help-0

[karmic solstice]

wassup

alr so

cubes

what do u

know abt them

about their

lengths

and also

how many sides faces does a cube have

[spiral coral]

the distribution table for this question is putting me off

would the probability of A still be 1/6?

considering the die is not fair?

and b = 0.2?

[sudden hinge]

consider opening your own channel

[lone heart]

@ivory sleet Has your question been resolved?

[lone heart]

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[stable gazelle]

Hello

[stable gazelle]

I have a problem on this exercice anyone can help me please

I can consider that F_k+2 = F_k+1 + F_k or i must write that with F_n+2 = …. ?

Can I change the letter k to n? 😅

It’s for the first question

[golden canyon]

F_k+2 = F_k+1 + F_k this holds doesn't matter if the letter is k or n

[stable gazelle]

Ok so i can write it with k

Thx !

[golden canyon]

only for k >= 0 though

[stable gazelle]

Yeah 0<=k<= n

.close

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[plucky jungle]

Hi guys ! i'd like to find a formula or algorithm that would generate this series of number :

1,2,4,3,5,6,8,7,9,10,12,11,13,14,16,15....

[plucky jungle]

It's basically counting above but every two number the counting is swaped if you get what I mean

I'm very unfamiliar with how to approach those kind of problem

+1,+2,-1,+2,+1,+2,-1,+2,+1,+2,-1

The logic is in that i guess

[daring patrol]

In code?

[golden canyon]

if its just a formula use sin

[plucky jungle]

Ye like in python

I want to generate a list of n number following this logic starting from 0

[daring patrol]

Arithmetic and geometric sequence might do the job

[plain flame]

well you could just use that for multiples of 4 this sequence is just the gaussian sum

and then deal with the last numbers if there are any

[plucky jungle]

Well the problem is a want a sequence like this with 13000 numbers

[plucky jungle]

I'm not even sure how to generate sequence ?

Sorry guys math aint my forte but willing to learn

[daring patrol]

You want to use python right?

Use Function that return list

[plucky jungle]

yes

Yes populating a list would be perfect

[rose sigil]

if you want to generate a list like that then I think recursion is fine

[daring patrol]

I think enumerate can also be used here

[plucky jungle]

Hmm im looking up all those terms 😄

Thanks for the help guys

[alpine sable]

just make some kind of loop, looping over 1,2,3,4,5,...
and then if the number mod 4 is 2, add 1, if the number mod 4 is 3, subtract 1

[plucky jungle]

Oh yea im kind of stupid !

I could actually just create a function that does the +2, -1

etc

[plucky jungle]

Ooh yeah !!

[alpine sable]

or alternatively make 4 numbers per loop cycle:
4i + 1, 4i+2, 4i+4, 4i+3
start i at 0

[plucky jungle]

oh that's clever too

Im really envious about yall math thinking mindset, wish I'd be able to do this 😄

Ok I think i'll be able to figure it out now, thanks fellas !!

[lone heart]

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[lament aspen]

Hello, I am asked to find the differential equation of this family (and am told I need to get rid of b to do so):

[lament aspen]

,tex x^2 + (y-b)^2 = 1 + b^2

[ocean seal]

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

I compile the code you give me by putting it into a template LaTeX document, between \begin{document} and \end{document} commands.
Please don't give me code that belongs outside of there!
See ,help tex for some examples of what I understand.

If you want to modify the template to add packages or your own macros, see ,help preamble.

Oct 12, 2022, 4:07 PM

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

[lament aspen]

Whoops

[lament aspen]

After that, I developed the (y-b)^2 and got rid of the b^2 on both sides, so now I have:

,tex x^2 + y^2 - 2yb = 1

[ocean seal]

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

[lament aspen]

But I am not sure how to get rid of the b, because if I take the derivate of -2yb, I will still have the b

[molten pivot]

$x^2 + (y-b)^2 = 1+b^2$

[ocean seal]

Mr. Gamer

[molten pivot]

this is the eq?

[lament aspen]

Yup

[molten pivot]

differentiate

[lament aspen]

But won't I still have the b after differentiation?

[molten pivot]

let me show you

x^2 + y^2 - 2by + b^2 = 1 + b^2
x^2 + y^2 - 2by = 1
y(y-2b) = (1-x^2)
y-2b = (1-x^2)/y
-2b = (1-x^2)/y - y

[lament aspen]

Oh so after that I can differentiate and the b will go away

That makes sense

[molten pivot]

yeah, it just takes a bit of algebra

[lament aspen]

but isn't (1-x^2)/y - y going to be a pain in the ass to differentiate?

