the radical

using $\sqrt{a\cdot b}=\sqrt{a}\cdot\sqrt{b}$

[ocean seal]

a disappointing son

[alpine sable]

Oh alright

.close

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[drifting bear]

someone mind lending a hand

[pale kestrel]

🤔

[tight locust]

Ok so basically part c is asking you to find the derivative

Do you know how to do that?

It's kind of tricky at first but you'll get the hang of it soon enough

[drifting bear]

Yea I understand the basic concept currently been up 30 hours and this due soon so brain isn't working

[tight locust]

Sounds rough buddy

So if you look carefully you can see that this function is two different functions being multiplied together

There is a rule for that

[drifting bear]

product rule?

[tight locust]

Yeah

[drifting bear]

This is what I have roughly but I feel I'm miles away

<@&286206848099549185>

[pale kestrel]

doing fine. factorise.

You're not done on c

[drifting bear]

a in that picture is c it was just labelled wrong in the question

what would the next step be

[pale kestrel]

.

[drifting bear]

6x(e^-x2)+e

?@pale kestrel

[pale kestrel]

?

That's not it, but just follow what the Q says

[drifting bear]

I'm not gonna lie I've been brain boggled for hour's no clue which part to factorise

[lone heart]

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[thorny pelican]

may someone check this for me, please? (:

[bright hedge]

you should use a calculator for things like that so you can do it quicker

but for now,

,w simplify (7-3xi)(2+5i) - (7+2x*i)(2+5i)

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[bright hedge]

you got the right answer

but you aren't allowed to 1) divide by a constant and 2) divide by x

you are SIMPLIFYING the original form not solving an equation

also dividing by x would cause you to miss the solution x = 0 in an equation so you really shouldn't ever do that

[thorny pelican]

Oh

Because the formula was a+bi I thought I had to include the x

So you keep the x’s

?

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[opal atlas]

I need help on this last question

[wary stream]

Use the triangle inequality theorem

[opal atlas]

i dont know where to begin

pj waot

oh wait

[wary stream]

It tells you what to use

[opal atlas]

i am the confusion

how do i know which one is the smallest angle @wary stream

after using the inequality theorem

[wary stream]

Do you know what the triangle inequality theorem is?

[opal atlas]

its where you add 2 sides of a triangle and it has to be bigger than the thrid

third*

A=11>8
B=14>5
C=13>6

D=13.6

13>6*

[wary stream]

Honestly, weird that it says to use that theorem but oh well

[opal atlas]

would it be B

[wary stream]

Yes

[opal atlas]

ty

.close

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[ashen trail]

How to split this into partial fraction

[wary stream]

Factor the denominator

@ashen trail

[ashen trail]

Then it’s (x-1)(x+1) , how bout the top

[wary stream]

You don't factor the top

You now can form the expression, $$\frac{x^2}{x^2 - 1} = \frac{A}{x -1}+ \frac{B}{x+ 1}$$

[ocean seal]

dldh06

[wary stream]

The right side is the partial fraction part

You need to find the values of A and B

[ashen trail]

1^2 /1^2 - 1 is undefined

[wary stream]

Clear the fractions by multiplying by the LCM

On both sides

[ashen trail]

I got it

Ty

[lone heart]

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[lone heart]

@cosmic nymph Has your question been resolved?

[tight locust]

systems of quadratic equations!!!

https://tenor.com/view/soy-soyjak-bugman-gif-21368596

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[wooden sapphire]

Hello, can someone show me a geometric proof of the cosine double angle identity and help me understand it?

[fathom mantle]

check youtube

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[alpine sable]

aa

[alpine sable]

is this correct

can someone explain

[lone heart]

@alpine sable Has your question been resolved?

[glad sluice]

is this an exam?

[alpine sable]

nope

<@&286206848099549185>

[fathom mantle]

Use algbera

solve for

r

[alpine sable]

is my answer i chose wrong or right

[fathom mantle]

And it does look like an exam

[alpine sable]

its maths online lol

[fathom mantle]

let me see if I get the same answer as you

[alpine sable]

proof

[glad sluice]

then it is correct

[fathom mantle]

yup

is correct

[alpine sable]

alrighty ty!

i just didnt wanna get too sure of myself hah 😅 tysm!

