help-0

[royal plank]

is ABC the base of the 3-sided pyramid ABCD and M is supposed to be the relative middle?

[nova swallow]

abcd are points of a parralelepiped

[limpid turret]

See I thought it was supposed to make a quad. Definitely feels like info is missing here.

[limpid turret]

Oh like corners?

[nova swallow]

yeah

[limpid turret]

Ok so abcd make some corners of a parraleliped and you need to find M such that abcm is one of its bases

Okay

You familiar with vectors?

[nova swallow]

yeah, but i have been stuck on this problem for hours

[limpid turret]

Define a b c and d as vectors.

Then m=(a-b)+(c-b)

[lone heart]

@nova swallow Has your question been resolved?

[long axle]

It definitely didn’t say that

#❓how-to-get-help

That was just an example

[long axle]

.

Go to one of the channels in Math Help (available)

[lone heart]

@nova swallow Has your question been resolved?

Channel closed

Closed by @nova swallow

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[keen iron]

hi

[keen iron]

im dum

and need help

[wary stream]

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

[wary stream]

@keen iron

[lone heart]

@keen iron Has your question been resolved?

[keen iron]

my question is whats 1+1

i dont know

i dont understand it

[wary stream]

Yeah... don't troll

.close

[lone heart]

Channel closed

Closed by @wary stream

Use .reopen if this was a mistake.

[lone heart]

Available help channel!

Send your question here to claim the channel.

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

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

[crimson cliff]

when you're determining the equation of a logarithmic graph, is there no horizontal strethc only when the xintercept is 1 away from the vertical asymptote?

[plain flame]

yes

[crimson cliff]

thx

.close

[lone heart]

Channel closed

Closed by @crimson cliff

Use .reopen if this was a mistake.

[lone heart]

Available help channel!

Send your question here to claim the channel.

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

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

[alpine sable]

Thesr righr?

[rocky grove]

1. is good except for the circle

2. same thing

[alpine sable]

How

It shows the value

[rocky grove]

Yeah but the circle being empty or closed is flipped

[lone heart]

@alpine sable Has your question been resolved?

[lone heart]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[naive flare]

How do I turn factored form to vertex form?

[high rapids]

Completing the square.

It seems you have already done most of the steps.

[rocky grove]

You're at the last step

Recall that

$(a+b)^2 = a^2 +2ab+b^2$

[ocean seal]

VulcanOne

[rocky grove]

And

$(a-b)^2 = a^2 -2ab+b^2$

[ocean seal]

VulcanOne

[naive flare]

how do I get rid of that -1 and -15??

[lone heart]

@naive flare Has your question been resolved?

[high rapids]

You add them?

What did you get?

[naive flare]

-16

and then i distribute to move it out?

[high rapids]

Move out where?

[naive flare]

like i distribute the a value to the c value so that it becomes the k value

[high rapids]

Show what you got

[naive flare]

uh one sec

[rocky grove]

That's it

That's your vertex form

[naive flare]

is it right?

[rocky grove]

Yeah

[naive flare]

oh, then what the hay is the lesser coordinate?

[rocky grove]

I think it's the minimum?

Or the one that is smaller than the other

Not sure

[naive flare]

i haven't learned about lesser coordinate i don't think 💀

[rocky grove]

💀💀💀

[naive flare]

well thanks for the help

.close

[lone heart]

Channel closed

Closed by @naive flare

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[gritty wing]

How to prove that when f(x) = 2, as x approaches infinity, f does not have a slant asymptote

[fallen verge]

Show that the limit doesnt go to infinity

[gritty wing]

thanks

.close

[lone heart]

Channel closed

Closed by @gritty wing

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[tacit arch]

,w Taylor series sin(x/3)/e^x

[ocean seal]

Results provided by WolframAlpha

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

Requested by riemann#2529

[tacit arch]

Do you know sin(x) = (e^(ix)-e^(-ix))/(2i)?

[tacit arch]

So no?

sin(x/3) =(a0 + a1x + a2x^2 +a3x^3+a4x^4) * (1+x+x^2 /2! +...)

Multiply and distribute and solve for the coefficients ai

[lone heart]

@wanton egret Has your question been resolved?

Channel closed

Closed by @wanton egret

Use .reopen if this was a mistake.

[tall reef]

wait

[lone heart]

Available help channel!

Send your question here to claim the channel.

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

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

[last ether]

<@&268886789983436800> porno moment

[sly mantle]

.close

[lone heart]

Channel closed

Closed by @sly mantle

Use .reopen if this was a mistake.

[last ether]

Calculate the velocity when I did your mom (please laugh I need emotional validation)

Man I'm so mature

[rocky grove]

Lmao

These people man

[last ether]

I sadly clicked on the video to see what Shitpost it was

And uh

Well I've seen worse from raids and shit but like

¯_(ツ)_/¯

[rose sigil]

i didn't laugh

[last ether]

😦

Im sad :(((

[pastel brook]

😵‍💫

[lone heart]

Available help channel!

Send your question here to claim the channel.

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

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

[eager furnace]

how to find y

would it work to set angle D to x and do 28 + y = 180?

[tribal haven]

construct some isosceles triangles

[eager furnace]

like this?

[tribal haven]

well i don't see how ADC is an isosceles triangle but keep going

[eager furnace]

how do i keep going

all i know is that the opposite angles equal 180

[tribal haven]

is M not the centre of the circle

[eager furnace]

idk 😭

does that big dot mean its the center?

