help-0

[supple tundra]

Ok the wolfram graph is in radians

but where do you think 19.5 degrees corresponds to in the graph

[silk steeple]

I don’t understand that graph sorry

we were only that in school for 1 lesson and were told to move on to cast diagram since it’s more ‘better’

[supple tundra]

hmm

graphs are important

very important

[silk steeple]

I need to learn graphs

[supple tundra]

uh

[silk steeple]

modelling is my weakest topic

[supple tundra]

Do you atleast know the shape of the sin(x) function

can u sketch that

[silk steeple]

yeah

We learnt how to sketch sin cos and tan graphs

[supple tundra]

ok good

What about $y=\frac{1}{3}$ can u sketch that

[ocean seal]

azeem321

[silk steeple]

Hm

isnt that a straight line

[supple tundra]

yh

horizontal or vertical

[silk steeple]

uh

has to be horizontal

if it intercepts with the y axis it has to be horizontal

[supple tundra]

right

so in words, it just says

y equals 1/3

So whatever the x value

[silk steeple]

yes

[supple tundra]

y=1/3

[silk steeple]

So we make the two equate each other to find points of intersection?

[supple tundra]

So $\sin{x} = \frac{1}{3}$ is just the intersection of sin(x) and 1/3

[ocean seal]

azeem321

[supple tundra]

yeah exactly

[silk steeple]

What

that’s it?

[supple tundra]

yh and graphically we get

,w graph sin(x) and 1/3

[ocean seal]

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[silk steeple]

😐 bruh they made me learn the whole cast diagram for that

This is so much more simpler

[supple tundra]

Have you learned radians

[silk steeple]

not yet in school but I’ve gone over it privately

it looks complicated

a lot of PI

I forgot the formula to calculate radians in a circle

[supple tundra]

When does sin(x) = 0

[silk steeple]

at 0?

[supple tundra]

yh

and

[silk steeple]

that’s all I know

Oh

360

[supple tundra]

why?

[silk steeple]

wait let me draw the graph

yeah it’s 0 and 360

That’s when it crosses the x axis

[supple tundra]

You are not wrong

but

What is this point in circle?

[silk steeple]

3?

that graph is different to the graph I learnt

my graph intercepts at 0 180 and 360

[supple tundra]

yes

yes

[silk steeple]

And -180 and -360

[supple tundra]

180 = pi

pi = 3.14

[silk steeple]

oh…

I forgot about that

[supple tundra]

Ok good we've established that

Ok have you learned that sin(x) represents itself every 360/2pi

[silk steeple]

why does this only have 2 intersection

[silk steeple]

yes

Both ways too

[supple tundra]

It doesn't go to $2\pi$

[ocean seal]

azeem321

[silk steeple]

huh

but 180 and 360

I’m confused

[supple tundra]

,w graph sin(x) (-2pi)<x<2pi

[ocean seal]

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[supple tundra]

ok finally

So now it goes up to $2\pi/360^{\circ}$

[ocean seal]

azeem321

[supple tundra]

So you've learned that $\sin(x) = \sin(x+360^{\circ})$?

[ocean seal]

azeem321

[silk steeple]

yes

azeem I don’t want to burden you with explain this whole concept do you have any video that helped you?

you helped me a lot already today

[supple tundra]

https://www.khanacademy.org/math/trigonometry

Watch all the videos

[silk steeple]

thank you

[supple tundra]

starting from trig functions

[silk steeple]

one last thing

is there a video for intergration

[supple tundra]

all there on khan academy

[silk steeple]

There’s something that came up in class

But I can’t find a video for it

[supple tundra]

its what i used mainly for learning

[silk steeple]

Like how would you find an area between 2 curves

there’s something you can do by equating the 2 curves together and intergrating that

[supple tundra]

https://www.khanacademy.org/math/integral-calculus

[silk steeple]

but i can’t find a video to explain the concept behind it

[supple tundra]

video will be there

[silk steeple]

I see

thank you azeem for helping me today

.close

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[dreamy nexus]

Can i get help

[grand lagoon]

type question here directly

[dreamy nexus]

What do we call these in english

[vale wigeon]

angles?

[grand lagoon]

angles at a point?

[dreamy nexus]

Thanks

[lone heart]

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[gilded vale]

How do I find the horizontal asymptote with that square root on the bottom?

[lone heart]

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[austere flax]

https://cdn.discordapp.com/attachments/954573780909428836/966833912569544724/unknown.png

[austere flax]

i need help with a couple questions

for my exan

exam*

this is algebra 1

<@&286206848099549185>

[hard patio]

idk its just on my side but i cant see the picture

[tacit arch]

can't see your picture either

[austere flax]

wdym

want me to dm it?