.close

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[latent lantern]

I'm really confused on what this question is even asking

oh, and these are the possible answers

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@latent lantern Has your question been resolved?

[latent lantern]

<@&286206848099549185>

:(

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[jade pumice]

anyone able to walk through this question

[supple tundra]

Do you know how to find normals/tangents to curve?

[jade pumice]

not really

[supple tundra]

have u learned differentiation

[jade pumice]

yes but im really rusty with most of the rules

[gray isle]

have you attempted differentiating what you've been given?

[jade pumice]

im just gonna say no because i really dk what im doing here

[gray isle]

do you know how to differentiate something like e^x

[jade pumice]

its just e^x

[gray isle]

do you know about chain rule?

[jade pumice]

not really

is that the derivative of the first term times the second + the derivative of the second times the first or is that product rule

[raw shard]

that’s the product rule

[jade pumice]

is chain the one u use if its a function inside a function

[raw shard]

yes

$\dv{y}{x} = \dv{y}{u}\dv{u}{x} \\ \dv{x}\left(f(g(x))\right) = f’(g(x))g’(x)$

[ocean seal]

quantum

[raw shard]

same thing but two different forms

[lone heart]

@jade pumice Has your question been resolved?

[jade pumice]

ok so how would i apply this to the question

[tacit arch]

f is the exponential function, g is the square function. Your problem is the composition

[lone heart]

@jade pumice Has your question been resolved?

[umbral orchid]

take the derivative at x=1 that’s the slope of the tangent

the slope of the line normal to the tangent is the negative reciprocal

and you know one point it crosses so that’s enough to write down the equation

[little drum]

[jade pumice]

is my point (1, e) then?

im not sure if im doing that process right

[little drum]

The point is supposed to be: ( x , y(x) )

because you want your normal at that point

so :o if you're plugging things right, ( 1 , 1/e ) is what you'd get

[little drum]

And follow this idea

[jade pumice]

wait can you show me how you got 1/e

[little drum]

e^(-1)?

[little drum]

[jade pumice]

where does the -1 come from again

cuz if i plug 1 into e^(-x^2) i get just e^1 dont i

[little drum]

e^(- (1^2)) and e^((-1)^2) are different :o

Anyways, write them down, and you'll know

[jade pumice]

how am i supposed to know if its the former and not the latter?

[alpine sable]

Bruh

Look at where the parenthesis are place

@jade pumice

[jade pumice]

ok and..? if im going off of (-x^2) and i plug in 1 for x why would it be (-(1^2)) and not ((-1)^2)?

[alpine sable]

Bruh

[jade pumice]

i dont believe i was ever taught that, theres no need to be rude

[alpine sable]

No I’m not being rude

[jade pumice]

saying bruh is not helpful

[alpine sable]

I’m just saying if it was just (-x)^2 would have just been written as x^2

[jade pumice]

ok so if had something like -x^3 and i wanted to plug in a number it would always be surrounded by parentheses?

making it -(n)^3 in my example?

[little drum]

Yes

(-x)^n is different from -(x)^n

[jade pumice]

i realize that but i what i did not know was that when u plug it in its the former

thanks

my maths level is very low lol

[little drum]

Hmm ^^" nvm and no, as you practice you get over the usual troupes but still keep tripping

so, can you follow from there? like you know the slope for normal and all right?

[jade pumice]

yes im up to here

[little drum]

then follow this

[jade pumice]

so i take the negative reciprocal of 1/e?

wait no its the negative reciprocal of 1 right

then i multiply that by the derivative of the original function?