[frozen hare]

yep

[eager furnace]

then what do i do now

[frozen hare]

ahhh so split the quadrilateral into triangles ABD and BDC

then you can find angle ABC in terms of x, and ADC in terms of x

since the quadrilateral is cyclic (all 4 vertices lie on the circumference)

ABD + BDC = 180º

[eager furnace]

how do i find angle ABC in terms of x?

[frozen hare]

yep, it worked

[frozen hare]

ABD is isosceles

and BDC is a right angle

[midnight vortex]

can u guys help me, if i dont finish i have a F and i need to finish by 4 hours

[frozen hare]

this channel is occupied

[eager furnace]

oh so angle ABD is 34º?

[frozen hare]

nope

wait you're using the angle in the centre is 2x the angle at the circumference right

[eager furnace]

umm idk

cuz u said triangle was isosceles

[frozen hare]

yeah the angle at the centre is 180º

so that can't help you here

[frozen hare]

ok, if the triangle is isosceles, then its base angles are....

[eager furnace]

the same

[frozen hare]

yep

[eager furnace]

and angle a is 112

so that means

[frozen hare]

forget about that

it's not 112

[eager furnace]

oh

[frozen hare]

oh wait it is

sorry, 180 - 68 = 112 (mental maths error)

yeah ok so it would help if you gave your reasoning for why

but I see now

[eager furnace]

then 180-112 = 68

[frozen hare]

shit I did this problem inefficiently, but that's okay

[eager furnace]

since both angles are the same

its half

34 no

[frozen hare]

yep, 4x = 112

it's just that

[alpine sable]

nhs i love 2turnt

[green talon]

nhs + 2t = winnipeg lrf

[frozen hare]

guys wrong channel

[eager furnace]

so abd is 34º?

[alpine sable]

nah we got the right one

#help-0 right?

[frozen hare]

no you want #discussion

check #rules for the rules

[frozen hare]

112/4 = 28º no?

[eager furnace]

yeah

[frozen hare]

yep

next time it would help if you gave a reason for how you found the angle

[eager furnace]

oh my bad

[frozen hare]

but it's also my bad because I totally missed the fact that it was a cyclic quad

and then mental maths error

[eager furnace]

so the answer i got is 56º

[frozen hare]

that answer doesn't make sense

because 4 * 56º > 180º

[tribal haven]

that's y not x..

[frozen hare]

and the maximum possible angle on the circumference is 180º when you have a straight line

[eager furnace]

yeah cuz i found x already

[eager furnace]

its right there

[frozen hare]

oh right, to find y

then yes you do need to break the quadrilateral apart into triangles ABD and BDC

[eager furnace]

so is it 56 or not

my brain hurts 😭

[frozen hare]

y = 56º yes

[eager furnace]

oo ok tysm

[tribal haven]

you can also save a lot of effort by drawing either AM or DM

but it works 20 ways because geometry

[eager furnace]

ohh ty

.close

[lone heart]

Channel closed

Closed by @eager furnace

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[rose lotus]

can someone help me figure out how you go from line 4 to 5?

I don’t know how you end up with a 1/2 and 1/3 in the brackets?

[deep compass]

can you factor 6x^2 + x - 1?

[rose lotus]

yeah

[last ether]

For which one

[rose lotus]

B

[last ether]

#❓how-to-get-help

Oh wait nvm

That's what they were replying to

Let u = cos(x)

Make the replacement

6u^2 + u - 1

Mb I thought it was a random question lol

[deep compass]

what do you get when you factor it

[rose lotus]

you get factors in two brackets

[rose lotus]

ohhhhh

(3x-1)(2x+1)

but like in this question

wait

[weary wyvern]

Line 5 is wrong

[rose lotus]

if i factor it the way ur saying u don’t get the 1/2 and 1/3 values but instead a 1 and -1

[rose lotus]

oh

[frozen hare]

you get -cos x

not cos x

[rose lotus]

-2cosx?

[frozen hare]

wait

[rose lotus]

man I just have no idea how they got those fractions there 😭

cause the answer is correct

[tribal haven]

looks right to me

[rose lotus]

but idk how you get the values 1/2 and 1/3

like u factor it

get two bracket

is it related to special triangles or the unit circle?

[tribal haven]

$$
\begin{align}
(3x-1)(2x+1) &= [3 \cdot (x-\frac{1}{3})][2 \cdot (x+\frac{1}{2})] = 0\
&\Rightarrow 6(x-\frac{1}{3})(x+\frac{1}{2}) = 0\
&\Rightarrow (x-\frac{1}{3})(x+\frac{1}{2}) = 0
\end{align}
$$

[ocean seal]

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

[rose lotus]

OHHHHHHH

wait where does the 6 go from the second last line

it just disappears

[tribal haven]

divide 6 on both sides

and 0/6 = 0

[rose lotus]

ohhhhhhhhhhhhhhhhhhhh

wow Tysm 🥹🙏🙏🙏

Lifesaver

.close

[lone heart]

Channel closed

Closed by @rose lotus

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[paper sigil]

Milk contains 3% butter fat and cream contains 15% butterfat. How many liters of milk and cream must be mixed together in order to produce 20L of a mixture that contains 6% butterfat?

[paper sigil]

I have no idea how to do this, all i know is that you have to use a linear system method

[tribal haven]

start by identifying your variables

[paper sigil]

let m be milk and cream be c

[tribal haven]

you might want to be a bit more clear,

let m, c both be in liters, then:

1. relate the amount of volume (in litres) of the target mixture with m,c
2. relate the amount of butterfat in the target mixture with m,c

[paper sigil]

ok

honestly this gotta be the hardest question in the world

[tribal haven]

eh, everything seems like the hardest problem when it's new

can you do part 1?

