help-0

[vale wigeon]

do you understand Y/N

[weary abyss]

什么

[vale wigeon]

...i don't speak chinese, but that apparently means "what"

[weary abyss]

我也不会说中文

[vale wigeon]

ok then why don't you stop sending messages in chinese

actually no

i'll take this as a sign that you consciously refuse to communicate clearly, to the point of absurdity

so yeah you're on your own now

[weary abyss]

thank god

[fading citrus]

Don't waste peoples' time, speak in English. Nobody is obligated to help you.

[lone heart]

Helpers are just people volunteering their time to help you. Be polite and patient.

[fading citrus]

Consider this a warning

[lone heart]

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[lone heart]

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[alpine sable]

How would I do this type of problem

[lone heart]

@alpine sable Has your question been resolved?

[alpine sable]

<@&286206848099549185>

[zealous lichen]

what are the domains of natural log and square root?

[valid acorn]

for ln functions, put the terms in parentheses >0 into the equation and solve the equation.

[zealous lichen]

@alpine sable

[alpine sable]

my bad im here now

[alpine sable]

anything bigger then 0

[zealous lichen]

so sketch x+y+1 >0

[alpine sable]

im not sure how that looks

[zealous lichen]

first sketch x+y+1=0

then determine which side is greater than 0

[alpine sable]

im sorry

idk how to do that either

[zealous lichen]

it's just a line

[alpine sable]

can i put in my calc

by solving for y

[zealous lichen]

you can try

have you graphed straight lines before?

[alpine sable]

yea i know what y=x is

[zealous lichen]

x+y+1=0 is same as y=-x-1

[alpine sable]

oh im slow

it has a slop of -1 and a y intercept of -1

[zealous lichen]

yep

[alpine sable]

immma try the next one onmy own i think its the same

[zealous lichen]

good luck

[alpine sable]

I think I did it right

[zealous lichen]

unfortunately no

you should consider the square roots seperately

also you need shade the area

[alpine sable]

oh so like one for negative and one for positive

[zealous lichen]

?

[alpine sable]

how the y is in between the negative sqrt n pos

[zealous lichen]

because 4-x^2-y^2 >= 0

y^2 <= 4-x^2

[alpine sable]

oh okay i see

also where did they get x=-1,1 from ?

[zealous lichen]

by solving 1-x^2>=0

[alpine sable]

where did the y go ?

[zealous lichen]

there's no y

we get $1-x^2\geq 0$ from $\sqrt{1-x^2}$

[ocean seal]

WhereWolf(ping if needed)

[alpine sable]

oh thats what you meant by treating the two square roots differently

[zealous lichen]

yes

[alpine sable]

oh okay thanks that opened my eyes

[lone heart]

@alpine sable Has your question been resolved?

[alpine sable]

do you know how to do these problems ?

[zealous lichen]

what problems

[alpine sable]

would it be just setting z to different values ?

[zealous lichen]

yes

draw f(x,y) = c

[alpine sable]

k

[alpine sable]

Can you do that

[zealous lichen]

ln(1)=0

[alpine sable]

kk so that would be one curve then

[zealous lichen]

you get x^2+y^2=0

[alpine sable]

which is y=-x

[zealous lichen]

what

[alpine sable]

nvm that lol

i forgot were doing z

which is x n y

[alpine sable]

how would i know how to graph this ?

[zealous lichen]

notice that both x^2 and y^2 are non-negative

[alpine sable]

k

[zealous lichen]

it means x and y are both 0

you can also think of it as circle of radius 0

[alpine sable]

yep

[alpine sable]

so if x and y are both 0 what does that mean for z ?

[zealous lichen]

we set z=1

so the only point where z=1 is (x,y)=(0,0)

[alpine sable]

oh so when z is 1 x n y are 0

so how do i sketch a space curve for that ?

[zealous lichen]

draw a point at 0,0

and mark it as z=1

[alpine sable]

k

oh thats much easier then i thought k thanks imma do two more numbers

so now that it doesnt = o what would be the difference ?

[zealous lichen]

x^2+y^2=r^2 is a circle

of radius r

you get x^2+y^2 =-ln(2)

[alpine sable]

yea

[zealous lichen]

which is impossible (for real numbers)

[alpine sable]

so do i need to pick a different number

[zealous lichen]

yes

actually it's easier if you set x^2+y^2=c

[alpine sable]

yea btw so if i dont know x^2 + y^2 is a circle im screwed ?

[zealous lichen]

ya

[alpine sable]

that sucks

[zealous lichen]

I mean you can also figure that out by your own lol

[alpine sable]

how without memorizing it ?

[zealous lichen]

use pythagoras theorem

[lone heart]

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[alpine sable]

.reopen

[lone heart]

✅

[lone heart]

@alpine sable Has your question been resolved?

[lone heart]

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[astral kelp]

If you're gonna find the probabilities of a number.Do you divide numbers by the big numbers first or small numbers?