[molten pivot]

sometimes you might have to differentiate twice though

to get rid of the b

and that's ok

[lament aspen]

Oh I see

Thank you, I think I'll be fine with this!

[molten pivot]

if we differentiated first without expanding:

we'd get:
2x + 2(y-b)y' = 0
x + (y-b)y' = 0
(y-b)y' = -x
y-b = -x/y'
-b = -x/y' + y

[lament aspen]

I see so it might even be simpler to differentiate first?

[molten pivot]

yeah

you can differentiate as many times as you need to

[lament aspen]

So differentiating at the beginning would give me:

$2xdx +2(y-b)dy=0$

[ocean seal]

Baylen

[molten pivot]

sure that works

[lament aspen]

and after I get:

$xdx + (y-b)dy=0$

[ocean seal]

Baylen

[lament aspen]

Do I just differentiate again to get rid of the b?

[molten pivot]

just differentiating again would leave the b in there

ideally get b on one side of the equation first

[lament aspen]

As in this?:

Don't mind the soul

failed experiment lol

We have b on both sides here I see

[molten pivot]

yeah i'd honestly go with this one even though it is a bit of a pain to differentiate

[lament aspen]

To be honest, I have no idea how I'd differentiate that... 😂

[molten pivot]

-2b = (1-x^2) * 1/y - y

[lament aspen]

Oh well, didn't see that path lol

Would make sense since the derivatives will end up with their corresponding variable

But do I differentiate the -2b with respect to y or x?

[molten pivot]

it becomes 0

and honestly i prefer using y' until the final step so you don't have to worry about what variable to differentiate wrt

[lament aspen]

I didn't know I could do that

Makes it a whole lot easier

[molten pivot]

yeah

then you can just multiply the whole equation through by dx at the end

[lament aspen]

When I differentiate the product I get two different terms through the product rule but do I stick a y' after each term or do I put a parenthesis around both and put the y' outside?

After differentiation I end up with:

$0=(\frac{-2xy-1+x^2}{y^2})\frac{dy}{dx}-y$

[ocean seal]

Baylen

[lament aspen]

Then I flip it over:

$-\frac{y^3}{2xy+1-x^2}=\frac{dy}{dx}$

[ocean seal]

Baylen

[lament aspen]

But their answer is:

$-\frac{2xy}{1-x^2+y^2}=\frac{dy}{dx}$

[ocean seal]

Baylen

[lone heart]

@lament aspen Has your question been resolved?

[molten pivot]

= 0

0 = (x^2 - 1)y'/y^2 - y' - 2x/y
multiply through by y^2:
0 = (x^2-1)y' - y^2y' - 2xy
2xy = y'(x^2-1-y^2)
y' = 2xy/(x^2-1-y^2)
y' = -2xy/(1-x^2+y^2)

@lament aspen

[lament aspen]

Let's gooo, I just got it too

A whole lot of mistakes and restarting but I got there

[lone heart]

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[mighty fulcrum]

Hello, how does the exercices goes from this: to this:

[keen pasture]

Factor out 5^x and subtract 5^3

[mighty fulcrum]

what has happened to the 5^x that like disapears?

[keen pasture]

It's still there. After the bracket

[mighty fulcrum]

and the first one?

[keen pasture]

Let's say 5^x = u

[mighty fulcrum]

okey

[keen pasture]

Then we have 5u -30u

What does this equal to?

[mighty fulcrum]

-25u

[keen pasture]

Very good

[mighty fulcrum]

that is the same as -5^3?

[keen pasture]

No, it's the same as (5-30) * 5^x

[mighty fulcrum]

okey

[keen pasture]

Because 5-30 = -25

[mighty fulcrum]

I got it, thanks, but one more thing sorry

[keen pasture]

Yes?

[mighty fulcrum]

5^x=5 -> x=1
what is the algebra for this?

[keen pasture]

Do you know log?

[mighty fulcrum]

I am studying it

is this log_5 5 ?

[keen pasture]

Yes

[mighty fulcrum]

so much thanks 🙂

[keen pasture]

You're welcome

[mighty fulcrum]

.close

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[steady basin]

help plz

[steady basin]

Am I along right lines?

[lone heart]

@steady basin Has your question been resolved?

[echo socket]

The negation of "For all x S(x) is true" is "For some x S(x) is false"

So you need to express the statement "Some nonempty subsets of the natural numbers don't have a smallest element"

[steady basin]

is the question asking me to write down both P and the negation of P?