[tacit arch]

no

fix your image on your machine and re-upload it

screenshot is probably fastest

[austere flax]

Sabina is baking cookies for a bake sale, but she wants to keep some for her friends to eat. Let x represent the number of cookies to be sold at the bake sale and let y represent the number of cookies to be shared with friends. Sabina wants to sell at least ten more than twice as many cookies as she shares with friends. Sabina plans to make at most 120 cookies and wants to share between 10 and 20 of them with friends.

Write the system of inequalities that represents these constraints.

@tacit arch

is it possible if i vc u

and stream

[tacit arch]

no

[lone heart]

@austere flax Has your question been resolved?

[austere flax]

.close

[lone heart]

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[worn cloud]

I have a percentage : say 50% how can i make it show as a negative number

[real solar]

What? Give more context

[worn cloud]

first number : 11

second number : 7

57% increase from 7 to 11

i want to go opposite

[real solar]

So 57% decrease?

[worn cloud]

because its a decrease

11 to 7 is good

7 to 11 bad

[real solar]

Oh i get what you are saying

[worn cloud]

what is the formula for that

[wet spindle]

find what 57% of 11 is first

[worn cloud]

my first number is 7

second number is 11

formula says +57%

but it is negative because going from 11 to 7 is bad

[real solar]

If you go from 11 to 7 you get a different number with the formula

It checks out

[worn cloud]

ty

.close

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[digital obsidian]

Hi, I seem to have entirely forgotten how to calculate this

[limpid spade]

factor

[zealous trench]

9sin^2(t) + 9cos^2(t) = 9(sin^2(t) + cos^2(t)) = 9

[limpid spade]

yes

[digital obsidian]

Oh my god I am

So

Oh

:)))

Well this is so awkward, sorry for taking your time

[zealous trench]

np

[digital obsidian]

And thanks for the swift answers ❤️

.close

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[austere torrent]

Anyone available to help with my homework

[lone heart]

Please don't occupy multiple help channels.

@austere torrent Has your question been resolved?

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[tropic oasis]

this problem is giving me a bit of an issue, if i'm correct it's asking for (-r, theta)

in order to obtain r i must use pythagorem therom

sqrt(x^2 + y^2)

but the arithmitic messes me up

i got r = 25

in order to obtain arccos and arcsin

i must do x/25?

y/25?

[worn fox]

@tropic oasis you sure r = 25? you may be forgetting something

[tropic oasis]

i can show my work

[worn fox]

You lost ya square root at the end

[tropic oasis]

h

oh

right..

so r = 5

[worn fox]

uh huh, so now find the angle for when r > 0, do you know the formula?

[tropic oasis]

yep

x/r

y/r

for arccos and arcsin

i got pi/6

which means (5, pi/6)

but now i must find (-r,theta)

(-5,7pi/6)?

[worn fox]

i agree!

just adding pi to the angle you found

[tropic oasis]

i think its against the rules to invade channels @alpine sable

just wait patiently like we all do man

[tropic oasis]

thanks for the help!

i'll work on keeping track of my sqrt lmao

[worn fox]

haha good stuff

[tropic oasis]

.close

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[tropic oasis]

in order to go from polar to rect coords

i would do x= r * cos theta

and y = r * sin theta

but i keep getting x = -1

and y = sqrt3

which doesnt make sense for my sin

[tacit arch]

what are you doing

[tropic oasis]

i sent my work

just now

[tacit arch]

,calc cos(-pi/3)

[ocean seal]

Result:

0.5

[tacit arch]

,calc sin(-pi/3)

[ocean seal]

Result:

-0.86602540378444

[tropic oasis]

-sqrt3/2

is the sin

-2/1 * -sqrt3/2

[tacit arch]

and why do you think this is wrong?

[tropic oasis]

bc there isnt an angle with (-1, sqrt3)

on my unit circle

and we're supposed to not use a calculator

[tacit arch]

why are you looking at the unit circle?

[tropic oasis]

bc we arent allowed calculators

[tacit arch]

you already calculated the rectangular coordinates and an angle is already given. what more are you looking for?

[tropic oasis]

wait.. i got confused

i dont know why my mind thought the provided question was in rect form

.close

[lone heart]

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[tropic oasis]

my brain died for a second zzz

[lone heart]

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[dim carbon]

Yo guys, does anyone know what to do when presented with a sequence where the "common difference" is alternating

[near hollow]

Can you send the example as this could mean a lot of things

[dim carbon]

yeah ur right i just dont want to be given a direct answer

I just want a push in the right direction

So basically the problem is the following: You have two lines A, B that are parallel to each other, and each line is given a number of dots. Let's say line A has 2 dots, we call this n. Line B will have m dots, which varies. Each dot on line A (with n dots, in this case 2) has to be connected to each of the dots on line B (with the varying dots, m). Then you make a table to find the intersections.

looks something like this

I've made a table for when m=2, and I was able to get a quadratic arithmetic sequence

then I tried it for when m=3, but the differences are a bit weird

I noticed that the third difference is constant, hinting a cubic sequence, but its alternating between -2 and 2

[lone heart]

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[tacit sable]

I don't think I'm stuck anywhere, I think I'm just not understanding the question. I got 1/50 * 1/49 = 1/2450 since when someone earns a place it is no longer available.