[vague coral]

probability of a number ?

I know that a number isnt a random event tho

[opal jolt]

ask your question properly

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[brave edge]

Can someone help me with this question

[round geyser]

what's the height of the equilateral triangle?

[brave edge]

X

[round geyser]

what

no

[brave edge]

3x

[round geyser]

no

height

not perimeter or anything else

[brave edge]

I don’t know

[round geyser]

use pythagoras' theorem

[brave edge]

X square root 2

[round geyser]

no

the base while using pythagoras' theorem is x/2 and the hypotenuse is x

[brave edge]

I’m not sure still

[round geyser]

what is the third side?

[lone heart]

@brave edge Has your question been resolved?

[brave edge]

is it x square root 3 /2

It’s x

[round geyser]

yes

this is correct

you have the height

and you also have the base of the equilateral triangle

so what's the area of the triangle

[brave edge]

4000/x^2square root 3

[lone heart]

@brave edge Has your question been resolved?

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[frail grove]

How can you tell from the graph of a function f that the second derivative at a certain point is 0 or diff of 0?
f''(x) = 0 or f''(x) ≠ 0

[frail grove]

.close

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[alpine sable]

[
F_G = mg \tss{and} \rho = \f m V
]

[alpine sable]

use those two equations

[stable sierra]

we dont have density of stone

[whole vine]

i am still confused

[alpine sable]

oh okay

you have to consider the boyunet force

[stable sierra]

yeo

yep

[lone heart]

@whole vine Has your question been resolved?

[hollow oriole]

Yes, -4x -x^2/20, as expected. My doubt is about how to get into that specific answer. Both are correct, I tested evaluating them on the same interval (-40<x<-20) and returned the same result (20). But what substitution is needed here to get in 40-(40+x)^2/20 ?

[harsh swallow]

no substitution needed

you should multiply out the square

[lone heart]

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[vapid bramble]

how do i approach this question?

[vapid bramble]

do i just do it normally?

[tardy stag]

why not

[vapid bramble]

i thought there would be somewhere to simplify it

i guess not

ima try doing it normally then

.close

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[alpine sable]

im trying to do 11. (C).. how do i do it using a method called subtistution??

[lone heart]

Please don't occupy multiple help channels.

[alpine sable]

.close

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[wheat isle]

I don’t get it what am I doing wrong

There’s still a y term

[vale wigeon]

why are you trying to integrate sin(y^2) dy symbolically

might it be that you are fucking up a SoR integral setup

[wheat isle]

i don’t know what that means

[vale wigeon]

you're trying to find the antiderivative of sin(y^2)

which exists, but is inexpressible in closed form

otherwise clarify which word or phrase you do not know the meaning of, or decline to do so and get sullied.

[daring rover]

kings rule

[wheat isle]

OH

wait I just had a Bruh moment

[vale wigeon]

might it be that you are fucking up a SoR integral setup

[daring rover]

I think its possible to evaluate since its a definite integral

[vale wigeon]

i'd like to see you try

[daring rover]

Give me a moment lol

[vale wigeon]

it's from 0 to sqrt(pi), not 0 to infinity

ftr

[daring rover]

gotta prove myself wrong

oh

[wheat isle]

the reason why it didn’t work is because I used the wrong formula for shell

[mortal trellis]

wolfram also just expresses it in terms of S(sqrt2)

[wheat isle]

I’m missing a y in my integral

lol

[mortal trellis]

where S is the antiderivative

[vale wigeon]

so i was right, and you DID fuck up a SoR integral.

[mortal trellis]

well that explains it

[wheat isle]

Anyways problem solved I forgor the shell formula 💀

[wheat isle]

Maybe

.close

[lone heart]

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[frosty totem]

Slept midway through Math class and now I have no idea how to do this problem. Can anyone help me find the degree measures?

[old heath]

no other information given???

[frosty totem]

thats it

no given thats why im quite confused with it

but all i know there are some specific measures to eventually build up to a full 360 circle

[old heath]

angle c= angle d

angle a = angle b

hmm isnt even given if e centre

[frosty totem]

maybe the half of measure CD is equal to measure BA?

[old heath]

you cannot assume that

[frosty totem]

yeah

BC = AD though

[old heath]

is it

[frosty totem]

it looks like it

but maybe not

[old heath]

if in a diagram

it looks like iy

u dont assume that

[frosty totem]

yea

[old heath]

for them to be equal they should be equidistant from centre

i feel like some info is missing

[frosty totem]

hmm yeah

pretty weird

meanwhile though there is another problem

there is a given here

i assume that x = 10 in here?

then i think once u get x, u substitute it right?

tho how do u get the arcs?

[old heath]

how can you just assume that

hmm idk

[frosty totem]

they are indeed equal

if u sub it

they're both 57

[old heath]

they are not meeting at the center

can you say with surity

[frosty totem]

it doesnt but we know its 57

[old heath]

they have to be equal

its given?