[paper sigil]

nah

[tribal haven]

what the number of liters you want to get in the end

[paper sigil]

20L

[tribal haven]

so how can you express the amount of milk and cream in your final mixture in liters

[paper sigil]

the amount of milk and cream is equal to 20L

[tribal haven]

express this with an equation involving m and c

[paper sigil]

m + c = 20L

[tribal haven]

now you have one of the equations

now think about how you might do something similar with the amount of butterfat

[paper sigil]

m+c = 6% butterfat?

[tribal haven]

not quite, what's the amount of butterfat in m liters of milk

[paper sigil]

3% butter fat in milk

am i supposed to convert or something

[tribal haven]

i mean you can work in percentages, but it ends up being the same thing

so thinking in amount should be a bit easier on you

[paper sigil]

3%=20L

[midnight hare]

Working in fractions would be easier

[paper sigil]

20/3

[midnight hare]

whats 20 divded by 3

[paper sigil]

6.6

.close

[lone heart]

Channel closed

Closed by @paper sigil

Use .reopen if this was a mistake.

[lone heart]

Available help channel!

Send your question here to claim the channel.

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

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

[tribal haven]

.close

[lone heart]

Channel closed

Closed by @tribal haven

Use .reopen if this was a mistake.

✅

[gusty gorge]

lol

[tribal haven]

.close

[lone heart]

Channel closed

Closed by @tribal haven

Use .reopen if this was a mistake.

[lone heart]

Available help channel!

Send your question here to claim the channel.

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

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

[mighty flower]

I understand

up until a=(-2w^2+46w)

how does completeing the square give us the width?

why would solving this using completing the square give us the width

[lone heart]

@mighty flower Has your question been resolved?

[gusty gorge]

so basically you've written the area as a function of the width yeah?

[mighty flower]

yes

[gusty gorge]

and you can see by inspection that it's quadratic

and you kinda also know that the quadratic is curved downward because otherwise you could get an unlimited area from your fencing (the problem wouldn't be so well posed)

[mighty flower]

and by solving for w by fineding the x intercepts of the parabola we fined the width

oh shoot

[gusty gorge]

no

[mighty flower]

?

[gusty gorge]

if you find the x-intercepts, you are finding where the area is 0

and I'm guessing that this problem is asking you to find the width such that the area is maximized

[mighty flower]

what does that mean

my teacher talked about maximizing area

but wont it be the same?

[gusty gorge]

If you have Area = (-2 * width^2 + 46 width), then if you solve (-2 * width^2 + 46 width) = 0, then you're really solving for the widths where the area is 0

that's not what you want to do

the problem is asking for the biggest area that you can get with this fencing

does that make sense?

[mighty flower]

a bit yes

[unkempt sundial]

you are minimizing the negative term so you can maximize the positive term

[gusty gorge]

wdym by a bit?

[mighty flower]

I tryed to do the same thing

[gusty gorge]

do you understand that the goal of this problem is to maximize the size of the fenced area?

[mighty flower]

on this problem

[haughty prawn]

hi

[mighty flower]

yea

but if that was tru why wont it work on this

[gusty gorge]

okay and you have written the area as a function of the width

[gusty gorge]

wdym by "won't work"

you have to be more specific

[mighty flower]

why cant I do

x(x+7)

[gusty gorge]

this is not a problem

[mighty flower]

than solve for x

[gusty gorge]

what are you supposed to do with that figure

[mighty flower]

and divide by 2

[mighty flower]

solve for x

[gusty gorge]

okay so why do you think that problem has anything to do with the fencing one?

in the fencing one, you're asked to maximize an area

in the triangle, you're asked to find the side lengths basically

[mighty flower]

what does maximzing the area mean tho?

[gusty gorge]

it means

look

if you have 46 feet of fencing and want to put it up

there are clearly many ways you can put the fence up, even if you're required to make it into a box shape

maximizing the area has basically the plain English meaning: how wide do I make the rectangle, so the space inside is as big as possible?

does that make sense?

[mighty flower]

the area will be the same regardless tho

[gusty gorge]

no it won't

[mighty flower]

how come 1 and 46 and 6.8

[gusty gorge]

Let's say I make the long side of the fence 45 feet long

that means that the two short sides are 0.5 feet long, since I only have 46 feet of fence

[mighty flower]

yea the area will be the sam

[gusty gorge]

no it won't stop arguing and listen

[mighty flower]

ok sorry

[gusty gorge]

what is the area of the space enclosed by my fence?

[mighty flower]

23

oh

[gusty gorge]

22.5

Area is equal to length times width

review the definition of area if you don't understand why

now let's say I make the long side of the fence 14 feet long

that means the short sides are each 16 feet long

what is the area of the part enclosed by the fence now?

[mighty flower]

224

[gusty gorge]

so clearly, some ideas for fencing are better than others, right?

[mighty flower]

yes

[gusty gorge]

the question is asking you to find the measurements that give you the biggest area

224 is not the biggest you can get

[mighty flower]

what would produce the biggest are tho

[gusty gorge]

that's literally what the question is asking you to figure out

[mighty flower]

I know

oh shoot

[gusty gorge]

so with any sort of problem, mathematical or otherwise, you need to look at what your goals are and what you know

and then you can figure out what sorts of tools you can use to solve it

one neat insight about the problem is that if you pick the width of the fence, you don't have any choice of the length

if I say that the width is 4 feet, then I really can't choose any length except 38 feet

and since the area is the width times the length, if we know the width of the fence, we can find the area of the fence

that is what your teacher has written: A = -2w^2 + 46w

that is an equation that tells you how to calculate the area of the enclosed space, given the width of the fence

does that make sense?