[ripe rain]

It's (or) & not (and)

So it'll be multiplied by 2!

Good example where changing 1 small word changes entire question

[tacit sable]

Ohhhh, I get it now.

Thank you so much.

.close

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[austere torrent]

Hello can anyone help me with my homework

[tacit sable]

What exactly would you like help with?

[austere torrent]

These questions @tacit sable

[tacit sable]

These look like they could be solved using a system of equations.

[austere torrent]

Yes and a “let” statement

[gray isle]

start by introducing some variables like
d to represent the number of dimes
n to represent the number of nickels

[austere torrent]

Yes I got that

[tacit sable]

Which part are you struggling with?

[austere torrent]

The equation

Finding the equation

[tacit sable]

Let's use the variables that Ramonov introduced. The first piece of information they give you is that if you took 46 less of n, you would have 4 times as many n as d. Do you have an idea on how you could set this up?

[austere torrent]

No not yet

What does 46 - n = like what thing

Like number of dimes or …

[tacit sable]

They tell you at the end of the sentence. It would equal 4 times that of the amount of d there is.

[austere torrent]

Ok got it

So we have the statement now we make the equation right

[tacit sable]

Yep.

[austere torrent]

How do we make the equation

[tacit sable]

However, it wouldn't be 46 - n, because the problems says that 46 less than n would be 4 times the amount of d.

[austere torrent]

Ok I’m confused

[tacit sable]

So, instead, it would be n - 46 = blank.

[austere torrent]

Oh

Now I get it

n - 46 = dimes

Right

[tacit sable]

n - 46 = 4 times the amount of dimes.

[austere torrent]

Ya that’s what I ment

[tacit sable]

Correct.

[austere torrent]

How do I make the equation

Can we talk in dms?

[tacit sable]

Yea, that's fine.

[austere torrent]

Ok

[lone heart]

@austere torrent Has your question been resolved?

[lone heart]

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[alpine sable]

hi! may i get help finding f(x) please

[buoyant kayak]

have you tried anything as of yet?

[alpine sable]

yes! so i tried to figure it out by reversing the product rule but then i realized that two things added wouldnt equate to a product. then i also tried seeing if i could use exponents and division but that didnt work out either so now im a bit stumped

[buoyant kayak]

well remember integration doesn't follow the same rules as differentiation

there isn't a "product" or "quotient" rule you can use

however, you can apply a power rule

do you know the power rule of integration?

[alpine sable]

i believe its when you use an exponent and divide the equation by the exponent?

[buoyant kayak]

what do you mean by "use" an exponent?

[alpine sable]

a power, so for example, if i had f'(x) = x^5, f(x) = x^6/6?

[buoyant kayak]

ah, yes

so you'd first want to do a bit of prep work before you start the calculus part

try distributing that sqrt(x)

[alpine sable]

okay done! that ended up with x√ x + √x

OH

i got it now, thank you!

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[alpine sable]

.close

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[drifting falcon]

I have simplified this problem to this point

I know the final answer is tan(b) but I am not sure how to get there from here

[manic wind]

The - in front of cos2b applies to the entire term

-(cos2b double angle)

So your first step is incorrect

[drifting falcon]

oh okay

let me see if I can work it out

[alpine sable]

there is a technique you can use to solve all of these problems without any worries

you need to read couple of papers first

those ain't hard either

it is by using euler's identity

[drifting falcon]

I'll look it up

anyways I figured it out thanks for the help

.close

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[short spear]

I get this

But then what

Because there are no tan values that give 3/2

[worn fox]

there definitely are, just no standard closed form values

i would guess the question isnt as intended

[short spear]

Like?

[worn fox]

,w arctan(3/2)

[ocean seal]

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[worn fox]

like that

[short spear]

Yeah true but I have to use fundamental formula

This

And I don't think I can use inverse tan for that

[worn fox]

ah okay i understand

so $tan^{-1}(3/2)$ is one solution we have found

[ocean seal]

iCaird

[worn fox]

now use the fundamental formula to write down another

[short spear]

Yeah it's just the first one + 180

Alright thanks

.close

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[waxen owl]

Quick question on this

[wicked light]

yo can i put in a question and u guys can give me the answer or nah

please i have a lot of them

[waxen owl]

Idk man'

[wicked light]

somebody be a king and help

[worn fox]

open your own thread dont hijack someone elses

[waxen owl]

When using the ratio test and finding an+1

Is it supposed to be (-10)^n+1 / (4)^2n+2(n+2)

[sweet chasm]

No

[waxen owl]

Why is it (4)^2n+3 instead of (4)^2n+2?