[frosty totem]

yes both of those are equal

no

i equated it both

[old heath]

thats what im saying

[frosty totem]

5x+7 = 4x+17

[old heath]

you cant just equate them both

[frosty totem]

u can

[old heath]

youre assuming they are equal

[frosty totem]

i wasnt

[old heath]

why are they equal?

[frosty totem]

try it

[frosty totem]

.

try to find the x

you'll get 10

[old heath]

i get that

but how can you be sure

they are equal

to equate it in the first place

they arent radii

[frosty totem]

5(10) + 7 = 57
4(10) + 17 = 57

they're the same

[old heath]

bro

youre putting a specific x

its not necessary

they are equal

ill send diagram wait

[frosty totem]

ok

[old heath]

You cant just say ac=bc

You have to prove it

[frosty totem]

thats true

but it is in fact given

and the proof is that they're both equal

[old heath]

where is it given 💀

[frosty totem]

its written man

on the diagram

[old heath]

not in the q or im blind

they just gave you the length in expression

doesnt mean they equal

[frosty totem]

this is another question thats not related to the first one

[old heath]

in my diagram i give you ac=x+2 bc=2x+5 you gonna say they are the same?

seems sus

idk ill let someone else figure it out

[frosty totem]

they're not even equal smh

[old heath]

its same diagram as yours

just by sight you cannot say they are equal or not

[frosty totem]

of course you cant

but there is literally the given

[old heath]

yes so how can you equate those

[frosty totem]

and they are in fact both equal

[old heath]

idk

[lone heart]

@frosty totem Has your question been resolved?

[lone heart]

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[spiral halo]

so in this problem they said 1/x is a constant, i dont get why

[ocean seal]

Jelle

[spiral halo]

but x can still be any number, or does it mean because it's any number then the rule that it can be taken out of the limit applies

is that right?

[golden canyon]

If something doesn't depend on the variable of the limit, $\Delta x$ in this case, then it can be taken out

[ocean seal]

Jelle

[spiral halo]

okay thank you!

.close

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[rigid tundra]

I was wondering if 8^14 is congruent to 1 mod 15 ? Or 4 mod 15 , I've worked out it's congruent to 4 mod 15 as counter example but calculators are saying 15 is a factor of 8^14 -1

[golden canyon]

It's congruent to 1, because $8^{14} = 8^{2^7} = 16^7$

[ocean seal]

Jelle

[golden canyon]

and 16 is congruent to 1

[rigid tundra]

Isn't 8^2 =64

[lone heart]

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[old heath]

It is

[lone heart]

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[waxen forge]

My brain isn't braining this help

[waxen forge]

I assume I first find the drivitave of the given functions

But then what

I'll just tell the teacher idk how to solve it👍

.closed

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[ruby vapor]

how this happened?

[lofty gorge]

there's another 6*6 term further right

[dim oasis]

$R^2 = 6^2 + 6^2 + 6(6) \implies R^2 = 6^2 + 6^2 + 6^2$

[ocean seal]

M. Frost

M. Frost

[ruby vapor]

how that 6(6) became to 3?

[dim oasis]

It didn't, there's 3 6^2's

Here try this

[ocean seal]

M. Frost

[ruby vapor]

there's 72 in the red square but when he simplified it, it became to 3

[dim oasis]

It didn't, the 72 simplification was unnecessary and not reflected in the next line

[dim oasis]

What do you think about this problem here?

[ruby vapor]

if x=2 answer is 12

it just 3(x^2)

oh i got it

ooohh i see that now

6*6 added to third 6^2

thanks

.solvede

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[silk thunder]

How do i simplify sin2x to tan2x

[limpid turret]

You don't

The whole expression is true, but sin = tan is not

The same way $(1-3)^2=(1-(-1))^2$, but $3\ne-1$

[ocean seal]

SWR

[silk thunder]

how do i show that the left side can be written as the right side?

both expressions are true, but the problem wants me to show how it is true by rewriting the left side as the right side

[limpid turret]

Try expanding both sides

Then use your trig properties to show they are true

[silk thunder]

ok

[silk thunder]

well... i couldn't solve it. can you walk me through how to solve?

[limpid turret]

!show

[lone heart]

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

[silk thunder]

after here: (1- 2tanx/tan2x)(1- 2tanx/tan2x) = 1 + (4tan²x / tan²2x)

am i correct up to this point?

.close

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[zenith flax]

I used the equation T(t) = C*e^kt + t(s)

So I had

110*e^kt + 70 = 110

k = -.0127664084

Evaluated and got t = ln(40/110)/k

Where did I go wrong

handwriting isn’t the neatest

[lone heart]

@zenith flax Has your question been resolved?

[zenith flax]

👋

[lone heart]

@zenith flax Has your question been resolved?

[lone heart]

@zenith flax Has your question been resolved?