[little drum]

Huhhhh?

negative reciprocal of 1 is -1 my guy

and no

Have you ever come across a theorem or statement that states the product of slopes of two mutually perpendicular lines equals -1?

given normal is mutually perpendicular with the tangent at your given point (1,1/e), I'm sure you only need to find out the slope of normal, and use the point-slope format of line equation to get done with it

[jade pumice]

i know that, i didnt say it was anything else?

i was just asking if u take the negative reciprocal of 1 or not

so how do u get the other point im still confused, i know its the negative reciprocal but of what

[little drum]

[little drum]

You don't need the other point, I just need the slope of tangent to deduce the slope of normal to deduce the equation of normal

[jade pumice]

i dont think so

[little drum]

You thinking doesn't help smh

Anyways

Just follow up with me,

So, you need the equation to the normal to

$y = e^{-x^2}$

[ocean seal]

Ansh

[little drum]

at point where x = 1

"at point" -> we figure out WHAT POINT

Plug x = 1, y = 1/e

so the point on the curve, where we're supposed to draw this normal is (1,1/e)

Now, we can't just draw a normal without the definition of what normal even is

Definition says: Normal is a line perpendicular to the tangent to the curve at any given point

or that's a rough definition at least

so next step is? how does knowing that helps?

well, because you've learnt to apply derivatives in curves

you now know that dy/dx is the slope of the curve at any given point (x,y)

Also, I'm assuming you realize that given the slope of a line and any 1 point that it passes through, you can write it's equation

[little drum]

then, if only you have the slope of tangent, and if only you know the relation between slope of tangent and the slope of normal, and if only you knew this point at which this normal is drawn, you'll be able to form the equation of normal at this point

[ocean seal]

Ansh

[little drum]

You now have the relations

[ocean seal]

Ansh

Ansh

[little drum]

@jade pumice Go through this once and tell me if you didn't understand something

[jade pumice]

im sorry, my level is just too low to comprehend anything in this unit so im just going to stop because i dont want to waste any more of your time

thanks for trying to help

.close

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[lethal tapir]

<@&286206848099549185>

[lone heart]

@lethal tapir Has your question been resolved?

[wanton jasper]

sorry, but we are not helping with tests, maybe after you done, someone could explain you this

[little drum]

Hmm, it shouldn't be 10:37 rn

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[whole wadi]

Two runners run a number of laps around the same loop. Both runners start at the same time from the same place. They run in the same direction, each with his own constant speed. After how long, the slower runner has been surpassed by the faster runner? After 9 minutes, the slower runner has run one and a half laps around the loop, which is 1200 meters. At the same time, the faster runner has run 2000 meters

[whole wadi]

If I am on a time crunch and want to know if it's possible to solve the question (that's all it takes since it's a multiple-choice), what would be the best route to find out?

[severe sluice]

what's the question?

[whole wadi]

After how long, the slower runner has been surpassed by the faster runner?

It's google translated

So, I was thinking 1200/9 = 100 + 30 + 3.333ish

That's the amount of seconds for him to run 1200m, and if you divide 1200m by 133.33s, we get 1200m/133s ≈ 1200m/130s ≈ 9m/s.

Actually I'm dumb, I don't know if what I did was correct

[bleak ridge]

Meters divided by minutes isn't seconds

[whole wadi]

Yeah

So it should be 1200/(9*60) right? :)))

And same with the other person, 2000/(9*60)

[bleak ridge]

That would be meters per second

[whole wadi]

Well how do we find ”after how long the slower runner has been surpassed by the faster runner”

That's what I'm struggling with

The ratio, I thought, is (2000/(9*60))/(1200/(9*60)

,w (2000/(960))/(1200/(960)

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[whole wadi]

so the faster runner is 5/3 as fast, which means that 3/5 * (9*60) is when he surpassed the slower runner, right? i.e at 5.4 minutes or 324 seconds.

[ocean seal]

The following error occured while calculating:
Error: Unexpected end of expression (char 14)

[whole wadi]

... Here is the question if anyone new is opening the channel

[bleak ridge]

Sorry I had to go for a bit

How long is a single lap

And how far apart do they need to be

[lone heart]

@whole wadi Has your question been resolved?