[mighty flower]

yea

[gusty gorge]

so then, naturally to solve our problem, we want to find the value of w that gives the biggest value of A

[mighty flower]

I still dont get how completing the square will give us the answer

[gusty gorge]

I'm getting there

it's important to actually understand the problem before trying to solve it

[mighty flower]

yea

[gusty gorge]

one thing that you can identify is that -2w^2 + 46w is quadratic in w

and it is a mathematical fact that's taught to you that it can be written in the form: a(w-c)^2 + b, for some numbers a, b, and c that are yet to determined

your teacher completes the square to write A = -2w^2 + 46w = -2(w-11.5)^2 + 264.6

do you know how to check that this is actually true?

[mighty flower]

not really

[gusty gorge]

you can literally just expand (w-11.5)^2 and verify that everything matches up

alternatively, because both are quadratic polynomials, you can check that they're equal at minimum 5 points

can you at least follow along and understand why we can write A = -2(w-11.5)^2 + 264.6?

[mighty flower]

yes

[gusty gorge]

now note that the first term -2(w-11.5)^2 is always less than or equal to 0

because (w-11.5)^2 is always 0 or bigger, and -2 makes it negative or 0

are you following along?

[mighty flower]

yes

[gusty gorge]

so basically we know that A is at most 264.6, yeah?

[mighty flower]

yes

[gusty gorge]

now, you can also observe that if we set the width = 11.5, the first term becomes 0, right?

[mighty flower]

yea

[gusty gorge]

so that means that if we set our fence width to 11.5, the area enclosed by the fence is 264.6, right?

[mighty flower]

yea

[gusty gorge]

and since we said before that you can't get any bigger than that

you have your answer to your question: if you set the width of the fence to 11.5, you get the biggest area, which is 264.6

[mighty flower]

thanks

I was working on this problem for a while cant couldnt get it

still kinda shaky but way better

[gusty gorge]

completing the square allows us to write the area of the fence as <something that can't get bigger than 0> + <a constant>

and then you know that if you can make the first thing get to 0, you can solve the problem

now

that's actually a rather confusing way of going about it

the simpler way is to observe that A = -2w^2 + 46w is a quadratic function of w

and you actually know a formula for the location of the vertex, which is the tip of the parabola

and that is w = -b/2a = -46/4 = 11.5

and then there's a calculus-based way of doing it too

[mighty flower]

really?

[gusty gorge]

yes

[mighty flower]

when will I be learning that?

[gusty gorge]

in calculus

[mighty flower]

what grade I mean

[gusty gorge]

depends on when you take calculus

some people it's first year of high school

some people it's second year of university lol

[mighty flower]

we wherent offered that option here

whelp thanks for the help

[woeful pulsar]

hmm i guess you can learn it yourself

i would recommend 3b1b's series

[mighty flower]

nope not with the way I am learning rn

kinda struggling with even simple crap like this

anyway gtg I have a test tmrw

[woeful pulsar]

o/

[mighty flower]

.close

[lone heart]

Channel closed

Closed by @mighty flower

Use .reopen if this was a mistake.

[lone heart]

Available help channel!

Send your question here to claim the channel.

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

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

[lime holly]

did i do something wrong?

[merry depot]

I don't think so, why?

[lime holly]

because the answer i got was incorrect

in the book it says i should multiply each term by 3^x

[merry depot]

oh, you said 3^-3 = 1/3^x which I don't think is true.....

[lime holly]

a^-b = 1/a^b

[merry depot]

sure....
on the left your b is 3
on the right your b is x

x is not 3

[lime holly]

i dont understand that

[merry depot]

3^-3 = 1/3^3

[lime holly]

wait i typed it out wrong

it was 3^x-3^-x=3

[merry depot]

then....

[lime holly]

these were le lesson notes

[merry depot]

,w solve 3^x -3^(-x) = 3

[ocean seal]

Results provided by WolframAlpha

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

Requested by Zybikron#5611

[merry depot]

that's what you have....

log(3.303)/log(3)

[lime holly]

i think i made a rounding error or something cause i was calculating it earlier and it gave me 1.7

[merry depot]

,w log(3.303)/log(3)

[ocean seal]

Results provided by WolframAlpha

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

Requested by Zybikron#5611

[lime holly]

alright i have one quick question

is this correct

sqrt(b) = b^1/2 and (n)sqrt(b) = b^1/n
logb(x^n) = (n)logbx
a^-b = 1/a^b

[merry depot]

assuming (n)sqrt(b) is b under a sqrt with a little n in it, then yes.