[zenith flax]

.close

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[brave meadow]

z

[brave meadow]

hello

this my channel

ok

nvm

u can have channel

[vale wigeon]

no, she needs to claim her own so it does not have your name on it still.

[brave meadow]

oh okay

one sec my laptop died its loading

[vale wigeon]

and you should post the question you need help with as the first message.

[brave meadow]

need help graphing

<@&286206848099549185>

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[lone heart]

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[frail grove]

if f=O(g) and g=O(f) then f and g have equal growth rates ?

[exotic canopy]

this implies that O(f)=O(g)

so yes

[frail grove]

what does that mean ?

f=O(g) means f is dominated by g

[exotic canopy]

oh?

[frail grove]

what does O(f)=O(g) mean?

[exotic canopy]

wait i am confused

why is there an equal there then

O(...) is big-O notation, right?

[frail grove]

yes

[exotic canopy]

i don't think that's right

it means that it grows "no faster than"

[strange zenith]

$f \in O(g), g \in O(f)$

[ocean seal]

ganbat

[frail grove]

that's what dominated mean xd

[exotic canopy]

and if f grows no faster than g, and g grows no faster than f, then they must have the same growth rate

[frail grove]

not the same exact growth rate though, right ?

.close

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[pine pilot]

Do you have an idea how I can describe the red circle in spherical coordinates using the delta distribution?

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[jagged cobalt]

h isnt actually 0

its just very very close to it

you could

youll just get the limit of 1/1

which is 1

[alpine sable]

just gets cancled out

[jagged cobalt]

youre doing the derivative with respect to h

h isnt a constant by any means

the fact youre taking a limit with respect to it means must be a variable

[ivory pivot]

if h is a constant i am brad pitt

[jagged cobalt]

h can be anything

youre finding it approaching 0

[tawny condor]

That's what he's supposed to do when using LHopitals rule.
Regardless I don't think it's a good idea to even use that right now

As h gets closer to 0, the value of the expression h/h is always 1.

No matter how close you get (as long as h != 0)

Therefore the value of the limit is 1

[ivory pivot]

very good!

[tawny condor]

h/h isn't continuous at 0

It's not even DEFINED at 0, how do you expect it to be continuous?

For continuity, you need to actually have a value there. You also need the limit to equal that value, but that doesn't matter right now

"With respect"?

[jagged cobalt]

i mean, yeah 'h' alone may be continuous at 0
but h/h isnt

[tawny condor]

It doesn't matter that the numerator is continuous.

The expression you're taking the limit of ISN'T continuous at h = 0.

[jagged cobalt]

because we're taking the limit

[tawny condor]

We do, that's correct

h/h = 1 when h != 0

Which is precisely why the limit is 1. You should probably revise what a limit means.

Getting a visualization might help

You aren't making any sense

The derivative of 1 is 0

No..

1 = x^0

Use the power rule here

1 is x^0

take the derivative using the power rule

No

x^1 != 1

??

Ok but "if x = 1" isn't helpful here

You are differentiating a function, not looking at a specific point.

[jagged cobalt]

1=x/x quotient rule (x-x)/x^2 =0/x^2=0 supposing x isnt 0, idk if thats a valid visualisation, maybe not

[tawny condor]

#❓how-to-get-help

@glad garnet Please get your own help channel

How is this related

[jagged cobalt]

probably better to use the definition of the derivative

it would actually be 1-1/h

if i define the function f(x)=1 for all x

then do the definition of the derivative

[f(x+h)-f(x)]/h = [1-1]/h

=0

[rose void]

Go to the "math help" category and take any open help thread by just entering your problem.

[tawny condor]

!occupied

[lone heart]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[tawny condor]

<@&268886789983436800>

I'm pretty sure this guy is just trolling

[lone heart]

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[light bridge]

can someone help me on how to satisfy both g) h) and j) at the same time

<@&286206848099549185>

[wild umbra]

!15m

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Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[lofty gorge]

I think if you make f perfectly flat in the correct location, it's possible

because then the limit of f(y) where y depends on f, i.e. either h or j, won't need to approach a value and instead you can plug straight in

that's worded poorly

essentially the idea is to e.g. plug a straight up 2 into the limit in h, rather than taking the limit of f(something that approaches but never equals 2)

and then use a single discontinuous point that you can set to whatever

[light bridge]

then i for j) i can just make a point?

if i understood what you said correctly

[light bridge]

at x= -2

[lofty gorge]

yes

[light bridge]

so essentially smt like this

[lofty gorge]

yes

[light bridge]

ok thx

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[storm zinc]

would i do this by getting the derivatives of both and plugging in 3 for t

and then getting the magnitude of both vectors to find the speeds of each?

<@&286206848099549185>

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@storm zinc Has your question been resolved?

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@storm zinc Has your question been resolved?

[storm zinc]

<@&286206848099549185>

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@storm zinc Has your question been resolved?

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@storm zinc Has your question been resolved?