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[whole wadi]

Hmm. I don't know. How do we find that out?

[whole wadi]

Is it 1200/(3/2) = 800m?

Two runners run a number of laps around the same loop. Both runners start at the same time from the same place. They run in the same direction, each with his own constant speed. After how long, the slower runner has been surpassed by the faster runner? After 9 minutes, the slower runner has run one and a half laps around the loop, which is 1200 meters. At the same time, the faster runner has run 2000 meters

[lone heart]

@whole wadi Has your question been resolved?

[bleak ridge]

What's 2000-1200

[whole wadi]

800

[bleak ridge]

Yes

So what does that mean

[whole wadi]

I don't know

That he's 800m ahead of him?

[bleak ridge]

Ye

[whole wadi]

The faster runner, I mean

[bleak ridge]

And how long is a lap

[whole wadi]

800, from what I've gathered

[bleak ridge]

Yeah

[whole wadi]

Wait

Can you show me a easy way of finding it out?

Because I did some hocus pocus lol

[bleak ridge]

Well is the question not asking when he will lap the guy?

[whole wadi]

The idea is that I am solving this question under a time crunch (2 minutes or less)

When he surpasses him, if the english is correct

[bleak ridge]

So wouldn't it just be 9 minutes

He's lapping him rn

[whole wadi]

🤔

Well I thought that we'd need to know the speed of each individual runner, with one variable, and then find the intersection, right?

I've underslept so my reasoning is of a unclear character

[bleak ridge]

Well the only intersection is at 0

But because the track is cyclical you look for where they're 800 meters apart

[whole wadi]

Well what's the point of this question

After how long, the slower runner has been surpassed by the faster runner?
if he's a faster runner, after all?

We're trying to find when the faster runner has surpassed him, so maybe he accelerated or some shit

A dog chased him, whatever

It's curious to me

How everything is formulated here

[bleak ridge]

,w plot y=x * (2000/9-1200/9)

[ocean seal]

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[bleak ridge]

This is a plot of how far ahead the fast runner is from the slow runner

[whole wadi]

lol idk what this means, what's the y axis and x axis

is it measured in m/s?

[bleak ridge]

Y axis is how far apart

X axis is time

[whole wadi]

so m/s

[bleak ridge]

S

Well minutes

[whole wadi]

hmm

[bleak ridge]

The slope is m/s

[whole wadi]

so let's say x = 1, then what? is that 1 minute?

I think it is

[bleak ridge]

Ye

So at 1 minute they're like 60 or so meters apart

[whole wadi]

Okay, well this is him being ahead of the slower runner, but this doesn't answer

After how long, the slower runner has been surpassed by the faster runner?

He has already been surpassed at x = 0.00000…1 then

No?

[bleak ridge]

Technically yes

[whole wadi]

Hahaha

[bleak ridge]

But you could probably assume they don't want that answer

[whole wadi]

Probably…

[bleak ridge]

You can solve for 800 in that equation

And get your time

[whole wadi]

Can you show me the reasoning behind this btw, for the future

y being m/s, yeah? and x being?

the time?

[bleak ridge]

m/s is a measure of speed

Y is how far apart the two runners are

In meters

Do you know the formula distance = speed * time

[whole wadi]

x = s
y = m/s
so y/x <=> m/s/s = m/s^2

are we finding the acceleration here?

[bleak ridge]

x = minutes
y = meters

[whole wadi]

ah ok

mb

[whole wadi]

yeah

s = v*t

[bleak ridge]

The speed of the faster runner is 2000/9 meters per minute yes

[whole wadi]

yup

[bleak ridge]

Then the slower is 1200/9 meters per minute

[whole wadi]

yup

[bleak ridge]

The distance of the faster is 2000/9 * t and the distance of the slower is 1200/9 * t

[whole wadi]

we multiply by x to get rid of the denominator, to get the distance, right?

[bleak ridge]

The difference between the two is just those subtracted

[whole wadi]

x being just the parameter

[whole wadi]

yup

[bleak ridge]

And that's the whole formula

I just factored out the t

Cause it's easier

[whole wadi]

and y is the distance between the two, not the distance between them and the starting point, right?