[sweet chasm]

4^[2(n+1)+1]

Because you multiply the 2 in

Before you add the 1

[waxen owl]

Okey dokey

[oak chasm]

@waxen owl You need to surround those exponents with parentheses because multiplication comes after exponents, so 4^2n+3 means (4^2)n + 3.

16n + 3 isn't the same as 4^(2n + 3).

[waxen owl]

I see I see

Thanks

.Close

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[drifting falcon]

How do I further simplify this?

[dry echo]

you could probably use the half angle identities

[ocean seal]

Denver Crossbourne

Denver Crossbourne

[drifting falcon]

one moment

Ok im at that step but wouldn't the exponent apply only to the top of the fraction?

[dry echo]

why would it?

[oak perch]

Not over 2, but over 4

((1-cos(6x))/2)^2, square 2 is 4

Again, 4

[ocean seal]

Denver Crossbourne

[oak perch]

cos^2(6x) can be further replaced though

[dry echo]

yeah

[oak perch]

(Cos(12x)+1)/2

[drifting falcon]

keep in mind I have to write this without any exponents larger then 1

[oak perch]

Then it’s done

(cos(12x)-4cos(6x)+3)/8

[drifting falcon]

jeez

alright one moment

[ocean seal]

Denver Crossbourne

[dry echo]

This is the final solution I got, but it can be simplified

Unless I made any mistakes

[dry echo]

yeah, pretty much this

[drifting falcon]

I see yeah okay I think I got there as well though it took me considerably longer

thanks for the help fellas

[dry echo]

you just use a bunch of half angle identities until there are no exponents greater than 1

[drifting falcon]

right

[dry echo]

np

[drifting falcon]

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[stuck geyser]

(A ∩ C') ∩ (B ∩ C') = (A ∩ B) Alright I know this is true just by intuition and drawing it out but I cant for the life of me place a law onto it

[oak perch]

This is not true

The left hand side equals intersection of A,B and C’

[stuck geyser]

Oh so it would be A∪B

Hang on I'm confused

Is the intersection of A, B, C' not A∩B

Like the intersection of A, B and everything but C which would just be the intersection of A and B.

I'm using C' as the compliment law which might be incorect

[lone heart]

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[alpine sable]

hi! so for the first question, was i supposed to be given the number of subintervals or do i just assume its infinite?

[lone heart]

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[alpine sable]

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[sweet chasm]

Do you know how to cross multiply

[near crypt]

ye

[sweet chasm]

You can cross multiply to find r

[near crypt]

ik but its asking for the error in the proportion used to find the value of r

and i dont really know whats the error

<@&286206848099549185>

[lone heart]

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[uncut depot]

what does $x^{min(a, b)}$ (or) $x^{max(a, b)}$ mean

[ocean seal]

azorfus

[stuck geyser]

min just returns the lowest of two values and max the highest of two

[uncut depot]

oh

[stuck geyser]

so if it was x^min( 2, 6) itd be x^2

[uncut depot]

oh then what about

$min{x>0|a_i$ divides x for i = 1, 2, ..., n$}$

stuff like this

[ocean seal]

azorfus

[stuck geyser]

maybe the lowest value of that series that divides x? Can't say for sure though

[uncut depot]

should i share the full thing

[stuck geyser]

If you want I'm not sure if I can fully answer though

just know what min and max does that's the extent of my intellegence

[uncut depot]

oh, i'll share anyways- if u are able

answer

the "min" in here

[stuck geyser]

Oh gotcha, so there are infinite mulitples of any two numbers, they put min in the formal definition to show that you should find the lowest of them.
like the numbers 3, 6 have multiples of 6, 18, 24, 36 . . . but you should return the lowest of them all which would be 6

and not zero

{x>0| a1 divides x for i = 1, 2, ... n} is just like a set of all the multiples of two numbers, putting min before it means just return the lowest of the entire set

[uncut depot]

oh

wait so

what

bro @stuck geyser

[stuck geyser]

hang on lol trying to also figure it out

[uncut depot]

are we saying [12, 18] = 36

because

24, 36

but both divide 36

not 24

[stuck geyser]

I mean they list that as an example

[uncut depot]

UhfUHf

[stuck geyser]

lol

[uncut depot]

idk, it makes sense

[5, 7]

25, 35

but still doesn't

ok yeah it does

[stuck geyser]

7, 5|35

[uncut depot]

first lowest common multiple

NIcE

[stuck geyser]

yeah

[uncut depot]

its in the name

[stuck geyser]

yep

and max is the max

which would ig be infinity

[uncut depot]

oh

nice

[stuck geyser]

min{1, 5, 7, 23, 2, -1} = -1

[uncut depot]

oh

i see

max[1, 2, 3, 4 ,5] = 5

[stuck geyser]

yepp

[uncut depot]

alr

thanks

[stuck geyser]

yeye

[uncut depot]

.close

[lone heart]

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[fossil bridge]

Plz help

https://media.discordapp.net/attachments/928502730971033731/967296481797230672/792953076894007307.png

But I'm stuck

Plz help

<@&286206848099549185>

Plz <@&286206848099549185>

[tacit arch]

stop abusing pings

[lone heart]

@fossil bridge Has your question been resolved?