[shy osprey]

Little boy why haven’t you done your math 😈😈😈😈😈

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[storm zinc]

.close

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[twilit gull]

Im new to permutations. Can anyone explain me this one?

So far I can clearly see that two places are already filled by 2 and that leaves with 2 ways each to fill the rest 5 digits giving $2^5=32$

[ocean seal]

Muffins

[twilit gull]

Also the two 2s can be in any of the place value.

I am unable to arrange these in a expression which should lead me to the answer

[lone heart]

@twilit gull Has your question been resolved?

[brazen copper]

Since you already have figured out that 32 is one part for the rest 5 remaining digits, all we have to calculate is the positioning of the 2s and multiply

which is simple

Since we have 7 places/digits

and we need to choose any 2 of these

we can do 7C2

The final answer being 7C2 x 32

672

[lone heart]

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[frozen pollen]

How to double differentiate a determinant

[frozen pollen]

.close

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[spice dock]

im translating english into predicate logic: "x is y's parent" and im not sure what the difference is between
Parent x z ∧ Parent z y

and

∃ z : People , Parent x z ∧ Parent z y

[steady mantle]

the first needs an explicitly defined person z. the second is saying that such a z exists, but we dont need to know who

[spice dock]

so the first would be more like "x is z's parent and z is y's parent"?

[steady mantle]

yes

[spice dock]

ty

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[sleek furnace]

%Hello,
I'm reading a book on group theory, and there are exercices in it, but a lot of them don't have any answers. The exercice is \
Determinate the sub-group of $(\mathbb R^, \cdot)$ generated by the set of prime numbers. \\
My imediate answer would be that there is no subset smaller than $\mathbb R^$ that is generated by the prime numbers given the fundamental theorem of arithmetic...

[ocean seal]

ταυταυ

[oak chasm]

What does R* mean? Nonzero reals?

[vale wigeon]

does sqrt(2) belong to the subgroup generated by the primes?

[sleek furnace]

oh wait

I meant $\mathbb N_*$ my bad

[sleek furnace]

also yes

it's supposed to be _ not ^ idk what i did there

[ocean seal]

ταυταυ

[sleek furnace]

especially since the fundamental theorem of arithmetic only applies to naturals kek

well, restricting it to non-negative and non-complex numbers

[oak chasm]

OK, so how would you produce an arbitrary a/b?

[vale wigeon]

hang on

@sleek furnace send us a picture of the problem

N_* is not a group

[sleek furnace]

the problem is in french

[sleek furnace]

oh true

[vale wigeon]

i speak french

[lone heart]

Please show the original problem, exactly as it was stated to you. A picture or screenshot is best.

If the original problem is not in English, then post it anyway! The additional context might still help helpers help you. Do your best to translate.

[sleek furnace]

oh i see

it's Q

without 0

ohhhhh

[vale wigeon]

post a picture so that we're 100% on the same page

[sleek furnace]

wait

there you go

[oak chasm]

So it is R*?

[oak chasm]

In that case, ^

[sleek furnace]

So If a prime is in the set, it's inverse is in the set too, so i would guess it would be $\mathbb Q_*^+$ since all primes are positive

[ocean seal]

ταυταυ

[oak chasm]

OK, how do you know it can't produce irrational numbers?

@sleek furnace

[sleek furnace]

irrational number can't be written as a fraction

[oak chasm]

Yes, but how do you know that nonfractions can't be produced?

[sleek furnace]

we are given prime numbers which are whole numbers

meaning that we also have the inverse of the prime numbers

soo i'd say $\langle \mathbb P \rangle = \left{ \frac{a}{b} \mid a, b \in \mathbb N\right}$

anyway i gotta go

[oak chasm]

OK.

[ocean seal]

ταυταυ

[sleek furnace]

i've got class now

[oak chasm]

I'd say that you start with fractions, and a fraction times a fraction is a fraction.

[sleek furnace]

boring physics lab

[sleek furnace]

ah i see

[oak chasm]

So, you can't leave the fractions by multiplying.

[alpine sable]

please do not flood help channels with this

[storm musk]

Why do I have to explain

It's like spamming

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@sleek furnace Has your question been resolved?

[lone heart]

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[deep crow]

yo help

[deep crow]

.close

[lone heart]

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[alpine sable]

This picture shows the graph of f(x) = 2x³ - 3x² - 3x + 2
How can I use that information to solve 2cos³x - 3cos²x - 3cosx + 2 = 0?

[vale wigeon]

substitute t := cos(x), and the equation becomes f(t) = 0

read off the roots of f from that graph

[alpine sable]

I came to the conclusion that cos(x) should equal those roots. But since the new function is a trigonometric function the new roots will be repeating forever. So I suppose I have to write it as x = angle + n * another angle, and I don't know how to do that.

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@alpine sable Has your question been resolved?

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[bold silo]

Where did I go wrong?

[fallen sierra]

hii

[lone heart]

@bold silo Has your question been resolved?