[bleak ridge]

Ye

Well not exactly the distance between the two because it doesn't account for lapping

You could use modulus or something to solve it but

[whole wadi]

i will try solving similar questions to see how better understanding i have on this, these questions are usually asked in my physics textbook

[bleak ridge]

You can just solve for 800

And when you solve for 800 you get

Drum roll

9 minutes

[whole wadi]

,w plot 800 = x(2000/9-1200/9)

[ocean seal]

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[bleak ridge]

So the initial condition they give you is when they lapped

At the 9 minute mark

Because 2000-1200 is 800

One lap

If you use mod you can see every time he laps the slow guy

[whole wadi]

i don't know anything about modulus lol

[bleak ridge]

,w plot 800 = (x(2000/9-1200/9) mod 800)

[ocean seal]

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Requested by PapaBread#3820

[bleak ridge]

It's more just interesting than applicable on a test

And it makes more logical sense

[whole wadi]

i don't think i'll need to know anything about modulus during these questions in the exam

but knowing that is good i suppose

what does that purple line mean

[bleak ridge]

That's just y=800

[whole wadi]

i meant violet sorry

[bleak ridge]

It's the distance between the two that gets "reset" every time he passes the slow guy

[whole wadi]

the one that says $\frac{800x}{9}mod:800$

[ocean seal]

Theophania

[bleak ridge]

So as soon as he passes it goes from 800 to 0

[whole wadi]

oh okay

[bleak ridge]

That's all the mod does really

[whole wadi]

so every 800 meters, he laps him

[bleak ridge]

It just resets when he laps

Yeah

Well not really

Every 800 meters of difference between the two he laps him

[whole wadi]

interesting

[bleak ridge]

Every 2000 meters he runs he laps

Not relative to the slow guy

[whole wadi]

well technically, he runs 1 and a half lap

After 9 minutes, the slower runner has run one and a half laps around the loop, which is 1200 meters. At the same time, the faster runner has run 2000 meters

800meters being one lap

[bleak ridge]

The slow guy gets lapped every 1200 meters he runs yes

But the fast guy laps the slow guy every 2000 meters he runs

[whole wadi]

every 2000 meters, or is it every 800 meter distance that he laps him? we know one lap is 800 meter

sorry if i'm being obtuse

[bleak ridge]

There's three diff values going on

The fast guy runs 800 meters further than the slow guy every time he laps him

[whole wadi]

true

[bleak ridge]

But in order to go 800 meters farther he has to run 2000 meters

Because the slow guy runs 1200 in that period of time (9 minutes)

1200+800=2000

[whole wadi]

yes

[bleak ridge]

So all three of those things are true in their own specific way

1. slow guy gets lapped every 1200 meters he runs
2. fast guy laps every 2000 meters he runs
3. fast guy had to run 800 meters more ahead of slow guy to lap each time

[whole wadi]

okay i see, this doesn't mean that he finishes one lap every 2000 meters right? xD

[bleak ridge]

Non

[whole wadi]

okay

well thanks for letting me bother you with these questions, was very educating

[bleak ridge]

Np

[whole wadi]

.close

[lone heart]

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[whole wadi]

.reopen

[lone heart]

✅

[whole wadi]

wanted to say smth?

.close

[lone heart]

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[lone heart]

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[grave sand]

How can I show that 2^x - 2^(x-1) equals 2^(x-1)?

[bright hedge]

$2^{x} = 2 \cdot 2^{x-1}$

[ocean seal]

Yottachad

[bright hedge]

Just properties of exponents

[grave sand]

.close

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[stable plume]

hello

[stable plume]

$f'(x)=3-x$

[ocean seal]

cakeee

[stable plume]

I know that when x=0 the f(x) is -4. x=0 f(x)=-4

of i can test that

$x=0 f(x)=-4$

[ocean seal]

cakeee

[buoyant kayak]

what is your question

[stable plume]

I want to know the original function

[buoyant kayak]

integrate

[stable plume]

I got $3*x-x^2/2+C$

[ocean seal]

cakeee

[buoyant kayak]

equate that to something and solve for C

[gray isle]

write the whole equation and apply the given condition

[stable plume]

$3x-x^2/2+C=-4$ like this?