[fossil bridge]

K sorry

I think endtimes is solving the problem

I think taking gcd of 2a^2 and a^2-b^2 will help?

[merry depot]

how did you get this?

[fossil bridge]

?

Which one

[merry depot]

click to see attachment...

[fossil bridge]

Bruh

[merry depot]

ok 🤷‍♂️

[fossil bridge]

@fossil bridge just basic manipulation

[merry depot]

which would be.....?

[lone heart]

@fossil bridge Has your question been resolved?

[fossil bridge]

@tight locust

[oak perch]

You can obtain that a^n-b^n divides 2b^n

So (2b^n)/(a^n-b^n)=2/((a/b)^n)-1) is an integer

Contradiction

( because (a/b)^n=2 or 3, but we know that 2^(1/n) or 3^(1/n) is irrational)

[lone heart]

@fossil bridge Has your question been resolved?

[strange palm]

pls help

hum

mhmh

mhmhmhmhmh

mhmhmh

mhh

mhmh

mhmh

mhmh

,h,h,h

BRUHHH

someone

pls

pls

pls

psl

spsdla

[limpid spade]

nobody wants to help you for a good reason

[glad sluice]

xD

[tidal grotto]

I wish my geometry hws were like that

😔

[limpid spade]

lol didn't even look at his question

that's literally dogshit easy lol

it's like asking help for x+2=0

[safe moss]

😐

don’t act like a jerk please

[warm cloud]

please google the definition of the radius and the diameter

you don't have to use any maths

you just have to recognize what the radius and diameter of a circle are

[limpid spade]

hes not even in the server rofl and not even his channel

[warm cloud]

bruh

.close

[safe moss]

yeah but why are you being an arse

[limpid spade]

am not

[safe moss]

you are

😐

some people struggle with maths

[limpid spade]

and also reading rules lol

[safe moss]

he could have dyscalculia

you don’t know if he has dyscalculia or not though

[safe moss]

i just did

[lone heart]

@fossil bridge Has your question been resolved?

[limpid spade]

.close

[lone heart]

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[sonic glade]

Explain why Pr(𝐴 ∩ 𝐵) = Pr(𝐴) ∘ P(𝐵 |𝐴) instead of Pr(𝐴) ∘ Pr(𝐵)

[sonic glade]

i can kinda "derive" it by drawing 4 quadrants and thinking of A and B | A as the area

i can't seem to put into words exactly why this is so

it's annoying because it means i most likely don't fully understand why

[placid zinc]

Is there ever a case where:
Pr(AB) = Pr(A)Pr(B)?

[sonic glade]

hm

that would be the general multiplicative rule

when the latter operation can be performed after every outcome of the prior operation

or did i misunderstand what that rule is about as well :X

actually that's a really good question

if the first outcome is in A ∩ B, then it is impossible to apply the general multiplicative rule of A × B

because it's simply impossible to have a second operation - that outcome has already been reached

[sonic glade]

did i interpret correctly what you meant by this?

wait shucks did i mix up the counting multiplication rule with probability

or are they actually the same thing

[placid zinc]

So if Pr(AB) = Pr(A)Pr(B), then A and B are said to be "independent"

A can be said to "not affect" B.

That's not always the case though. There's many examples where the outcome of one event affects the probability of the other event

That's why in the first formula, we see a conditional probability to account for this

[sonic glade]

oh i see - so basically its a disproof by counterexample that Pr(𝐴 ∩ 𝐵) = Pr(𝐴) ∘ Pr(𝐵) because of the case where 𝐴 and 𝐵 are not independent.

and Pr(𝐴 ∩ 𝐵) = Pr(𝐴) ∘ P(𝐵 |𝐴) works when they are independent because it would just return 0 for the latter

thank you - i think my biggest confusion was i mistook the generalised rule of multiplication to apply to probability of events instead of permutations

[placid zinc]

P(AB) = P(A)P(B|A)
Is actually the definition for conditional probability and we can't "prove" a definition haha.

But the second equation is not good for non-independent cases

So I figure that's the angle the teacher wants

[sonic glade]

oh we cant prove definitions?

[placid zinc]

One might ask "well what does P(B|A) mean?"

Well, P(B|A) = P(AB)/P(A) of course!