[bold silo]

It's not 3[(1-2/27x)^8], it's [3(1-2/27x)^8]

Ohh k thanks

.close

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[thorn niche]

help me with this question please

[sullen geode]

yep

[thorn niche]

ok

[vale wigeon]

!da2a

[lone heart]

No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/

[thorn niche]

Ok here is the question then

[vale wigeon]

what's troubling you with this

[thorn niche]

the question i dont know it

[sullen geode]

um

it would be 25 x 10^13

right?

[thorn niche]

how did u get that tho

what are the steps

[sullen geode]

like u write it as

50 x 10^13

[vale wigeon]

right value wrong form.

standard form requires the mantissa to be between 1 and 10, not including 10.

[vale wigeon]

do you know what "standard form"/"scientific notation" is?

[sullen geode]

2.5 x 10^14 then?

[vale wigeon]

• not x, but yes.

the question in fact amounts to nothing more than dividing 5 by 2.

[sullen geode]

ye ;-;

[thorn niche]

no i dont

[vale wigeon]

since that does not take you outside of the 1 to 10 range.

[vale wigeon]

ok then you have to read up / watch videos on it

[thorn niche]

ye i watched the video i dont know it

Too complicated

[vale wigeon]

what video did you watch

[thorn niche]

the video on

the

website

[vale wigeon]

ok hold on

im gonna ask this to get an idea of how much you know or don't know

what grade are you in

[thorn niche]

9

[vale wigeon]

so that's... like 15 years old right

give or take one

[thorn niche]

No 13

[vale wigeon]

hm

well alright

do you know how decimals work

[thorn niche]

yes

[vale wigeon]

and do you know how exponents work

[thorn niche]

no

[vale wigeon]

uh oh

well there's the hole in your knowledge innit

actually, wait.

are you in the UK

[thorn niche]

i didnt get taught exponents ever

yea

[vale wigeon]

they might be called "indices" instead

[thorn niche]

no not that either

[vale wigeon]

damn ok

well at least now we know what you gotta learn

[thorn niche]

i did the same question with multiplying but i dont know the dividing

what can i do @vale wigeon

[vale wigeon]

honestly dont know what to tell you there sorry

[vale wigeon]

you need to learn how exponents work, and this is too big of a topic to teach over discord (+ i dont have the energy for it rn)

i mean like ok

in THIS case

the 10^14 can just be left alone

you know how to divide 5 by 2 right

[thorn niche]

2.5

[vale wigeon]

right

2.5 * 10^14 is what'll happen

and that's already in standard form with no need to readjust

[thorn niche]

What is * and ^

• is X and ^ is divide right?

[vale wigeon]

* means multiplication, ^ is exponentiation

division is /

[thorn niche]

The answer has to be this

So how will we figure out that equation

[vale wigeon]

.

you know like, 2 people have already told you the answer even

[thorn niche]

2.5 x 10?

[vale wigeon]

no

$2.5 \times 10^{14}$

[ocean seal]

AnnGhost

[vale wigeon]

this

[thorn niche]

Ye but how

[vale wigeon]

AnnGhost — Today at 19:32
i mean like ok
in THIS case
the 10^14 can just be left alone
you know how to divide 5 by 2 right

ali — Today at 19:32
2.5

AnnGhost — Today at 19:32
right
2.5 * 10^14 is what'll happen
and that's already in standard form with no need to readjust

[thorn niche]

I dont really know the 10^14 can just be left alone

How can i know what can be left alone and not

[vale wigeon]

because you have admitted that you don't know anything about exponents

you're refusing to go learn about them

idk like go to http://khanacademy.org/

watch organic chemistry tutor

search "organic chemistry tutor exponents" on youtube

youve gotta put in the effort

[thorn niche]

I do

Its not that easy to learn

.close

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[thorn niche]

how do i solve this in easy fast way

<@&286206848099549185>

[exotic canopy]

divide the numbers before the 10^... and subtract the exponents of 10 from each other

[thorn niche]

Im not sure what exponents are

[exotic canopy]

in 10^18, the exponent is 18

[thorn niche]

The bigger number?

[exotic canopy]

the number above

written in superscript

[thorn niche]

Whats that

[exotic canopy]

look at your question

$10^{18}$

[ocean seal]

artemetra

[unkempt robin]

$a^b$

[ocean seal]

USS-Enterprise

[unkempt robin]

This is called a power.

[exotic canopy]

oh

[unkempt robin]

It translates to a being multiplied by itself b times

[exotic canopy]

okay my bad then

[unkempt robin]

a is called the base, b is called the exponent

[thorn niche]

ok

exponent = power?