[ocean seal]

cakeee

[buoyant kayak]

yep, but when does f(x)=-4?

[stable plume]

When x=0

[buoyant kayak]

right

so what is C?

[stable plume]

$C=-4-3x+x^2/2$

[ocean seal]

cakeee

[buoyant kayak]

plug in your initial condition

[stable plume]

what do you mean

[buoyant kayak]

you just told me f(x)=-4 when x=0

you equated f(x) to -4 but didn’t use your other condition

[stable plume]

I dont get it

[stable plume]

isnt this one the original function?

[buoyant kayak]

that’s you solving for C

[buoyant kayak]

this is f(x)

and you’re given that f(0)=-4

solve for C

[stable plume]

$f(x)=3*x-x^2/2+C$

[ocean seal]

cakeee

[stable plume]

$f(0)=3*0-0^2/2+C$

[ocean seal]

cakeee

[stable plume]

$C=-3*0+0^2/2=0$

[ocean seal]

cakeee

[stable plume]

i dont get this

[gray isle]

what is the given value of f(0)?

[stable plume]

-4

[gray isle]

yes

apply that

in your equation

[stable plume]

I got 20

[gray isle]

whats 20 supposed to be?

[stable plume]

no idea

[gray isle]

you have
$$\red{f(0)} = -3\cdot 0 + \frac{0^2}{2} + C$$
apply the given fact that $\red{f(0)} = -4$

[ocean seal]

ℝamonov

[gray isle]

(and don't overthink it)

you should have 0 issue with this step

[stable plume]

$-4=-3*0+0^2/2+C$

[ocean seal]

cakeee

[gray isle]

yes

and then simplify and identify the value of C

[stable plume]

Ok thanks

😄

[stable plume]

So what f(1) should be?

[gray isle]

well once you determined C, you now know exactly what f(x) is

[stable plume]

$why -3\cdot 0 + \frac{0^2}{2} + C?$

[ocean seal]

cakeee

[gray isle]

sry messed up some signs, was doing copy paste

as those two terms are 0 anyway

[stable plume]

yep

[lone heart]

@stable plume Has your question been resolved?

[lone heart]

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[harsh acorn]

how can I prove q>p?

[solar merlin]

add the numbers

[ocean seal]

!!!

[harsh acorn]

oh yes zeta function

[alpine sable]

Yes

[harsh acorn]

I completely forgot it bcs it is a 9th grade question lol

[wanton junco]

you can prove it's bounded

its bound being 1-1/100

exactly what you're looking for

[alpine sable]

I'm not getting you 🤔

[harsh acorn]

same here

[wanton junco]

its a sum of a series right?

[harsh acorn]

yes

[alpine sable]

Yes

[wanton junco]

E n=1->100 1/n^2

n=2*

[harsh acorn]

can you latex it

[wanton junco]

which is smalelr than En=2 -> 100 1/n(n-1)

ummm

im not too competent with latex

@alpine sable

[alpine sable]

But i didn't understand what you mean.

[harsh acorn]

zeta function is enough for me

[umbral orchid]

he means compare

[alpine sable]

But how will you use that here?

[umbral orchid]

the other thing is telescoping

[wanton junco]

,rotate

[wanton junco]

^

[harsh acorn]

in my question there is no 1 and estimating p^2/6 is not that hard

[harsh acorn]

I tried, but failed to do so

[wanton junco]

does the question allow you to assume that you know the sum of 1/n^2?

can you PROVE its converging to p^2 / 6?