[echo socket]

Hmm, well I'm not sure so I'd write both lol

[steady basin]

is S(x) same as A in this case?

[echo socket]

A is a set and S(x) is a statement, so no

I meant S to denote some statement for x

[steady basin]

Would this be it for p

[echo socket]

Ugh just forget the x and S

[steady basin]

Or this

@echo socket

[echo socket]

You've declared the variable but not the statement

How'd you write "has a smallest element?"

[steady basin]

yh thats wat im unsure about

[echo socket]

Try rephrasing "has a smallest element"

[steady basin]

something like min?

minimum

[echo socket]

Not necessary to refer to some function for a set

[steady basin]

element which is the smallest?

[echo socket]

If a set has a smallest element, it means that there exists an element in that set which is smaller than or equal to all of the elements in that set

[steady basin]

right

[echo socket]

That'll be easier to express with quantifiers

[steady basin]

icl im stuck on what i need to write now

could u show me how the final answer looks and then we can go through it together?

so i understand

[echo socket]

∀S⊂N S≠∅ (∃x∈S (∀y∈S x ≤ y))

This is p

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[lone heart]

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[last rampart]

I have dy/dx = (1 +t^-1)/(1-t^-1)

but my textbook says its (t+1)/(t-1)

its not obvious to me if these are equivalent

or did I do something wrong

[sudden hinge]

multiply numerator & denominator by t

[minor needle]

$$\frac{1+\frac{1}{t}}{1-\frac{1}{t}}=\frac{\frac{t+1}{t}}{\frac{t-1}{t}}=$$
$$=\frac{t+1}{t} \cdot \frac{t}{t-1}=\frac{t+1}{t-1}$$

[ocean seal]

Modus

[last rampart]

Oh alright I see

[lone heart]

@last rampart Has your question been resolved?

[last rampart]

TB says the second derivative is -2t/(t-1)^3

but I only got -2/(t-1)^3

cause d(dy/dx)/dt = -2/(t-1)^2 and dx dt = t-1

so how is -2/(t-1)^2 *1/(t-1) = -2t/(t-1)^3

@sudden hinge

[mystic orchid]

The tb has a misprint your answer is correct

[last rampart]

ok cool thanks, had me stuck scratching my head here for no reason

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[lone heart]

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[alpine sable]

I genuinely don't understand how to solve a problem like this

[alpine sable]

Like i dont know how it's possible

[lone heart]

@alpine sable Has your question been resolved?

[lone heart]

@alpine sable Has your question been resolved?

[alpine sable]

<@&286206848099549185>

[mossy laurel]

Use the Newton equations

[alpine sable]

I tried

Its like i dont have enough to solve it

Oh wait

I just got 1.95deg

🤔

Damn im dumb

Lmao

[raven haven]

This is a projectile motion question

Oh you solved it

[alpine sable]

Yeah i think i just erased my right answer before because 1.95degrees seemed ridiculous

But i just realized 120m/s going at a 100m target doesn't take much of an angle

.close

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[round zealot]

I know that you can use mass point geometry to solve this, but the numbers are weird and not working

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@round zealot Has your question been resolved?

[round zealot]

<@&286206848099549185>

[lone heart]

@round zealot Has your question been resolved?

[round zealot]

If the bottom one is too hard, then help with the top one?

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[lone heart]

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[fathom horizon]

Need help with factoring a polynomial

[fathom horizon]

2x^2-10x+8

[karmic solstice]

aye aye

alr

hm

got any

attempt

or nah

[fathom horizon]

Yes

[karmic solstice]

aye aye

alr

got a pic

[fathom horizon]

The app i use it says this isnt the answer instead its 2(x-1)(x-4)????

[karmic solstice]

ye the app

is right

so

hm

alr

to make it

easier

for urself

first

when u see

the polynomial

the have

a common factor

right

it’s 2

[fathom horizon]

Yes

[karmic solstice]

so

to

make it easier

factor it out

so u work

with smaller

numbers

so u get

$2(x^2 -5x +4)$

[ocean seal]

Springsskateboard

[karmic solstice]

now

don’t wry abt that 2

focus

on what’s inside

the bracket

what are 2 numbers

that add up

[fathom horizon]

Howd u get the -5??