[unkempt robin]

It's used interchangeably, but technically a power is the whole thing while the exponent is just the number on top of the base

So $10^{14}$

[ocean seal]

USS-Enterprise

[unkempt robin]

Means 10 being multiplied by 10 fourteen times

[thorn niche]

Yes

[unkempt robin]

$2^3 = 2 \cdot 2 \cdot 2$

[ocean seal]

USS-Enterprise

[thorn niche]

2x2x2

[unkempt robin]

We read this as "2 raised to the power of 3"

Or 10 raised to the power of 14

[thorn niche]

Okay

[unkempt robin]

But this just means multiplication

As multiplication means addition (for example 2 x 3 = 2 + 2 + 2, so adding 2 three times), powers mean multiplication (2^3 = 2 x 2 x 2, so multiplying 2 three times)

[thorn niche]

ok

[unkempt robin]

Anyway, to your original problem

We can write everything as a fraction, we rarely use the divison symbol

$\frac{8 \cdot 10^{18}}{4 \cdot 10^3}$

[ocean seal]

USS-Enterprise

[thorn niche]

How can we answer that

[unkempt robin]

Well

Have you heard about cancelling?

[thorn niche]

no

[unkempt robin]

You've got a fraction with the main operation being multiplication

Let's take a, b for some number and write an expression like this:

$\frac{a \cdot b}{a}$

[ocean seal]

USS-Enterprise

[thorn niche]

ok

[unkempt robin]

You can cancel common factors in both the numerator and the denominator

Given your main operation is multiplication

We see we have a common factor a in both the numerator and denominator

They can cancel

[thorn niche]

So only b is left?

[unkempt robin]

Because if we take it seperately, we get $\frac{a}{a}$

[ocean seal]

USS-Enterprise

[unkempt robin]

Which is just 1

[thorn niche]

ok

[unkempt robin]

And we are left with b

So yes, $\frac{ab}{a} = b$

[ocean seal]

USS-Enterprise

[unkempt robin]

So let's try this

$\frac{2 \cdot 9 \cdot 4}{3 \cdot 4 \cdot 9}$

[ocean seal]

USS-Enterprise

[unkempt robin]

What's this equal to?

[thorn niche]

I dont know

[unkempt robin]

Think of this

You've only got multiplication

$\frac{a \cdot b \cdot c}{d \cdot c \cdot b}$

[ocean seal]

USS-Enterprise

[unkempt robin]

Commutativity can be used here

Means you may rearrange factors as you wish

[thorn niche]

okay

[unkempt robin]

So if we rearrange the denominator, we get $\frac{a \cdot b \cdot c}{d \cdot b \cdot c}$

[ocean seal]

USS-Enterprise

[unkempt robin]

See anything similar

[thorn niche]

They can cancel out

[unkempt robin]

What can

[thorn niche]

bc get canceled out

[unkempt robin]

Exactly

[thorn niche]

Leaving only a and d

[unkempt robin]

We end up with $\frac{a}{d}$

[ocean seal]

USS-Enterprise

[unkempt robin]

And if we get back to numbers

[unkempt robin]

What can be done here

[thorn niche]

Hm what numbers

[unkempt robin]

$\frac{2 \cdot 9 \cdot 4}{3 \cdot 4 \cdot 9}$

[ocean seal]

USS-Enterprise

[thorn niche]

So it should be 2/3 left out

[unkempt robin]

Exactly

[thorn niche]

4/4 and 9/9 together

Ok

[unkempt robin]

Are 1 times 1

1 times 1 is 1

[thorn niche]

Yes

[unkempt robin]

And anything multiplied by 1 is just the same anything

So it's irrelevant to have it there

Here we learn that you can multiply the denominator and the numerator by the same non-zero number

And the value of the fraction remains unchanged!

If we take for example $\frac{5}{2}$

[ocean seal]

USS-Enterprise

[unkempt robin]

We can multiply both the numerator and denominator by 3

[thorn niche]

15/6

[unkempt robin]

And we get $\frac{15}{6}$

[ocean seal]

USS-Enterprise

[unkempt robin]

Yes

$\frac{5}{2} = \frac{15}{6}$

[ocean seal]

USS-Enterprise

[unkempt robin]

But most of the time you have to do it the other way round

'simplify' 15/6

You see both the numerator and denominator have the same factor 3

So you cancel out 3 (or divide both numerator and denominator by 3)

[thorn niche]

Correct

[unkempt robin]

Because you can think of 15/6 as $\frac{5 \cdot 3}{2 \cdot 3}$

[ocean seal]

USS-Enterprise

[unkempt robin]

And 3 cancel out

So, try simplifying this: $\frac{24}{14}$

[ocean seal]

USS-Enterprise

[thorn niche]

12/7

[unkempt robin]

There you go!

But remember this only works when the main operation is multiplication

If we for example had addition, $\frac{5 + 3}{2 + 3}$

[ocean seal]

USS-Enterprise

[unkempt robin]

You can not cancel out the 3 here

[thorn niche]

Ohh ok,

[unkempt robin]

$\frac{5 + 3}{2 + 3} \neq \frac{5}{2}$

[ocean seal]

USS-Enterprise

[unkempt robin]

The left one is 1.6 while the right is 2.5

Not the same 😄

Anyway

Let's get to the original question

[thorn niche]

ok

[unkempt robin]

$\frac{8 \cdot 10^{18}}{4 \cdot 10^3}$

[ocean seal]

USS-Enterprise

[unkempt robin]

You get this right?