[harsh acorn]

oooh I got what you mean now

[harsh acorn]

it is actually multiple choice question, it asks for relationship ( > ,<,=) between p and q and I assumed q>p bcs it looks like it

anyways, thx

.close

[lone heart]

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[wanton junco]

Oh

well now you know how to prove that exactly then lol

[lone heart]

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[alpine sable]

I'm not sure if this is the appropriate place to ask this question, but, how was it decided/discovered that complex are the building blocks for all real numbers and things in nature?

[minor pumice]

im having trouble with this hw question

[alpine sable]

Post your question in other available channels.

[minor pumice]

this is my first time on the serber

[gilded quarry]

go to help 2 and post there

[alpine sable]

What does “complex numbers are the building blocks for all real numbers” mean?

I'm not sure, it's something I heard so I probably worded it wrong or got misinformed

Heard where?

[tacit arch]

you probably want something like the history of real numbers

[gilded quarry]

There are a dozen of youtube videos on the topic

[alpine sable]

https://www.youtube.com/watch?v=cUzklzVXJwo

I think it was this video but I don't remember really

[gilded quarry]

and its not a quesitons that can really be answered in less than 10 min

[alpine sable]

i see

What are some good sources u guys can suggest then

[gilded quarry]

im pushing it a bit tbf but yeah there is no single sentence answer

[alpine sable]

I’m not sure what I can suggest for learning what “complex numbers are the building blocks for all real numbers” means because that’s…

An odd thing to say, I guess

Are there any things to help learn for what complex numbers generally are and how they exist in nature?

[lone heart]

@alpine sable Has your question been resolved?

[alpine sable]

whatever i'll just look online

.close

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[hard wing]

6. As a promotion, a cereal company randomly inserts one of a set of six different baseball cards into each box of its product. There are equal numbers of the six different cards. Determine the average number of boxes you would have to buy to get a complete set of cards.

[hard wing]

I have a math homework question for statistics

Please help I am stuck for over an hour

<@&286206848099549185>

[wary stream]

You have to wait at least 15 minutes before pinging helpers

[hard wing]

my bad

<@&286206848099549185>

pls assist

[wintry lotus]

What do you have so far?

[hard wing]

nothing

[wintry lotus]

Ah, so we are given that there are 6 different cards and the probability of getting any one of the 6 is the same (so 1/6) since there are equal numbers

What sort of distribution is something with equal probability?

[lone heart]

@hard wing Has your question been resolved?

[lone heart]

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• Be polite and have a nice day!

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[magic terrace]

Simplify and write the trigonometric expression in terms of sine and cosine:

[magic terrace]

$\frac{1 + cos y}{1 + sec y} $

[ocean seal]

Eyesonjune
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[magic terrace]

woops

$\frac{1 + cos y}{1 + sec y}

$\frac{1 + cos y}{1 + sec y}$

[ocean seal]

Eyesonjune

[untold knot]

Okay

What is it asking for?

[magic terrace]

this

[strong zinc]

writing the trigonometric expression in terms of sine and cosine means getting rid of that sec function, do you know of any way to transform that sec y into something you can simplify later?

[magic terrace]

So I know I could do like uhhh

1/cosy

But how do I go from (1+cosy)/(1+(1/cosy)) to anything else

[untold knot]

Somebody check this

[magic terrace]

Well apparently it accepts (1+cosy)/(1+(1/cosy)) but is there any further way to reduce it

[strong zinc]

I think it's wrong @untold knot

[magic terrace]

$\frac {1 + cos(y)}{1 + \frac{1}{cos(y)}}$

[ocean seal]

Eyesonjune
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[untold knot]

[magic terrace]

$\frac {1 + cos(y)}{1 + \frac{1}{cos(y)}}$

[ocean seal]

Eyesonjune

[magic terrace]

yeet

[strong zinc]

$\frac {1 + cos(y)}{\frac{cos(y)}{cos(y)} + \frac{1}{cos(y)}}$

[ocean seal]

Jojotes

[untold knot]

Where did I go wrong?

Is it the fraction?

[strong zinc]

You could continue using the fact that 1 = cos(y)/cos(y)

[magic terrace]

Now it wants me to reduce this monstrosity