[karmic solstice]

to -5

[karmic solstice]

well

[fathom horizon]

And 4

[karmic solstice]

-10x divided by 2

and 8 divided by 2

rmb

we

factored out

2

from the entire

polynomial

[fathom horizon]

Ahh yes

[karmic solstice]

yeye

so

[fathom horizon]

Why do u need to facyor the 2 out btw and when can i do that

[karmic solstice]

alr so

we don’t NEED to

yk

but

it’ll make it

easier

esp

if

ure working with

much bigger numbers

in those cases

we’d usually

[fathom horizon]

Ahhh

[karmic solstice]

use the formul

formula

but idk if u learnt that

[fathom horizon]

Which one

Idk

[karmic solstice]

ah then nvm

so

ye

it makes it easier

cuz

we’ll work with

smaller numbers

[fathom horizon]

Okayy

[karmic solstice]

$2(x^2 -5x+4)$

[ocean seal]

Springsskateboard

[karmic solstice]

this

is what we have now

ye

so

think of two numbers

that add up to -5

and multiply to give +4

[fathom horizon]

2 and 3?

[karmic solstice]

what is 2 times 3

and also

2+3 is 5

not -5

[fathom horizon]

Nvm

[karmic solstice]

good try

aye

so

try again

[fathom horizon]

1 and 5?

[karmic solstice]

what is 1+5

it does not equal -5

ye

[fathom horizon]

Idkk:((

[karmic solstice]

alr so

it’s -1 and -4

[fathom horizon]

Ahh

[karmic solstice]

what is -1 + (-4)

-5

[fathom horizon]

Yes

[karmic solstice]

what’s -1 times -4

positive 4

[fathom horizon]

4

[karmic solstice]

so ye

like that

we get

[fathom horizon]

Yess i got it now

[karmic solstice]

$2(x-1)(x-4)$

aye aye

[ocean seal]

Springsskateboard

[karmic solstice]

nice

[fathom horizon]

Thank uu so much omg

[karmic solstice]

npnp

[fathom horizon]

Heyy i forgot to ask

Can u also do the same for a coefficient 3?

Like take it out

@karmic solstice

[karmic solstice]

aye aye

wassup

hm

[fathom horizon]

Sorry to @ need ur help

[karmic solstice]

alr so

nah issokay

idm

so

we can only

factor out

a number

if every term

is divisible

by it

and gives u whole number

ykwim

so just now

we had ur qn

look at

the first term

2x^2

is the coefficient

which is 2

divisible by 3

2*

[fathom horizon]

Ohhh so lets say if the other 2 teerms in a trinomial is divisible by 3 we can do the same as what u just did?

[karmic solstice]

yeye

if every term

is divisible by it

[fathom horizon]

Thank you so much

[karmic solstice]

npnp

[lone heart]

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[lone heart]

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[tacit dirge]

Help

[tacit dirge]

My question is

This and I have my work

Where did I do wrong??

ANYONE?

BROOOOOO

[little drum]

x = 0, y² = 1/d ? y = 0, x² = 1/d ?

Don't those points comply as well?

[tacit dirge]

Hmm

Yeah

So

I did x=0 and y=0 but

Still the min is not 0

[little drum]

... of course x = 0, y = 0 would not give you the min.

[tacit dirge]

Then what will???

[little drum]

yk that Del g should not be 0 vector, right?

x = 0, y = 0 is not allowed

[little drum]

...

[tacit dirge]

Oh

...........

Then what should be the answer sry I have 1 min left

.............

Like last min sorry

[little drum]

shouldn't you check these points as well?

[tacit dirge]

I did but idk the answer still

I tried

And got -4

But that's not the answer also

Ok could you just tell me the answer

I just don't get it

[little drum]

I can't tell the answer (#rules ) but you really would've got your answer if you tried those points

[tacit dirge]

....

So -3 is the answer then?

Could you at least confirm if its right or wrong

[little drum]

no.. of course not lol.

f(x, y) will always be positive since x² and y² are always > 0

If you'd tried (x, y) = (1/d², 0), d = 1, f(1, 0) = 2 should give you the minimum

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[rustic crest]

any idea how i can solve this ?

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[fiery hazel]

ok so im not good at math but i was wondering why does a triangle have 180 degrees but a circle has 360 when they both close at the same point?

[karmic solstice]

aye aye

wassup

so

hm

what’s ur qn exactly?

why a triangle

angles add up to

180?

[fiery hazel]

sry its not clear

[karmic solstice]

nah it’s okay bro

wait so

is that ur qn?