[thorn niche]

Kinda

[unkempt robin]

Okay so

We see the main (and only) operation is multiplication

So we can do whatever we want 🙃

Try simplifying 8/4 first

[thorn niche]

Isnt it division?

[unkempt robin]

Yes but that's irrelevant at this

[thorn niche]

So if the question is division we start answering it with multiplication Then we get to division

[unkempt robin]

And division is just multiplying the first number by the reciprocal of the other 🙂

So $3 : 2 = 3 \cdot \frac{1}{2}$

[ocean seal]

USS-Enterprise

[unkempt robin]

Right now you are dividing two numbers

That's the horizontal line

Division

Your job is to simplify this fraction as much as you can

[thorn niche]

2/1

For this one

[unkempt robin]

Exactly

2/1 is just 2

[thorn niche]

Ok

What next

[unkempt robin]

So we gwt

$\frac{2 \cdot 10^{18}}{1 \cdot 10^3}$

[ocean seal]

USS-Enterprise

[unkempt robin]

And the one really isn't doing much

$\frac{2 \cdot 10^{18}}{10^3}$

[ocean seal]

USS-Enterprise

[unkempt robin]

Because 8 divided by 4 is 2

Now we come to a property of exponents, though you can use canceling method as well

[thorn niche]

How can we know if a number isnt doing much

So we can remove it

[unkempt robin]

Well a multiplied by 1 is just a right

1 is the identity of multiplication

$1 \cdot a = a$

[ocean seal]

USS-Enterprise

[unkempt robin]

No point in writing the one

[thorn niche]

So of there is 1 in the division we have to take it out

[unkempt robin]

That's not what I am saying

$\frac{8 \cdot 10^{18}}{4 \cdot 10^3}$

We had this

[ocean seal]

USS-Enterprise

[unkempt robin]

You simplified 8/4

Which is 2/1

$\frac{2 \cdot 10^{18}}{1 \cdot 10^3}$

[ocean seal]

USS-Enterprise

[unkempt robin]

But 2 divided by 1 is just 2

[thorn niche]

10 18 and 10 3 is 10 21

[unkempt robin]

Careful

We've got division

You add exponents if you are multiplying

But substract if dividing

[thorn niche]

So 15

[unkempt robin]

Yes, we substract 3 from 18

And we end up with $2 \cdot 10^{15}$

[ocean seal]

USS-Enterprise

[thorn niche]

But we had a fraction before

How did it change to one decimal

[unkempt robin]

We had $\frac{2 \cdot 10^{18}}{10^3}$

[ocean seal]

USS-Enterprise

[unkempt robin]

You can kick the 2 out, because $\frac{2a}{b} = 2 \cdot \frac{a}{b}$

[thorn niche]

Yes.

[ocean seal]

USS-Enterprise

[unkempt robin]

We have $2 \cdot \frac{10^{18}}{10^3}$

[ocean seal]

USS-Enterprise

[unkempt robin]

Do you understand this?

[thorn niche]

Yeah but not this part

[unkempt robin]

Well let's say we have $\frac{1}{2}$

[ocean seal]

USS-Enterprise

[unkempt robin]

And we multiply this by 2

[thorn niche]

2/4

[unkempt robin]

No.

We get $2 \cdot \frac{1}{2}$

[ocean seal]

USS-Enterprise

[thorn niche]

Decimals and fractions can be together?

[unkempt robin]

We multiply a fraction by a whole number

[thorn niche]

2 . 1/2?

[unkempt robin]

By multiplying the numerator with the whole number

This isn't decimal!

This is multiplication

[thorn niche]

But why does it have a dot

[unkempt robin]

$\cdot$

[ocean seal]

USS-Enterprise

[unkempt robin]

Dot is used by the vast majority

For multiplication

[thorn niche]

So . just means x

[unkempt robin]

dot in the middle

[thorn niche]

Ye that

[unkempt robin]

$\cdot \neq .$

[ocean seal]

USS-Enterprise

[thorn niche]

Dot on the bottom means decimal the one in the middle means x

[unkempt robin]

Exactly

But I would suggest getting used to using the dot

[thorn niche]

Alright thank you for clarifying

[unkempt robin]

Because you'll eventually move to it from x

[thorn niche]

Wdym

by move to it from x

[unkempt robin]

We move from using "x" for multiplication to the dot

As we get older

In school

[thorn niche]

Okay

[unkempt robin]

In highschool+

You won't see x for multiplication there anymore

[thorn niche]

For me i think i stay with x

Is it only in US

[unkempt robin]

Okay, no problem

No

Universally

[thorn niche]

Seriously?

[unkempt robin]

dot in the middle means multiplication

Yeah