Getting real circular real quick

[hollow shale]

You can get intuition for it using a venn diagram though

[placid zinc]

A natural question is "Why does it capture the probability of something happening, given something else?"

I'm, uh, adding more to this conversation than I intended to haha

[sonic glade]

how would that look like? i was trying to do exactly that for a while but the only diagram i could draw that would represent P(A) * P(B | A) is

[placid zinc]

Let's say that you know A happens. So, we restrict ourselves to cases where only A happens. The "total number of outcomes" is P(A).

We want to see how many of them also include B happening. That's P(AB).

Favorable/Total = P(AB)/P(A)

We can ignore that I conflated "number of outcomes" with "probability" pfft I mean who cares really

[lone heart]

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[lone heart]

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[alpine sable]

I’ve learned how to do this, but I don’t understand the logic behind the process quite well, can someone explain why we do what we do here? Thank you!

[gloomy thorn]

its same as x ÷ 8 then × 8, so we simplify it by deleting both 8

cuz the answer will be same

take 8 as x, 8×4=32, 32÷4=8
or we delete both 4, answer is still 8 which is correct

[slender gull]

Answer is not 8...

[gloomy thorn]

its an example as i clearly wrote

[scenic grove]

Thats 6

[slender gull]

That wasn't for you.

Yes off set you did.

Now I see it.

[gloomy thorn]

so u got it @scenic grove

[scenic grove]

You multiply 8 on both sides so that x is alone on one side, and u get the value of x

[slender gull]

so that x is cancelled
Um no.

x is not what you're cancelling.

[scenic grove]

Yea that was wrong haha

[slender gull]

Yes, now it's correct.

[scenic grove]

So that x is alone on one side

[alpine sable]

I don’t really get it. I think what prevents me from understanding it is this question: how 8 gets canceled by multiplying it by 8? Why the inverse of division is multiplication and vice versa?

[gloomy thorn]

well it is divisio and multiplications are inverse

[alpine sable]

And the term canceled means to become zero, right?

[scenic grove]

8 has imaginary denominator 1. So 8/1
x/8 * 8/1
If thats the case you cqn cancel similar terms in numerator and denominator

x/8 * 8/1 is the same as 8x/8

[gloomy thorn]

the most simple explaining is examples.
take 4, and assume the both multiplication and divisions are 5.
now:
4 × 5 = 20 => 20 ÷ 5 = 4
which are the same.
so you just delete them as they are same whether you actually calculate or nor.

[alpine sable]

That makes some sense now!

[gloomy thorn]

hahah

cool

foundation is very important like a root as you learn more advanced stuff or there is nothing
to lean on the root if you dont have it

[alpine sable]

Yeah it’s very cool when it makes sense 😄

I guess these questions get me to the foundation, or how I learn it best?

[pure tree]

don't write 1 before x

it is illegal

[alpine sable]

Ikr 😅

[gloomy thorn]

u just learn thorough thats it

1x seems perfectly fine to me xD

[scenic grove]

Thats when you cancel, but yea for it not to be confused, put it simewhere top or maybe northwest/east(haha)

[lone heart]

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[limpid spade]

@deep veldt resend the question here

[limpid spade]

if u still need halp

[thorny citrus]

i need help

okay so this question is asking us to identify what sampling method is used and the text says: a school guidance counsellor arranges interviews with every fifth student on the alphabetized attendance roster

I'm not sure if it would be systematic random sampling or convenience

[limpid spade]

its occupied

[lone heart]

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[pearl vortex]

having trouble solving this problem

[pearl vortex]

here's my requisite work, i've checked it over and can't find a problem

[worn fox]

in your second line of calculation you started doing $DPP^{-1}$

[ocean seal]

iCaird

[bitter vault]

Should be
{4,0}
{-4.5,-5}

[pearl vortex]

gosh darn it

lemme work it out the proper and see if it works

got it!

thank you all

.close

[worn fox]

nice!

[lone heart]

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[upbeat kayak]

How do you find the period of a function such as f(x)=cos2x*sin2x ?

[winter tangle]

do you know the period of cos and sin seperately?

[upbeat kayak]

2pi

[winter tangle]

do you know how the 2x changes it?

[upbeat kayak]

(2pi)/2 ?

[winter tangle]

yes

[upbeat kayak]

Okay got it

1/2*sin(4x) when you convert it and so the period is pi/2

[winter tangle]

yh you just find the compound periodicity

[winter tangle]

yessss

[upbeat kayak]

aight, ty

.close

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[warm sage]

need help

[slender gull]

What have you tried?

[warm sage]

i think its 8 but someone told me t was wrong

[slender gull]

8 is wrong.

Why do you think it's 8?

[warm sage]

4*2

[slender gull]

WHY

[warm sage]

idk its so hard idk what to try anymore

[slender gull]

No, but why did you do 4*2

Because it might lead you to the correct answer.