[fiery hazel]

no sry i type slow

[karmic solstice]

ohh alr

nah

take ur time

np

also I don’t get

what u mean

by “close at the same point”

[fiery hazel]

sry i mean like if u have point "a" its on the circumfrence of a circle and is a point on a triangle

it closes at the same point

is that any better?

[karmic solstice]

uhh

sry bro

I still don’t get

it

[fiery hazel]

its fine im not great with words

[karmic solstice]

nah it’s fine

im not great at understanding

[fiery hazel]

ok imagine u have point "a" on the circumference of a circle. Point "a" is also a vertex on a triangle. Why is Point "a" to Point "a" on a circle 360 degrees but on a triangle only 180 degrees.

[tall topaz]

Like this?

[fiery hazel]

yeah i think

[tall topaz]

A point doesn’t have an angle tho

[karmic solstice]

aye aye

wassup

do u

have a picture

of the qn

[fiery hazel]

uh yeah i can get one real quike

quick

[iron wraith]

Hola anyone fan of billy joel is from east coast dm me or @ me?

[fiery hazel]

not sure if this helps at all

sry took a while

.close

[lone heart]

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[misty kayak]

I'm stuck on these two questions

I just want to know how to solve them

do i use b^2-4ac

[karmic solstice]

aye aye

wassup

so

hm

yeye

suppose to use

discriminant

nice

[lone heart]

@misty kayak Has your question been resolved?

[lone heart]

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[graceful echo]

.reopen

Hi

[graceful echo]

<@&286206848099549185>

.close

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[lone heart]

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[stable grotto]

suppose we have 15 boy and 10 girl . we wont to make pairs 1 boy and 1 girl. how many ways we can pair them ?

[stable grotto]

my thought is that if there were 10 boy and 10 girl the answer would be 10 !

and not we have to calculate

how many ways we can choose 10 boy from 15 and order does not matter

and multiply that number by 10!

Is this correct ?

[lone heart]

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[stable grotto]

.close

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[alpine sable]

DC1194A: 3.3V @ 200mA, 4.5 ~ 36V in, Inductor On-Chip ; how it's used "@" here ? I mean I can guess that 200mA is the max output, but it's the first time seeing this notation

[prime badge]

it's used as the english word "at" i assume

[lone heart]

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[lone heart]

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[waxen forge]

Any one know what is going on??

[harsh girder]

$f(9) = 81$

[ocean seal]

秋水

[waxen forge]

?

[trim wagon]

substitute 9 in x for ur f(x) and that should be =81

[waxen forge]

Ah okay thank you

That's all I need

.close

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[frail lantern]

Hello

[frail lantern]

I have a rather simple doubt: When a circle touches all 4 sides of a parallelogram, what shape is the parallelogram? The answer is Rhombus but there's square in the options as well. If the paralleogram can be a rhombus then why not a square?

Ik the answer is Rhombus from 4 sources but none of them ever explain why it can't be Square

please ping

[fierce prairie]

@frail lantern squares are included in the definition of a rhombus

because it just needs equal angles and sides

[frail lantern]

So, you're suggesting square is an acceptable answer?

[fierce prairie]

nah, Rhombus is correct

but like a square is in its category

but.. you can’t say it just makes a square

because it also makes this kind of rhombus

[frail lantern]

Oh I see yeah, I shoudln't go into the specifics, Im supposed to mark the most appropriate answer

the most general answer

[fierce prairie]

yeah

[frail lantern]

gotchu gotchu

That's all then, been bothering me for a hot minute

Thanks a lot

take care ❤️

++done

-done

.done

[fierce prairie]

no problem

[frail lantern]

whats the code lol

[fierce prairie]

it’s .close lol

[frail lantern]

right too many help servers xd

.close

[lone heart]

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[quick anvil]

Can someone please help me with my homework with the solving too

[quiet laurel]

do you guys help in homeworks?

[languid bolt]

yes, but in other channels

this one is occupied

[quiet laurel]

okk

[quick anvil]

I litteraly hate math omg I hate online class fr

[languid bolt]

Do you know what the quadratic formula is?

[quick anvil]

Gurl I have no idea

[frail lantern]

I hate math too, I strongly recommend getting better at it if you wanna win at life though

[quick anvil]

Yeah

Might as well just close this

.close

[lone heart]

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[frail lantern]

Fair play

[languid bolt]

$x_{1, 2} = \frac{-b\pm\sqrt{b^2 - 4ac}}{2a}$

[ocean seal]

help

[languid bolt]

this is the quadratic equation

wait it's closed

[simple wadi]

it is unfortunatly

ur nice @languid bolt

[languid bolt]

thanks

[lone heart]

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[steady basin]

R my answers correct

[lone heart]

@steady basin Has your question been resolved?