[lime holly]

my test is tomorrow and im scared of blanking when i get there 🥲

but thank you for the help

[merry depot]

write out a note card 'cheat sheet'
then try to do it again from memory.
then do it again reading the rules,
then do it again

[lime holly]

i can do it without the cheat sheet but i feel like when i look at new questions i blank

i already finished all of the revision

its just the laws about like log(n) + log(n) = log(n x n) and log(n) - log(n) = log(n/n)

that im worried about

[merry depot]

for situations like that, I try to go through the problems and see when I used those rules and why. Write it down to help you remember it.
Even reworking the problem you've already solved can help

[rose sigil]

you cn also try to remember those ones are like the exponent rules

[lime holly]

maybe it would be best to sleep now since i have to wake up for this in about 6 hours

[lime holly]

i feel like i know all the laws but i dont want to get there and use the wrong ones

[rose sigil]

yea maybe it would be best to sleep then 🙂

[lime holly]

my test criteria things are
I agree that the logarithmic function is the reciprocal of the exponential function.
I compare the main characteristics of graphs of exponential and logarithmic functions (domain, range, coordinates at the origin, intervals of growth/decline, asymptote).
I relate the logarithm of a number to the corresponding exponential expression.
I evaluate simple logarithm expressions using reciprocal expressions.
I demonstrate and describe transformations applied to graphs of logarithmic functions.
I recognize equivalent expressions involving logarithms and simplify them.
I solve exponential equations using a common base to write powers.
I establish the links between the laws of exponents and the laws of logarithms.
I simplify and evaluate logarithmic expressions using the laws of logarithms.
I solve logarithmic equations by expressing it in its equivalent exponential form.
I formulate and solve algebraically problems drawn from various applications that can be modeled by an exponential or logarithmic function.

i hope it works out alright thats all 😅

[rose sigil]

sounds kinda poetic

[lime holly]

its translated from french to english

i go to french school

[rose sigil]

oh haha

[lime holly]

😅 my bad

i think i should be alright for the test im just worried about solving complex equations

[rose sigil]

it’s okkk just sleep so you feel your best for tomorrow if you think you’re ready enough c:

[lime holly]

Yes i will sleep now thank you guys 🥹

[rose sigil]

.close

[lone heart]

Channel closed

Closed by @rose sigil

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[pliant nymph]

how do I complete the diagram?

[molten pivot]

it's just a bit of algebra really

A + B + (A U B)' - (A n B) = 20

three of those unknowns are given

just solve for the intersection of A and B

[pliant nymph]

Why is it A + B + (A U B)' - (A n B) = 20
I mean like, where does A + B + (A U B)' - (A n B) come from

[molten pivot]

The whole is the sum of the parts.

[pliant nymph]

and why are there a subtract in this, when everything add together should be 20

[molten pivot]

inclusion exclusion principle

[pliant nymph]

I dont really understand whats the concept of finding this

[molten pivot]

A n B is counted twice

[molten pivot]

let's say there are 10 red and blue marbles in a box. 5 of them are red. how many are blue?

[pliant nymph]

5

[molten pivot]

how did you know that?

[pliant nymph]

because 10 subtract 5

[molten pivot]

no, but conceptually

what's the equation

[pliant nymph]

R + B = O

idk

[molten pivot]

Red + Blue = Total

[pliant nymph]

red + blue = overall

[molten pivot]

yes

[pliant nymph]

Yes

but like, how are the - in the + B + (A U B)' - (A n B)

part

[molten pivot]

The whole is the sum of the parts. Are you with me on that?

so the entire rectangle must be the sum of what's inside the rectangle

[pliant nymph]

not really, the "of the parts"

[pliant nymph]

yes make sense

[molten pivot]

alright we can proceed from here

[pliant nymph]

?

[molten pivot]

what do you see inside the rectangle

how many distinct regions are there

[pliant nymph]

depend on the size of the rectangle?

[molten pivot]

the size doesn't matter

[pliant nymph]

?

[molten pivot]

we just want to identify what makes up the rectangle

what is inside the rectangle?

[pliant nymph]

lots of little square?

[pliant nymph]

Rectangle

[molten pivot]

no, this rectangle in the problem

what's inside it

[pliant nymph]

Some solid object that made up this rectangle

[molten pivot]

do you see some circles perhaps?

let me repost the image

[pliant nymph]

ohhhh

ok

i got it

yes

2 circles

intersecting each other

sorry my bad

[molten pivot]

how many distinct regions are in the rectangle

[pliant nymph]

4

[molten pivot]

name them

[pliant nymph]

Union, intersect, A and B

am I right? im not sure

[molten pivot]

are those distinct?

[pliant nymph]

No

1. theres a Intersect region between B and A
2. Area in the A circle
3. Area in the B circle
4. The outside of the circle

[molten pivot]

ok sure that's a starting point

how about this

does this match what you're saying

[pliant nymph]

so you just label each part?

[pliant nymph]

yes

[molten pivot]

alright

now what is w?

[pliant nymph]

10

[molten pivot]

nope

[pliant nymph]

why?

[molten pivot]

don't worry about the numbers yet

can you find w in terms of A and B

[pliant nymph]

A

w is A

[molten pivot]

not quite

A is the entire left circle

[pliant nymph]

A is W that doesnt intersect with B

[pliant nymph]

oh

yes

[molten pivot]

but W is just the part of A that doesn't intersect with B

[pliant nymph]

yes

[molten pivot]

so in set theory language, couldn't we say that

W = A - (A n B)

[pliant nymph]

wait im trying to catch up

so A is the entire circle

and to find the W I need to subtract A by the intersect

right?

[molten pivot]

yes

[pliant nymph]

how is knowing that going to help me answer the question

[molten pivot]

trust me

[pliant nymph]

ok

[molten pivot]

alright

so W = A - (A n B)

what is X

[pliant nymph]

X = (W +Y)/2?

is it?

[molten pivot]

not quite

find X in terms of A and B

[pliant nymph]

x = (A+B)/2

[molten pivot]

there's no division here

we're working with sets

[pliant nymph]

oh

[molten pivot]

X is the region where the two circles overlap, isn't it?