[warm sage]

because it was the only numbers they gave me so

[slender gull]

Lol

Okay now that's messed up.

Anyway

Do you know the formula to figure the area of a triangle?

[warm sage]

yep

base

times height

divided by 2

[slender gull]

Correct.

You already have the base.

All you need is the height.

[warm sage]

ya

[slender gull]

Right?

[warm sage]

which is DF

[slender gull]

Have you studied congruent triangles?

[warm sage]

doing it right now

WAIT

DE

[slender gull]

ye

[warm sage]

IS CONGURENT DF

SO

ITS 2

[slender gull]

it is, that was the hint.

Although

You might wanna justify all this.

And not just write DE is congruent to DF.

So yeah.

Well done.

[warm sage]

wait its not 2 its 4

LOl

ok thanks

cya 😄

[slender gull]

@warm sage

DF is 2.

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[coral rock]

ok so I am asked to evaluate the 1st derivative of $f(x)=x^{\frac{1}{x}}$

[ocean seal]

Xyz.

[coral rock]

which i use implicit diff and get $(\frac{1-\ln{x}}{x^{2}})x^{\frac{1}{x}}$

[ocean seal]

Xyz.

[coral rock]

then the next part asks for "The expansion to second order in (pi - e) of f(pi)/f(e) about x=e."
drk what the "(pi - e) of f(pi)/f(e)" part means

[tacit arch]

Can you take a picture or screenshot of the actual question

[lone heart]

@coral rock Has your question been resolved?

[coral rock]

sure its very raw there is no context what so ever,

This looked promising but its not what they want

[lone heart]

@coral rock Has your question been resolved?

[proper tangle]

sosad students nowadays has to type math 😦

on paper would be easier for writing, but more difficult to read

graders are readers, students are on the other side, so ... 😦

,w derivative x^{1/x}

[ocean seal]

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Requested by vin100#3191

[proper tangle]

,w second derivative x^{1/x}

[ocean seal]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by vin100#3191

[proper tangle]

i wonder if getting the calc right can help you understand the general theory (e..g. disadvantages of Riemann Integration and the need for Lebesgue's Integrals)

since it's a series expansion about $x = e$, so $\ln(x) = 1$.

[ocean seal]

vin100

[coral rock]

ahhh

just realised i made a mistake in the taylor expansion for f(pi) about x=e

should be like this

[coral rock]

dont worry i have my notebook and pen 🙂 its just this would be quite tedious to write in latex like i normally do

[lone heart]

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[coral rock]

.reopen

[lone heart]

✅

[coral rock]

so then plugging in f'(e)(=0) and f''(e) i should be good?

??

looks good ngl

says its wrong, how could this be

im gonna cry

[proper tangle]

,ask second derivative x^{1/x} at x = e

[ocean seal]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by vin100#3191

[coral rock]

ohhh i seeeee

brother

ily

i wish u the very best in life

[lone heart]

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[vast bobcat]

if I could get some help on this it'd be great

[lone heart]

@vast bobcat Has your question been resolved?

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@vast bobcat Has your question been resolved?

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[faint pond]

The problem states:
Numbers 5, x, y are given in an increasing order to create a geometric sequence, wherein x - y = 10. Calculate X and Y.
I understand most of it, I just don't understand where they got 10, -5 and =5 from in the 3rd last line.

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[reef trout]

.close

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[charred musk]

Solve the equation 10^x = 15

[charred musk]

im doing natural logarithms and i don't understand how to answer this question without using the "log" function on my calculator

Solve the equation 10^x = 15

im brand new to logarithms but i understand certain stuff like log2(8)=3

[little drum]

umm, you might not have been asked to report the approx value maybe?

[charred musk]

yeah approximate value

[little drum]

you should just report the exact value if it's much troublesome

Were you made to learn the values of $\log 2$ and $\log 3$ ?

[ocean seal]

Arya

[charred musk]

i haven't

[little drum]

then you'd have to use the calculator or you can at best answer with the exact value

$x = \log_{10} 15$

[ocean seal]

Arya

[charred musk]

hmm

ok but how do i calculate log 8

by itself

[little drum]

or $x = 1 + \log_{10} 3 - \log_{10} 2$

[ocean seal]

Arya

[little drum]

hmmm? 3log 2?

if you're thinking about calculating the approx value, you'd need the logarithm chart or the calculator

or learn the values of log 2 and log 3

[charred musk]

so im not supposed to actually know the answer to these without a calculator?