[gilded vessel]

seems alright

only one im unsure on would be f) cause idk if those events would necessarily be independent

actually it should be fine

cause every one with one coin gold and silver has at least one gold

so seems good

[lone heart]

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[shell iron]

hihi

[shell iron]

stuck on…all of this

[sudden hinge]

okay so lets start with the first one

do you know some log properties that could simplify this equation?

[shell iron]

um

no i do t

dont*

[tall topaz]

What is $\log{(a^m)}$

[ocean seal]

Pure

[shell iron]

m

right?

[tall topaz]

Would be if it was log base a

But in general?

[shell iron]

ifs just a ^m?

then

[tall topaz]

Do you know this formula $\log{ab} = \log a + \log b$

[ocean seal]

Pure

[shell iron]

yes

so log a^m would be log a + log a^m?

[tall topaz]

So $\log{(a^m)} = \log{(a \cdot a \cdot a \cdot … \cdot a)}$ m times

[ocean seal]

Pure

[shell iron]

ohhh

right

so log 2048 = 4 x 4 x 4, x times?

[tall topaz]

No no wait

[tall topaz]

Continue from this

Can you simplify further

[shell iron]

simply this?

[tall topaz]

Yes

[tall topaz]

Using this

[shell iron]

if would be log (2048^x) = log (4^x)

fhat doesnt seem right

how about log (4^x) = log 2048 x times

[tall topaz]

[\log{(a \cdot a \cdot a \cdot … \cdot a)} = \underbrace{\log a + \log a + … + \log a}_\text{m times} ]

[ocean seal]

Pure

[shell iron]

log (4^x) = log 4 + log 4 + log 4….) x times

trying to think like the problem

[tall topaz]

$=m\log a$

[ocean seal]

Pure

[shell iron]

or x log 4

[tall topaz]

Yes

[shell iron]

so that’s all i need to write?

[tall topaz]

$4^x = 2048 \implies x=\frac{\ln 4}{\ln {2048}}$

[ocean seal]

Pure

[shell iron]

ohh

can u explain the last step

how u got to ln

[tall topaz]

You can use any log

[shell iron]

so ln would replace log

[tall topaz]

But generally you use ln

Here you can just use log base 4

[shell iron]

in this context

[tall topaz]

$4^x = 2048 \implies x=\log_4 2048$

[ocean seal]

Pure

[tall topaz]

Here I accidentally flipped the fraction

[shell iron]

ohg

oh

this makes sense

yes

[shell iron]

for number 2, is the first one vaid

valid

[tall topaz]

What do you think

[shell iron]

so it has to be bigger than 0

and for everything but the last two, i would say yes

wait no

sorry

um

so 2 for x-2=0

so the first two are invalid

right

[tall topaz]

x-2 is not relevant here

I think that was specific to the question

Let’s think about it logically

$\log_2 (e)$

[ocean seal]

Pure

[tall topaz]

This is asking 2 raised to some power is e

$2^m = e$

[ocean seal]

Pure

[tall topaz]

Is this possible?

[shell iron]

no

[tall topaz]

Why not

[shell iron]

because 2 raised to a power is an integer

not a variable

[tall topaz]

e is not a variable it’s just a constant 2.71…

And

,calc 2^1.173

[ocean seal]

Result:

2.2548008242908

[tall topaz]

It’s not always an integer

,w plot y=2^x

[ocean seal]

Results provided by WolframAlpha

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

Requested by Pure#9389

[tall topaz]

2^m can be anything as long as it’s positive

So there’s definitely a solution to 2^m = e

[shell iron]

ohh

ok yes

didnt know about e

[tall topaz]

Okay so what about the second one

[shell iron]

i think that it is valid

because e raised to a power could be two..but

then again no

because its 2.17

[tall topaz]

Well

[shell iron]

and nothing raised to a power from 2.17 can be =2

[tall topaz]

You can raise it to negative power

[shell iron]

unless its like a negative or something?

yeah

so yes for that

[tall topaz]

,calc e^-1

[ocean seal]

Result:

0.36787944117144

[tall topaz]

Yeah

[shell iron]

and yes for 3 because

1 can be raised to a power for 10

[tall topaz]

How?