[pliant nymph]

I just know that the intersect is the numbers that exist in A and B

[pliant nymph]

yes

[molten pivot]

so X is the intersection of A and B

[pliant nymph]

yes

[molten pivot]

so X = (A n B)

[pliant nymph]

OH yes

[molten pivot]

alright

now try finding Y in terms of A and B

[pliant nymph]

so you're just teaching me to understand stand of the W, X, Y, Z concept?

[pliant nymph]

Y = B-X

[molten pivot]

sure that's a start

but what is X

[pliant nymph]

Y=B-(A n B)

[molten pivot]

yes! you're getting it

finally

we just need to find Z

in terms of A and B

[pliant nymph]

i really have no idea

doesn't we need another unit to do that?

[molten pivot]

can you put it in words

what is the region Z

[pliant nymph]

Region Z is every numbers but are not in the A, B or intersect

that are already given but not are any of those

[molten pivot]

ok yeah

[pliant nymph]

criteria

[molten pivot]

Z is everything not in A or B

so how we write that is:
Z = (A u B)'

Z is the complement of the union of A and B

[pliant nymph]

?

i dont understand by your term

your phrase

[molten pivot]

i'm just giving you the definition

[pliant nymph]

complement of the union

yes it is

it sounds correct but doesnt at the same time for some reason

it logically correct

but like

[molten pivot]

the union of A and B is just A and B together

the complement of that is everything not in A or B

[pliant nymph]

yes

[pliant nymph]

the whole B and A and the intersect too

but the )' make its not any of those

[molten pivot]

yep

you should also know that the intersection is part of both A and B

[pliant nymph]

yes

[molten pivot]

so when we say A+B+(intersection of A and B), that's the same thing as A+B

alright

[pliant nymph]

no?

[molten pivot]

yes

[pliant nymph]

doesnt A+B have an extra intersect?

[molten pivot]

nope

[pliant nymph]

?

[molten pivot]

the '+' symbol doesn't mean adding here

it means the union of sets

[pliant nymph]

oh

So A U B U (A n B)?

you mean that?

[molten pivot]

A U B U (A n B) = A U B

so there's no reason to write A U B U (A n B)

the intersection is already a part of A and B

[pliant nymph]

yes

a and b are

[molten pivot]

now

[pliant nymph]

now

[molten pivot]

we have formulas for W,X,Y,Z in terms of A and B

W = A - (A n B)
X = (A n B)
Y = B - (A n B)
Z = (A u B)'

[pliant nymph]

i can either remember that, or just work it out right? if it pop up on an exam

[molten pivot]

you just need more practice

i can tell this is all very new to you

[pliant nymph]

how could i do that, are there like some website link that have copies of those question? cuz when i tried, i only sees the probability one

[pliant nymph]

;-;

[molten pivot]

let's just try solving this problem first

would you agree that W+X+Y+Z makes up the entire rectangle?

[pliant nymph]

yes

i agree

[molten pivot]

so let's call the entire rectangle R

W + X + Y + Z = R

[pliant nymph]

ok

[molten pivot]

(A - (A n B)) + (A n B) + (B - (A n B)) + (A u B)' = R

let's simplify the left side

what do we get

[pliant nymph]

R = (A - (A n B)) + (A n B) + (B - (A n B)) + (A u B)'

wait

let me rephase it

i need some logical thinking

its hard

[molten pivot]

think about what happens to the (A n B)

you subtract it twice

and add it once

-2 + 1 = ?

[pliant nymph]

-1

[molten pivot]

yes

so that's the same thing as just subtracting it once

so we finally get

A + B + (A u B)' - (A n B) = R

[pliant nymph]

R = (A - (A n B)) + (A n B) + (B - (A n B)) + (A u B)'

wait

let me try to understand

how do you get these equation again?

R = (A - (A n B)) + (A n B) + (B - (A n B)) + (A u B)'

[molten pivot]

W+X+Y+Z=R

[pliant nymph]

and when i look carefully i see there's 4 intersect, 2 of those have + infront of another 2 have subtract

[pliant nymph]

oh yes

[molten pivot]

then we just plug in the formulas we derived here

[pliant nymph]

ok

[molten pivot]

there's only 3 intersections

[pliant nymph]

oh sorry, im mistaken with the union

A + B + (A u B)' - (A n B) = R

R = (A - (A n B)) + (A n B) + (B - (A n B)) + (A u B)'

R = A + (B - (A n B)) + (A u B)'

?

i got that

[molten pivot]

yes

A + B + (A u B)' - (A n B) = R

[pliant nymph]

yes according to the formula

[molten pivot]

now let's look back at what we had

[molten pivot]

we know that the entire rectangle is 20, so R = 20

[pliant nymph]

yes

im writing it down in my note

[molten pivot]

R = 20, A = 10, B = 13, (A u B)' = 3

[pliant nymph]

A + B + (A u B)' - (A n B) = R

now we just put all of those into the formula?

[molten pivot]

yes

[pliant nymph]

oh ok i think i kinda got it

how about the B, theres an (A' n B)

doesnt that means that they just told us to get the number in Y?

[molten pivot]

yes

you get it

what was our formula for Y again?

[pliant nymph]

Y = B - (AUB)

[molten pivot]

not quite

[pliant nymph]

13 - 3?

[molten pivot]

Y = B - (A n B)

[pliant nymph]

am I right?

[molten pivot]

nope

what did you get for part a

[pliant nymph]

6

[molten pivot]

yes

Y = B - intersection of A and B

[pliant nymph]

oh

so its 13 - 6

my bad

so it 7

[molten pivot]

yes

[pliant nymph]

thank you alot

you really help me

ill spend rest of today revising for the theory you just teach me, thank you

[molten pivot]

👍

might want to search up on khan academy

basic set theory

[pliant nymph]

ok ill do it

when we got the help and understand, what do we do?