[little drum]

yeah

[charred musk]

first of all, what does log of any number mean

[little drum]

I mean

ehhhhhhhhhhhh

[charred musk]

[little drum]

logarithm is just the

ummm

opposite of exponents

something to the power of something is something is the way of an exponent

then

log of something to the base of something is something is the way of logarithm

🐖

[charred musk]

uhh

[little drum]

for example,

$4^5 = 1024$

[ocean seal]

Arya

[little drum]

that's exponents alright

now,

[charred musk]

[little drum]

$4^{\boxed{5}} = 1024 \iff \log_{4} 1024 = \boxed{5}$

[ocean seal]

Arya

[little drum]

logarithm reports the exponent

exponent reports the value

[charred musk]

i think i understand but at the same time i dont

is it possible to get

log4^1024=x as a question

and solve it without a calculator

[little drum]

Y S

yes

because

you can write 1024

as an exponent form of 4

[charred musk]

squarrooted

[little drum]

which is 4^5

[charred musk]

wtf

[little drum]

and logarithm... reports this "5"

however you cannot write 15 as a natural exponent of 10

therefore, you cannot evaluate $\log_{10} 15$ without a calculator

[ocean seal]

Arya

[charred musk]

hmm

ok wait lets go back to the original question

Solve the equation 10^x = 15

my teacher solved it

as

"log both sides"

log10^x =log15

x=lg15

x=1.176

what does log both sides mean

@little drum

[little drum]

mwans

means

you take the log of both sides

as you know log is an operation, so taking log just means what it means

taking log of 10 means writing log 10, which is just 1

taking log of 15 base 10 means writing $\log_{10} 15$

[ocean seal]

Arya

[charred musk]

im so confusedddd

how is log 15 = log10^15

why am i not understanding this lol

[little drum]

🐖

[little drum]

$\log_{10} 10^x = x$

[ocean seal]

Arya

[little drum]

Anyways, let me try and rewrite the shit for you

[charred musk]

just explain it in kid terms

[little drum]

$\rightarrow 10^x = 15$ \ $\implies \log_{10} 10^x = \log_{10} 15$ \ $\implies x = \log_{10} 15$

[ocean seal]

Arya

[charred musk]

log10^10=1 right?

[little drum]

Skondar

empty your frickin brain and TRY TO UNDERSTAND the difference between writing something in SUBSCRIPT versus writing something with a ^ on superscript

$\log_{10} 10 = 1$ is true. \ However, what you wrote $\log 10^{10} = 1$ is ...

[ocean seal]

Arya

[little drum]

but I'm guessing you have understood the gist of it

[charred musk]

[little drum]

just note the fundamental rule of thumb: $$a^b = c \implies \log_a c = b$$

[charred musk]

how tf should i write it then

[ocean seal]

Arya

[charred musk]

ok so now i have log10^15, what does this mean exactly

how much of something can be multiplied 10 times to get 15?

@little drum

[remote heron]

it means what power do you have to raise 10 to get 15

[charred musk]

hmm

[charred musk]

can i do this without a calculator

[remote heron]

probably not

[charred musk]

ok, what does

log8 mean

[remote heron]

as in $\log 8$ or $\log _8$

[ocean seal]

jan Niku (Shuri for Honorable)

[charred musk]

what's the difference

[remote heron]

logs have a base and an argument

without a base and argument log means nothing

[charred musk]

hm

the first one

what does it mean

[remote heron]

idk can you provide context or something

what is the question

if you just want to learn about logs i can try to find videos

[charred musk]

yes please, but more specifically natural logarithms

[remote heron]

mos tpeople here are better helpers than teachers

[charred musk]

i've tried finding a few but they don't correlate to what im studying

[remote heron]

so natural logs are just a special kind of logs

they have a specific base

$\log _e (x) = \ln (x)$

[ocean seal]

jan Niku (Shuri for Honorable)

[charred musk]

bro 20min here i learned more then 5 hours with teachers

[remote heron]

natural logs are nice for reasons you usually dont learn when youre learning logs

but theyre important enough to get their own name

[charred musk]

hmm ok

[charred musk]

idk man, i have a test on this next week, and i need to learn y=a^x after this

and i apparently need to know log before doing this

[remote heron]

you learn them at the same time

[charred musk]

yeah im doing that now

but im doing natural log before learning what log is before hand

[remote heron]

logs are just inverses of exponentiation, right

like youd learn about subtraction and addition around the same time

[charred musk]

yeah

[remote heron]

nothing super magical

but confusing yea

[charred musk]

ok but why am i super confused

[remote heron]

if you try to understand exponent properties it will help you understand log

like $x^a x^b = x^{a+b}$

[ocean seal]

jan Niku (Shuri for Honorable)

[remote heron]

and $\qty( x^a )^b = x^{ab}$

[ocean seal]

jan Niku (Shuri for Honorable)

[charred musk]

hmm

[remote heron]

and i guess $x^{-a} = \frac{1}{x^a}$

[ocean seal]

jan Niku (Shuri for Honorable)

[remote heron]

stuff like these

[charred musk]

i know these

[remote heron]

log properties come directly from these

so then if you see a log property thats like uhh

[charred musk]

no but like