[shell iron]

1^10?

wait

sorry

lol

[tall topaz]

,calc 1^28188372

[ocean seal]

Result:

1

[shell iron]

multiplies

yeah =1

so no for that

[tall topaz]

Yeah

[shell iron]

i would say no for the next

because

[tall topaz]

Log of negative base not not defined

[shell iron]

nothing times 10 =1?

unless

no

its no

for part 4 of 2

and yes for part 5 because -1 times negative 36 = 36

[tall topaz]

10^m = 1

You mix up the definitions

it’s not -1 times something = 36

[shell iron]

oh

[tall topaz]

It’s -1 to the power of something = 36

[shell iron]

umm

the i dont think theres a power

that = 36

[tall topaz]

Yes so it doesn’t work

Wait come back to $\log_{10} 1$

[ocean seal]

Pure

[tall topaz]

It’s asking $10^m = 1$

[ocean seal]

Pure

[tall topaz]

Can you find such m

[shell iron]

for part 4

i think no

[tall topaz]

What about $10^0$

[ocean seal]

Pure

[shell iron]

its 1

so its valid

oh

[tall topaz]

Ye

[shell iron]

um last part of 2

36 to the power of something

=-1

its not valid

cant find anything

[tall topaz]

Correct

[shell iron]

how do u come up with the numbers

[tall topaz]

You can’t raise a number to some power and get a negative number

[shell iron]

like i didnt think of 0

[tall topaz]

It’s just a standard thing

Log of 0 is 1

[shell iron]

for part 3

right lol

it takes time for me

[tall topaz]

This uses some of the log properties

[shell iron]

is it just

u add 3+4+5

12 log (a + b + c)

[tall topaz]

No no no

[shell iron]

well log 2

ooh

um can u send the properties?

[ocean seal]

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

[shell iron]

so we r using

log a + log b

um just add?

[tall topaz]

Use the first law first

[shell iron]

lol like 3log 2 (a)+ 4 log(b)= 7 log2(ab)

[tall topaz]

No

That’s not how it works

You can only use the laws when there’s number in front of log

You need to use the first law I sent to simplify the logs first

[shell iron]

so 3log 2(a) = log 3^a

um log 2. 3^a

[tall topaz]

Yes

Do the same for the other ones

Then apply the addition and substraction laws

[shell iron]

and log2 4 ^b

and log2 5^c

[tall topaz]

Yes

[shell iron]

do i combine them now?

so like its log 2 (3+4+5) ^ abc

[lone heart]

@shell iron Has your question been resolved?

[lone heart]

@shell iron Has your question been resolved?

[lone heart]

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[somber lantern]

Are you still in the exam?

Yes?

<@&268886789983436800>

[trim wagon]

<@&268886789983436800>

[night geyser]

.close

[lone heart]

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[shell iron]

hihi sorry

[shell iron]

i reesponded so late but no i didnt finish it

its my pre work - like the work i bring to class its considerd as homework, but also 'prep" so not the exam

im still confused on number 3

i solved for each log, but what ould the last step be? to combine them?

.close

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[bronze pilot]

if U(n+1)=2/3U(n)-n-8/3, and U(0)=2;
for V(n)=U(n)+an-1;
how much does a has to be for this serie to be geometrique

[bronze pilot]

for V(n) to be geometrique

could it even be geometrique?

[harsh granite]

Can u use latex or an img of the problem would be good.

[bronze pilot]

. thx for that but i found the anwser

just now

[harsh granite]

K

[bronze pilot]

it's 2 i think

.close

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[desert drum]

how do i use sin, tan, to find x? Does my exact value triangles help or

[gray isle]

the idea is not to explicitly find x

you are told x is acute, drawing your triangle will tell you all the trig ratios you need for this question

[desert drum]

oh okay

okay i think i know what to do

ive got my, sinx, and sin60, and now to do sin(x+60) i'm at 24/25+root3/2

do i make the denominators the same and then add them?

[gray isle]

ugh show work

[desert drum]

ok

[gray isle]

looks like you did some illegal stuff

[desert drum]

aw man

[gray isle]

$\sin(a+b)\neq \sin(a) + \sin(b)$

[ocean seal]

ℝamonov

[desert drum]

oh wait yeah, the formulas much longer

ill do it again, but with the proper formula

does it matter what i make my a, and b? like can they be interchangable

such as, x=a 60=b, or does it need to be 60=a x=b

got it

thanks!

.close

[lone heart]

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[lavish surge]

HELLO

[plain night]

Hi

[somber lantern]

Hi

[plain night]

How to convert 7_10 into mixed fraction

I have dought

[lavish surge]

i like math

[plain night]

Oh nice

[lavish surge]

like algebra

[plain night]

?