[molten pivot]

nothing lol

you're all good

[pliant nymph]

oh ok, so theres no like command to tell the server that I already got help and this chat is free for the next person

ok

[molten pivot]

https://www.khanacademy.org/math/statistics-probability/probability-library/basic-set-ops/v/intersection-and-union-of-sets

this is what you need practice on

gg

[pliant nymph]

ok thank you

[pliant nymph]

do you mind if im asking why are you helping me for? cuz Ik that you also probably have something else busy to do in life

[molten pivot]

i'm on break

i'm usually very busy with my job and school and everything

but i'm home right now and it's getting kind of boring already haha

[pliant nymph]

oh ok, thanks alot Mr. Gamer

[molten pivot]

gl

[lone heart]

@pliant nymph Has your question been resolved?

Channel closed

Closed by @pliant nymph

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[unkempt birch]

I wanna show that N and M have the same cardinality

So I need to define a function f(x) which maps each element x in N to the element x in M

And vice versa ofc

[vale wigeon]

$M = [3,5] \cup [7,10]$ and $N = [0,5]$?

[ocean seal]

Ann

[unkempt birch]

Yes

[vale wigeon]

does the problem say "construct a bijection between M and N" or does it say "prove M and N have the same cardinality"

[unkempt birch]

I guess they want me to construct a bijection yes

[vale wigeon]

the former is going to be nasty

[vale wigeon]

wdym "guess"???

[unkempt birch]

Wait, I have to translate it

[vale wigeon]

from what language

[unkempt birch]

German

Prove that |M| = |N| holds

[mortal trellis]

give the original german

or just a picture of the whole exercise

[unkempt birch]

Its about (1)

[vale wigeon]

so it's "prove M and N have the same cardinality".

and you are not asked for a bijection. not explicitly.

so the question becomes "are you a masochist"

[unkempt birch]

lmao

[alpine sable]

yes

[vale wigeon]

you know how to show that any two closed intervals have the same cardinality right

[rose sigil]

idt it would be that bad to construct one explicitly?

[unkempt birch]

Okay how to proof this? I mean I have to deal with real numbers so.. dont I need a bijective function for that??

[mortal trellis]

do you know schröder bernstein?

[unkempt birch]

Yes

[vale wigeon]

oh yeah that's gonna be easier

just construct injective functions both ways

[mortal trellis]

a bijective function wouldn't be that bad but you would have to worry about a few details. injective functions are much easier

also btw the first set is [3, 5) and not [3,5] so glueing them together isnt annoying with having to account for a double 5

[unkempt birch]

So I need two injective functions from M->N and N->M right?

[mortal trellis]

that's one way to show it, yes

[keen plinth]

surely just gluing the two intervals together is fine

the problem statement even made the first interval half open for that to be easy

[unkempt birch]

How to "glue" them together?

[mortal trellis]

shift the second interval down by 2

(that's clearly a bijection)

then your union is now just [3,8]

or well, same cardinality and all that

[unkempt birch]

Am I allowed to do that?

[mortal trellis]

and now you have to find a bijection between [3,8] and [0,5] and that's hopefully easy

why not

[keen plinth]

kinda looks like uh

[keen plinth]

this lmfao

[mortal trellis]

technically the function would look like that
$f(x) = \begin{cases} x & x \in [3,5) \ x-2 & x\in [7,10] \end{cases}$

[ocean seal]

Denascite

[mortal trellis]

and then you compose it with your bijection of [3,8] -> [0,5]

[unkempt birch]

The cardinality is the same for both okay

[mortal trellis]

yes but that so far does not count as a proof

[unkempt birch]

Ye I know

Isnt it just f(x) = x -3?

[mortal trellis]

a key idea of these "show sets have the same cardinality" questions is to do it step by step and then in the end compose all the bijections you used along the way

[mortal trellis]

the bijection [3,8] -> [0,5]? yes

[unkempt birch]

And vice versa f(x) = x + 3

[mortal trellis]

yes

[unkempt birch]

Ahh yes thank u

[mortal trellis]

although you should not use the same letter for both directions

[unkempt birch]

So f(x) = x -3 and its Reverse function g(x) = x + 3 are bijective

[mortal trellis]

as functions on those sets, yes

[lone heart]

@unkempt birch Has your question been resolved?

[unkempt birch]

Thanks Denascite!!

.close

[lone heart]

Channel closed

Closed by @unkempt birch

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[atomic coral]

can anybody explain how the centripetal force changes along the simple pendulum? can we know the centripetal force even if there are not given the highest point of the motion?

[atomic coral]

I already asked before, but I'm still confused I don't know what I'm missing for now

[outer lark]

[placid zinc]

Given by v^2/r

Well, mv^2/r

Force vs acceleration

[atomic coral]

yes if I have to get the centripetal force in the lowest point

I can utilize the cons of energy right

Ug = KE

[outer lark]

depends

[atomic coral]

mgh = 0.5mv^2

[outer lark]

well yes but

[placid zinc]

It really does depend on what you are given, haha

[atomic coral]

but we don't know the h

there are only given the mass of the ball and the length of the string

[outer lark]

at the very bottom of the circle

[atomic coral]

yes

[placid zinc]

Nothing else at all? Then we don't have enough info.

[outer lark]

the force due to gravity is balanced through the string,

mg = mv^2 / r

[placid zinc]

For all we know, it isn't even moving

[atomic coral]

then we are unable to determine the centripetal force in this case?

[outer lark]

so v = sqrt(gr)

we can make expressions for it

[placid zinc]

Actually, maybe I'm speaking too soon haha

[atomic coral]

what is si

[atomic coral]

lol

[outer lark]

also to answer your question

you probably want to think about theta and how the components are split

as the ball moves at different stages

like this

[placid zinc]

No I'm back to my original thought. We have no info on the speed at all. The pendulum may not even be moving for all we know. Not enough info here.

[atomic coral]

there's given

the pendulum is moving back and forth

but we dont know the speed

[outer lark]

you can create expressions for it but not obtain a numerical value

using the diagram posted

[atomic coral]

can you let me know the expression?

let me see

F_c = T - mg, right

[outer lark]

dude I have completely forgot since I have last looked at this and have been up for like 36 hours, so I would give the worst possible explanation even if I could

head to the physics server and make a post there

theres a rlly good guy in there who will help you out

[unkempt sundial]

what is this?

[outer lark]

centripetal force = tension - weight

[atomic coral]

I tried to find active physics server

but I couldn't

[unkempt sundial]

but centripetal force is the tension

[outer lark]

#old-network

https://discord.gg/physics

[outer lark]

yes

[atomic coral]

wdym

[outer lark]

the tension in the string is due to mv^2/r

[atomic coral]

I searched a lot and still confused

[outer lark]

or supplied through it

idk how to word it perfectly

[unkempt sundial]

what are you still confused about @atomic coral ?

[atomic coral]

do you agree with the equation: centripetal force = tension - weight?

[unkempt sundial]

no I don't, where did you get it

or how

[outer lark]

I would agree 👀

[atomic coral]

googling...

I have no idea how to approach this

[outer lark]

gl, brain too fuzzy

post in physics server

petshge will sort you out

[unkempt sundial]

ill leave this to Clarkie, i was never given Centripetal force while learning pendulum

[atomic coral]

the centripetal acc cannot be constant

right/

[outer lark]

[atomic coral]

if so, the centripetal force should change as well

[outer lark]

yes, and its balanced by the differing components in theta I believe

at y_max you have max acceleration and minimum velocity

max potential energy

[atomic coral]

y max means the highest point

?

[outer lark]

yes.

[atomic coral]

that is mgh, right

[outer lark]

potential energy is

[atomic coral]

the potential energy

ya

[outer lark]

have you done simple harmonic motion?

[atomic coral]

and the lowest point is max kinatic energy

yes but little confused with it

[outer lark]

it describes the acceleration and velocity , also displacement through the motion

[atomic coral]

that is why I'm wandering

[outer lark]

well

I dont know what else to say

your question was answered long ago

[atomic coral]

then can you answer the only question

if there are given the mass and the length of the string, and the simple pendulum is moving

[outer lark]

ok

[atomic coral]

can we get the centripetal force at the lowest point?

you said at first it depends

[outer lark]

at the very lowest point?

[atomic coral]

I don't get what else variable that should be handled

yes

[outer lark]

see simple harmonic motion helps here

the answer is 0

[atomic coral]

because the tension is the same as the weight?

[outer lark]

and you can get it from deriving a wave equation for a simple pendulum modelled as a sin/cos wave

[unkempt sundial]

oh i see now, centripetal force is F_net in pendulum

[atomic coral]

I haven't learn about it

[atomic coral]

then you agree with the equation that I mentioned?

[unkempt sundial]

yah i agree, i thought centripetal force is tension force

[atomic coral]

thanks

for your clarification

do you think the tension is the same as the weight at the lowest point

[outer lark]

it is

f=ma=mg=mv^2/r

and then as soon as you want an individual point on a higher value you have to think about components

[atomic coral]

i see

[outer lark]

still, I dont trust what im saying with 100% accuracy , I would still go physics server and the absolute god that is in there will answer your question with ease

so

[atomic coral]

ok thanks

.close

[lone heart]

Channel closed

Closed by @atomic coral

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[cosmic orbit]

I was going to use the multiplication rule, but I dont know how to work out the intersection

I need to find out the probability of it being R B R B R and also B R B R B

[outer lark]

<@&268886789983436800>

[cosmic orbit]

Do you think you could help me?

[outer lark]

no I dont have a clue in the world about anything to do with probability

[cosmic orbit]

ok

[naive valley]

ha what does the giant size of the playing cards have to do with anything...

[cosmic orbit]

no clue

[naive valley]

hint: the probability of RBRBR is the same as the probability of RRRBB

[cosmic orbit]

Ive been stuck on this for 15 mins

[cosmic orbit]

How

They r both ordered differently

[naive valley]

either way you're drawing three reds and two blacks without replacement from a shuffled deck

but if you don't like that you can just work out RBRBR directly

probability that the first card is red is 26/52

[cosmic orbit]

Ok so i got

[naive valley]

probability that the second card is black is 26/51

...

and so on

[cosmic orbit]

Yh i jsut worked that out

so the final black is 25/49

probBILITY

probability*

Red 1: 26/52, Red 2:25/51, Red3: 24/50, Black1:26/49, Black 2 25/48

Do I multiply them together?

[naive valley]

wait

your denominators should include 49 and 48..

[cosmic orbit]

yeah my bad

fixed it

[naive valley]

yep that looks better

notice that by rearranging the numerators you can change RRRBB to RBRBR

without changing the value of the product

in any case yeah multiply them together

[cosmic orbit]

then do i do it for B R B R B