[lavish surge]

btw im in 6 grade

[plain night]

Me too

[somber lantern]

What is this?

[plain night]

Where are u from

[lavish surge]

Norway

[plain night]

Ok

Im from India

[plain night]

In which school you study

[lone heart]

@lavish surge Has your question been resolved?

[lavish surge]

im back

i was just watching a video on how to beat the calculator in division

[lone heart]

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[smoky perch]

I'm confused about how to use the "execute" command in geogebra. Especially where I should open and close the quotation mark. I found a couple of examples on the internet.
Execute(Sequence("C"+i+"=Circle((4 random(), 4 random()), RandomUniform(0.2, 1))", i, 1, 10))
.In this example, when I try to replace the diameter with an element of a list or the i itself, the program does not run.
like this.
Execute(Sequence("C"+i+"=Circle((4 random(), 4 random()), Element(l1,i))", i, 1, 10))
Execute(Sequence("C"+i+"=Circle((4 random(), 4 random()), i)", i, 1, 10))
where is the problem?

[lone heart]

@smoky perch Has your question been resolved?

[smoky perch]

<@&286206848099549185>

[waxen flame]

I think you may be better off using the Zip command.

Are you trying to create 10 random circles?

@smoky perch

[smoky perch]

I want to generate random circles whose red color component is equal to its radius.

[neat locust]

Ok?

[smoky perch]

but its not my final goal

my main task is different and i want to learn to use execute command for this task

[waxen flame]

Try making three lists of random numbers for x, y, and r.

You should then be able to use the Zip command like so

Zip( Circle( (a,b),c), a, x_list, b, y_list, c, r_list)

As far as setting the color, you will likely need to use Javascript.

[smoky perch]

okey

[smoky perch]

ım gonna use that

thanks

.close

[lone heart]

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[real idol]

Yo I'm confused on how to calculate this quick without using a calculator

[sudden hinge]

group the 10^x terms, then cancel with the denominator appropriately

[real idol]

Lemme try

Like this right?

Or anything else to make it more quick?

[gray isle]

converting 0.25 to the fraction 1/4 helps

[real idol]

Hmm yeah

thanks guys

.close

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[alpine sable]

$$
|{X:X \in P(B),|X|=6}|=28 \text{ find |B|}
$$
$$
\text{ let a1,a2... be elements of P(B), suppose we are constructing P(B), first step: include a1 or not, second step: include a2 or not, etc...}
$$
$$
\text{chossing 6 times to include the item yields 28 sets thus}
$$
$$
|B|=C\binom{2^n}{6}=28 \text{ whatever it is}
$$

[ocean seal]

Zermelon

[alpine sable]

it this proof rigorous ?

[lone heart]

@alpine sable Has your question been resolved?

[lone heart]

@alpine sable Has your question been resolved?

[lone heart]

@alpine sable Has your question been resolved?

[lone heart]

@alpine sable Has your question been resolved?

[hollow oracle]

hello

[trim galleon]

Hey Im not in highschool but i wanna try understanding and try to learn calculus, can someone mind showing me the steps on how to do it?

[lone heart]

@alpine sable Has your question been resolved?

[formal fiber]

Yes

I can

Im a math professor

A pretty young one

[lone heart]

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[bright void]

how can the sum $\sum_{k=1}^{n}\frac{1}{k(k+1)(k+2)}$ evaluated? I tried something like partial fraction then cancelling out some terms as I was suspecting it was a telescoping series, but stuck right now

[ocean seal]

임도현

[molten pivot]

What do you get after partial fraction

[bright void]

i got $\frac{1}{2k} - \frac{1}{k+1} + \frac{1}{2k+4}$

[ocean seal]

임도현

[tiny turtle]

i'm gay kkkkk

[molten pivot]

I can show you an advanced method

Easy conceptually but fairly tedious

[bright void]

uhm may i see it

[molten pivot]

Let me write it on paper

[bright void]

thank you owo

[molten pivot]

Lots of integrating and multiplying by x to shift the index of the power series

@bright void

We start with a known series (geometric)

Then we can do all the calculus we want to both sides of the equation to make the series match up with the desired summation

Then we can just let x = 1

We end up with:

$\int (x (\int (\frac{\int f_n(x) dx}{x^2} dx) dx$

[ocean seal]

Mr. Gamer

[molten pivot]

Now the problem reduces to integration